diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/0Hnc-SfI61E_raw.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/0Hnc-SfI61E_raw.srt
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index 0000000000000000000000000000000000000000..144bc5f07e51549e299fb2c94ac804cc64d383f3
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@@ -0,0 +1,1300 @@
+1
+00:00:01,940 --> 00:00:06,400
+بسم الله الرحمن الرحيم بنستكمل مع محاضرات ال
+
+2
+00:00:06,400 --> 00:00:12,080
+physical optics وتوقفنا عند موضوع ال
+
+3
+00:00:12,080 --> 00:00:19,560
+bacteriorhodopsin وإنه موجود في بكتيريا قديمة اللي
+
+4
+00:00:19,560 --> 00:00:23,300
+هي ال halobacterium halobium وقلنا هذا ال
+
+5
+00:00:23,300 --> 00:00:28,090
+bacteriorhodopsinهو العين بتاعة البكتيريا بمعنى هو
+
+6
+00:00:28,090 --> 00:00:32,850
+الجزيء الحيوي أو المركب الكيميائي داخل البكتيريا
+
+7
+00:00:32,850 --> 00:00:37,070
+التي يستطيع فهم الضوء وحكينا أن هذا البكتيريو
+
+8
+00:00:37,070 --> 00:00:42,190
+رودوبسين الموجود في الهالو بكتيريوم هالوبيوم مكون
+
+9
+00:00:42,190 --> 00:00:46,030
+من شقين الأوبسين بورشين أو الجزء البروتيني
+
+10
+00:00:46,030 --> 00:00:49,930
+والريتينال بورشين اللي هو أحد مركبات أو أحد أشكال
+
+11
+00:00:49,930 --> 00:00:53,970
+فيتامين A هدول الجزئين مع بعضهم بكونوا البكتيريو
+
+12
+00:00:53,970 --> 00:01:00,400
+رودوبسينوقلنا كيف عرفوا العلماء أنه بيتأثر ال
+
+13
+00:01:00,400 --> 00:01:05,800
+bacteriorhodopsin بالضوء فوجدوا العلماء أنه بمجرد
+
+14
+00:01:05,800 --> 00:01:09,860
+سقوط الضوء على هذا المركب أو هذا الجزء الحيوي اللي
+
+15
+00:01:09,860 --> 00:01:14,440
+هو ال bacteriorhodopsinبحصل في شقاه .. في شقاه
+
+16
+00:01:14,440 --> 00:01:19,500
+بحصل تغير والتغير هذا بسرعة هائلة جدا ال obscene
+
+17
+00:01:19,500 --> 00:01:24,520
+portion .. ال obscene portion بتغير وال retinal
+
+18
+00:01:24,520 --> 00:01:28,260
+portion بتغير ببدأ التغير في ال retinal portion
+
+19
+00:01:28,260 --> 00:01:32,460
+اللي هو الجزء اللي هو عبارة عن شكل من أشكال .. من
+
+20
+00:01:32,460 --> 00:01:35,540
+أشكال vitamin A اللي هو جزء من مكونات ال
+
+21
+00:01:35,540 --> 00:01:42,740
+bacteriorhodopsin بيصير في ..isomerization بمعنى
+
+22
+00:01:42,740 --> 00:01:48,000
+ان ال form بتتحول لل transform بسرعة شاهقة جدا
+
+23
+00:01:48,000 --> 00:01:54,980
+تقدر بعشرة أصناق ستماشر second يعني واحد على مليون
+
+24
+00:01:54,980 --> 00:02:00,100
+مليون ثانية واحد على أو جزء من مليون مليون جزء من
+
+25
+00:02:00,100 --> 00:02:06,260
+الثانية وهذا بيتبع ال debrotonation إعطاء لبروتون
+
+26
+00:02:06,750 --> 00:02:12,170
+من ال obscene portion اللي هو الجزء البروتيني تمام
+
+27
+00:02:12,170 --> 00:02:17,210
+في عشرة أص ناقص خمسة من الثانية يعني في واحد من
+
+28
+00:02:17,210 --> 00:02:21,590
+مائة ألف جزء من الثانية وهذا يعتبر سرعة شاهقة أو
+
+29
+00:02:22,810 --> 00:02:27,090
+يعني شديدة السرعة في الاستجابة لضوء .. في
+
+30
+00:02:27,090 --> 00:02:31,850
+الاستجابة لضوء، اذا ال bacteriorhodopsin يستجيب
+
+31
+00:02:31,850 --> 00:02:37,830
+لضوء و الخلية بتفيد من استجابة bacteriorhodopsin و
+
+32
+00:02:37,830 --> 00:02:43,790
+بتقوم بالعمليات الحيوية اللازمة لها و اتوقفنا عند
+
+33
+00:02:43,790 --> 00:02:50,560
+هذا القضيةطبعا سألوا العلماء أنفسهم ال rodopsin أو
+
+34
+00:02:50,560 --> 00:02:53,940
+ال bacteriorodopsin الموجود في ال helobacterium
+
+35
+00:02:53,940 --> 00:02:59,040
+helobium يترى باستجيب لأي نوع من الطول أو لأي طول
+
+36
+00:02:59,040 --> 00:03:03,780
+موجي أكتر هل باستجيب للأحمر أو للبرتقالي أو للأصفر
+
+37
+00:03:03,780 --> 00:03:08,560
+أو للأخضر أو للأزرق يعني أي من الموجات الطيفية
+
+38
+00:03:08,560 --> 00:03:15,950
+بتستحث ال bacteriorodopsinبشكل أكتر من غيرها و
+
+39
+00:03:15,950 --> 00:03:22,590
+وجدوا أن طول الموج الأزرق 495 نانومتر هو يعني
+
+40
+00:03:22,590 --> 00:03:26,910
+بينشط معاه ال bacteriorhodopsin بتتغير التفاعلات
+
+41
+00:03:26,910 --> 00:03:33,120
+أو بتحدث التفاعلاتالكيميائية فيه بشكل انشط مما لو
+
+42
+00:03:33,120 --> 00:03:38,760
+تعرض لموجات ضوئية من أطوال موجية أخرى، اذا this
+
+43
+00:03:38,760 --> 00:03:44,400
+early rodopsin absorbed light maximally at 495
+
+44
+00:03:44,400 --> 00:03:48,460
+nanometer but responded to almost all visible
+
+45
+00:03:48,460 --> 00:03:52,220
+lightيعني هو بيستجيب الـ bacteriorhodopsin بيستجيب
+
+46
+00:03:52,220 --> 00:03:57,060
+لكل الأطوال الموجية بس الأكثر استجابة لطول الموج
+
+47
+00:03:57,060 --> 00:04:02,560
+الأزرق لطول الموج الأزرق اللي هو تقريبا اربعمية و
+
+48
+00:04:02,560 --> 00:04:06,540
+خمسة و تسعين نانو متر اربعمية و خمسة و تسعين يعني
+
+49
+00:04:06,540 --> 00:04:11,660
+حوالين الأزرق estimates suggest that the ancestor
+
+50
+00:04:11,660 --> 00:04:16,560
+of human color pigment genesDiverged from the
+
+51
+00:04:16,560 --> 00:04:21,020
+rhodopsin gene about 800 million years ago and
+
+52
+00:04:21,020 --> 00:04:24,720
+eventually resulted in a series of pigments with
+
+53
+00:04:24,720 --> 00:04:28,740
+maximal absorption peaks in the blue, green and
+
+54
+00:04:28,740 --> 00:04:32,480
+red areas of the spectrum. These specially adapted
+
+55
+00:04:32,480 --> 00:04:35,380
+molecules are needed for accurate color vision
+
+56
+00:04:35,380 --> 00:04:40,700
+.الان العلماء سألوا نفسهم عشان نفهم هذه الفقرة، يا
+
+57
+00:04:40,700 --> 00:04:48,610
+ترى أول ما بدأيظهر الـRhodopsin أو أول ما خُلِق
+
+58
+00:04:48,610 --> 00:04:53,030
+الـRhodopsin أو الكائنات الأولية الشديدة البداية
+
+59
+00:04:53,030 --> 00:04:58,590
+الـRhodopsin اللي فيها هل هو بيستجيب لطول موجي
+
+60
+00:04:58,590 --> 00:05:03,650
+معين ولا بيستجيب يعني أو في منه أنواع خلينا نقول
+
+61
+00:05:03,650 --> 00:05:06,730
+في منه أنواع مختلفة من الـRhodopsin كل واحد منها
+
+62
+00:05:06,730 --> 00:05:13,270
+بيستجيب لطول موجي بذاته فقدروا العلماء أن ظهور
+
+63
+00:05:13,270 --> 00:05:20,070
+الجيناتظهور الجينات طبعا على الكروموسومات المسئولة
+
+64
+00:05:20,070 --> 00:05:25,310
+عن إنتاج ال Rodopsin ممكن إنسان يقول إيش علاقة
+
+65
+00:05:25,310 --> 00:05:28,910
+الجينات في الموضوع هذا، ما ننساش أن ال Rodopsin
+
+66
+00:05:28,910 --> 00:05:35,600
+مكوّن منجزء بروتيني وجزء vitamin E الجزء البروتيني
+
+67
+00:05:35,600 --> 00:05:40,560
+لبروتينات معروف إنها أحماض أمينية مت .. مترابطة مع
+
+68
+00:05:40,560 --> 00:05:47,300
+بعضها البعض ويعني بتكون polypeptide chain و بتكون
+
+69
+00:05:47,300 --> 00:05:51,420
+منها البروتين اللي هو طبعا سلاسل اللي هو عديدة ال
+
+70
+00:05:51,420 --> 00:05:56,030
+peptideفبالتالي طالب مكوّن من amino acids، معناته
+
+71
+00:05:56,030 --> 00:06:00,350
+هذه أنتجت في الريبوسومات، الريبوسومات مين اللي
+
+72
+00:06:00,350 --> 00:06:04,640
+أعطاها الإشارة؟إنها تنتج الجينات أو الكرموسومات
+
+73
+00:06:04,640 --> 00:06:08,680
+الموجودة في النواء عبر ال messenger RNA أرسلت
+
+74
+00:06:08,680 --> 00:06:13,940
+رسالة عن طريق ال messenger RNA لرايبوسومات اللي هي
+
+75
+00:06:13,940 --> 00:06:18,320
+مصانع البروتينات فأنتجت اللي هو ال amino acids أو
+
+76
+00:06:18,320 --> 00:06:21,900
+جمعت ال amino acids وكونت لي ال obscene portion
+
+77
+00:06:21,900 --> 00:06:25,640
+بتاعة ال bacteriorhodopsin العلماء لما سألوا
+
+78
+00:06:25,640 --> 00:06:30,700
+أنفسهم سؤال هل في أكتر من نوعمن ال Rodopsin يعني
+
+79
+00:06:30,700 --> 00:06:33,700
+نوع يستجيب مثلا الطول الموجي أو يمتص الطول الموجي
+
+80
+00:06:33,700 --> 00:06:37,020
+الأزرق، نوع يمتص الطول الموجي الأخضر، نوع يمتص
+
+81
+00:06:37,020 --> 00:06:40,460
+الطول الموجي الأحمر و هكذا، هل في أنواع كتيرة يعني
+
+82
+00:06:40,460 --> 00:06:45,380
+و لا هو نوع واحد و خلاص، فالدراسات
+
+83
+00:06:45,380 --> 00:06:52,160
+قادت إلى أن الجينات الجينات اللي بتتحكم في إنتاج
+
+84
+00:06:52,160 --> 00:06:57,200
+أنواع مختلفة من ال Rodopsinأنواع مختلفة من الـ
+
+85
+00:06:57,200 --> 00:07:03,110
+Rhodopsinيعني بدأت بالظهور تقديريا تقريبا 800
+
+86
+00:07:03,110 --> 00:07:08,530
+مليون سنة قبل عصرنا الحالي يعني قبل عصرنا الحالي
+
+87
+00:07:08,530 --> 00:07:12,890
+يعني الحفريات أوجدت أو استطاعوا العلماء التوصل
+
+88
+00:07:12,890 --> 00:07:17,710
+لكائنات فيها أنواع متعددة من الجينات هذه الجينات
+
+89
+00:07:17,710 --> 00:07:23,070
+مسئولة عن إنتاج أنواع مختلفة من الرضبسين لما درست
+
+90
+00:07:23,070 --> 00:07:27,330
+هذه الأنواع المختلفة وجدوا أنهكل نوع منها باستجيب
+
+91
+00:07:27,330 --> 00:07:32,810
+لطول موجي معين و هكذا بدأ بالظهور يعني أنواع
+
+92
+00:07:32,810 --> 00:07:40,390
+مختلفة من الجينات و استنتج أنها تنتج
+
+93
+00:07:40,390 --> 00:07:45,470
+أنواع مختلفة من الريدوبسينو كل نوع منها حساس لطول
+
+94
+00:07:45,470 --> 00:07:49,830
+موجي معين فبالتالي بدأت قصة ال color vision في
+
+95
+00:07:49,830 --> 00:07:55,530
+الظهور منذ ذلك الوقت و وصلنا لأعلى الكائنات اللي
+
+96
+00:07:55,530 --> 00:08:01,970
+هو الإنسان اللي عنده سلسلة من الصبغات اللي بيصير
+
+97
+00:08:01,970 --> 00:08:05,910
+ال maximum absorption لل light فيها بعضها عند ال
+
+98
+00:08:05,910 --> 00:08:08,750
+blue بعضها عند ال green و بعضها عند ال red و عشان
+
+99
+00:08:08,750 --> 00:08:13,300
+هي كدهالإنسان عنده تلت أنواع من ال cones اللي هي
+
+100
+00:08:13,300 --> 00:08:18,200
+المستقبلات الألوان red sensitive cone و green
+
+101
+00:08:18,200 --> 00:08:21,800
+sensitive cone و blue sensitive cone، الآن بس بدأ
+
+102
+00:08:21,800 --> 00:08:26,320
+نوح لقضية خارج عن المحاضرة بس مهمة جدامن الخطأ ..
+
+103
+00:08:26,320 --> 00:08:30,060
+من الخطأ أني أقول blue cones و green .. green
+
+104
+00:08:30,060 --> 00:08:34,500
+cones و red cones لأنه هذه مش ألوان لخلايا،
+
+105
+00:08:34,500 --> 00:08:39,940
+الخلايا ليست .. أو ليست ملونة و إنما ال pigment
+
+106
+00:08:39,940 --> 00:08:43,220
+اللي فيها أو ال protein اللي فيها أو الrodopsin
+
+107
+00:08:43,220 --> 00:08:48,090
+عشان نكون دقيقين جداتركيبة ال Rodopsin هنا تختلف
+
+108
+00:08:48,090 --> 00:08:53,050
+عن تركيبة ال Rodopsin هنا تختلف عن تركيبة ال
+
+109
+00:08:53,050 --> 00:08:57,430
+Rodopsin هنا Rodopsin ترتيب الأحماض الأمينية فيه
+
+110
+00:08:57,430 --> 00:09:01,710
+بيجعله حساس للطول الموجي الأزرق هنا ترتيب الأحماض
+
+111
+00:09:01,710 --> 00:09:06,150
+الأمينيةاللي هي قولنا عنها ميتين وتمانية واربعين
+
+112
+00:09:06,150 --> 00:09:08,850
+حمض أميني في ال بكتيريو رودوبسين بس في الإنسان
+
+113
+00:09:08,850 --> 00:09:12,750
+يعني بتختلف التركيبة بس برضه في ال obscene portion
+
+114
+00:09:12,750 --> 00:09:18,050
+مكون من عدد معين من الأحماض الأمينية ترتيبتها
+
+115
+00:09:18,270 --> 00:09:22,850
+ترتيبتها وتشابكها مع بعض البعض بتخلي أحيانا بعض
+
+116
+00:09:22,850 --> 00:09:26,590
+الخلايا حساس للطول الموجي الأزرق بعضها حساس للطول
+
+117
+00:09:26,590 --> 00:09:32,090
+الموجي الأخضر وبعضها حساس للطول الموجي الأحمر إذا
+
+118
+00:09:32,090 --> 00:09:37,050
+الكلمة blue و green و red cones هذه كلمة خاطئ و
+
+119
+00:09:37,050 --> 00:09:41,150
+هنا بقول blue sensitive cone green sensitive cone
+
+120
+00:09:41,150 --> 00:09:45,730
+و red sensitive cone يعني حسب حساسيتها لأي طيف من
+
+121
+00:09:45,730 --> 00:09:53,030
+الضوء المرئيإذا التقديرات بتقول أنه ال ancestor of
+
+122
+00:09:53,030 --> 00:10:00,310
+human color pigment genes أنه الجد أو السلف بتاعه
+
+123
+00:10:00,310 --> 00:10:05,600
+human color pigment genes الجيناتاللي بدأت بالظهور
+
+124
+00:10:05,600 --> 00:10:10,020
+طبعا هذه وفق نظريات التطور عندهم بس احنا بالنسبة
+
+125
+00:10:10,020 --> 00:10:15,280
+للإنسان خلق الإنسان في أحسن تقويم ويعني معروف أنه
+
+126
+00:10:15,280 --> 00:10:19,280
+من بداية خلق الإنسان من آدم عليه السلام أنه هذه
+
+127
+00:10:19,280 --> 00:10:22,920
+الجينات كلها موجودة عند آدم عليه السلام وذريته
+
+128
+00:10:22,920 --> 00:10:28,100
+وصولا إلى عصرنا الحالي وحتى يعني تقوم الساعةكله
+
+129
+00:10:28,100 --> 00:10:31,480
+يستطيع رؤية الألوان إلا إذا كان عنده مرض عمى
+
+130
+00:10:31,480 --> 00:10:36,980
+الألوان بس كله موجود عنده ال genes بتاعت اللي هي
+
+131
+00:10:36,980 --> 00:10:41,320
+الرؤية اللونية وزي ما بنقول و بنذكر مش الجينات هي
+
+132
+00:10:41,320 --> 00:10:45,080
+اللي بترا الألوان الجينات تتحكم في إنتاج ال
+
+133
+00:10:45,080 --> 00:10:49,600
+proteinات اللي هي بتدخل في تكوين الأبسين بتاع ال
+
+134
+00:10:49,600 --> 00:10:52,180
+Rodopsin بتاع ال Rodopsin
+
+135
+00:10:54,170 --> 00:10:57,990
+لما بنقول أربعمية و خمسة و تسعين نرجع للبكتيريو
+
+136
+00:10:57,990 --> 00:11:02,710
+رودوبسين أكتر حساسية البكتيريو رودوبسين الموجود في
+
+137
+00:11:02,710 --> 00:11:06,390
+الهالو بكتيريوم هالوبيوم عند الطول الموجي أربعمية
+
+138
+00:11:06,390 --> 00:11:10,950
+و خمسة و تسعين نانومتر هي الأطياف من عند أربعمية
+
+139
+00:11:10,950 --> 00:11:15,870
+تقريبا لسبعمية لو جينا نقول تقريبا أربعمية و خمسة
+
+140
+00:11:15,870 --> 00:11:20,330
+و تسعين نانومتر يعني هو جاي بين الأزرق و الأخضر
+
+141
+00:11:20,330 --> 00:11:25,230
+بين الأزرق و الأخضر بين اللون الأزرقو الأخضر فهنا
+
+142
+00:11:25,230 --> 00:11:30,730
+بيكون ال maximum .. ال maximum sensitivity ل ال
+
+143
+00:11:30,730 --> 00:11:35,070
+bacteriorhodopsin بس هو بنذكر ايضا ان هو حساس لكل
+
+144
+00:11:35,070 --> 00:11:40,240
+الأطياف الموجية .. لكل الأطياف الموجيةthus early
+
+145
+00:11:40,240 --> 00:11:43,700
+animals used something akin to the original
+
+146
+00:11:43,700 --> 00:11:48,300
+rhodopsin and a very simple optical system to see
+
+147
+00:11:48,300 --> 00:11:53,900
+الآن قبل ما نشرح هذه الفقرة بنقول كالقاتل أبسط ..
+
+148
+00:11:53,900 --> 00:12:00,260
+أبسط جزيء .. أبسط جزيء حساس للضوءووجد في
+
+149
+00:12:00,260 --> 00:12:06,840
+الhalobacterium halobium واطلقوا عليه العلماء اسم
+
+150
+00:12:06,840 --> 00:12:11,160
+bacteriorhodopsin هاي الشكل او ال simulation بتاعه
+
+151
+00:12:12,660 --> 00:12:17,360
+بدنا الأن ننتقل لكائنات أكثر تعقيدا قليلا مش كتير
+
+152
+00:12:17,360 --> 00:12:21,680
+أكثر تعقيدا ولكن أكثر تعقيدا بشكل يعني الدرجة اللي
+
+153
+00:12:21,680 --> 00:12:27,300
+بعديها في التعقيد هنا هذا الجزيء موجود داخل خلية
+
+154
+00:12:27,300 --> 00:12:30,120
+الhalobacterium halobium وسمينا ال
+
+155
+00:12:30,120 --> 00:12:34,920
+bacteriorhodopsin بسيط للغاية لا يتطلب أي شروط
+
+156
+00:12:34,920 --> 00:12:40,580
+للتفاعل مع الضوء بمعنى أخر لو إيجاد ضوء من الناحية
+
+157
+00:12:40,580 --> 00:12:43,770
+هايهيستجيب إله، لو إجاء الضوء من الناحية high،
+
+158
+00:12:43,770 --> 00:12:46,830
+هيستجيب إله، لو إجاء الضوء من الناحية high،
+
+159
+00:12:46,830 --> 00:12:49,890
+هيستجيب إله، من وين ما إجا الضوء، من تحت، من فوق،
+
+160
+00:12:49,890 --> 00:12:53,510
+من شماله، من يمينه، من وين ما سقط الضوء على هذه
+
+161
+00:12:53,510 --> 00:12:57,210
+الخلية البكتيرية، هيصل ل .. اللي هو ال
+
+162
+00:12:57,210 --> 00:13:01,950
+bacteriorhodopsin ويسبب التغيرات اللي حكينا عنها
+
+163
+00:13:01,950 --> 00:13:05,870
+في الجزئين إبتعينه طيب ممكنسان يقولوا هل هذا يعني
+
+164
+00:13:05,870 --> 00:13:10,010
+.. إيش علاقته؟قضيت إنه يستجيب من وين ما إيجاه
+
+165
+00:13:10,010 --> 00:13:16,330
+الضوء، معناته هذا الجهاز بسيط للغاية، ممكن نقول
+
+166
+00:13:16,330 --> 00:13:21,430
+هذا يعني أفضل، يعني نقول لأ وكل ما تم التعقيد
+
+167
+00:13:21,430 --> 00:13:26,230
+بيصير حاجة بيسموها ال directionality أو الاستجابة
+
+168
+00:13:26,230 --> 00:13:30,230
+أو الاتجاهية في الاستجابة، بمعنى آخر الإنسان اللي
+
+169
+00:13:30,230 --> 00:13:35,350
+هو أعلى الكائنات لو إيجاله الضوء من خلف رأسه مش
+
+170
+00:13:35,350 --> 00:13:41,340
+هيشوفه، مش هيشوفهفبالتالي ليش؟ لأنه عنده الاستجابة
+
+171
+00:13:41,340 --> 00:13:44,880
+directional بمعنى إنه عشان يشوف الضوء لازم الضوء
+
+172
+00:13:44,880 --> 00:13:49,720
+يكون موجه باتجاه جهاز الإبصار لدى الإنسان وهو
+
+173
+00:13:49,720 --> 00:13:56,220
+العين .. وهو العينالان نيجي لل step الأعلى من ال
+
+174
+00:13:56,220 --> 00:14:00,260
+bacteriorhodopsin بنقول thus early animals used
+
+175
+00:14:00,260 --> 00:14:03,940
+something akin to the original rhodopsin and very
+
+176
+00:14:03,940 --> 00:14:09,200
+simple optical system الان ال rodopsin ال original
+
+177
+00:14:09,200 --> 00:14:13,500
+rhodopsin وال bacteriorhodopsin موجودفي الخلية
+
+178
+00:14:13,500 --> 00:14:19,640
+البكتيرية ليس له مثلا عضي من عضيات الخلية معين لأو
+
+179
+00:14:19,640 --> 00:14:23,380
+انهم موجود في ال cytoplasm بتاع الخلية و من وين ما
+
+180
+00:14:23,380 --> 00:14:27,700
+اجاله الضوء بيستجيب الان الكائنات اللي أعلى طبقة
+
+181
+00:14:27,700 --> 00:14:33,580
+من ال helobacterium helobium او من عالم البكتيريا
+
+182
+00:14:33,580 --> 00:14:38,380
+الكائنات الأعلى طبقة قليلة فيها موجود ال rodopsin
+
+183
+00:14:39,020 --> 00:14:41,980
+اللي بيشبه الrodopsin بتاع الhalobacterium
+
+184
+00:14:41,980 --> 00:14:46,080
+halobium بس مضاف له very simple optical system
+
+185
+00:14:46,080 --> 00:14:50,040
+يعني في مضاف له جهاز إبصار موجود ال rodopsin في
+
+186
+00:14:50,040 --> 00:14:53,860
+هذا الجهاز الإبصار عشان نوضح الفكرة بنقول for
+
+187
+00:14:53,860 --> 00:14:58,520
+example early worms الديدان القديمة and shellfish
+
+188
+00:14:58,520 --> 00:15:03,720
+والمحارات المحارلي الأصدافالبحرية had light
+
+189
+00:15:03,720 --> 00:15:07,440
+sensing cells that lined a small cup-like
+
+190
+00:15:07,440 --> 00:15:11,520
+structure فيها هذه الـ shellfish اللي هي المحارات
+
+191
+00:15:11,520 --> 00:15:17,040
+أو الأصداف و الديدان القديمة فيها خلايا حساسة
+
+192
+00:15:17,040 --> 00:15:20,500
+للضوء طبعا ليش حساسة للضوء لأن فيها ال Rodopsin
+
+193
+00:15:20,500 --> 00:15:24,140
+فيها ال Rodopsin الخاص فيها طب وين موجودة هذه
+
+194
+00:15:24,140 --> 00:15:27,960
+الخلايا الحساسة موجودة ضمن very simple optical
+
+195
+00:15:27,960 --> 00:15:32,720
+system عبارة عن إيش ال optical systemعبارة عن cup
+
+196
+00:15:32,720 --> 00:15:37,580
+-like structure هي كتركيبة زي الفنجان أو زي الوعاء
+
+197
+00:15:37,580 --> 00:15:42,520
+الصغير المفتوح بالظبط زي الصحن أو الفنجان طبعا هذه
+
+198
+00:15:42,520 --> 00:15:46,240
+الخلايا الحساسة للضوء و اللي فيها رودوبسين تبطن
+
+199
+00:15:46,240 --> 00:15:52,100
+تبطن او تكسو من الداخلsmall cup-like structure ..
+
+200
+00:15:52,100 --> 00:15:57,060
+small cup-like structure نرجع للصورة هنا، بنقول هي
+
+201
+00:15:57,060 --> 00:16:00,580
+.. هي صورة للمحارة، المحارة عبارة عن cup-like
+
+202
+00:16:00,580 --> 00:16:05,040
+structures طبعا مبطنة من الداخل .. مبطنة من
+
+203
+00:16:05,040 --> 00:16:08,770
+الداخل، طبعا احنا ما بدنا .. يعنيهذه اللي هي
+
+204
+00:16:08,770 --> 00:16:12,850
+الإفرازات المحارة أو شيء من هذا القبيل وإنما في
+
+205
+00:16:12,850 --> 00:16:16,370
+ابطانة للمحارة تمام لتوضيح الفكرة طبعا هذه
+
+206
+00:16:16,370 --> 00:16:21,150
+الابطانة موجود فيها light sensing cells light
+
+207
+00:16:21,150 --> 00:16:24,650
+sensing cells بمعنى في خلايا حساسة للضوء ليش هذه
+
+208
+00:16:24,650 --> 00:16:28,930
+الخلايا اللي بتبطن هذا ال cup؟حساسة للضوء لأنه
+
+209
+00:16:28,930 --> 00:16:32,610
+موجود فيها ال Rodopsin الان مش هسميه Rodopsin
+
+210
+00:16:32,610 --> 00:16:35,730
+بكتيريو Rodopsin هسميه Rodopsin لأنه احنا اهداك
+
+211
+00:16:35,730 --> 00:16:38,810
+سميناه بكتيريو Rodopsin لأنه موجود ضمن البكتيريا
+
+212
+00:16:38,810 --> 00:16:43,710
+هذا Rodopsin يشبه في التركيب ولكن مع إضافة هذا ال
+
+213
+00:16:43,710 --> 00:16:47,110
+optical systemليش سميناها optical system؟ لأنه
+
+214
+00:16:47,110 --> 00:16:51,650
+بلعب دور أنه الضوء إذا إجا من ورا مش هيصل لل light
+
+215
+00:16:51,650 --> 00:16:55,730
+sensing cells فبالتالي مش .. مش هيستفيد هذا الكائن
+
+216
+00:16:55,730 --> 00:17:00,510
+الحقيقي أو هذا الحيوان منه بينما لو إجا مباشر ..
+
+217
+00:17:00,510 --> 00:17:05,970
+مباشر ووصل لل light sensing cell إذا ساعتها
+
+218
+00:17:05,970 --> 00:17:10,490
+هيستجيب للضوء طب هذا إيش فادني؟ فادني في شغل تاني
+
+219
+00:17:10,490 --> 00:17:16,080
+أنه في optical system أضيفالـ Bacteriorhodopsin مش
+
+220
+00:17:16,080 --> 00:17:20,560
+optical system مجرد جزء كيميائي .. جزء كيميائي أو
+
+221
+00:17:20,560 --> 00:17:24,060
+مركب عضوي داخل خلية و خلصنا، اذا هذا مش optical
+
+222
+00:17:24,060 --> 00:17:28,860
+system و انما مركب عضوي يستطيع التأثر بالضوء أما
+
+223
+00:17:28,860 --> 00:17:34,900
+بالنسبة لأ المحار والديدان القديمة، في عندهغير
+
+224
+00:17:34,900 --> 00:17:38,260
+قضية الردوبسين الموجود في خلايا سميناها light
+
+225
+00:17:38,260 --> 00:17:42,540
+sensing cells، في عندي optical system، very simple
+
+226
+00:17:42,540 --> 00:17:46,760
+optical system، هو عبارة عن cup-like structure،
+
+227
+00:17:46,760 --> 00:17:50,600
+يعني تركيبة هيك بتشبه الفنجان أو بتشبه الصحن
+
+228
+00:17:50,720 --> 00:17:55,020
+بالإضافة إنه أضيفت قضية ال directionality إنه
+
+229
+00:17:55,020 --> 00:17:58,820
+الضوء إذا إجا على ال cup من وجهه بينشاف لأنه بيصل
+
+230
+00:17:58,820 --> 00:18:01,980
+لل light sensing cells إذا ما إجا من .. من .. من
+
+231
+00:18:01,980 --> 00:18:06,580
+دهر المحارة مش هينشاف أبدا لأنه مش هيصل لل light
+
+232
+00:18:06,580 --> 00:18:10,540
+sensing cells because each cell is shielded from
+
+233
+00:18:10,540 --> 00:18:13,620
+light that approaches the cup from the non-seeing
+
+234
+00:18:13,620 --> 00:18:17,420
+side ليش مش هينشاف؟ لأنه كل خلية من الخلايا
+
+235
+00:18:17,420 --> 00:18:22,730
+الحساسة للضوءيعني محمية من الضوء إذا إجا الضوء لل
+
+236
+00:18:22,730 --> 00:18:27,970
+cup من ال non-seeing side .. من ال non-seeing side
+
+237
+00:18:27,970 --> 00:18:33,190
+اتطورت الحياة أكتر أو خلينا نقول مش اتطورت الحياة
+
+238
+00:18:33,190 --> 00:18:36,350
+أكتر يعني هي الحياة متطورة من .. من ذو بدء الخليقة
+
+239
+00:18:36,350 --> 00:18:40,550
+أو ننتقل لطبقة أعلى من الكائنات طبقة أعلى من
+
+240
+00:18:40,550 --> 00:18:44,950
+المحارات و من ال .. الديدان القديمة بنقول if the
+
+241
+00:18:44,950 --> 00:18:50,110
+cup is made deeperand the sides are turned over a
+
+242
+00:18:50,110 --> 00:18:54,710
+lensless spin hole system is produced نرجع للمحار
+
+243
+00:18:54,710 --> 00:19:00,570
+ونقول المحار أعقد من البكتيريا في شغلتين انه ال
+
+244
+00:19:00,570 --> 00:19:04,770
+light sensing cells اللي فيها الرضبسين محمية من
+
+245
+00:19:04,770 --> 00:19:08,750
+جهةبال optical system هذا اللي أنا بأشير عليه اللي
+
+246
+00:19:08,750 --> 00:19:12,550
+هو cup-like structure وتتمتع بخاصية ال
+
+247
+00:19:12,550 --> 00:19:16,830
+directionality طيب لو هذا ال cup سألوا العلماء
+
+248
+00:19:16,830 --> 00:19:22,670
+سؤال هل يوجد كائنات أعلى من المحار أعلى من المحار
+
+249
+00:19:22,670 --> 00:19:28,090
+فيها هذا ال optical system أعمق؟وحوافه متقاربة ليش
+
+250
+00:19:28,090 --> 00:19:31,990
+العلماء صاروا يدوروا على مخلوقات تتمتع بهذه
+
+251
+00:19:31,990 --> 00:19:38,930
+الخاصية لأنهم بدهم يقتربوا في التركيب بما يشبه
+
+252
+00:19:38,930 --> 00:19:42,590
+الإنسان .. بما يشبه عين الإنسان قالوا يا ترى الآن
+
+253
+00:19:42,590 --> 00:19:45,910
+لو في عندنا .. لو ش .. لو شفنا أو .. أو لجينا
+
+254
+00:19:45,910 --> 00:19:50,030
+مخلوقات أو كائنات عندها optical system يشبه ال
+
+255
+00:19:50,030 --> 00:19:54,230
+optical system بتاع المحار بس أطور شوية منه بمعنى
+
+256
+00:19:54,230 --> 00:20:01,290
+آخرإنه ال cup هذا صار عميق .. صار عميق وتقاربة
+
+257
+00:20:01,290 --> 00:20:05,650
+الحواف بتاعته يعني ال light sensing cells الخلايا
+
+258
+00:20:05,650 --> 00:20:11,730
+الحساسة للضوء المبطنة لل .. لل cup هذا بدنا نجيلنا
+
+259
+00:20:11,730 --> 00:20:15,430
+أي كائن حي آخر غير المحار يكون فيه عنده نفس الفكرة
+
+260
+00:20:15,430 --> 00:20:19,810
+بس مع اختلاف بسيط إنه ال cup عميق عشان يصير يشبه
+
+261
+00:20:19,810 --> 00:20:24,170
+العينوإن الحواف بتاعة ال cup متقاربة مع بعضها
+
+262
+00:20:24,170 --> 00:20:27,750
+البعض عشان تصير تشبه ال pupil بدناش crystalline
+
+263
+00:20:27,750 --> 00:20:30,910
+lens و بدناش cornي احنا بدنا بس المرحلة اللي بعدها
+
+264
+00:20:30,910 --> 00:20:36,710
+فبالتالي if the cup is made deeper and the sides
+
+265
+00:20:36,710 --> 00:20:42,450
+الحواف are turned off over يعني متقاربة أو بدت
+
+266
+00:20:42,450 --> 00:20:46,820
+تتسكر على بعضها البعضبساعتها هيكون هذا الكائن الحي
+
+267
+00:20:46,820 --> 00:20:52,380
+عنده ما يسمى بال lensless pinhole system lensless
+
+268
+00:20:52,380 --> 00:20:56,600
+pinhole system يعني optical system عبارة عن
+
+269
+00:20:56,600 --> 00:21:01,150
+pinhole لأنه إذا تقاربت الحوافو سكرت ع بعضها هيصير
+
+270
+00:21:01,150 --> 00:21:06,130
+عندى كأنه pupil او pin hole يعني مع شكل كروي مغلق
+
+271
+00:21:06,130 --> 00:21:09,790
+فقط مفتوح من عند ال pin hole ومافيش crystalline
+
+272
+00:21:09,790 --> 00:21:14,030
+lens اذا بسميه lensless optical system بدنا نأكد
+
+273
+00:21:14,030 --> 00:21:17,210
+على نقطة ان احنا هذا الكلام اللى انا بحكيه مش
+
+274
+00:21:17,210 --> 00:21:21,850
+مقصود فيه المحار وانما العلماء بدوروا على كائن ..
+
+275
+00:21:21,850 --> 00:21:27,600
+على كائن أرقى قليلا من المحارو هم ما يقصدوا أن
+
+276
+00:21:27,600 --> 00:21:32,280
+المحار يتطور بذاته و يسير هذا المحار، هيضله محار
+
+277
+00:21:32,280 --> 00:21:35,980
+من حد ما يفلق لغاية ما تنتهي حياته، الآن هم ده
+
+278
+00:21:35,980 --> 00:21:39,240
+بدهم يدوروا على درجة أعلى من الحياة أو درجة أعلى
+
+279
+00:21:39,240 --> 00:21:43,060
+من الكائنات الحية، بمعنى إيش يعني أعلى؟ يعني
+
+280
+00:21:43,060 --> 00:21:46,660
+الجهاز الإبصار اللي ديها مطور أكثر، إيش يعني مطور
+
+281
+00:21:46,660 --> 00:21:52,120
+أكثر؟ يعني يشبه أكثر، جهاز يشبه أكثر قليلاجهاز
+
+282
+00:21:52,120 --> 00:21:56,280
+الإبصار بتاع أعلى الكائنات وهو الإنسان، الإنسان
+
+283
+00:21:56,280 --> 00:22:02,800
+وان ننساش انه لين .. انه لين عبارة عن كب مغلقمغلق
+
+284
+00:22:02,800 --> 00:22:06,060
+و فيه pinhole اللي هو ال pupil تمام و فيه
+
+285
+00:22:06,060 --> 00:22:09,920
+crystalline lens العلماء بدهم بس تطور قليل جدا او
+
+286
+00:22:09,920 --> 00:22:14,060
+كائن أرقى قليلا من المحار بس انه يكون ال .. ال cup
+
+287
+00:22:14,060 --> 00:22:17,920
+بتاعه more deep جهاز الإبصار بتاعه more deep و
+
+288
+00:22:17,920 --> 00:22:22,340
+الحواف تتتقاربت عشان تشبه ال pupil بدناش نسأل الآن
+
+289
+00:22:22,340 --> 00:22:25,240
+عن ال .. ال crystalline lens بدناش نسأل عن
+
+290
+00:22:25,240 --> 00:22:30,180
+الكورنيا و ما إلى ذلك وجدوا العلماء طلبهمفي كائن
+
+291
+00:22:30,180 --> 00:22:34,300
+يسمى ال neutralist ال neutralist اللي هو نوع من ال
+
+292
+00:22:34,300 --> 00:22:39,760
+swimming مولوسك اللي هي الحلزونات التي العائمة ..
+
+293
+00:22:39,760 --> 00:22:43,260
+الحلزون العائم و احنا جبنا صورة هنا ل ال
+
+294
+00:22:43,260 --> 00:22:48,100
+neutralist neutralist
+
+295
+00:22:48,100 --> 00:22:53,540
+هينوع من أنواع الحلزونات العائمة، هاي جهاز الإبصار
+
+296
+00:22:53,540 --> 00:22:57,900
+فيه، هاي جهاز الإبصار فيه، أنا كبرت جهاز الإبصار
+
+297
+00:22:57,900 --> 00:23:01,400
+عشان نشوف إنه عبارة عن كأنه عين بس بدون
+
+298
+00:23:01,400 --> 00:23:05,140
+crystalline lens أو كورن، يعني مجرد .. يعني تجويف
+
+299
+00:23:05,140 --> 00:23:10,240
+عميق بالظبط زي كورة العين و الحواف تقاربت لدرجة
+
+300
+00:23:10,240 --> 00:23:14,790
+إنه ..أصبح عندي ما يسمى بال lensless spin hole
+
+301
+00:23:14,790 --> 00:23:19,250
+system طبعا هذا الكلام لجوه such a system is used
+
+302
+00:23:19,250 --> 00:23:22,590
+by a very primitive swimming mollusc طبعا هذا ال
+
+303
+00:23:22,590 --> 00:23:26,230
+mollusc مش .. مش رقي، very primitive، بداي جدا بس
+
+304
+00:23:26,230 --> 00:23:33,080
+هو أرقىمن إبصاريا .. أرقى إبصاريا من المحار .. إذا
+
+305
+00:23:33,080 --> 00:23:37,780
+this system is used by a very primitive swimming
+
+306
+00:23:37,780 --> 00:23:41,760
+mollusc called Nutilus thus with visible light
+
+307
+00:23:41,760 --> 00:23:45,300
+falling .. الآن بدنا نلخص كل المحاضرات اللي ..
+
+308
+00:23:45,300 --> 00:23:51,960
+اللي سبقت بالفقرة هاي بنقول هكذا بمجردعرفنا طبعا
+
+309
+00:23:51,960 --> 00:23:55,260
+thus with visible light falling on the earth
+
+310
+00:23:55,260 --> 00:24:00,000
+androdopsin already present the stage was set for
+
+311
+00:24:00,000 --> 00:24:03,280
+the development from simple light sensing to
+
+312
+00:24:03,280 --> 00:24:08,130
+natural or living optics يعنيالضوء وصل نقم من
+
+313
+00:24:08,130 --> 00:24:13,030
+مصدره اللي هو الشمس صار على سطح الأرض بشكل آمن ال
+
+314
+00:24:13,030 --> 00:24:17,590
+Rodopsin اللي هو الجزء الحساس للضوء و اللي هيقدر
+
+315
+00:24:17,590 --> 00:24:21,150
+يترجم أن الضوء موجود في خلايا نقم .. خلايا
+
+316
+00:24:21,150 --> 00:24:25,270
+الإنسان، خلايا الحيوان، خلايا البكتيريا، الاخرى ال
+
+317
+00:24:25,270 --> 00:24:30,320
+Rodopsin موجود، اذا الأن أصبحالمرحلة أو الحياة
+
+318
+00:24:30,320 --> 00:24:35,000
+انتقلت لطور من ال very simple light sensing اللي
+
+319
+00:24:35,000 --> 00:24:38,060
+هو موجود في ال bacteriorhodopsin مجرد light
+
+320
+00:24:38,060 --> 00:24:43,420
+sensing to natural or living optics يعني ل .. اللي
+
+321
+00:24:43,420 --> 00:24:48,560
+هو الإبصار اللي بي .. بي .. بي .. بنستخدمه لتأدية
+
+322
+00:24:48,560 --> 00:24:54,050
+كل مهام الحياة أو الغالبية العظمى من مهامالحياة و
+
+323
+00:24:54,050 --> 00:24:58,250
+هيك احنا وصلنا للجزء التاني اللي هو ال physical
+
+324
+00:24:58,250 --> 00:25:02,030
+optics و الصفات الفيزيائية للضوء و المرة القادمة
+
+325
+00:25:02,030 --> 00:25:06,530
+هنستكمل معاه ان شاء الله تعالى و يعطيكم العافية
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/9_PW6XMKhCw_raw.json b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/9_PW6XMKhCw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e30248885543910ed50c0104962eb5b525df3f5f
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/9_PW6XMKhCw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2303, "start": 2.23, "end": 23.03, "text": "بسم الله الرحمن الرحيم هذه تجربة او جهاز بيجيس لل optical density و لل transmittance كل ما زادت ال optical density بيقل لل transmittance كل ما زادت ال optical density بيقل لل transmittance الجهاز عبارة عن قطعتين موصلين في جهاز computer يعني بيحسب ال", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 29538, 6055, 7435, 25513, 3660, 1975, 2407, 10874, 3224, 31377, 4724, 1829, 7435, 1829, 3794, 24976, 20674, 10305, 4032, 24976, 7715, 593, 719, 28242, 19446, 30767, 18513, 2655, 2423, 20674, 10305, 4724, 1829, 4587, 1211, 24976, 7715, 593, 719, 28242, 19446, 30767, 18513, 2655, 2423, 20674, 10305, 4724, 1829, 4587, 1211, 24976, 7715, 593, 719, 25724, 3224, 31377, 6225, 3555, 9640, 3660, 18871, 12174, 9566, 34268, 9957, 3714, 2407, 36520, 9957, 8978, 10874, 3224, 31377, 3820, 37495, 22653, 4724, 1829, 5016, 35457, 2423], "avg_logprob": -0.12710013312678184, "compression_ratio": 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"probability": 0.55548095703125}, {"start": 238.74, "end": 238.96, "word": " الضوء", "probability": 0.84332275390625}, {"start": 238.96, "end": 239.3, "word": " صدر", "probability": 0.9886067708333334}, {"start": 239.3, "end": 239.48, "word": " 100", "probability": 0.83349609375}, {"start": 239.48, "end": 239.98, "word": "%", "probability": 0.9833984375}, {"start": 239.98, "end": 240.4, "word": " اللي", "probability": 0.76220703125}, {"start": 240.4, "end": 240.76, "word": " نفذ", "probability": 0.9510091145833334}, {"start": 240.76, "end": 241.06, "word": " عبر", "probability": 0.982666015625}, {"start": 241.06, "end": 241.82, "word": " الزرقونيا", "probability": 0.6998697916666666}, {"start": 241.82, "end": 242.74, "word": " 48", "probability": 0.97705078125}, {"start": 242.74, "end": 243.14, "word": "%", "probability": 0.99072265625}, {"start": 243.14, "end": 243.42, "word": " نجيب", "probability": 0.7913818359375}, {"start": 243.42, "end": 243.66, "word": " مادة", "probability": 0.97021484375}, {"start": 243.66, "end": 244.06, "word": " أكسف", "probability": 0.8067626953125}, {"start": 244.06, "end": 244.62, "word": " وأكسف", "probability": 0.8880615234375}, {"start": 244.62, "end": 245.2, "word": " اللي", "probability": 0.927001953125}, {"start": 245.2, "end": 245.34, "word": " هي", "probability": 0.80517578125}, {"start": 245.34, "end": 245.76, "word": " غطاء", "probability": 0.9562174479166666}, {"start": 245.76, "end": 246.22, "word": " لمبة", "probability": 0.7578125}, {"start": 246.22, "end": 247.3, "word": " كهربائية", "probability": 0.9814453125}, {"start": 247.3, "end": 248.38, "word": " يعني", "probability": 0.81787109375}, {"start": 248.38, "end": 260.68, "word": " الآن", "probability": 0.63232421875}, {"start": 260.68, "end": 261.08, "word": " هاي", "probability": 0.599609375}, {"start": 261.08, "end": 261.4, "word": " قطعة", "probability": 0.9661458333333334}, {"start": 261.4, "end": 261.44, "word": " ..", "probability": 0.4013671875}, {"start": 261.44, "end": 261.86, "word": " قطعة", "probability": 0.9609375}, {"start": 261.86, "end": 262.44, "word": " الإصدار", "probability": 0.95361328125}, {"start": 262.44, "end": 262.68, "word": " تحت", "probability": 0.5753173828125}, {"start": 262.68, "end": 262.96, "word": " الضوء", "probability": 0.979736328125}, {"start": 262.96, "end": 263.4, "word": " وقطعة", "probability": 0.8470052083333334}, {"start": 263.4, "end": 264.12, "word": " الاستقبال", "probability": 0.97353515625}, {"start": 264.12, "end": 264.4, "word": " تحت", "probability": 0.993408203125}, {"start": 264.4, "end": 264.84, "word": " الضوء", "probability": 0.9886474609375}], "temperature": 1.0}, {"id": 11, "seek": 29324, "start": 269.04, "end": 293.24, "text": "هنا تقريبا الكثافة البصرية ال optical density تقريبا 15% اللى نفذ من اجزاز اللمبة high تقريبا 73% يعني لو حطينا مصباح كهربائي وغطينا بهذه ال cover هينفذ من ضوء المصباح تقريبا 72% ويعطيكم العافية والسلام عليكم ورحمة الله وبركاته", "tokens": [3224, 8315, 6055, 4587, 16572, 3555, 995, 33251, 12984, 31845, 3660, 29739, 9381, 2288, 10632, 2423, 20674, 10305, 6055, 4587, 16572, 3555, 995, 2119, 4, 13672, 7578, 8717, 5172, 8848, 9154, 1975, 7435, 11622, 31377, 13672, 2304, 49401, 1090, 6055, 4587, 16572, 3555, 995, 28387, 4, 37495, 22653, 45164, 11331, 9566, 1829, 8315, 3714, 9381, 3555, 39319, 9122, 3224, 25513, 16373, 1829, 4032, 17082, 9566, 1829, 8315, 39627, 24192, 2423, 2060, 8032, 9957, 5172, 8848, 9154, 48812, 2407, 38207, 9673, 9381, 3555, 39319, 6055, 4587, 16572, 3555, 995, 18731, 4, 4032, 40228, 9566, 1829, 24793, 18863, 31845, 10632, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.14322916457527562, "compression_ratio": 1.6916299559471366, "no_speech_prob": 2.193450927734375e-05, "words": [{"start": 269.04, "end": 269.44, "word": "هنا", "probability": 0.83740234375}, {"start": 269.44, "end": 270.06, "word": " تقريبا", "probability": 0.97763671875}, {"start": 270.06, "end": 270.64, "word": " الكثافة", "probability": 0.896728515625}, {"start": 270.64, "end": 271.34, "word": " البصرية", "probability": 0.9560546875}, {"start": 271.34, "end": 272.54, "word": " ال", "probability": 0.70703125}, {"start": 272.54, "end": 272.92, "word": " optical", "probability": 0.83447265625}, {"start": 272.92, "end": 273.34, "word": " density", "probability": 0.8544921875}, {"start": 273.34, "end": 273.82, "word": " تقريبا", "probability": 0.99140625}, {"start": 273.82, "end": 274.18, "word": " 15", "probability": 0.7861328125}, {"start": 274.18, "end": 274.74, "word": "%", "probability": 0.7548828125}, {"start": 274.74, "end": 275.2, "word": " اللى", "probability": 0.7294921875}, {"start": 275.2, "end": 275.68, "word": " نفذ", "probability": 0.9742838541666666}, {"start": 275.68, "end": 276.12, "word": " من", "probability": 0.98046875}, {"start": 276.12, "end": 277.1, "word": " اجزاز", "probability": 0.73114013671875}, {"start": 277.1, "end": 277.56, "word": " اللمبة", "probability": 0.56201171875}, {"start": 277.56, "end": 277.86, "word": " high", "probability": 0.364013671875}, {"start": 277.86, "end": 278.7, "word": " تقريبا", "probability": 0.99541015625}, {"start": 278.7, "end": 279.3, "word": " 73", "probability": 0.91162109375}, {"start": 279.3, "end": 280.14, "word": "%", "probability": 0.9677734375}, {"start": 280.14, "end": 281.08, "word": " يعني", "probability": 0.77294921875}, {"start": 281.08, "end": 281.4, "word": " لو", "probability": 0.97265625}, {"start": 281.4, "end": 281.84, "word": " حطينا", "probability": 0.8812255859375}, {"start": 281.84, "end": 282.26, "word": " مصباح", "probability": 0.8707275390625}, {"start": 282.26, "end": 282.82, "word": " كهربائي", "probability": 0.8830078125}, {"start": 282.82, "end": 283.32, "word": " وغطينا", "probability": 0.857470703125}, {"start": 283.32, "end": 283.8, "word": " بهذه", "probability": 0.4654541015625}, {"start": 283.8, "end": 284.42, "word": " ال", "probability": 0.87939453125}, {"start": 284.42, "end": 284.78, "word": " cover", "probability": 0.90966796875}, {"start": 284.78, "end": 285.9, "word": " هينفذ", "probability": 0.74169921875}, {"start": 285.9, "end": 286.16, "word": " من", "probability": 0.984375}, {"start": 286.16, "end": 286.48, "word": " ضوء", "probability": 0.9684244791666666}, {"start": 286.48, "end": 287.0, "word": " المصباح", "probability": 0.989013671875}, {"start": 287.0, "end": 287.52, "word": " تقريبا", "probability": 0.991015625}, {"start": 287.52, "end": 288.14, "word": " 72", "probability": 0.9736328125}, {"start": 288.14, "end": 289.62, "word": "%", "probability": 0.9873046875}, {"start": 289.62, "end": 290.22, "word": " ويعطيكم", "probability": 0.90888671875}, {"start": 290.22, "end": 290.64, "word": " العافية", "probability": 0.9620768229166666}, {"start": 290.64, "end": 291.04, "word": " والسلام", "probability": 0.8541666666666666}, {"start": 291.04, "end": 291.5, "word": " عليكم", "probability": 0.945556640625}, {"start": 291.5, "end": 291.92, "word": " ورحمة", "probability": 0.9847412109375}, {"start": 291.92, "end": 292.22, "word": " الله", "probability": 0.97216796875}, {"start": 292.22, "end": 293.24, "word": " وبركاته", "probability": 0.987890625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 293.4538125, "duration_after_vad": 270.736875}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/CQeq0bGJeVc.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/CQeq0bGJeVc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4cb8755fc8fc45e213e7d2a4f3516df4c5985e76
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/CQeq0bGJeVc.srt
@@ -0,0 +1,1902 @@
+1
+00:00:01,400 --> 00:00:04,780
+بسم الله الرحمن الرحيم نبدأ في مراجعة الامتحان
+
+2
+00:00:04,780 --> 00:00:08,820
+النسخة الأولى اللي هو الصباحية طبعا إن شاء الله
+
+3
+00:00:08,820 --> 00:00:15,240
+تعالَ نبدأ السؤال الأول if 
+
+4
+00:00:15,240 --> 00:00:18,380
+the magnetic field of light propagates vertically
+
+5
+00:00:18,380 --> 00:00:21,840
+then the light is polarized طالما الـ magnetic
+
+6
+00:00:21,840 --> 00:00:25,960
+field vertical معناته الـ electric field horizontal
+
+7
+00:00:25,960 --> 00:00:29,500
+وإحنا الـ polarization مرتبط بالـ electric field مش
+
+8
+00:00:29,500 --> 00:00:33,560
+..بالـ magnetic field، الـ magnetic field بينه وبين
+
+9
+00:00:33,560 --> 00:00:36,060
+الـ electric field فيه زاوية قائمة طالما الـ
+
+10
+00:00:36,060 --> 00:00:40,100
+magnetic field vertical معناته الـ electric field
+
+11
+00:00:40,100 --> 00:00:43,100
+horizontal وبالتالي الـ polarization horizontal
+
+12
+00:00:43,100 --> 00:00:48,770
+ننتقل للسؤال اللي بعده a dropping of an electron
+
+13
+00:00:48,770 --> 00:00:52,030
+from higher energy state to lower energy state
+
+14
+00:00:52,030 --> 00:00:56,170
+must be accompanied by absorption of a photon الـ
+
+15
+00:00:56,170 --> 00:00:59,690
+absorption of a photon بيصعد مع الإلكترون مش بيهبط
+
+16
+00:00:59,690 --> 00:01:04,490
+هنا لما بيهبط بيفقد فوتون مش بيكتسب فوتون ما بيعملش
+
+17
+00:01:04,490 --> 00:01:08,890
+absorption بيعمل emission فبالتالي هذا غلط هذا غلط
+
+18
+00:01:12,170 --> 00:01:15,330
+The theory that can explain the behavior of light
+
+19
+00:01:15,330 --> 00:01:19,210
+waves at atomic and molecular levels اللي هي الـ
+
+20
+00:01:19,210 --> 00:01:23,800
+quantum theory قولنا الـ electromagnetic wave الـ
+
+21
+00:01:23,800 --> 00:01:28,100
+electromagnetic wave theory ما بتصلح على الظواهر
+
+22
+00:01:28,100 --> 00:01:32,900
+المرئية بالعين الـ reflection الـ refraction الـ
+
+23
+00:01:32,900 --> 00:01:36,440
+diffraction وما إلى ذلك لما بنيجي على مستوى
+
+24
+00:01:36,440 --> 00:01:39,240
+الذرات والجزئيات الـ electromagnetic wave بتقدرش
+
+25
+00:01:39,240 --> 00:01:43,060
+تفسر هذه الظواهر فبالتالي الـ quantum theory هي
+
+26
+00:01:43,060 --> 00:01:44,920
+اللي بتفسر لهذه الظواهر
+
+27
+00:01:48,440 --> 00:01:51,480
+According to the wave theory, collimated light
+
+28
+00:01:51,480 --> 00:01:54,280
+should remain so after traversing an aperture
+
+29
+00:01:57,470 --> 00:02:00,570
+الـ wave theory هذه حسب الـ corpuscular theory اللي
+
+30
+00:02:00,570 --> 00:02:03,970
+أقدم نظرية واللي عفى عليها الزمن أنه بعد ما يعدي
+
+31
+00:02:03,970 --> 00:02:09,150
+من فتحة في جدار بيظل collimated يعني موازي لبعض و
+
+32
+00:02:09,150 --> 00:02:12,130
+لبعض الصحيح أنه ما بيظلش collimated أنه بعد ما يعدي
+
+33
+00:02:12,130 --> 00:02:15,290
+في فتحة في جدار بيصير له ظاهرة الـ diffraction اللي
+
+34
+00:02:15,290 --> 00:02:19,130
+هي أنه بتبعد عن بعض ويصير له divergence حسب الـ wave
+
+35
+00:02:19,130 --> 00:02:22,840
+theory أما قضية أنه يظل collimated هذه الفرضية
+
+36
+00:02:22,840 --> 00:02:26,900
+فرضتها الـ corpuscular theory وبالتالي الإجابة خطأ
+
+37
+00:02:26,900 --> 00:02:33,900
+..الإجابة خطأ طيب what is the critical angle
+
+38
+00:02:33,900 --> 00:02:37,820
+between when .. the critical angle when light
+
+39
+00:02:37,820 --> 00:02:43,080
+travels from air and تساوي واحد to glass and تساوي
+
+40
+00:02:43,080 --> 00:02:46,980
+واحد ونصف هذه القضية بدها شوية تفكير بسيط جدا
+
+41
+00:02:46,980 --> 00:02:50,880
+الضوء بينتقل من الهواء low refractive index لأ
+
+42
+00:02:50,880 --> 00:02:54,570
+للجلاس عمره ما بيصير critical angle إحنا قلنا لـ
+
+43
+00:02:54,570 --> 00:02:58,490
+critical angle لما الضوء بينتقل من مادة أعلى في الـ
+
+44
+00:02:58,490 --> 00:03:01,690
+refractive index أو أعلى في الكثافة لمادة أقل
+
+45
+00:03:01,690 --> 00:03:05,850
+العكس ما بيصيرش فبالتالي الإجابة فورا بدون حسابات
+
+46
+00:03:05,850 --> 00:03:11,010
+none لأنه بينتقل من الهواء لل glasses ما فيش critical
+
+47
+00:03:11,010 --> 00:03:13,910
+angle لما ينتقل من الهواء لل glasses أما في
+
+48
+00:03:13,910 --> 00:03:18,360
+critical angle لما ينتقل من ال glasses للهواء طيب
+
+49
+00:03:18,360 --> 00:03:21,780
+according to quantum theory red light has less
+
+50
+00:03:21,780 --> 00:03:25,700
+energy than yellow light، الآن مين أطول موجتا؟ الـ
+
+51
+00:03:25,700 --> 00:03:28,360
+red light أطول من الـ yellow light، الـ red light
+
+52
+00:03:28,360 --> 00:03:33,000
+أطول الـ visible light، أحمر، برتقالي، أصفر، أخضر،
+
+53
+00:03:33,000 --> 00:03:37,770
+أزرق، نيلي، بنفسجي إذا الأحمر أطولهم، البرتقالي أقل
+
+54
+00:03:37,770 --> 00:03:40,510
+طول منه، والأصفر أقل طول، إحنا بهمنا الأحمر
+
+55
+00:03:40,510 --> 00:03:45,670
+والأصفر، إذا طالما الأصفر أقل طولا من الأحمر، إذا
+
+56
+00:03:45,670 --> 00:03:49,050
+الـ frequency بتاعته أعلى، تردده، عدد الموجات في
+
+57
+00:03:49,050 --> 00:03:53,850
+وحدة الزمن أكثر، فبالتالي الـ yellow light إن الـ
+
+58
+00:03:53,850 --> 00:03:57,490
+energy بتاعته أعلى أو الـ red light اللي has less
+
+59
+00:03:57,490 --> 00:04:00,750
+energy than yellow light حسب الـ quantum theory
+
+60
+00:04:00,750 --> 00:04:02,270
+وهذا إجابة صحيحة
+
+61
+00:04:06,110 --> 00:04:10,170
+reflected light is completely polarized if the
+
+62
+00:04:10,170 --> 00:04:14,350
+angle of incidence equals the critical angle، وهذا
+
+63
+00:04:14,350 --> 00:04:17,730
+غلط، if the angle of incidence equals the Brewster
+
+64
+00:04:17,730 --> 00:04:18,910
+angle مش الـ critical
+
+65
+00:04:24,870 --> 00:04:28,470
+dark absorption lines in the emitted spectrum from
+
+66
+00:04:28,470 --> 00:04:33,190
+a star من نجم enables us بتمكننا to know the
+
+67
+00:04:33,190 --> 00:04:36,530
+composition of that star طبعا الـ dark absorption
+
+68
+00:04:36,530 --> 00:04:41,940
+line المناطق من الضوء المرئي المنبعث من هذا النجم
+
+69
+00:04:41,940 --> 00:04:45,000
+البعيد واللي إحنا شايفينه بواسطة التليسكوبات
+
+70
+00:04:45,000 --> 00:04:48,460
+الضوء الواصل منه فيه dark absorption line في مناطق
+
+71
+00:04:48,460 --> 00:04:52,660
+معينة هذه بتخلينا نعرف إيش العناصر المكونة لهذا
+
+72
+00:04:52,660 --> 00:04:54,140
+النجم وهذا كلام صحيح
+
+73
+00:04:58,840 --> 00:05:02,640
+When the reflected and refracted rays form a right
+
+74
+00:05:02,640 --> 00:05:05,980
+angle, all the reflected light is linearly
+
+75
+00:05:05,980 --> 00:05:09,060
+polarized parallel to the interface وهذا كلام
+
+76
+00:05:09,060 --> 00:05:12,660
+صحيح لأنه لما الـ reflected والـ refracted اللي هو
+
+77
+00:05:12,660 --> 00:05:16,800
+الـ transmitted rays بيصير بينهم زاوية قائمة معناته
+
+78
+00:05:16,800 --> 00:05:21,110
+الضوء سقط بالـ Brewster angle بالـ Brewster angle إذا
+
+79
+00:05:21,110 --> 00:05:24,370
+كل الـ reflected light اللي كان نصيبه أن يصير له
+
+80
+00:05:24,370 --> 00:05:27,790
+reflection بيكون linearly polarized parallel to
+
+81
+00:05:27,790 --> 00:05:30,690
+the interface between the two media، هذا الكلام
+
+82
+00:05:30,690 --> 00:05:31,230
+صحيح
+
+83
+00:05:35,420 --> 00:05:39,680
+in Young's experiment as the wave-transition of
+
+84
+00:05:39,680 --> 00:05:43,320
+light overlap less and less fringe contrast
+
+85
+00:05:43,320 --> 00:05:47,220
+increases معروف أنه لما الـ wave-transition of
+
+86
+00:05:47,220 --> 00:05:51,260
+light في الـ Young's two slit experiment لما يصير
+
+87
+00:05:51,260 --> 00:05:55,180
+الـ overlapping أقل وأقل بين القطارين من الموجات
+
+88
+00:05:55,180 --> 00:05:58,900
+الضوئية الـ fringe contrast مش increases، decreases
+
+89
+00:05:58,900 --> 00:06:01,720
+يعني على الأطراف بتروح، على الأطراف بتروح وبالتالي
+
+90
+00:06:01,720 --> 00:06:03,140
+الإجابة خطأ
+
+91
+00:06:06,220 --> 00:06:10,440
+superposition of two waves of identical frequency
+
+92
+00:06:10,440 --> 00:06:15,220
+.. identical frequency تم تراكب موجتين اللهم نفس
+
+93
+00:06:15,220 --> 00:06:18,120
+الـ frequency produce stable destructive
+
+94
+00:06:18,120 --> 00:06:22,220
+interference pattern only produce stable
+
+95
+00:06:22,220 --> 00:06:26,580
+interference بنقول نعم صحيح destructive only لأ
+
+96
+00:06:26,580 --> 00:06:29,760
+ممكن يكون destructive يلغوا بعضهم البعض وممكن يكون
+
+97
+00:06:29,760 --> 00:06:33,960
+constructive يصيروا موجة لها twice the amplitude
+
+98
+00:06:34,430 --> 00:06:38,890
+وممكن يكون بين البنين بين صفر واثنين زي ما شرحنا
+
+99
+00:06:38,890 --> 00:06:42,230
+في المحاضرات إذا لما بيقول كلمة only معناته خطأ
+
+100
+00:06:42,230 --> 00:06:46,030
+لأنه ممكن يكون constructive interference ممكن يكون
+
+101
+00:06:46,030 --> 00:06:50,910
+destructive interference and
+
+102
+00:06:50,910 --> 00:06:54,010
+electronic transitions between energy states
+
+103
+00:06:54,010 --> 00:06:58,770
+results in visible all electron مش يعني all
+
+104
+00:06:58,770 --> 00:07:01,850
+electrons transitions between energy states
+
+105
+00:07:01,850 --> 00:07:05,870
+results in visible photons لو كلمة visible شيلناها
+
+106
+00:07:05,870 --> 00:07:10,850
+وقلنا results in photons حصص من الطاقة بنقول صحيح
+
+107
+00:07:10,850 --> 00:07:17,010
+بس بعض الأحيان لما ينزل الإلكترون من مدار لمدار
+
+108
+00:07:17,010 --> 00:07:22,770
+بيعطي فوتون مرئي أحمر أزرق أخضر أي شيء وأحيانا لما
+
+109
+00:07:22,770 --> 00:07:25,470
+بيكون طاقته عالية بيعطي فوتون في range الـ
+
+110
+00:07:25,470 --> 00:07:29,950
+ultraviolet يعني ما بنشوفهوش أو لما تكون المدارين
+
+111
+00:07:29,950 --> 00:07:33,310
+متقاربين والفرق في الطاقة بينهم قليل جدا هيعطي
+
+112
+00:07:33,310 --> 00:07:36,690
+فوتون طاقته قليلة جدا إذا هيكون في الـ infrared
+
+113
+00:07:37,160 --> 00:07:40,640
+وبالتالي هيكون أحيانا invisible photons وأحيانا
+
+114
+00:07:40,640 --> 00:07:46,060
+invisible photons يعني مش مرئية فهذا الكلام غلط مش
+
+115
+00:07:46,060 --> 00:07:49,460
+دائما الإلكترون مش all electron transitions
+
+116
+00:07:49,460 --> 00:07:52,260
+between energy states results in visible photons
+
+117
+00:07:52,260 --> 00:07:56,220
+أحيانا results in visible photons وأحيانا results
+
+118
+00:07:56,220 --> 00:07:58,820
+in invisible غير مرئي photons
+
+119
+00:08:03,420 --> 00:08:07,280
+طيب at which temperature a piece of steel قطعة من
+
+120
+00:08:07,280 --> 00:08:10,340
+الصلب .. من الحديد الصلب cannot be considered
+
+121
+00:08:10,340 --> 00:08:14,780
+thermally agitated؟ قلنا أي جسم حرارته أكثر من
+
+122
+00:08:14,780 --> 00:08:18,800
+ناقص 273 تحت الصفر يعتبر مهتاج
+
+123
+00:08:18,800 --> 00:08:25,070
+حراريا، طب هذه أكثر محتاج حراريا وهذه محتاج حراريا
+
+124
+00:08:25,070 --> 00:08:30,290
+والصفر المئوي محتاج حراريا الوحيد اللي أقل من 273
+
+125
+00:08:30,290 --> 00:08:34,070
+تحت الصفر هي الـ 274 تحت الصفر إذا هي الإجابة
+
+126
+00:08:34,070 --> 00:08:38,330
+الوحيدة اللي بقدر أعتبر فيها أنه لو بردت قطعة حديد
+
+127
+00:08:38,330 --> 00:08:42,430
+لدرجة الحرارة high ساعتها هذه القطعة لا تعتبر
+
+128
+00:08:42,430 --> 00:08:45,230
+cannot be considered thermally agitated
+
+129
+00:08:47,990 --> 00:08:51,830
+طيب، visible light comprises which percentage of
+
+130
+00:08:51,830 --> 00:08:55,230
+the electromagnetic spectrum؟ قلنا الـ .. الـ .. الضوء
+
+131
+00:08:55,230 --> 00:08:59,650
+المرئي بشكل نسبة قليلة جدا، تشكل 1% من
+
+132
+00:08:59,650 --> 00:09:01,830
+كل الطيف الكهرومغناطيسي
+
+133
+00:09:04,990 --> 00:09:08,150
+According to quantum theory, the energy carried by
+
+134
+00:09:08,150 --> 00:09:11,450
+the wave is proportional to the square of its
+
+135
+00:09:11,450 --> 00:09:14,590
+amplitude and does not depend at all on the
+
+136
+00:09:14,590 --> 00:09:18,730
+frequency of the wave هذا الكلام صحيح للـ wave
+
+137
+00:09:18,730 --> 00:09:21,730
+theory، مش للـ quantum theory، الـ quantum theory
+
+138
+00:09:21,730 --> 00:09:29,030
+الطاقة المحمولة بالفوتون أو اللي بيحملها الفوتون أو
+
+139
+00:09:29,030 --> 00:09:31,930
+الـ .. الـ .. الـ wave الـ light wave بتعتمد على الـ
+
+140
+00:09:31,930 --> 00:09:34,710
+frequency على التردد حسب الـ quantum theory إذا
+
+141
+00:09:34,710 --> 00:09:41,010
+الجواب خطأ .. الجواب خطأ
+
+142
+00:09:41,010 --> 00:09:46,830
+what is the Brewster angle when light travels from
+
+143
+00:09:46,830 --> 00:09:54,210
+glass to air إذا الـ air NT والـ glass NI من الـ
+
+144
+00:09:54,210 --> 00:09:56,990
+Glass وده تروح على الهواء بنقول كالقاعدة بدنا الـ
+
+145
+00:09:56,990 --> 00:09:57,510
+calculator
+
+146
+00:10:23,210 --> 00:10:28,290
+هيتنقص ناقص 1 مللي جلاس هو هينتقل مللي جلاس
+
+147
+00:10:28,290 --> 00:10:34,950
+للهواء إذا الهواء NT تنقص ناقص 1 NT اللي هو 1
+
+148
+00:10:34,950 --> 00:10:39,550
+على
+
+149
+00:10:39,550 --> 00:10:52,190
+NI لأ مش هيك 1 على NI اللي هو 1 ونصف
+
+150
+00:10:54,430 --> 00:11:00,950
+إذا يساوي أنت 33.69،
+
+151
+00:11:00,950 --> 00:11:03,950
+يعني 33.7، 33
+
+152
+00:11:03,950 --> 00:11:07,150
+و7 من عشرة، إذا هذا هو الجواب الصحيح
+
+153
+00:11:10,090 --> 00:11:13,250
+Earth's atmosphere is held in position by the
+
+154
+00:11:13,250 --> 00:11:17,250
+gravitational pull of the mass of the earth وهذا
+
+155
+00:11:17,250 --> 00:11:21,470
+كلام منطقي وواقعي وصحيح أنه الغلاف الجوي بيظل
+
+156
+00:11:21,470 --> 00:11:24,950
+مكانه حوالين الأرض، محيط بالأرض، ما بتطيرش، اللي هو
+
+157
+00:11:24,950 --> 00:11:27,730
+ثاني أكسيد الكربون وبخار الماء والأوزون وما إلى
+
+158
+00:11:27,730 --> 00:11:32,230
+ذلك بسبب الجاذبية الأرضية، هذا كلام صحيح، هذا كلام
+
+159
+00:11:32,230 --> 00:11:32,930
+صحيح
+
+160
+00:11:35,750 --> 00:11:38,590
+The pressure inside gas discharged tube is lower
+
+161
+00:11:38,590 --> 00:11:41,870
+than atmospheric pressure والكلام صحيح ما بيكون
+
+162
+00:11:41,870 --> 00:11:44,710
+أعلى ولا مساويا للـ atmospheric pressure لازم يكون
+
+163
+00:11:44,710 --> 00:11:48,950
+أقل من الضغط الجو المحيط بالـ gas discharged tube
+
+164
+00:11:48,950 --> 00:11:51,210
+أقل بكثير من الضغط الجو
+
+165
+00:11:54,220 --> 00:11:58,100
+طيب، what is the brightest of the four Birkin J
+
+166
+00:11:58,100 --> 00:12:00,780
+images؟ طبعا الأولى هي الـ brightest لأنها هي
+
+167
+00:12:00,780 --> 00:12:04,920
+الانعكاس من السطح الأمامي بتاع القرانية .. من
+
+168
+00:12:04,920 --> 00:12:11,280
+السطح الأمامي بتاع القرانية طيب، which is true؟
+
+169
+00:12:11,280 --> 00:12:13,780
+الصحيح هو the greater the difference in the
+
+170
+00:12:13,780 --> 00:12:17,140
+refractive indices between the two media or the
+
+171
+00:12:17,140 --> 00:12:22,040
+greater the angle of incidence لأ هنا طبعا خربت
+
+172
+00:12:22,040 --> 00:12:25,300
+الإجابات أنا طالب منه خربت الإجابات يعني كل طالب
+
+173
+00:12:25,300 --> 00:12:28,440
+ممكن يظهر عنده الإجابات بهذا فخلينا احنا نقرأهم
+
+174
+00:12:28,440 --> 00:12:30,940
+كلهم the smaller the difference in the refractive
+
+175
+00:12:30,940 --> 00:12:34,280
+index أو the refractive indices between the two
+
+176
+00:12:34,280 --> 00:12:37,640
+media or the smaller the angle of incidence, the
+
+177
+00:12:37,640 --> 00:12:41,080
+smaller the amount of reflection and consequently
+
+178
+00:12:41,080 --> 00:12:44,720
+the less light transmitted كل هالجملة صحيحة معادة
+
+179
+00:12:44,720 --> 00:12:47,220
+كلمة the less لو .. لو قلنا the more light
+
+180
+00:12:47,220 --> 00:12:50,730
+transmitted كانت أصبحت صحيحة ننتقل للجملة الثانية،
+
+181
+00:12:50,730 --> 00:12:54,030
+the greater the difference between refractive
+
+182
+00:12:54,030 --> 00:12:56,750
+indices between the two media or the greater the
+
+183
+00:12:56,750 --> 00:12:59,530
+angle of incidence, the smaller the amount of
+
+184
+00:12:59,530 --> 00:13:02,990
+reflection، هذه غلط، the smaller the difference in
+
+185
+00:13:02,990 --> 00:13:06,130
+the refractive indices between the two media or
+
+186
+00:13:06,130 --> 00:13:09,350
+the smaller the angle of incidence, the smaller of
+
+187
+00:13:09,350 --> 00:13:13,130
+the amount of reflection and consequently the more
+
+188
+00:13:13,130 --> 00:13:16,190
+light transmitted، هذه الإجابة هي الصحيحة، هذه
+
+189
+00:13:16,190 --> 00:13:21,280
+الإجابة هي الصحيحة واللي مش متأكد يرجع للمحاضرات،
+
+190
+
+201
+00:14:04,110 --> 00:14:07,750
+effect of external photon
+
+202
+00:14:17,000 --> 00:14:20,700
+Close spacing between two energy states هذه 
+
+203
+00:14:20,700 --> 00:14:24,840
+المادة أو أي مادة فيها close spacing between two
+
+204
+00:14:24,840 --> 00:14:27,560
+energy states بنقول بتنفع هذه المادة تكون
+
+205
+00:14:27,560 --> 00:14:31,140
+fluorescent material، fluorescent material لازم
+
+206
+00:14:31,140 --> 00:14:34,520
+يكون فيها مدارين متقاربين، يعني ال close spacing
+
+207
+00:14:34,520 --> 00:14:38,700
+في الطاقة بينهم بيظل الخيار الأخير drop of an
+
+208
+00:14:38,700 --> 00:14:42,180
+electron to lower energy level without any
+
+209
+00:14:42,180 --> 00:14:45,140
+external الحالة spontaneous emission، spontaneous
+
+210
+00:14:45,140 --> 00:14:51,560
+emission، هيك بيكون خلص السؤال هذا In Young's two
+
+211
+00:14:51,560 --> 00:14:54,760
+slit experiment, if the light source consists of
+
+212
+00:14:54,760 --> 00:14:58,620
+many point sources distributed over a broad area,
+
+213
+00:14:58,780 --> 00:15:03,580
+the net result will be total loss of contrast and
+
+214
+00:15:03,580 --> 00:15:08,040
+no fringes will be evident لأن المناطق الواضحة تحت
+
+215
+00:15:08,040 --> 00:15:11,220
+صورة النقطة الأولى هتيجي على المناطق المعتمة تحت
+
+216
+00:15:11,220 --> 00:15:15,300
+صورة النقطة الثانية وهيبهتوا بعض فإذا كان عندي
+
+217
+00:15:15,300 --> 00:15:18,300
+أكثر من نقطتين ال object مكون من عدد لانهائي من
+
+218
+00:15:18,300 --> 00:15:21,700
+النقاط هيصير عندي total loss of contrast and no
+
+219
+00:15:21,700 --> 00:15:25,080
+fringes will be evident وبالتالي اللي .. اللي بده
+
+220
+00:15:25,080 --> 00:15:28,680
+يتأكد ممكن نرجع للمحاضرة لإن فيها شريح وافي مع ال
+
+221
+00:15:28,680 --> 00:15:34,560
+simulation طيب ال coherence length of laser light
+
+222
+00:15:34,560 --> 00:15:38,180
+is longer than that of the sunlight، هذا صحيح لأن
+
+223
+00:15:38,180 --> 00:15:41,780
+ال laser light عبارة عن narrow band وبالتالي ال
+
+224
+00:15:41,780 --> 00:15:43,780
+coherence length بتاعه أطول
+
+225
+00:15:49,290 --> 00:15:52,590
+Electron cannot drop more than one energy level
+
+226
+00:15:52,590 --> 00:15:59,390
+هذا خطأ ممكن ينزل أكثر من energy level حسب الفوتون
+
+227
+00:15:59,390 --> 00:16:03,550
+اللي فقده ممكن يقفز مدارين أو ثلاثة للأسفل أو
+
+228
+00:16:03,550 --> 00:16:06,990
+مدارين أو ثلاثة للأعلى أو مدار واحد فعنده الخيارات
+
+229
+00:16:06,990 --> 00:16:11,050
+متاع حسب الفوتون طاقة الفوتون اللي اكتسبه أو اللي
+
+230
+00:16:11,050 --> 00:16:11,630
+فقده
+
+231
+00:16:14,290 --> 00:16:17,550
+طيب، the energy emitted at any frequency from
+
+232
+00:16:17,550 --> 00:16:21,130
+transition of electrons between energy states can
+
+233
+00:16:21,130 --> 00:16:25,050
+only change by discrete amounts equaling multiples
+
+234
+00:16:25,050 --> 00:16:30,330
+of hν وهذا كلام صحيح وشرحناه في المعرض يعني ما فيش
+
+235
+00:16:30,330 --> 00:16:32,690
+أنصاف وأرباع للـ hν
+
+236
+00:16:35,180 --> 00:16:39,560
+ال energy اللي بيتم بثها أو إشعاعها سواء .. بغض
+
+237
+00:16:39,560 --> 00:16:42,480
+النظر عن ترددها، يعني عن تردد الفوتون، ما الفوتون
+
+238
+00:16:42,480 --> 00:16:47,840
+هو energy تم إشعاعه تمام؟ إله frequency معينة،
+
+239
+00:16:47,840 --> 00:16:53,740
+بيقدر تتغير طاقته بكميات محددة عبارة عن مضاعفات ال
+
+240
+00:16:53,740 --> 00:16:56,560
+hν في V، المضاعفات ال hν في V
+
+241
+00:17:01,830 --> 00:17:07,110
+يعني 2 hν 3 hν 4 hν وهكذا atoms of
+
+242
+00:17:07,110 --> 00:17:10,430
+all elements have the same energy state and the
+
+243
+00:17:10,430 --> 00:17:13,630
+same difference between energy states هذا الكلام
+
+244
+00:17:13,630 --> 00:17:17,770
+خطأ مائة بالمائة كل عنصر له يعني توزيعة معينة هذا
+
+245
+00:17:17,770 --> 00:17:20,970
+الكلام شرحناه وقولنا هذه تعتبر بصمة العنصر وعن
+
+246
+00:17:20,970 --> 00:17:25,710
+طريقها بنقدر نعرف العناصر المكونة للنجوم والكواكب
+
+247
+00:17:25,710 --> 00:17:30,050
+البعيدة بدراسة الضوء المنبعث منها بدراسة الضوء
+
+248
+00:17:30,050 --> 00:17:31,410
+المنبعث أو المنعكس
+
+249
+00:17:34,220 --> 00:17:38,020
+In quantum theory electrons present around a
+
+250
+00:17:38,020 --> 00:17:41,140
+nucleus in non-radiating state وهذه اللي بتفرج
+
+251
+00:17:41,140 --> 00:17:44,320
+وهذا صحيح وهي اللي بيفسر لإنه ليش الإلكترون
+
+252
+00:17:44,320 --> 00:17:48,200
+ما بفقدش الطاقة أثناء حركته بيصطاد مش بالنواع هذا
+
+253
+00:17:48,200 --> 00:17:50,960
+إذا بنفسره حسب ال wave theory بس ال quantum theory
+
+254
+00:17:50,960 --> 00:17:55,500
+بيقول لأ هذه الإلكترون حالة خاصة إنه بيوجد في non
+
+255
+00:17:55,500 --> 00:18:02,670
+-radiating state هيك خلصنا احنااللي هو الإجابات
+
+256
+00:18:02,670 --> 00:18:06,090
+submit
+
+257
+00:18:06,090 --> 00:18:12,650
+and finish all تمام؟
+
+258
+00:18:12,650 --> 00:18:17,170
+وبالتالي هذه الإجابات الصحيحة الآن ننقلها للنسخة
+
+259
+00:18:17,170 --> 00:18:24,090
+الثانية من الإختبار النصفة ونحلها مع بعض
+
+260
+00:18:30,230 --> 00:18:33,810
+طيب regarding the two slit experiment if the light
+
+261
+00:18:33,810 --> 00:18:36,610
+source consists of many point sources distributed
+
+262
+00:18:36,610 --> 00:18:39,990
+over a broad area the net result will be هذا
+
+263
+00:18:39,990 --> 00:18:45,050
+جوابناه قبل شوية total loss of contrast and no
+
+264
+00:18:45,050 --> 00:18:52,570
+fringes will be evident هذا الجواب الصحيح in
+
+265
+00:18:52,570 --> 00:18:55,270
+destructive interference, the resulting wave is
+
+266
+00:18:55,270 --> 00:18:58,630
+twice the amplitude، لأ، في ال destructive، في
+
+267
+00:18:58,630 --> 00:19:01,370
+ال destructive مش twice، هتصير صفر، في ال
+
+268
+00:19:01,370 --> 00:19:04,390
+constructive interference هتصير twice the
+
+269
+00:19:04,390 --> 00:19:07,990
+amplitude، اذا هادي خطأ، في ال destructive هتصير
+
+270
+00:19:07,990 --> 00:19:12,130
+صفر مش twice،
+
+271
+00:19:12,130 --> 00:19:15,190
+طيب، the superposition of two waves of differing
+
+272
+00:19:15,190 --> 00:19:20,490
+frequencies produce changing interference pattern
+
+273
+00:19:20,490 --> 00:19:23,490
+طالما differing frequencies إذا هتعطيني changing
+
+274
+00:19:23,490 --> 00:19:31,250
+interference pattern وهذا كلام صحيح
+
+275
+00:19:31,250 --> 00:19:37,340
+نجي لسؤال هذا يعني بحتاج لتفكير قليل نقول كالعادى
+
+276
+00:19:37,340 --> 00:19:41,500
+in the image هذه الصورة the reflected part of
+
+277
+00:19:41,500 --> 00:19:46,320
+light سقط ضوء سواء سقط من هنا سقط من هنا سقط من
+
+278
+00:19:46,320 --> 00:19:49,460
+هنا سقط من هنا لسه مش عارفين من وين سقط احتمالية
+
+279
+00:19:49,460 --> 00:19:52,900
+سقوطه لسه مش معروفة إنه خلنا نقرأ in the image the
+
+280
+00:19:52,900 --> 00:19:55,820
+reflected part احنا قولنا لما بيصل الضوء للسطح
+
+281
+00:19:55,820 --> 00:20:00,160
+الفاصل بين الهواء والزجاج هذا مكعب من الزجاج الآن
+
+282
+00:20:00,160 --> 00:20:03,080
+الجزء اللي انعكس، الآن بيحكيلي عن ال reflected
+
+283
+00:20:03,080 --> 00:20:07,700
+part اللي ارتدت للهواء، ضرب في الزجاج و ارتد للهواء
+
+284
+00:20:07,700 --> 00:20:13,600
+was totally polarized إيش يعني totally polarized؟
+
+285
+00:20:13,600 --> 00:20:18,720
+يعني كل الجزء اللي انعكس polarized and the
+
+286
+00:20:18,720 --> 00:20:24,280
+direction of polarization was vertical طيب كلمة
+
+287
+00:20:24,280 --> 00:20:28,970
+totally polarized معناته سقط بال Brewster angle و
+
+288
+00:20:28,970 --> 00:20:32,910
+هذا بيقدي إلى إنه totally polarized الجزء اللي
+
+289
+00:20:32,910 --> 00:20:37,270
+انعكس is totally polarized طيب totally polarized
+
+290
+00:20:37,270 --> 00:20:40,030
+هيكون parallel to the surface طالما ال direction
+
+291
+00:20:40,030 --> 00:20:43,490
+of polarization was vertical معناته ال surface أو
+
+292
+00:20:43,490 --> 00:20:48,730
+ال interface أيضا vertical إذا الاحتماليات الضوء
+
+293
+00:20:48,730 --> 00:20:54,620
+سقط على أي أسطح اما على السطح هذا بال Brewster angle أو
+
+294
+00:20:54,620 --> 00:20:57,460
+على السطح هذا بال Brewster angle ليش؟ لأن هدول
+
+295
+00:20:57,460 --> 00:21:01,940
+السطحين vertical وطالما ال polarization vertical
+
+296
+00:21:01,940 --> 00:21:06,060
+ال direction of polarization vertical وكل اللي
+
+297
+00:21:06,060 --> 00:21:09,200
+انعكس polarized واتجاه ال polarization vertical
+
+298
+00:21:09,200 --> 00:21:12,600
+معناته هو اتجاه ال polarization parallel to the
+
+299
+00:21:12,600 --> 00:21:16,000
+surface أو parallel to the interface فبالتالي اما
+
+300
+00:21:16,000 --> 00:21:20,000
+الضوء سقط من هنا أو سقط من هنا مستحيل الضوء يسقط
+
+301
+00:21:20,000 --> 00:21:25,010
+بال Brewster angle على سطح أفقي وينعكس ويكون totally
+
+302
+00:21:25,010 --> 00:21:27,950
+polarized ما اختلفناش بس يكون vertical اتجاه ال
+
+303
+00:21:27,950 --> 00:21:32,550
+polarization لأنه لو سقط على سطح أفقي هينعكس ..
+
+304
+00:21:32,550 --> 00:21:35,950
+هينعكس ويكون totally polarized ما فيش نقاش بس
+
+305
+00:21:35,950 --> 00:21:38,590
+هيكون ساعتها اتجاه ال polarization horizontal مش
+
+306
+00:21:38,590 --> 00:21:42,890
+vertical زي ما هنا يعني مذكور فبالتالي الاحتمالين
+
+307
+00:21:42,890 --> 00:21:47,190
+إنه اما سقط على السطح العمودي هذا للوح الزجاج اللي
+
+308
+00:21:47,190 --> 00:21:52,690
+هو الحب أو مكعب الزجاج أو على هذا أما هنا وهنا لأ،
+
+309
+00:21:52,690 --> 00:22:01,010
+إذا بنقول from here و from here أما إذا كانوا
+
+310
+00:22:01,670 --> 00:22:05,350
+vertical بي polarize بيكون .. بنفعش يكون سقط من
+
+311
+00:22:05,350 --> 00:22:08,730
+هنا ولا سقط من هنا، هذه الإجابة الصحيحة، هذه
+
+312
+00:22:08,730 --> 00:22:11,970
+الإجابة الصحيحة مائة بالمائة، إذا الاحتماليات
+
+313
+00:22:11,970 --> 00:22:15,390
+طالما ال .. طالما كل اللي انعكس polarized، ماشي،
+
+314
+00:22:15,390 --> 00:22:19,970
+بس اتجاه ال polarization وين؟ vertical، بفهم من كل
+
+315
+00:22:19,970 --> 00:22:22,950
+.. من كلمة كل اللي انعكس polarized إنه سقط بالـ
+
+316
+00:22:22,950 --> 00:22:26,160
+Brewster angle طيب طالما اتجاه ال polarization
+
+317
+00:22:26,160 --> 00:22:29,080
+vertical معناته .. احنا بنعرف ال Brewster angle
+
+318
+00:22:29,080 --> 00:22:32,780
+معناته هي انعكس باتجاه polarization موازي لل
+
+319
+00:22:32,780 --> 00:22:37,520
+interface اذا هيكون اما سقط على هذا السطح أو على
+
+320
+00:22:37,520 --> 00:22:41,000
+هذا السطح ال two vertical surfaces بس مش ممكن من
+
+321
+00:22:41,000 --> 00:22:47,140
+هنا عفوا هنا هذه الخطأ not from here هيك .. هيك
+
+322
+00:22:47,140 --> 00:22:54,100
+الإجابات صحيحة مائة بالمائة Atoms of all elements
+
+323
+00:22:54,100 --> 00:22:56,700
+have different energy states and the difference
+
+324
+00:22:56,700 --> 00:23:00,120
+between energy states is unique يعني فريد for each
+
+325
+00:23:00,120 --> 00:23:03,580
+element and compound هذا كلام واضح اللي هو بصمة
+
+326
+00:23:03,580 --> 00:23:08,960
+العنصر أو بصمة المركب الكيميائي calculate the
+
+327
+00:23:08,960 --> 00:23:13,390
+critical angle between water لأن تساوي 1.3
+
+328
+00:23:13,390 --> 00:23:17,090
+من عشرة والهواء إذا الضوء بدي انتقل من ال .. 1
+
+329
+00:23:17,090 --> 00:23:20,730
+و3 من عشرة من ال .. من ال water للهواء إذا في
+
+330
+00:23:20,730 --> 00:23:24,750
+critical angle بروح على ال calculator بقول بدي
+
+331
+00:23:24,750 --> 00:23:30,890
+الدالة هنا بدي sin و sin 1 برجع للأساسية
+
+332
+00:23:30,890 --> 00:23:37,850
+بنقول 1 و n اللي هو الهواء على و n1 تقسيم
+
+333
+00:23:37,850 --> 00:23:46,040
+1 و 3 من عشرة بنقول له enter 50 و 2
+
+334
+00:23:46,040 --> 00:23:49,540
+من عشرة تقريبا، هل فيه في الإجابات 50 و 2
+
+335
+00:23:49,540 --> 00:23:54,620
+2 8؟ 50 2 8 صحيح، إذا 50
+
+336
+00:23:54,620 --> 00:24:01,400
+2 8، degree، هذه ال critical angle The
+
+337
+00:24:01,400 --> 00:24:04,820
+energy emitted at any frequency from transition of
+
+338
+00:24:04,820 --> 00:24:08,040
+electrons between energy states can only change by
+
+339
+00:24:08,040 --> 00:24:11,940
+discrete amounts equaling multiples of hν هذا
+
+340
+00:24:11,940 --> 00:24:14,360
+السؤال مر في النسخة الأولى من الامتحان، بنقول
+
+341
+00:24:14,360 --> 00:24:21,950
+صحيح، next page light waves are not objects so they
+
+342
+00:24:21,950 --> 00:24:25,770
+can overlap and superposition can take place وهذا
+
+343
+00:24:25,770 --> 00:24:28,390
+كلام صحيح يعني الموجات الضوئية حكيناها في
+
+344
+00:24:28,390 --> 00:24:32,510
+المحاضرات إنه مش عبارة عن .. مش object ممكن
+
+345
+00:24:32,510 --> 00:24:35,730
+يتداخلوا مع بعضهم البعض لو الموجات الضوئية عبارة
+
+346
+00:24:35,730 --> 00:24:39,710
+عن object .. objects صعب أنهم يت .. مش صعب يعني
+
+347
+00:24:39,710 --> 00:24:42,690
+ما فيش إمكانية أنهم يحلوا في بعضهم البعض أو يتحدوا
+
+348
+00:24:42,690 --> 00:24:48,530
+في بعضهم البعض طيب ممكن يتداخلوا في بعضهم البعض if
+
+349
+00:24:48,530 --> 00:24:51,430
+the light source consists of many points sources
+
+350
+00:24:51,430 --> 00:24:54,850
+distributed over a broad area, the net result will
+
+351
+00:24:54,850 --> 00:24:59,950
+be زي هذا السؤال مكرر a total loss of contrast and
+
+352
+00:24:59,950 --> 00:25:06,510
+no fringes will be evident reflected
+
+353
+00:25:06,510 --> 00:25:09,710
+light is completely polarized if the angle of
+
+354
+00:25:09,710 --> 00:25:14,100
+reflection هذا السؤال فيه خدعة بسيطة reflected
+
+355
+00:25:14,100 --> 00:25:18,120
+light is completely polarized if the angle of
+
+356
+00:25:18,120 --> 00:25:22,920
+reflection equals the Brewster angle احنا عارفين
+
+357
+00:25:22,920 --> 00:25:25,380
+إنه the angle of incidence equals the Brewster
+
+358
+00:25:25,380 --> 00:25:29,020
+angle ساعتها كله بيكون completely polarized مظبوط
+
+359
+00:25:29,020 --> 00:25:34,060
+بس لما ال angle of reflection ماهي تساوي ال angle
+
+360
+00:25:34,060 --> 00:25:39,290
+of incidence حسب قانون الانعكاس θi تساوي θr زاوية
+
+361
+00:25:39,290 --> 00:25:43,490
+الانعكاس تساوي زاوية السقوط وطالما زاوية الانعكاس
+
+362
+00:25:43,490 --> 00:25:47,150
+تساوي ال Brewster angle معناته زاوية السقوط تساوي
+
+363
+00:25:47,150 --> 00:25:51,950
+ال Brewster angle فالجواب صحيح هنا بس غيرنا كلمة if
+
+364
+00:25:51,950 --> 00:25:54,890
+the angle of incidence equals the Brewster angle
+
+365
+00:25:54,890 --> 00:25:58,450
+وبدلناها بكلمة if the angle of reflection ما هو
+
+366
+00:25:58,450 --> 00:26:00,810
+معروف أن ال angle of reflection و ال angle of
+
+367
+00:26:00,810 --> 00:26:05,510
+incidence هما نفس القيمة إذا واحدة منهم 50
+
+368
+00:26:05,510 --> 00:26:08,030
+degree الثانية 50 degree إذا واحدة 30 degree
+
+369
+00:26:08,030 --> 00:26:12,630
+الثانية يعني دائما قانون للإعكاس أول قانون ناخده θi
+
+370
+00:26:12,630 --> 00:26:16,670
+تساوي θr فبالتالي هذه لو أنا شيلتها وبدلت قلت
+
+371
+00:26:16,670 --> 00:26:18,850
+ما هي ال angle of reflection هي ال angle of
+
+372
+00:26:18,850 --> 00:26:22,450
+incidence بدلت هنا في خيال في مخي اللي اتقول if
+
+373
+00:26:22,450 --> 00:26:25,250
+the angle of incidence equals the Brewster angle
+
+374
+00:26:25,250 --> 00:26:26,830
+هيطلع معايا الجواب صحيح
+
+375
+00:26:30,550 --> 00:26:33,810
+if the electric field is oriented vertically then
+
+376
+00:26:33,810 --> 00:26:36,610
+polarization of light هذا سؤال مباشر electric
+
+377
+00:26:36,610 --> 00:26:39,870
+field vertically is a vertical polarization بدأهاش
+
+378
+00:26:39,870 --> 00:26:43,690
+يعني لأن حسب ال electric field بيعتبر ال
+
+379
+00:26:43,690 --> 00:26:47,170
+polarization which of the Purkinje images is the
+
+380
+00:26:47,170 --> 00:26:50,490
+least clinically visible الثانية الثانية الأولى
+
+381
+00:26:50,490 --> 00:26:53,630
+أوضح واحدة والثانية أقل واحدة وضوحا الثالثة
+
+382
+00:26:53,630 --> 00:26:58,390
+والرابعة تقريبا نفس الوضوح تقريبا نفس الوضوح بس
+
+383
+00:26:58,390 --> 00:27:01,590
+بيجوا أقل من الأولى، can total internal reflection
+
+384
+00:27:01,590 --> 00:27:04,950
+occur inside the air if the interface between air
+
+385
+00:27:04,950 --> 00:27:08,250
+and water؟
+
+386
+00:27:08,250 --> 00:27:12,410
+يعني هل
+
+401
+00:28:07,130 --> 00:28:10,690
+higher energy state to lower energy state بتحفيز 
+
+402
+00:28:10,690 --> 00:28:15,920
+من external photon، هذا stimulated emission لأن هذه
+
+403
+00:28:15,920 --> 00:28:19,340
+هي فكرة ال laser هذه هي ال stimulated emission
+
+404
+00:28:19,340 --> 00:28:23,660
+jumping of an electron to higher energy state كلمة 
+
+405
+00:28:23,660 --> 00:28:26,940
+jumping يعني يطلع على فوق هذا الوحيد اللي هو
+
+406
+00:28:26,940 --> 00:28:33,420
+absorption و هذا حلناها قبل شوية طيب what is the
+
+407
+00:28:33,420 --> 00:28:38,360
+optical density of a material if the transmittance
+
+408
+00:28:38,360 --> 00:28:45,820
+equals واحد من مية في المية نيجي هنا بنقول إن شاء
+
+409
+00:28:45,820 --> 00:28:52,420
+الله نجي للوغارتمات هنا logarithm
+
+410
+00:28:52,420 --> 00:29:01,400
+.. نرجع للأساسية الواحد تقسيم واحد من مية في المية
+
+411
+00:29:01,400 --> 00:29:07,620
+يعني واحد من عشرة آلاف عفوًا
+
+412
+00:29:07,620 --> 00:29:13,100
+ال logarithm العشري لواحد تقسيم
+
+413
+00:29:14,940 --> 00:29:26,220
+واحد على عشرة آلاف كان
+
+414
+00:29:26,220 --> 00:29:30,340
+واحد على ال transmittance واحد لوغاريتم العشر لـ
+
+415
+00:29:30,340 --> 00:29:34,060
+واحد ال optical density ال optical density تساوي
+
+416
+00:29:34,060 --> 00:29:37,360
+واحد على ال transmittance طب ل transmittance واحد
+
+417
+00:29:37,360 --> 00:29:39,860
+من مية في المية ممكن سايا نقول لا يعني أنا ما بديش
+
+418
+00:29:39,860 --> 00:29:45,020
+أبديها زي ما هي مكتوبة بالضبط نقوله ماشي فضلها ال
+
+419
+00:29:45,020 --> 00:29:53,440
+logarithm واحد على واحد من مية في المية طيب نشوف
+
+420
+00:29:53,440 --> 00:29:59,340
+تظبط معانا ولا لأ واحد من مية في المية إن شاء الله
+
+421
+00:29:59,340 --> 00:30:03,860
+تظبط لأ هيك ما ضبطتش ال logarithm واحد من مية في
+
+422
+00:30:03,860 --> 00:30:10,240
+المية يعني واحد من عشرة آلاف ال logarithm واحد
+
+423
+00:30:10,240 --> 00:30:14,440
+تقسيم لأ آسف
+
+424
+00:30:20,420 --> 00:30:32,180
+ولو غاريتم واحد تقسيم واحد من عشرة آلاف لأ
+
+425
+00:30:32,180 --> 00:30:35,460
+واحد على واحد هي آه ده هي اللي زادت واحد على عشرة
+
+426
+00:30:35,460 --> 00:30:35,980
+آلاف
+
+427
+00:30:48,760 --> 00:30:53,120
+آه هيك ضبطت .. لازم نحط zero هنا على الشمال .. إذا
+
+428
+00:30:53,120 --> 00:31:01,460
+أربعة .. إذا أربعة .. نرجع للامتحان .. إذا أربعة
+
+429
+00:31:01,460 --> 00:31:06,120
+.. إذا ال .. ال transmittance واحد من مية في المية
+
+430
+00:31:06,120 --> 00:31:10,680
+يعني واحد من مية على مية يعني واحد على مية على مية
+
+431
+00:31:10,680 --> 00:31:16,730
+يعني واحد على عشرة آلاف .. إذا أربعة Dark absorption
+
+432
+00:31:16,730 --> 00:31:19,610
+lights in the emitted spectrum from a star enables
+
+433
+00:31:19,610 --> 00:31:22,630
+us to know the composition of that star هذا سؤال
+
+434
+00:31:22,630 --> 00:31:29,510
+ورد في النسخة الأولى، قول صحيح In Yang's
+
+435
+00:31:29,510 --> 00:31:32,030
+experiment, as the wave transition of light
+
+436
+00:31:32,030 --> 00:31:35,390
+overlap less and less, fringe contrast decreases، 
+هذا صحيح
+
+437
+00:31:35,390 --> 00:31:36,010
+هذا صحيح
+
+438
+00:31:40,510 --> 00:31:43,310
+طيب all of the following mechanisms are helpful
+
+439
+00:31:43,310 --> 00:31:46,070
+for protection against harmful sun radiation
+
+440
+00:31:46,070 --> 00:31:50,170
+except .. طبعًا except Jupiter's magnetic field
+
+441
+00:31:50,170 --> 00:31:55,170
+يعني المجال المغناطيسي لكوكب المشتري ما إله علاقة
+
+442
+00:31:55,170 --> 00:31:58,830
+في إنه يحمينا من الأشعة اللي صادرة من الشمس اللي 
+
+443
+00:31:58,830 --> 00:32:01,630
+هي الأشعة ال harmful ال gamma ray و ال X-ray و ال
+
+444
+00:32:01,630 --> 00:32:05,520
+ultraviolet و ما إلى ذلك أما البعد الشاهق للـ
+
+445
+00:32:05,520 --> 00:32:10,940
+للأرض عن الشمس آه، عشان إنه بيصلنا حصة قليلة جدًا 
+
+446
+00:32:10,940 --> 00:32:14,580
+من الإشعاع الشمسي، ال solar wind المحيطة بالشمس،
+
+447
+00:32:14,580 --> 00:32:17,900
+الرياح الشمسية صحيح، ال earth atmosphere اللي 
+
+448
+00:32:17,900 --> 00:32:21,220
+بيمتص يعني مثلًا طبقة الأوزون في ال atmosphere بتمتص
+
+449
+00:32:21,220 --> 00:32:24,240
+ال ultraviolet و هكذا تمام؟ فبالتالي ال Jupiter
+
+450
+00:32:24,240 --> 00:32:28,460
+magnetic field ما إله دعوة فهو الوحيد ال exception
+
+451
+00:32:28,460 --> 00:32:33,830
+.. ال exceptionعندما يصيب الرايس المظهرة و المظهرة
+
+452
+00:32:33,830 --> 00:32:39,450
+الصحيحة، فكل الضوء المظهر يصيب بطريقة مرتبطة 
+
+453
+00:32:39,450 --> 00:32:42,950
+بطريقة عادية للوظيفة لما ال reflected و ال
+
+454
+00:32:42,950 --> 00:32:46,690
+refracted rays يكونوا right angle بينهم تسعين
+
+455
+00:32:46,690 --> 00:32:49,990
+درجة، معناته فيه سقوط بال broaster angle، ساعتها 
+
+456
+00:32:49,990 --> 00:32:54,090
+كل ال reflected light is linearly polarized، صحيح،
+
+457
+00:32:54,090 --> 00:32:57,710
+parallel لإيش؟ لل interface، مش ال service normal،
+
+458
+00:32:57,710 --> 00:33:01,130
+لل interface، مش ال service normal، فبالتالي هذا
+
+459
+00:33:01,130 --> 00:33:04,470
+الإجابة خطأ، في ناس وجعت فكرت كلمة service
+
+460
+00:33:04,470 --> 00:33:06,670
+normal هي ال interface، هي ال interface
+
+461
+00:33:09,410 --> 00:33:13,210
+visible lights is considered a type of ionizing
+
+462
+00:33:13,210 --> 00:33:15,970
+radiation غلط، visible light مش ionizing
+
+463
+00:33:15,970 --> 00:33:19,910
+radiation، أما الأشعة اللي هي ال ionizing radiation زي
+
+464
+00:33:19,910 --> 00:33:22,950
+الجمرة و ال X-ray و ال ultraviolet
+
+465
+00:33:27,500 --> 00:33:31,100
+the time .. the coherence time is in a broad .. in 
+
+466
+00:33:31,100 --> 00:33:34,340
+a broad band light source is longer than the
+
+467
+00:33:34,340 --> 00:33:37,360
+coherence time in narrow band light sources وده 
+
+468
+00:33:37,360 --> 00:33:41,400
+خطأ لأن ال coherence time في ال broad band .. ال
+
+469
+00:33:41,400 --> 00:33:43,940
+broad band ال sections قصيرة فال coherence time
+
+470
+00:33:43,940 --> 00:33:47,020
+قصير مش longer than shorter than فبالتالي هذه
+
+471
+00:33:47,020 --> 00:33:48,220
+إجابة خطأ
+
+472
+00:33:51,900 --> 00:33:54,980
+and electron .. all electron .. all electron 
+
+473
+00:33:54,980 --> 00:33:57,600
+transitions between energy states results in
+
+474
+00:33:57,600 --> 00:34:01,340
+visible photons طبعًا مش كلها بعضها بتنتج عنها 
+
+475
+00:34:01,340 --> 00:34:04,340
+invisible photons إذا الإجابة غلط و هذا سؤال مر 
+
+476
+00:34:04,340 --> 00:34:08,080
+معنا طيب
+
+477
+00:34:08,080 --> 00:34:13,800
+light was travelling from air أنواعه to glass and
+
+478
+00:34:13,800 --> 00:34:17,040
+at a specific angle of incidence you noted that
+
+479
+00:34:17,040 --> 00:34:19,660
+the reflected light and transmitted light are 
+
+480
+00:34:19,660 --> 00:34:23,200
+perpendicular to each other يعني سقطت بالبروستر
+
+481
+00:34:23,200 --> 00:34:26,540
+angle what was the angle of incidence؟ بدنا نحسب 
+
+482
+00:34:26,540 --> 00:34:31,820
+البروستر angle من الهوى اللي هو Ni لجلس اللي هو Nt
+
+483
+00:34:31,820 --> 00:34:37,280
+بدنا نروح على الحاسبة ونقول تان او ناقص واحد Nt
+
+484
+00:34:37,280 --> 00:34:40,440
+اللي هو الجلس قلنا قداش واحد و أربعة من عشرة
+
+485
+00:34:53,870 --> 00:35:03,130
+لأ نقول تان اثنين او ناقص واحد NT
+
+486
+00:35:03,130 --> 00:35:08,870
+واحد و أربعة من عشرة تقسيم
+
+487
+00:35:08,870 --> 00:35:16,310
+NI الواحد عندي أربعة و خمسين و أربعة من عشرة
+
+488
+00:35:16,310 --> 00:35:18,970
+أو أربعة و خمسين و ستة و أربعين من مية، هلفي في 
+
+489
+00:35:18,970 --> 00:35:22,090
+الإجابات أربعة و خمسين و ستة و أربعين من مية
+
+490
+00:35:22,090 --> 00:35:27,580
+degree؟ هذا نية الإجابة طيب according to quantum
+
+491
+00:35:27,580 --> 00:35:29,980
+theory the energy carried by the wave is
+
+492
+00:35:29,980 --> 00:35:33,100
+proportional to the square of its amplitude قولنا 
+
+493
+00:35:33,100 --> 00:35:35,920
+هذا الكلام بظبط مع ال wave theory إنها بتتناسب 
+
+494
+00:35:35,920 --> 00:35:39,260
+الطاقة مع مربع ال amplitude أما في ال quantum
+
+495
+00:35:39,260 --> 00:35:42,780
+theory بتتناسب مع ال frequency and does not depend 
+
+496
+00:35:42,780 --> 00:35:47,060
+at all on the frequency طبعًا غلط هذا و هذا سؤال
+
+497
+00:35:47,060 --> 00:35:51,400
+مكرر و هيك بنكون انتهينا من الامتحان الثاني طبعًا
+
+498
+00:35:51,400 --> 00:35:52,220
+عملنا finishing
+
+499
+00:35:56,910 --> 00:35:59,990
+هيك بنقول لكم يعطيكم العافية والسلام عليكم ورحمة 
+
+500
+00:35:59,990 --> 00:36:01,670
+الله وبركاته
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/CQeq0bGJeVc_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/CQeq0bGJeVc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..79683a6e1d444a1e4822af10a20906c6fb8ef8ae
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/CQeq0bGJeVc_postprocess.srt
@@ -0,0 +1,2000 @@
+1
+00:00:01,400 --> 00:00:04,780
+بسم الله الرحمن الرحيم نبدأ في مراجعة الامتحان
+
+2
+00:00:04,780 --> 00:00:08,820
+النسخة الأولى اللي هو الصباحية طبعا ان شاء الله
+
+3
+00:00:08,820 --> 00:00:15,240
+تعالى نبدأ السؤال الأول if
+
+4
+00:00:15,240 --> 00:00:18,380
+the magnetic field of light propagates vertically
+
+5
+00:00:18,380 --> 00:00:21,840
+then the light is polarized طالما ال magnetic
+
+6
+00:00:21,840 --> 00:00:25,960
+field vertical معناته ال electric field horizontal
+
+7
+00:00:25,960 --> 00:00:29,500
+واحنا ال polarization مرتبط بال electric field مش
+
+8
+00:00:29,500 --> 00:00:33,560
+..بال magnetic field، ال magnetic field بينه وبين
+
+9
+00:00:33,560 --> 00:00:36,060
+ال electric field فيه زاوية قائمة طالما ال
+
+10
+00:00:36,060 --> 00:00:40,100
+magnetic field vertical معناته ال electric field
+
+11
+00:00:40,100 --> 00:00:43,100
+horizontal وبالتالي ال polarization horizontal
+
+12
+00:00:43,100 --> 00:00:48,770
+ننتقل للسؤال اللي بعدهa dropping of an electron
+
+13
+00:00:48,770 --> 00:00:52,030
+from higher energy state to lower energy state
+
+14
+00:00:52,030 --> 00:00:56,170
+must be accompanied by absorption of a photon ال
+
+15
+00:00:56,170 --> 00:00:59,690
+absorption of a photon بيصعد مع الإلكترون مش بيهبط
+
+16
+00:00:59,690 --> 00:01:04,490
+هنا لما بيهبط بيفقد فوتون مش بيكتسب فوتون مابيعملش
+
+17
+00:01:04,490 --> 00:01:08,890
+absorption بيعمل emission فبالتالي هذا غلط هذا غلط
+
+18
+00:01:12,170 --> 00:01:15,330
+The theory that can explain the behavior of light
+
+19
+00:01:15,330 --> 00:01:19,210
+waves at anatomic and molecular levels اللي هي ال
+
+20
+00:01:19,210 --> 00:01:23,800
+quantum theory قولنا ال electromagnetic waveالـ
+
+21
+00:01:23,800 --> 00:01:28,100
+electromagnetic wave theory ما بتصلح على الظواهر
+
+22
+00:01:28,100 --> 00:01:32,900
+المرئية بالعين ال reflection ال refraction ال
+
+23
+00:01:32,900 --> 00:01:36,440
+diffraction و ما إلى ذلك لما بنيجي على مستوى
+
+24
+00:01:36,440 --> 00:01:39,240
+الذرات والجزائيات ال electromagnetic wave بتقدرش
+
+25
+00:01:39,240 --> 00:01:43,060
+تفسر هذه الظواهر فبالتالي ال quantum theory هي
+
+26
+00:01:43,060 --> 00:01:44,920
+اللي بتفسر لهذه الظواهر
+
+27
+00:01:48,440 --> 00:01:51,480
+According to the wave theory, collimated light
+
+28
+00:01:51,480 --> 00:01:54,280
+should remain so after traversing an aperture
+
+29
+00:01:57,470 --> 00:02:00,570
+ال web theory هذه حسب ال corpuscular theory اللي
+
+30
+00:02:00,570 --> 00:02:03,970
+أقدم نظرية و اللي عفى عليها الزمن أنه بعد ما يعد
+
+31
+00:02:03,970 --> 00:02:09,150
+من فتحة في جدار بيظله collimated يعني موازي لبعض و
+
+32
+00:02:09,150 --> 00:02:12,130
+لبعض الصحيح أنه ما بيظل collimated أنه بعد ما يعدي
+
+33
+00:02:12,130 --> 00:02:15,290
+في فتحة في جدار بيصيرله ظاهرة ال diffraction اللي
+
+34
+00:02:15,290 --> 00:02:19,130
+هي أنه بتبعد عن بعض و يصيرله divergence حسب ال web
+
+35
+00:02:19,130 --> 00:02:22,840
+theory أماقضية انه يظل collimated هذه الفرضية
+
+36
+00:02:22,840 --> 00:02:26,900
+فرضتها ال corpuscular theory وبالتالي الإجابة خطأ
+
+37
+00:02:26,900 --> 00:02:33,900
+.. الإجابة خطأ طيبwhat is the critical angle
+
+38
+00:02:33,900 --> 00:02:37,820
+between when .. the critical angle when light
+
+39
+00:02:37,820 --> 00:02:43,080
+travels from air and تساوي واحد to glass and تساوي
+
+40
+00:02:43,080 --> 00:02:46,980
+واحد و نص هذه القضية بدها شوية تفكير بسيط جدا
+
+41
+00:02:46,980 --> 00:02:50,880
+الضوء بينتقل من الهواء low refractive index لأ
+
+42
+00:02:50,880 --> 00:02:54,570
+لجلس عمره ما بيصير critical angleاحنا قلنا لـ
+
+43
+00:02:54,570 --> 00:02:58,490
+critical angle لما الضوء بينتقل من مادة أعلى في ال
+
+44
+00:02:58,490 --> 00:03:01,690
+refractive index أو أعلى في الكثافة لمادة أقل
+
+45
+00:03:01,690 --> 00:03:05,850
+العكس مابيصيرش فبالتالي الإجابة فورا بدون حسابات
+
+46
+00:03:05,850 --> 00:03:11,010
+none لأنه بنتقل من الهوى لل glasses مافيش critical
+
+47
+00:03:11,010 --> 00:03:13,910
+angle لما ينتقل من الهوى لل glasses أما في
+
+48
+00:03:13,910 --> 00:03:18,360
+critical angle لما ينتقل من ال glasses للهوىطيب
+
+49
+00:03:18,360 --> 00:03:21,780
+according to quantum theory red light has less
+
+50
+00:03:21,780 --> 00:03:25,700
+energy than yellow light، الآن مين أطول موجتا؟ ال
+
+51
+00:03:25,700 --> 00:03:28,360
+red light أطول من ال yellow light، ال red light
+
+52
+00:03:28,360 --> 00:03:33,000
+أطول ال visible light، أحمر، برتقالي، أصفر، أخضر،
+
+53
+00:03:33,000 --> 00:03:37,770
+أزرق، نيلي، بنفسجيإذا الأحمر أطولهم، البرتقالي أقل
+
+54
+00:03:37,770 --> 00:03:40,510
+طول منه، والأصفر أقل طول، احنا بهمنا الأحمر
+
+55
+00:03:40,510 --> 00:03:45,670
+والأصفر، إذا طالما الأصفر أقل طولا من الأحمر، إذا
+
+56
+00:03:45,670 --> 00:03:49,050
+ال frequency بتاعته أعلى، تردده، عدد الموجات في
+
+57
+00:03:49,050 --> 00:03:53,850
+وحدة الزمن أكتر، فبالتالي ال yellow light إن ال
+
+58
+00:03:53,850 --> 00:03:57,490
+energy بتاعته أعلى أو ال red light اللي has less
+
+59
+00:03:57,490 --> 00:04:00,750
+energy than yellow light حسب ال quantum theory
+
+60
+00:04:00,750 --> 00:04:02,270
+وهذا إجابة صحية
+
+61
+00:04:06,110 --> 00:04:10,170
+reflected light is completely polarized if the
+
+62
+00:04:10,170 --> 00:04:14,350
+angle of incidence equals the critical angle، وهذا
+
+63
+00:04:14,350 --> 00:04:17,730
+غلط، if the angle of incidence equals the Brewster
+
+64
+00:04:17,730 --> 00:04:18,910
+angle مش ال critical
+
+65
+00:04:24,870 --> 00:04:28,470
+dark absorption lines in the emitted spectrum from
+
+66
+00:04:28,470 --> 00:04:33,190
+a star من نجم enables us بتمكننا to know the
+
+67
+00:04:33,190 --> 00:04:36,530
+composition of that star طبعا ال dark absorption
+
+68
+00:04:36,530 --> 00:04:41,940
+line المناطق من الضوء المرئي المنبعثمن هذا النجم
+
+69
+00:04:41,940 --> 00:04:45,000
+البعيد و اللي احنا شايفينه بواسطة التليسكوبات
+
+70
+00:04:45,000 --> 00:04:48,460
+الضوء الواصل منه فيه dark absorption line في مناطق
+
+71
+00:04:48,460 --> 00:04:52,660
+معينة هذه بتخلينا نعرف ايش العناصر المكونة لهذا
+
+72
+00:04:52,660 --> 00:04:54,140
+النجم و هذا كلام صحيح
+
+73
+00:04:58,840 --> 00:05:02,640
+When the reflected and refracted rays form a right
+
+74
+00:05:02,640 --> 00:05:05,980
+angle, all the reflected light is linearly
+
+75
+00:05:05,980 --> 00:05:09,060
+polarized parallel to the interface و هذا كلام
+
+76
+00:05:09,060 --> 00:05:12,660
+صحيح لأنه لما ال reflected و ال refracted اللي هو
+
+77
+00:05:12,660 --> 00:05:16,800
+ال transmitted rays بيصير بينهم زاوية قائمة معناته
+
+78
+00:05:16,800 --> 00:05:21,110
+الضوء سقط بالبروستر angleبالـ Brewster angle إذا
+
+79
+00:05:21,110 --> 00:05:24,370
+كل الـ reflected light اللي كان نصيبه أن يصير له
+
+80
+00:05:24,370 --> 00:05:27,790
+reflection بيكون linearly polarized parallel to
+
+81
+00:05:27,790 --> 00:05:30,690
+the interface between the two media، هذا الكلام
+
+82
+00:05:30,690 --> 00:05:31,230
+صحيح
+
+83
+00:05:35,420 --> 00:05:39,680
+in young's experiment as the wave-transition of
+
+84
+00:05:39,680 --> 00:05:43,320
+light overlap less and less fringe contrast
+
+85
+00:05:43,320 --> 00:05:47,220
+increases معروف أنه لما ال wave-transition of
+
+86
+00:05:47,220 --> 00:05:51,260
+light في ال young's two slit experiment لما يصير
+
+87
+00:05:51,260 --> 00:05:55,180
+ال overlapping أقل وأقل بين القطارين من الموجات
+
+88
+00:05:55,180 --> 00:05:58,900
+الضوئية ال fringe contrast مش increases، decreases
+
+89
+00:05:58,900 --> 00:06:01,720
+يعني على الأطراف بتروح، على الأطراف بتروح وبالتالي
+
+90
+00:06:01,720 --> 00:06:03,140
+الإجابة خطأ
+
+91
+00:06:06,220 --> 00:06:10,440
+superposition of two waves of identical frequency
+
+92
+00:06:10,440 --> 00:06:15,220
+.. identical frequency تم تراكب موجتين اللهم نفس
+
+93
+00:06:15,220 --> 00:06:18,120
+ال frequency produce stable destructive
+
+94
+00:06:18,120 --> 00:06:22,220
+interference pattern only produce stable
+
+95
+00:06:22,220 --> 00:06:26,580
+interference بنقول نعم صحيح destructive only لأ
+
+96
+00:06:26,580 --> 00:06:29,760
+ممكن يكون destructive يلغوا بعضهم البعض وممكن يكون
+
+97
+00:06:29,760 --> 00:06:33,960
+constructive يصيروا موجة اللها twice the amplitude
+
+98
+00:06:34,430 --> 00:06:38,890
+و ممكن يكون بين البنين بين صفر و اتنين زي ما شرحنا
+
+99
+00:06:38,890 --> 00:06:42,230
+في المحاضرات إذا لما بيقول كلمة only معناته خطأ
+
+100
+00:06:42,230 --> 00:06:46,030
+لأنه ممكن يكون constructive interference ممكن يكون
+
+101
+00:06:46,030 --> 00:06:50,910
+destructive interference and
+
+102
+00:06:50,910 --> 00:06:54,010
+electronic transitions between energy states
+
+103
+00:06:54,010 --> 00:06:58,770
+results in visible all electronمش يعني all
+
+104
+00:06:58,770 --> 00:07:01,850
+electrons transitions between energy states
+
+105
+00:07:01,850 --> 00:07:05,870
+results in visible photons لو كلمة visible شيلناها
+
+106
+00:07:05,870 --> 00:07:10,850
+وقولنا results in photons حصص من الطاقة بنقول صحيح
+
+107
+00:07:10,850 --> 00:07:17,010
+بس بعض الأحيان لما ينزل ال электرون من مدار لمدار
+
+108
+00:07:17,010 --> 00:07:22,770
+بيعطي فوتون مرئيأحمر أزرق أخضر أي إشي و أحيانا لما
+
+109
+00:07:22,770 --> 00:07:25,470
+بيكون طاقته عالية بيعطي فوتون في range ال
+
+110
+00:07:25,470 --> 00:07:29,950
+ultraviolet يعني ما بنشوفهوش أو لما تكون المدارين
+
+111
+00:07:29,950 --> 00:07:33,310
+متقاربين و الفرق في الطاقة بينهم قليل جدا هيعطي
+
+112
+00:07:33,310 --> 00:07:36,690
+فوتون طاقته قليلة جدا إذا هيكون في ال infrared
+
+113
+00:07:37,160 --> 00:07:40,640
+وبالتالي هيكون أحيانا invisible photons و أحيانا
+
+114
+00:07:40,640 --> 00:07:46,060
+invisible photons يعني مش مرئية فهذا الكلام غلط مش
+
+115
+00:07:46,060 --> 00:07:49,460
+دائما ال electron مش all electron transitions
+
+116
+00:07:49,460 --> 00:07:52,260
+between energy states results in visible photons
+
+117
+00:07:52,260 --> 00:07:56,220
+أحيانا results in visible photons وأحيانا results
+
+118
+00:07:56,220 --> 00:07:58,820
+in invisible غير مرئي photons
+
+119
+00:08:03,420 --> 00:08:07,280
+طيب at which temperature a piece of steel قطعة من
+
+120
+00:08:07,280 --> 00:08:10,340
+الصلب .. من الحديد الصلب cannot be considered
+
+121
+00:08:10,340 --> 00:08:14,780
+thermally agitated؟ قولنا أي جسم حرارته أكتر من
+
+122
+00:08:14,780 --> 00:08:18,800
+ماينس متين و تلاتة و سبعين تحت الصفر يعتبر مهتاج
+
+123
+00:08:18,800 --> 00:08:25,070
+حراريا، طب هذه أكترمحتاج حراريا و هذه محتاج حراريا
+
+124
+00:08:25,070 --> 00:08:30,290
+و الصفر المئوي محتاج حراريا الوحيد اللي أقل من 273
+
+125
+00:08:30,290 --> 00:08:34,070
+تحت الصفر هي ال 274 تحت الصفر إذا هي الإجابة
+
+126
+00:08:34,070 --> 00:08:38,330
+الوحيدة اللي بقدر اعتبر فيها أنه لو بردت قطعة حديد
+
+127
+00:08:38,330 --> 00:08:42,430
+لدرجة الحرارة high ساعتها هذه القطعة لا تعتبر
+
+128
+00:08:42,430 --> 00:08:45,230
+cannot be considered thermally agitated
+
+129
+00:08:47,990 --> 00:08:51,830
+طيب، visible light comprises which percentage of
+
+130
+00:08:51,830 --> 00:08:55,230
+electromagnetic spectrum؟ قلنا ال .. ال .. الضوء
+
+131
+00:08:55,230 --> 00:08:59,650
+المرئي بشكل نسبة قليلة جدا، تشكل واحد في المية من
+
+132
+00:08:59,650 --> 00:09:01,830
+كل الطيف الكهرو مغناطيسي
+
+133
+00:09:04,990 --> 00:09:08,150
+According to quantum theory, the energy carried by
+
+134
+00:09:08,150 --> 00:09:11,450
+the wave is proportional to the square of its
+
+135
+00:09:11,450 --> 00:09:14,590
+amplitude and does not depend at all on the
+
+136
+00:09:14,590 --> 00:09:18,730
+frequency of the wave هذا الكلام صحيح لل wave
+
+137
+00:09:18,730 --> 00:09:21,730
+theory، مش لل quantum theory، ال quantum theory
+
+138
+00:09:21,730 --> 00:09:29,030
+الطاقة المحمولة بالفوتون أو اللي بيحملها الفوتونأو
+
+139
+00:09:29,030 --> 00:09:31,930
+ال .. ال .. ال wave ال light wave بتعتمد على ال
+
+140
+00:09:31,930 --> 00:09:34,710
+frequency على التردد حسب ال quantum theory إذا
+
+141
+00:09:34,710 --> 00:09:41,010
+الجواب خطأ .. الجواب خطأ
+
+142
+00:09:41,010 --> 00:09:46,830
+what is the Pruster angle when light travels from
+
+143
+00:09:46,830 --> 00:09:54,210
+glass to air إذا ال air NT و ال glass NIمن الـ
+
+144
+00:09:54,210 --> 00:09:56,990
+Glass و ده تروح على الهواء بنقول كالقاعدة بدنا ال
+
+145
+00:09:56,990 --> 00:09:57,510
+calculator
+
+146
+00:10:23,210 --> 00:10:28,290
+هيتنقص ناقص واحد ميلي جلاس هو هينتقل ميلي جلاس
+
+147
+00:10:28,290 --> 00:10:34,950
+للهوا إذا الهوا NT تنقص ناقص واحد NT اللي هو واحد
+
+148
+00:10:34,950 --> 00:10:39,550
+على
+
+149
+00:10:39,550 --> 00:10:52,190
+NI لأ مش هيك واحد على NI اللي هو واحد ونص
+
+150
+00:10:54,430 --> 00:11:00,950
+إذا يساوي انت تلاتة و تلاتين و تسعة و ستين من مية،
+
+151
+00:11:00,950 --> 00:11:03,950
+يعني تلاتة و تلاتين و سبعة من عشرة، تلاتة و تلاتين
+
+152
+00:11:03,950 --> 00:11:07,150
+و سبعة من عشرة، إذا هذا هو الجواب الصحيح
+
+153
+00:11:10,090 --> 00:11:13,250
+Earth's atmosphere is held in position by the
+
+154
+00:11:13,250 --> 00:11:17,250
+gravitational pull of the mass of the earth وهذا
+
+155
+00:11:17,250 --> 00:11:21,470
+كلام منطقي وواقعي وصحيح أنه الغلاف الجوي بيظل
+
+156
+00:11:21,470 --> 00:11:24,950
+مكانه حوالين الأرض، محيط بالأرض، مابتطيرش، اللي هو
+
+157
+00:11:24,950 --> 00:11:27,730
+ثاني أكسيد الكربون وبخار الماء والأوزون وما إلى
+
+158
+00:11:27,730 --> 00:11:32,230
+ذلك بسبب الجاذبية الأرضية، هذا كلام صحيح، هذا كلام
+
+159
+00:11:32,230 --> 00:11:32,930
+صحيح
+
+160
+00:11:35,750 --> 00:11:38,590
+The pressure inside gas discharged tube is lower
+
+161
+00:11:38,590 --> 00:11:41,870
+than atmospheric pressure و التكلام صحيح ما بيكون
+
+162
+00:11:41,870 --> 00:11:44,710
+أعلى ولا مساوى لل atmospheric pressure لازم يكون
+
+163
+00:11:44,710 --> 00:11:48,950
+أقل من الضغط الجو المحيط بال gas discharged tube
+
+164
+00:11:48,950 --> 00:11:51,210
+أقل بكتير من الضغط الجو
+
+165
+00:11:54,220 --> 00:11:58,100
+طيب، what is the brightest of the four Birkin J
+
+166
+00:11:58,100 --> 00:12:00,780
+images؟ طبعا الأولى هي ال brightest لأنها هي
+
+167
+00:12:00,780 --> 00:12:04,920
+الانعكاس من السطح الأمامي بتاع القرانية .. من
+
+168
+00:12:04,920 --> 00:12:11,280
+السطح الأمامي بتاع القرانية طيب، which is true؟
+
+169
+00:12:11,280 --> 00:12:13,780
+الصحيح هو the greater the difference in the
+
+170
+00:12:13,780 --> 00:12:17,140
+refractive indices between the two media or the
+
+171
+00:12:17,140 --> 00:12:22,040
+greater the angle of incidenceلأ هنا طبعا خربت
+
+172
+00:12:22,040 --> 00:12:25,300
+الإيجابات أنا طالب منه خربت الإيجابات يعني كل طالب
+
+173
+00:12:25,300 --> 00:12:28,440
+ممكن يظهر عنده الإيجابات بهذا فخلينا احنا نقرأهم
+
+174
+00:12:28,440 --> 00:12:30,940
+كلهم the smaller the difference in the refractive
+
+175
+00:12:30,940 --> 00:12:34,280
+index او the refractive indices between the two
+
+176
+00:12:34,280 --> 00:12:37,640
+media or the smaller the angle of incidence, the
+
+177
+00:12:37,640 --> 00:12:41,080
+smaller the amount of reflection and consequently
+
+178
+00:12:41,080 --> 00:12:44,720
+the less light transmitted كل هالجملة صحيحة معادة
+
+179
+00:12:44,720 --> 00:12:47,220
+كلمة the less لو .. لو قلنا the more light
+
+180
+00:12:47,220 --> 00:12:50,730
+transmitted كان أصبحت صحيحةانتقل للجملة التانية،
+
+181
+00:12:50,730 --> 00:12:54,030
+the greater the difference between refractive
+
+182
+00:12:54,030 --> 00:12:56,750
+indices between the two media or the greater the
+
+183
+00:12:56,750 --> 00:12:59,530
+angle of incidence, the smaller the amount of
+
+184
+00:12:59,530 --> 00:13:02,990
+reflection، هذه غلط، the smaller the difference in
+
+185
+00:13:02,990 --> 00:13:06,130
+the refractive indices between the two media or
+
+186
+00:13:06,130 --> 00:13:09,350
+the smaller the angle of incidence, the smaller of
+
+187
+00:13:09,350 --> 00:13:13,130
+the amount of reflection and consequently the more
+
+188
+00:13:13,130 --> 00:13:16,190
+light transmitted، هذه الإجابة هي الصحية، هذه
+
+189
+00:13:16,190 --> 00:13:21,280
+الإجابة هي الصحيةواللي مش متأكد يرجع للمحاضرات،
+
+190
+00:13:21,280 --> 00:13:24,680
+الان matching، matching بنقول jumping of electron
+
+191
+00:13:24,680 --> 00:13:28,420
+to higher energy state، يعني كان في مدار أدنى و
+
+192
+00:13:28,420 --> 00:13:33,500
+اكتسب فوتون، صار في مدار أعلى، بيسموها stimulated
+
+193
+00:13:33,500 --> 00:13:38,180
+absorptionemission مابنفعش لأن كلمة emission و
+
+194
+00:13:38,180 --> 00:13:42,820
+emission هدول الخيارين مابنفعش ليش؟ لأنه لو صار
+
+195
+00:13:42,820 --> 00:13:45,420
+emission .. emission معناته فقد فوتون معناته بده
+
+196
+00:13:45,420 --> 00:13:49,140
+ينزل مش يطلع طالما أنه بده يطلع jump ل higher
+
+197
+00:13:49,140 --> 00:13:52,600
+energy state معناته absorption طب الفلوريسانس أيضا
+
+198
+00:13:52,600 --> 00:13:55,960
+الفلوريسانس بده ينزل إذا الإجابة الوحيدة الممكنة
+
+199
+00:13:55,960 --> 00:14:00,450
+stimulated absorption طيبDrop of an electron from
+
+200
+00:14:00,450 --> 00:14:04,110
+higher energy state to lower energy state by the
+
+201
+00:14:04,110 --> 00:14:07,750
+effect of external photon
+
+202
+00:14:17,000 --> 00:14:20,700
+Close spacing between two energy states هذه ال
+
+203
+00:14:20,700 --> 00:14:24,840
+media أو أي مادة فيها close spacing between two
+
+204
+00:14:24,840 --> 00:14:27,560
+energy states بنقول بتنفع هذه المادة تكون
+
+205
+00:14:27,560 --> 00:14:31,140
+fluorescent material، fluorescent material لازم
+
+206
+00:14:31,140 --> 00:14:34,520
+يكون فيها مدارين متقاربين، يعني ال close spacing
+
+207
+00:14:34,520 --> 00:14:38,700
+في الطاقة بينهمبيظل الخيار الأخير drop of an
+
+208
+00:14:38,700 --> 00:14:42,180
+electron to lower energy level without any
+
+209
+00:14:42,180 --> 00:14:45,140
+external الحالة spontaneous emission، spontaneous
+
+210
+00:14:45,140 --> 00:14:51,560
+emission، هيك بيكون خلص السؤال هذا In Yang's two
+
+211
+00:14:51,560 --> 00:14:54,760
+slit experiment, if the light source consists of
+
+212
+00:14:54,760 --> 00:14:58,620
+many point sources distributed over a broad area,
+
+213
+00:14:58,780 --> 00:15:03,580
+the net result will be total loss of contrast and
+
+214
+00:15:03,580 --> 00:15:08,040
+no fringes will be evidentلأن المناطق الواضحة تحت
+
+215
+00:15:08,040 --> 00:15:11,220
+صورة النقطة الأولى هتيجي على المناطق المعتمة تحت
+
+216
+00:15:11,220 --> 00:15:15,300
+صورة النقطة التانية و هيبهتوا بعض فإذا كان عندي
+
+217
+00:15:15,300 --> 00:15:18,300
+أكتر من نقطتين ال object مكوّن من عدد لانهائي من
+
+218
+00:15:18,300 --> 00:15:21,700
+النقاط هيصير عندي total loss of contrast and no
+
+219
+00:15:21,700 --> 00:15:25,080
+fringes will be evident وبالتالي اللي .. اللي بدى
+
+220
+00:15:25,080 --> 00:15:28,680
+يتأكد ممكن نرجع للمحاضرة لإن فيها شريح وافي مع ال
+
+221
+00:15:28,680 --> 00:15:34,560
+simulationطيب ال coherence length of laser light
+
+222
+00:15:34,560 --> 00:15:38,180
+is longer than that of the sunlight، هذا صحيح لأن
+
+223
+00:15:38,180 --> 00:15:41,780
+ال laser light عبارة عن narrow band وبالتالي ال
+
+224
+00:15:41,780 --> 00:15:43,780
+coherence length بتاعه أطول
+
+225
+00:15:49,290 --> 00:15:52,590
+Electron cannot drop more than one energy level
+
+226
+00:15:52,590 --> 00:15:59,390
+هذا خطأ ممكن ينزل أكتر من energy level حسب الفوتون
+
+227
+00:15:59,390 --> 00:16:03,550
+اللي فقده ممكن يقفز مدارين أو تلاتة للأسفل أو
+
+228
+00:16:03,550 --> 00:16:06,990
+مدارين أو تلاتة للأعلى أو مدار واحد فعنده الخيارات
+
+229
+00:16:06,990 --> 00:16:11,050
+متاع حسب الفوتون طاقة الفوتون اللي اكتسبه أو اللي
+
+230
+00:16:11,050 --> 00:16:11,630
+فقده
+
+231
+00:16:14,290 --> 00:16:17,550
+طيب، the energy emitted at any frequency from
+
+232
+00:16:17,550 --> 00:16:21,130
+transition of electrons between energy states can
+
+233
+00:16:21,130 --> 00:16:25,050
+only change by discrete amounts equaling multiples
+
+234
+00:16:25,050 --> 00:16:30,330
+of HVB وهذا كلام صحيح وشرحناه في المعرض يعني مافيش
+
+235
+00:16:30,330 --> 00:16:32,690
+أنصاف وأرباع للـ HVB
+
+236
+00:16:35,180 --> 00:16:39,560
+ال energy اللي بيتم بثها أو إشعاعها سواء .. بغض
+
+237
+00:16:39,560 --> 00:16:42,480
+النظر عن ترددها، يعني عن تردد الفوتون، ما الفوتون
+
+238
+00:16:42,480 --> 00:16:47,840
+هو energy تم إشعاعه تمام؟ إله frequency معينة،
+
+239
+00:16:47,840 --> 00:16:53,740
+بيقدر تتغير طاقته بكميات محددة عبارة عن مضاعفات ال
+
+240
+00:16:53,740 --> 00:16:56,560
+edge في V، المضاعفات ال edge في V
+
+241
+00:17:01,830 --> 00:17:07,110
+يعني اتنين HPV تلاتة HPV اربع HPV و هكذا atoms of
+
+242
+00:17:07,110 --> 00:17:10,430
+all elements have the same energy state and the
+
+243
+00:17:10,430 --> 00:17:13,630
+same difference between energy states هذا الكلام
+
+244
+00:17:13,630 --> 00:17:17,770
+خطأ مائة بالمائة كل عنصر له يعني توزيعة معينة هذا
+
+245
+00:17:17,770 --> 00:17:20,970
+الكلام شرحناه وقولنا هذه تعتبر بصمة العنصر وعن
+
+246
+00:17:20,970 --> 00:17:25,710
+طريقها بنقدر نعرف العناصر المكونة للنجوم و الكواكب
+
+247
+00:17:25,710 --> 00:17:30,050
+البعيدة بدراسة الضوء المنبعث منها بدراسة الضوء
+
+248
+00:17:30,050 --> 00:17:31,410
+المنبعث او المنعكس
+
+249
+00:17:34,220 --> 00:17:38,020
+In quantum theory electrons present around a
+
+250
+00:17:38,020 --> 00:17:41,140
+nucleus in non-radiating state وهذه اللي بتفرج
+
+251
+00:17:41,140 --> 00:17:44,320
+وهذا صحيح وهي اللي بيفسر لإنه ليش الإلكترون
+
+252
+00:17:44,320 --> 00:17:48,200
+مابفقدش الطاقة أثناء حركته بيصطاد مش بالنواع هذا
+
+253
+00:17:48,200 --> 00:17:50,960
+إذا بنفسره حسب ال wave theory بس ال quantum theory
+
+254
+00:17:50,960 --> 00:17:55,500
+بيقول لأ هذه الإلكترون حالة خاصة إنه بيوجد في non
+
+255
+00:17:55,500 --> 00:18:02,670
+-radiating state هيك خلصنا احنااللي هو الإجابات
+
+256
+00:18:02,670 --> 00:18:06,090
+submit
+
+257
+00:18:06,090 --> 00:18:12,650
+and finish all تمام؟
+
+258
+00:18:12,650 --> 00:18:17,170
+وبالتالي هذه الإجابات الصحيحة الآن ننقلها للنسخة
+
+259
+00:18:17,170 --> 00:18:24,090
+التانية من الإختبار النصفة ونحلها مع بعض
+
+260
+00:18:30,230 --> 00:18:33,810
+طيب regarding the two slit experiment if the light
+
+261
+00:18:33,810 --> 00:18:36,610
+source consists of many point sources distributed
+
+262
+00:18:36,610 --> 00:18:39,990
+over a broad area the net result will be هذا
+
+263
+00:18:39,990 --> 00:18:45,050
+جوابناه قبل شوية total loss of contrast and no
+
+264
+00:18:45,050 --> 00:18:52,570
+fringes will be evident هذا الجواب الصحيحin
+
+265
+00:18:52,570 --> 00:18:55,270
+destructive interference, the resulting wave is
+
+266
+00:18:55,270 --> 00:18:58,630
+twice the amplitude، لأ، في الـ destructive، في
+
+267
+00:18:58,630 --> 00:19:01,370
+الـ destructive مش twice، هتصير صفر، في ال
+
+268
+00:19:01,370 --> 00:19:04,390
+constructive interference هتصير twice the
+
+269
+00:19:04,390 --> 00:19:07,990
+amplitude، اذا هادي خطأ، في ال destructive هتصير
+
+270
+00:19:07,990 --> 00:19:12,130
+zero مش twice،
+
+271
+00:19:12,130 --> 00:19:15,190
+طيب، the superposition of two waves of differing
+
+272
+00:19:15,190 --> 00:19:20,490
+frequenciesproduce changing interference pattern
+
+273
+00:19:20,490 --> 00:19:23,490
+طالما differing frequencies إذا هتعطيني changing
+
+274
+00:19:23,490 --> 00:19:31,250
+interference pattern و هذا كلام صحيح
+
+275
+00:19:31,250 --> 00:19:37,340
+نجي لسؤال هذا يعني بحتاج لتفكير قليلنقول كالعادى
+
+276
+00:19:37,340 --> 00:19:41,500
+in the image هذه الصورة the reflected part of
+
+277
+00:19:41,500 --> 00:19:46,320
+light سقط ضوء سواء سقط من هنا سقط من هنا سقط من
+
+278
+00:19:46,320 --> 00:19:49,460
+هنا سقط من هنا لسه مش عارفين من وين سقط احتمالية
+
+279
+00:19:49,460 --> 00:19:52,900
+سقوطه لسه مش معروفة انه خلنا نقرأ in the image the
+
+280
+00:19:52,900 --> 00:19:55,820
+reflected part احنا قولنا لما بيصل الضوء للسطح
+
+281
+00:19:55,820 --> 00:20:00,160
+الفاصل بين الهواء والجزاز هذا مكعب من الزجاجالان
+
+282
+00:20:00,160 --> 00:20:03,080
+الجزء اللي انعكس، الان بيحكيلي عن ال reflected
+
+283
+00:20:03,080 --> 00:20:07,700
+part اللي ارتدت للهوى، ضرب في الزجاج و ارتد للهوى
+
+284
+00:20:07,700 --> 00:20:13,600
+was totally polarized إيش يعني totally polarized؟
+
+285
+00:20:13,600 --> 00:20:18,720
+يعني كل الجزء اللي انعكس polarized and the
+
+286
+00:20:18,720 --> 00:20:24,280
+direction of polarization was vertical طيب كلمة
+
+287
+00:20:24,280 --> 00:20:28,970
+totally polarized معناته سقط بال prostrate angleو
+
+288
+00:20:28,970 --> 00:20:32,910
+هذا بيقدّي إلى انه totally polarized الجزء اللي
+
+289
+00:20:32,910 --> 00:20:37,270
+انعكس is totally polarized طيب totally polarized
+
+290
+00:20:37,270 --> 00:20:40,030
+هيكون parallel to the surface طالما ال direction
+
+291
+00:20:40,030 --> 00:20:43,490
+of polarization was vertical معناته ال service او
+
+292
+00:20:43,490 --> 00:20:48,730
+ال interface ايضا vertical اذا الاحتماليات الضوء
+
+293
+00:20:48,730 --> 00:20:54,620
+سقط على اي أسطح اما على السطح هذابالبروستر أنجل أو
+
+294
+00:20:54,620 --> 00:20:57,460
+على السطح حادة بالبروستر أنجل ليش؟ لأن هدول
+
+295
+00:20:57,460 --> 00:21:01,940
+السطحين vertical وطالما ال polarization vertical
+
+296
+00:21:01,940 --> 00:21:06,060
+ال direction of polarization vertical وكل اللي
+
+297
+00:21:06,060 --> 00:21:09,200
+انعكس polarized واتجاه ال polarization vertical
+
+298
+00:21:09,200 --> 00:21:12,600
+معناته هو اتجاه ال polarization parallel to the
+
+299
+00:21:12,600 --> 00:21:16,000
+surface او parallel to the interface فبالتالي اما
+
+300
+00:21:16,000 --> 00:21:20,000
+الضوء سقط من هنا او سقط من هنا مستحيل الضوء يسقط
+
+301
+00:21:20,000 --> 00:21:25,010
+بالبروستر أنجل على سطح أفقيوينعكس ويكون totally
+
+302
+00:21:25,010 --> 00:21:27,950
+polarized ما اختلفناش بس يكون vertical اتجاه ال
+
+303
+00:21:27,950 --> 00:21:32,550
+polarization لأنه لو سقط على سطح أفقه هينعكس ..
+
+304
+00:21:32,550 --> 00:21:35,950
+هينعكس ويكون totally polarized مافيها نقاش بس
+
+305
+00:21:35,950 --> 00:21:38,590
+هيكون ساعتها اتجاه ال polarization horizontal مش
+
+306
+00:21:38,590 --> 00:21:42,890
+vertical زي ما هنا يعني مذكور فبالتالي الاحتمالين
+
+307
+00:21:42,890 --> 00:21:47,190
+انه اما سقط على السطح العمودي هذا للوح الجزاز اللي
+
+308
+00:21:47,190 --> 00:21:52,690
+هو الحب أو مكعب الزجاج او على هذاأما هنا و هنا لأ،
+
+309
+00:21:52,690 --> 00:22:01,010
+إذا بنقول from here و from here أما إذا كانوا
+
+310
+00:22:01,670 --> 00:22:05,350
+vertical بي polarize بيكون .. بنفعش يكون سقط من
+
+311
+00:22:05,350 --> 00:22:08,730
+هنا ولا سقط من هنا، هاي الإجابة الصحيحة، هاي
+
+312
+00:22:08,730 --> 00:22:11,970
+الإجابة الصحيحة مائة بالمائة، إذا الاحتماليات
+
+313
+00:22:11,970 --> 00:22:15,390
+طالما ال .. طالما كل اللي انعكس polarized، ماشي،
+
+314
+00:22:15,390 --> 00:22:19,970
+بس اتجاه ال polarization وين؟ vertical، بفهم من كل
+
+315
+00:22:19,970 --> 00:22:22,950
+.. من كلمة كل اللي انعكس polarized إنه سقط بالـ
+
+316
+00:22:22,950 --> 00:22:26,160
+poster angleطيب طالما اتجاه ال polarization
+
+317
+00:22:26,160 --> 00:22:29,080
+vertical معناته .. احنا بنعرف ال browser angle
+
+318
+00:22:29,080 --> 00:22:32,780
+معناته هي انعكس باتجاه polarization موازي لل
+
+319
+00:22:32,780 --> 00:22:37,520
+interface اذا هيكون اما سقط على هذا السطح او على
+
+320
+00:22:37,520 --> 00:22:41,000
+هذا السطح ال two vertical surfaces بس مش ممكن من
+
+321
+00:22:41,000 --> 00:22:47,140
+هنا عفوا هنا هذه الخطأ not from here هيك .. هيك
+
+322
+00:22:47,140 --> 00:22:54,100
+الإجابات صحيحة مئة بالمائةAtoms of all elements
+
+323
+00:22:54,100 --> 00:22:56,700
+has different energy states and the difference
+
+324
+00:22:56,700 --> 00:23:00,120
+between energy states is unique يعني فريد for each
+
+325
+00:23:00,120 --> 00:23:03,580
+element and compound هذا كلام واضح اللي هو بصمة
+
+326
+00:23:03,580 --> 00:23:08,960
+العنصر أو بصمة المركب الكيميائي calculate the
+
+327
+00:23:08,960 --> 00:23:13,390
+critical angle between waterلأن تساوي واحد و تلاتة
+
+328
+00:23:13,390 --> 00:23:17,090
+من عشرة و الهواء إذا الضوء بدي انتقل من ال .. واحد
+
+329
+00:23:17,090 --> 00:23:20,730
+و تلاتة من عشرة من ال .. من ال water للهواء إذا في
+
+330
+00:23:20,730 --> 00:23:24,750
+critical angle بروح على ال calculator بقول بدي
+
+331
+00:23:24,750 --> 00:23:30,890
+الدالة هنا بدي sign و اصناقس واحد برجع للأساسية
+
+332
+00:23:30,890 --> 00:23:37,850
+بنقول واحد and T اللي هو الهواء على and I تقسيم
+
+333
+00:23:37,850 --> 00:23:46,040
+واحد و تلاتة من عشرةبنقول له enter خمسين و اتنين
+
+334
+00:23:46,040 --> 00:23:49,540
+من عشرة تقريبا، هل فيه في الإجابات خمسين و اتنين
+
+335
+00:23:49,540 --> 00:23:54,620
+اتنين تمانية؟ خمسين اتنين تمانية صحيح، اذا خمسين
+
+336
+00:23:54,620 --> 00:24:01,400
+اتنين تمانية، degree، هاي ال critical angleThe
+
+337
+00:24:01,400 --> 00:24:04,820
+energy emitted at any frequency from transition of
+
+338
+00:24:04,820 --> 00:24:08,040
+electrons between energy states can only change by
+
+339
+00:24:08,040 --> 00:24:11,940
+discrete amounts equaling multiples of HPV هذا
+
+340
+00:24:11,940 --> 00:24:14,360
+السؤال مر في النسخة الأولى من الامتحان، بنقول
+
+341
+00:24:14,360 --> 00:24:21,950
+صحيح، next pagelight waves are not objects so they
+
+342
+00:24:21,950 --> 00:24:25,770
+can overlap and superposition can take place و هذا
+
+343
+00:24:25,770 --> 00:24:28,390
+كلام صحيح يعني الموجات الضوئية حاكيناها في
+
+344
+00:24:28,390 --> 00:24:32,510
+المحاضرات أنه مش عبارة عن .. مش object ممكن
+
+345
+00:24:32,510 --> 00:24:35,730
+يتداخلوا مع بعضهم البعض لو الموجات الضوئية عبارة
+
+346
+00:24:35,730 --> 00:24:39,710
+عن object .. objects صعب أنهم يت .. مش صعب يعني
+
+347
+00:24:39,710 --> 00:24:42,690
+مافيش إمكانية أنهم يحلوا في بعضهم البعض أو يتحدوا
+
+348
+00:24:42,690 --> 00:24:48,530
+في بعضهم البعض طيبممكن يتدافل في بعضهم البعض if
+
+349
+00:24:48,530 --> 00:24:51,430
+the light source consists of many points sources
+
+350
+00:24:51,430 --> 00:24:54,850
+distributed over a broad area, the net result will
+
+351
+00:24:54,850 --> 00:24:59,950
+be زي هذا السؤال مكرر a total loss of contrast and
+
+352
+00:24:59,950 --> 00:25:06,510
+no fringes will be evident reflected
+
+353
+00:25:06,510 --> 00:25:09,710
+light is completely polarized of the angle of
+
+354
+00:25:09,710 --> 00:25:14,100
+reflection هذا السؤال فيه خدعة بسيطةreflected
+
+355
+00:25:14,100 --> 00:25:18,120
+light is completely polarized if the angle of
+
+356
+00:25:18,120 --> 00:25:22,920
+reflection equals the Brewster angle احنا عارفين
+
+357
+00:25:22,920 --> 00:25:25,380
+انه the angle of incidence equals the Brewster
+
+358
+00:25:25,380 --> 00:25:29,020
+angle ساعتها كله بيكون completely polarized مظبوط
+
+359
+00:25:29,020 --> 00:25:34,060
+بس لما ال angle of reflection ماهي تساوي ال angle
+
+360
+00:25:34,060 --> 00:25:39,290
+of incidence حسب قانون الانعكاس θI تساوي θRزاوية
+
+361
+00:25:39,290 --> 00:25:43,490
+الانعكاس تساوي زاوية السقوط وطالما زاوية الانعكاس
+
+362
+00:25:43,490 --> 00:25:47,150
+تساوي ال browser angle معناته زاوية السقوط تساوي
+
+363
+00:25:47,150 --> 00:25:51,950
+ال browser angle فالجواب صحيح هنا بس غيرنا كلمة if
+
+364
+00:25:51,950 --> 00:25:54,890
+the angle of incidence equals the browser angle
+
+365
+00:25:54,890 --> 00:25:58,450
+وبدلناها بكلمة if the angle of reflection ما هو
+
+366
+00:25:58,450 --> 00:26:00,810
+معروف أن ال angle of reflection و ال angle of
+
+367
+00:26:00,810 --> 00:26:05,510
+incidence هما نفس القيمة إذا واحدة منهم خمسين
+
+368
+00:26:05,510 --> 00:26:08,030
+degree اتانى خمسين degree إذا واحدة تلاتين degree
+
+369
+00:26:08,030 --> 00:26:12,630
+اتانىيعني دائما قانون للإعكاس أول قانون ناخده θ I
+
+370
+00:26:12,630 --> 00:26:16,670
+تساوي θ R فبالتالي هذه لو أنا شيلتها و بدلت قولت
+
+371
+00:26:16,670 --> 00:26:18,850
+ما هي ال angle of reflection هي ال angle of
+
+372
+00:26:18,850 --> 00:26:22,450
+incidence بدلت هنا في خياه في مخيي اللي اتقول if
+
+373
+00:26:22,450 --> 00:26:25,250
+the angle of incidence equals the Brewster angle
+
+374
+00:26:25,250 --> 00:26:26,830
+هيطلع معايا الجواب صحيح
+
+375
+00:26:30,550 --> 00:26:33,810
+if the electric field is oriented vertically then
+
+376
+00:26:33,810 --> 00:26:36,610
+polarization of light هذا سؤال مباشر electric
+
+377
+00:26:36,610 --> 00:26:39,870
+field vertically is a vertical polarization بداهاش
+
+378
+00:26:39,870 --> 00:26:43,690
+يعني لأن حسب ال electric field بيعتبر ال
+
+379
+00:26:43,690 --> 00:26:47,170
+polarization which of the bourkinje images is the
+
+380
+00:26:47,170 --> 00:26:50,490
+least clinically visible التانية التانية الأولى
+
+381
+00:26:50,490 --> 00:26:53,630
+أوضح واحدة والتانية أقل واحدة وضوحاً التالتة
+
+382
+00:26:53,630 --> 00:26:58,390
+والرابعة تقريبا نفس الوضوح تقريبا نفس الوضوحبس
+
+383
+00:26:58,390 --> 00:27:01,590
+بيجوا أقل من الأولى، can total internal reflection
+
+384
+00:27:01,590 --> 00:27:04,950
+occurs inside the air if the interface between air
+
+385
+00:27:04,950 --> 00:27:08,250
+and water؟
+
+386
+00:27:08,250 --> 00:27:12,410
+يعني هل ممكن يحصل total internal reflection داخل
+
+387
+00:27:12,410 --> 00:27:16,150
+الهوى؟إذا كان السطح الفاصل هو يفصل بين الهواء
+
+388
+00:27:16,150 --> 00:27:19,490
+والميء كأنه بيقول الضوء إجا من جلب الهواء من جوا
+
+389
+00:27:19,490 --> 00:27:22,490
+الهواء وراح على السطح الفاصل بين الهواء والميء
+
+390
+00:27:22,490 --> 00:27:26,190
+بنفع يصير total internal reflection inside the air
+
+391
+00:27:26,190 --> 00:27:29,430
+يعني ينعكس مرة تانية في الهواء بيقولوا لأ مابنفعش
+
+392
+00:27:29,430 --> 00:27:33,370
+لأنه الضوء طالما في الهواء وبينتقل للميء من .. من
+
+393
+00:27:33,370 --> 00:27:36,390
+وسط أقل كثافة لأعلى كثافة بينفعش يصير total
+
+394
+00:27:36,390 --> 00:27:39,730
+internal reflection بتادة ال total internal
+
+395
+00:27:39,730 --> 00:27:42,630
+reflection من أعلى لأقل فبالتالي غلط
+
+396
+00:27:47,770 --> 00:27:51,790
+طيب match the following sentences close spacing
+
+397
+00:27:51,790 --> 00:27:55,350
+between two energy states اللي هو ال fluorescence
+
+398
+00:27:55,350 --> 00:27:59,150
+هذا السؤال جوابناه قبل شوية drop of electron to
+
+399
+00:27:59,150 --> 00:28:02,370
+lower energy level بدون ما حد يكلمه، بنقوله
+
+400
+00:28:02,370 --> 00:28:07,130
+spontaneous emission drop of an electron from
+
+401
+00:28:07,130 --> 00:28:10,690
+higher energy state to lower energy state بتحفيز
+
+402
+00:28:10,690 --> 00:28:15,920
+من external photon، هذا stimulated emissionلأن هذه
+
+403
+00:28:15,920 --> 00:28:19,340
+هي فكرة ال laser هذه هي ال stimulated emission
+
+404
+00:28:19,340 --> 00:28:23,660
+jumping of an electron to higher energy state كلمة
+
+405
+00:28:23,660 --> 00:28:26,940
+jumping يعني يطلع على فوق هذا الوحيد اللي هو
+
+406
+00:28:26,940 --> 00:28:33,420
+absorption و هذا حلناها قبل شوية طيب what is the
+
+407
+00:28:33,420 --> 00:28:38,360
+optical density of a material if the transmittance
+
+408
+00:28:38,360 --> 00:28:45,820
+equals واحد من مية في المية نيجي هنا بنقولإن شاء
+
+409
+00:28:45,820 --> 00:28:52,420
+الله نجي اللوجارتمات هنا logarithm
+
+410
+00:28:52,420 --> 00:29:01,400
+.. نرجع للأساسية الواحد تقسيم واحد من مية في المية
+
+411
+00:29:01,400 --> 00:29:07,620
+يعني واحد من عشر تلاف عفوا
+
+412
+00:29:07,620 --> 00:29:13,100
+ال logarithm العشري لواحد تقسيم
+
+413
+00:29:14,940 --> 00:29:26,220
+واحد على عشرة تلاف كان
+
+414
+00:29:26,220 --> 00:29:30,340
+واحد على ال transmittance واحد لغريتم العشر إلى
+
+415
+00:29:30,340 --> 00:29:34,060
+واحد ال optical density ال optical density تساوي
+
+416
+00:29:34,060 --> 00:29:37,360
+واحد على ال transmittance طب ل transmittance واحد
+
+417
+00:29:37,360 --> 00:29:39,860
+من مية في المية ممكن سايا نقول لا يعني انا مابديش
+
+418
+00:29:39,860 --> 00:29:45,020
+ابيديها زي ما هي مكتوبة بالضبط نقوله ماشي فضلهي ال
+
+419
+00:29:45,020 --> 00:29:53,440
+logarithm واحد على واحد من مية في المية طيب نشوف
+
+420
+00:29:53,440 --> 00:29:59,340
+تظبط معانا ولا لأ واحد من مية في المية ان شاء الله
+
+421
+00:29:59,340 --> 00:30:03,860
+تظبط لأ هيك مازبطتش ال logarithm واحد من مية في
+
+422
+00:30:03,860 --> 00:30:10,240
+المية يعني واحد من عشر تلف ال logarithm واحد
+
+423
+00:30:10,240 --> 00:30:14,440
+تقسيم لأ اسف
+
+424
+00:30:20,420 --> 00:30:32,180
+ولو جاريتم واحد تقسيم واحد من عشر تلاف لأ
+
+425
+00:30:32,180 --> 00:30:35,460
+واحد على واحد هي اه ده هي اللي زادت واحد على عشر
+
+426
+00:30:35,460 --> 00:30:35,980
+تلاف
+
+427
+00:30:48,760 --> 00:30:53,120
+أه هيك اضطط .. لازم نحط zero هنا على الشمال .. اذا
+
+428
+00:30:53,120 --> 00:31:01,460
+اربعة .. اذا اربعة .. نرجع للامتحان .. اذا اربعة
+
+429
+00:31:01,460 --> 00:31:06,120
+.. اذا ال .. ال transmittance واحد من مية في المية
+
+430
+00:31:06,120 --> 00:31:10,680
+يعني واحد من مية على مية يعني واحد على مية على مية
+
+431
+00:31:10,680 --> 00:31:16,730
+يعني واحد على عشر اكتر .. اذا اربعةDark absorption
+
+432
+00:31:16,730 --> 00:31:19,610
+lights in the emitted spectrum from a star enables
+
+433
+00:31:19,610 --> 00:31:22,630
+us to know the composition of that star هذا سؤال
+
+434
+00:31:22,630 --> 00:31:29,510
+ورد في النسخة الأولى، قول صحيح In Yang's
+
+435
+00:31:29,510 --> 00:31:32,030
+experiment, as the wave transition of light
+
+436
+00:31:32,030 --> 00:31:35,390
+overlap less and less, fringe contrast decreases،
+
+437
+00:31:35,390 --> 00:31:36,010
+هذا صحيح
+
+438
+00:31:40,510 --> 00:31:43,310
+طيب all of the following mechanisms are helpful
+
+439
+00:31:43,310 --> 00:31:46,070
+for protection against harmful sun radiation
+
+440
+00:31:46,070 --> 00:31:50,170
+except .. طبعا except Jupiter's magnetic field
+
+441
+00:31:50,170 --> 00:31:55,170
+يعني المجال المغناطيسي لكوكب المشتري مايله علاقة
+
+442
+00:31:55,170 --> 00:31:58,830
+في إنه يحمينا من الأشعة اللي صادرة من الشمس اللي
+
+443
+00:31:58,830 --> 00:32:01,630
+هي الأشعة ال harmful ال gamma ray و ال X-ray و ال
+
+444
+00:32:01,630 --> 00:32:05,520
+ultraviolet و ما إلى ذلكأما البعد الشاهق لل ..
+
+445
+00:32:05,520 --> 00:32:10,940
+للأرض عن الشمس أه، عساس أنه بيصلنا حصة قليلة جدا
+
+446
+00:32:10,940 --> 00:32:14,580
+من الإشعاع الشمسي، ال solar wind المحيطة بالشمس،
+
+447
+00:32:14,580 --> 00:32:17,900
+الرياح الشمسية صحيح، ال earth atmosphere اللي
+
+448
+00:32:17,900 --> 00:32:21,220
+بيمتص يعني مثلا طبقة الوزون في ال atmosphere بتمتص
+
+449
+00:32:21,220 --> 00:32:24,240
+ال ultraviolet و هكذا تمام؟ فبالتالي ال Jupiter
+
+450
+00:32:24,240 --> 00:32:28,460
+magnetic field مايله دعوة فهو الوحيد ال exception
+
+451
+00:32:28,460 --> 00:32:33,830
+.. ال exceptionعندما يصيب الرايس المظهرة و المظهرة
+
+452
+00:32:33,830 --> 00:32:39,450
+الصحيحة، فكل الضوء المظهر يصيب بطريقة مرتبطة
+
+453
+00:32:39,450 --> 00:32:42,950
+بطريقة عادية للوظيفةلما ال reflected و ال
+
+454
+00:32:42,950 --> 00:32:46,690
+refracted rays يكونوا right angle بينهم تسعين
+
+455
+00:32:46,690 --> 00:32:49,990
+درجة، معناته فيه سقوط بال broaster angle، ساعتها
+
+456
+00:32:49,990 --> 00:32:54,090
+كل ال reflected light is linearly polarized، صحيح،
+
+457
+00:32:54,090 --> 00:32:57,710
+parallel لإيش؟ لل interface، مش ال service normal،
+
+458
+00:32:57,710 --> 00:33:01,130
+لل interface، مش ال service normal، فبالتالي هذا
+
+459
+00:33:01,130 --> 00:33:04,470
+الإجابة خطأ، في ناس و جاعت فكرت كلمة service
+
+460
+00:33:04,470 --> 00:33:06,670
+normal هي ال interface، هي ال interface
+
+461
+00:33:09,410 --> 00:33:13,210
+visible lights is considered a type of ionizing
+
+462
+00:33:13,210 --> 00:33:15,970
+radiation غلط، visible light مش ionizing
+
+463
+00:33:15,970 --> 00:33:19,910
+radiation، أما الأشعة ليه ال ionizing radiation زي
+
+464
+00:33:19,910 --> 00:33:22,950
+الجمرة و ال X-ray و ال ultraviolet
+
+465
+00:33:27,500 --> 00:33:31,100
+the time .. the coherence time is in a broad .. in
+
+466
+00:33:31,100 --> 00:33:34,340
+a broad band light source is longer than the
+
+467
+00:33:34,340 --> 00:33:37,360
+coherence time in narrow band light sources وده
+
+468
+00:33:37,360 --> 00:33:41,400
+خطأ لأن ال coherence time في ال broad band .. ال
+
+469
+00:33:41,400 --> 00:33:43,940
+broad band ال sections قصيرة فال coherence time
+
+470
+00:33:43,940 --> 00:33:47,020
+قصير مش longer than shorter than فبالتالي هذه
+
+471
+00:33:47,020 --> 00:33:48,220
+إجابة خطأ
+
+472
+00:33:51,900 --> 00:33:54,980
+and electron .. all electron .. all electron
+
+473
+00:33:54,980 --> 00:33:57,600
+transitions between energy states results in
+
+474
+00:33:57,600 --> 00:34:01,340
+visible photons طبعا مش كلها بعضها بتنتج عنها
+
+475
+00:34:01,340 --> 00:34:04,340
+invisible photons إذا الإجابة غلط و هذا سؤال مر
+
+476
+00:34:04,340 --> 00:34:08,080
+معناه طيب
+
+477
+00:34:08,080 --> 00:34:13,800
+light was travelling from air أنواعة to glassand
+
+478
+00:34:13,800 --> 00:34:17,040
+at a specific angle of incidence you noted that
+
+479
+00:34:17,040 --> 00:34:19,660
+the reflected light and transmitted light are
+
+480
+00:34:19,660 --> 00:34:23,200
+perpendicular to each other يعني سقطت بالبروستر
+
+481
+00:34:23,200 --> 00:34:26,540
+angle what was the angle of incidence؟ بدنا نحسب
+
+482
+00:34:26,540 --> 00:34:31,820
+البروستر angle من الهوى اللي هو Ni لجلس اللي هو Nt
+
+483
+00:34:31,820 --> 00:34:37,280
+بدنا نروح على الحاسبة ونقول تام او ناقص واحد Nt
+
+484
+00:34:37,280 --> 00:34:40,440
+اللي هو الجلس قلنا قداش واحد واربعة من عشرة
+
+485
+00:34:53,870 --> 00:35:03,130
+لأ نقول تان أثناقس واحد NT
+
+486
+00:35:03,130 --> 00:35:08,870
+واحد وأربعة من عشرة تقسيم
+
+487
+00:35:08,870 --> 00:35:16,310
+NI الواحدانت فعندي اربعة و خمسين و اربعة من عشرة
+
+488
+00:35:16,310 --> 00:35:18,970
+او اربعة و خمسين و ستة و اربعين من مية، هلفي في
+
+489
+00:35:18,970 --> 00:35:22,090
+الإجابات اربعة و خمسين و ستة و اربعين من مية
+
+490
+00:35:22,090 --> 00:35:27,580
+degree؟ هذا نية الإجابةطيب according to quantum
+
+491
+00:35:27,580 --> 00:35:29,980
+theory the energy carried by the wave is
+
+492
+00:35:29,980 --> 00:35:33,100
+proportional to the square of its amplitude قولنا
+
+493
+00:35:33,100 --> 00:35:35,920
+هذا الكلام بظبط مع ال wave theory إنها بتتناسب
+
+494
+00:35:35,920 --> 00:35:39,260
+الطاقة مع مربع ال amplitude أما في ال quantum
+
+495
+00:35:39,260 --> 00:35:42,780
+theory بتتناسب مع ال frequency and does not depend
+
+496
+00:35:42,780 --> 00:35:47,060
+at all on the frequency طبعا غلط هذا و هذا سؤال
+
+497
+00:35:47,060 --> 00:35:51,400
+مكرر و هيك بنكون انتهينا من الامتحان التاني طبعا
+
+498
+00:35:51,400 --> 00:35:52,220
+عملنا finishing
+
+499
+00:35:56,910 --> 00:35:59,990
+هيك بنقولكم يعطيكم العافية والسلام عليكم ورحمة
+
+500
+00:35:59,990 --> 00:36:01,670
+الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/HIX23ALIN7Q_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/HIX23ALIN7Q_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0ad34fa5783efe9901bb9222f4630ee55ecb97ed
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/HIX23ALIN7Q_postprocess.srt
@@ -0,0 +1,1272 @@
+1
+00:00:02,210 --> 00:00:07,230
+بسم الله الرحمن الرحيم بنستكمل محاضرات ال physical
+
+2
+00:00:07,230 --> 00:00:12,690
+optics و اتعرفنا في المحاضرة السابقة على وسائل
+
+3
+00:00:12,690 --> 00:00:17,190
+الحماية من الضوء او من الموجات الكهرومغناطسية
+
+4
+00:00:17,190 --> 00:00:21,890
+الدارة المرافقة للضوء و حكينا انه بيوصل على سطح
+
+5
+00:00:21,890 --> 00:00:27,190
+الأرض الضوء المرئي بمعنى ال visible light و قليل
+
+6
+00:00:27,190 --> 00:00:32,570
+من ال ultraviolet و قليل من ال infraredوقليل جدا
+
+7
+00:00:32,570 --> 00:00:38,170
+جدا جدا من باقي الإشعاعات و .. اللي هي إشعاعات
+
+8
+00:00:38,170 --> 00:00:43,530
+ضارة زي ال ionizing radiation وصل الضوء لسطح الأرض
+
+9
+00:00:43,530 --> 00:00:49,730
+لابد من أنه نتكلم الآن عن المرحلة التانية بعد وصول
+
+10
+00:00:49,730 --> 00:00:55,130
+الضوء وهي مرحلة ال visible light sensing الإحساس
+
+11
+00:00:55,130 --> 00:00:59,310
+بالضوء المرئي أو فهم الضوء المرئي أو التعامل مع
+
+12
+00:00:59,310 --> 00:01:04,630
+الضوء المرئيأو الاستفادة للكائنات الحية من الضوء
+
+13
+00:01:04,630 --> 00:01:09,370
+المري و قبل ما نوصل لاستفادة الإنسان من الضوء
+
+14
+00:01:09,370 --> 00:01:13,030
+المري و استخدامه في عملية الرؤية و التعرف على
+
+15
+00:01:13,030 --> 00:01:19,700
+الأشياءو استخدام جهاز الإبصار للتنقل و للقراة و
+
+16
+00:01:19,700 --> 00:01:26,640
+لأشياء و وظائف عديدة جدا لابد انه يعني نذكر و
+
+17
+00:01:26,640 --> 00:01:31,740
+نستعرض الكائنات الأدنى من الإنسان وصولها لأدنى
+
+18
+00:01:31,740 --> 00:01:37,100
+الكائنات مثل البكتيريا كيف هي بتتعامل مع الضوء و
+
+19
+00:01:37,100 --> 00:01:43,420
+كيف هي بتفهم الضوءWe have traced the origins of
+
+20
+00:01:43,420 --> 00:01:46,620
+visible light from the sun to the earth surfaces
+
+21
+00:01:46,620 --> 00:01:53,460
+احنا اتبعنا نشوء الضوء المرئي من الشمس وصوله لسطح
+
+22
+00:01:53,460 --> 00:01:59,640
+الأرض و ايضا تتبعنا وسائل الحماية من الأشعة الغير
+
+23
+00:01:59,640 --> 00:02:05,360
+مرئية و الموجات الكهرومغناطيسية الضارة زي الجامعة
+
+24
+00:02:05,360 --> 00:02:10,220
+و ال X-ray و ما شابهequally instructive are the
+
+25
+00:02:10,220 --> 00:02:13,180
+mechanisms by which the biological molecule
+
+26
+00:02:13,180 --> 00:02:16,720
+absorbs visible light and then informs the animal
+
+27
+00:02:16,720 --> 00:02:21,180
+of that event بنفس الطريقة يعني يداش مهم احنا
+
+28
+00:02:21,180 --> 00:02:26,300
+نتعرف على نشوء الضوء في داخل الشمسومصوله إلى سطح
+
+29
+00:02:26,300 --> 00:02:31,660
+الأرض بشكل آمن وسليم وغير ضارب أيضًا يعني على نفس
+
+30
+00:02:31,660 --> 00:02:36,560
+المستوى وعلى نفس القدر من الأهمية أنه نتعرف على
+
+31
+00:02:36,560 --> 00:02:41,760
+الآليات اللي بوسطتها الأجزاء الحيوية أو الجزيئات
+
+32
+00:02:41,760 --> 00:02:45,960
+الحيوية أو المركبات الكيميائية الموجودة في الخلايا
+
+33
+00:02:45,960 --> 00:02:53,020
+يعني كيف إنها بتمتص الضوء المرئي وبيتعطي معلومات
+
+34
+00:02:53,370 --> 00:03:02,210
+للكائن الحي أو للحيوان عن وجود حدث ما أمامه مثال،
+
+35
+00:03:02,210 --> 00:03:07,800
+إنسان واقف أماميفتحت عينيا وجيت هذا الإنسان يعني
+
+36
+00:03:07,800 --> 00:03:13,020
+واقف أمامي عرفت هذا الشخص مين هو وعرفت مين اسمه
+
+37
+00:03:13,020 --> 00:03:16,680
+وإيش علاقته فيا سواء إنسان قريب أو غريب أو ما إلى
+
+38
+00:03:16,680 --> 00:03:21,640
+ذلك اللي حدث إنه الضوء اللي صدر من هذا الجسم نتيجة
+
+39
+00:03:21,640 --> 00:03:25,940
+سقوط ضوء الشمس أو ضوء الغرفة أو أي ضوء عليه وانعكس
+
+40
+00:03:25,940 --> 00:03:32,400
+باتجاه عيني ووصل ل ..يعني مركب كيميائي موجود في
+
+41
+00:03:32,400 --> 00:03:36,540
+مستقبلات الضوء ال photo receptors اللي هي ال cones
+
+42
+00:03:36,540 --> 00:03:40,580
+و ال rods اللي هي من ضمن مكونات الشبكية دخل الضوء
+
+43
+00:03:40,580 --> 00:03:45,140
+على ال photo receptors وصل لمركب كيميائي بيسموه ال
+
+44
+00:03:45,140 --> 00:03:49,560
+rodopsin أو الصبغة البصرية الصبغة البصرية أو ال
+
+45
+00:03:49,560 --> 00:03:53,600
+rodopsin أو هذا المركب الكيميائي هو الوحيد القادر
+
+46
+00:03:53,600 --> 00:03:59,070
+على فهم الضوءوإيصال هذا الفهم للدماغ ثم يقوم
+
+47
+00:03:59,070 --> 00:04:04,690
+الدماغ بعمليات تحليل عليا ينتج عنها إدراكي لمين
+
+48
+00:04:04,690 --> 00:04:09,390
+الشخص أو الشيء اللي واقف أمامي أو الحدث اللي بيحدث
+
+49
+00:04:09,390 --> 00:04:14,070
+أمامي، إذا بقدر ما هو مهم نعرف من شاء الضوء ووصوله
+
+50
+00:04:14,070 --> 00:04:19,660
+لسطح الأرض بنفس الأهمية مهم أنه نعرف الآلياتاللي
+
+51
+00:04:19,660 --> 00:04:24,580
+بواسطتها الأجزاء الحيوية .. الأجزاء الجزيئيات
+
+52
+00:04:24,580 --> 00:04:27,400
+الحيوية اللي موجودة في داخل الخلايا ونقصد فيها
+
+53
+00:04:27,400 --> 00:04:31,560
+خلايا ال photo receptors كيف هي بتنتصط ضوء المرء
+
+54
+00:04:31,560 --> 00:04:37,640
+وكيف بتعطينا معلومات عن الحدث اللي بيحدث أمامنا أو
+
+55
+00:04:37,640 --> 00:04:45,000
+أمام أي كائن حي هذا بيشبهحق كتير جدا، ظاهرة
+
+56
+00:04:45,000 --> 00:04:48,980
+فيزيائية، طبعا مالاش علاقة مباشرة في .. في .. في
+
+57
+00:04:48,980 --> 00:04:53,660
+قضية الرؤية، ولكن من وجه الشبه يعني تضرب كمثال In
+
+58
+00:04:53,660 --> 00:04:57,000
+a sense, this represents the equivalent of
+
+59
+00:04:57,000 --> 00:05:02,120
+Einstein photoelectric effectإيش هو ال Einstein
+
+60
+00:05:02,120 --> 00:05:06,100
+photoelectric effect و ليش بيشبه هذه العملية؟
+
+61
+00:05:06,100 --> 00:05:09,320
+بنقول كالاتي أول إشي بدنا نعرف إيش هو ال Einstein
+
+62
+00:05:09,320 --> 00:05:18,360
+photoelectric effect بنرجع للرسمة التالية Einstein
+
+63
+00:05:18,360 --> 00:05:24,920
+وجد أن أي مادة .. أي مادة لما بيسقط عليها الضوء
+
+64
+00:05:24,920 --> 00:05:33,080
+يعني لما بتوصلها فوتو ناتو الضوءبتخليها ينبعث منها
+
+65
+00:05:33,080 --> 00:05:37,520
+إلكترونات هاي عندي أنا صفيحة من المعدن metal plate
+
+66
+00:05:37,520 --> 00:05:42,520
+.. metal plate سقط عليه كمية من الضوء دخلت
+
+67
+00:05:42,520 --> 00:05:46,840
+الفوتونات أو ضربت الفوتونات في صفيحة المعدن تسببت
+
+68
+00:05:46,840 --> 00:05:51,500
+في انبعاث عدد من الإلكترونات لما شدت الإضاءة بتكون
+
+69
+00:05:51,500 --> 00:05:57,650
+أقل .. عفوا أكتر عدد الإلكترونات المنبعثةبيكون
+
+70
+00:05:57,650 --> 00:06:03,770
+أكتر إذا هذه الصفيحة المعدنية تأثرت بالضوء وصارت
+
+71
+00:06:03,770 --> 00:06:09,130
+تطلق الإلكترونات حسب شدة الضوء الساقط عليها وكمية
+
+72
+00:06:09,130 --> 00:06:12,970
+الضوء الساقط عليه إذا هي تأثرت ما الدليل على إنها
+
+73
+00:06:12,970 --> 00:06:18,010
+تأثرت هذه الصفيحة من المعدن إنه أطلقت يعني أو بعثت
+
+74
+00:06:18,010 --> 00:06:21,610
+إلكترونات من ذراتها من ذراتها زي ما الصورة بتوضع
+
+75
+00:06:21,610 --> 00:06:25,830
+أيضا لما بسقط الضوء على الجزائي الحيوي
+
+76
+00:06:28,710 --> 00:06:33,030
+بيعمل تغيير في الجزء الحيوي، هذا الجزء الحيوي لما
+
+77
+00:06:33,030 --> 00:06:37,270
+يتغير بتبعت إشارات بس مش في الفرار، بتبعت إشارات
+
+78
+00:06:37,270 --> 00:06:42,150
+عبر العصب البصري إلى الدماغ و من ثم الدماغ بيحلل
+
+79
+00:06:42,150 --> 00:06:45,630
+هذه الإشارات و بالنهاية الإنسان بدرق أن اللي قدامه
+
+80
+00:06:45,630 --> 00:06:52,810
+بني آدم، سيارة، شجرة، لعبة، جوال، إلى آخرى،
+
+81
+00:06:52,810 --> 00:06:56,350
+فبالتالي بيعرف إيش الحدث اللي بيحدث أماما، زي ما
+
+82
+00:06:56,350 --> 00:07:02,760
+تأثرت صفيحة المعدنبالضوء و بعثت إلكترونات أيضًا
+
+83
+00:07:02,760 --> 00:07:07,660
+بنفس الفكرة الجزاء الحيوي الموجود في ال photo
+
+84
+00:07:07,660 --> 00:07:10,560
+-receptors ال photo-receptors اللي هم ال cones و
+
+85
+00:07:10,560 --> 00:07:14,020
+ال rods اللي خلايا من ضمن خلايا الشبكية موجود فيها
+
+86
+00:07:14,020 --> 00:07:17,620
+الصبغة البصرية اللي اسمها Rodopsin احنا لأ مش
+
+87
+00:07:17,620 --> 00:07:21,370
+هنسميه Rodopsin هنسميه الجزاء الحيويالجزء الحيوي
+
+88
+00:07:21,370 --> 00:07:25,410
+هو الجزء الكيميائي أو المركب العضوي الموجود داخل
+
+89
+00:07:25,410 --> 00:07:29,430
+خلايا الـ photoreceptor والوحيد القادر على فهم
+
+90
+00:07:29,430 --> 00:07:34,250
+الضوء بدليل أنه لما بيسقط عليه الضوء بيجوم بعمليات
+
+91
+00:07:34,250 --> 00:07:39,580
+معينة، هذه العمليات المعينة تشبهالـ Photoelectric
+
+92
+00:07:39,580 --> 00:07:43,340
+Effect بتاع Einstein أنه زي ما الضوء بيسقط على
+
+93
+00:07:43,340 --> 00:07:47,740
+صفيحة معدن صفيحة المعدن بتتأثر و ذراتها بتصير تطلق
+
+94
+00:07:47,740 --> 00:07:51,620
+إلكترونات أيضا الضوء لما بيسقط على الجزيء الحيوي
+
+95
+00:07:51,620 --> 00:07:55,400
+اللي موجود في الخلايااللي هي ال photoreceptors أو
+
+96
+00:07:55,400 --> 00:07:59,020
+مستقبلات الضوء في الشبكية، أيضًا لما بسقط عليه
+
+97
+00:07:59,020 --> 00:08:03,800
+الضوء، بيعمل أو بيحدث فيه أثر، هذا الأثر بتنشأ عنه
+
+98
+00:08:03,800 --> 00:08:08,460
+إشارة كهربائية تصل للدماغ، الدماغ بيقوم بما تبقى
+
+99
+00:08:08,460 --> 00:08:13,280
+من العملية، وهي عملية إدراك ما الذي يحدث أمام
+
+100
+00:08:13,280 --> 00:08:19,670
+العين، ما الذي يحدث أمام العينإذن in essence this
+
+101
+00:08:19,670 --> 00:08:23,550
+represents the equivalent هذا يكافئ لل Einstein
+
+102
+00:08:23,550 --> 00:08:27,490
+photoelectric effect طيب إيش هو ال biological
+
+103
+00:08:27,490 --> 00:08:31,490
+molecule? Rhodopsin is the biological molecule
+
+104
+00:08:31,490 --> 00:08:35,730
+typically used for this purposeممكن سنقول و القصة
+
+105
+00:08:35,730 --> 00:08:39,490
+هاي الكبيرة، يعني إيش الهدف منها؟ يعني بنقول
+
+106
+00:08:39,490 --> 00:08:44,330
+كالقاتي، لو احنا تعبنا عشان نجيب شخص من أسبانيا،
+
+107
+00:08:44,330 --> 00:08:50,610
+يعني هذا الشخص مثلا بارع جدا في جراحة العيون و
+
+108
+00:08:50,610 --> 00:08:55,900
+جراحة الشبكية و لا يتكلم إلا اللغة الأسبانيةالخطوة
+
+109
+00:08:55,900 --> 00:08:59,960
+التانية بعد مجيءه، ضروري جدا أن يكون عندنا إنسان
+
+110
+00:08:59,960 --> 00:09:04,520
+يستطيع فهم اللغة الأسبانية عشان يترجم بيننا وبينه
+
+111
+00:09:04,520 --> 00:09:09,040
+فبالتالي إذا الضوء وصل من سطح الشمس إلى الأرض
+
+112
+00:09:09,040 --> 00:09:14,580
+وعدّى عبر وسائل الأمان كلها وماكانش فيه أي ضرر
+
+113
+00:09:16,380 --> 00:09:22,020
+فلابد من وجود جزئ حيوي يفهم على الضوء ويستفيد من
+
+114
+00:09:22,020 --> 00:09:29,100
+الضوء ويعطي معلومات ضوئية .. ضوئية للكائن الحي
+
+115
+00:09:29,100 --> 00:09:33,890
+عشان يفهم الكائن الحيإيش الأشياء المحيطة فيه و
+
+116
+00:09:33,890 --> 00:09:39,670
+يفهمها من ناحية بصرية أو من ناحية رؤية يا ترى إيش
+
+117
+00:09:39,670 --> 00:09:43,170
+هو الجزء الحيوي؟ الجزء الحيوي هو ال Rodopsin هو ال
+
+118
+00:09:43,170 --> 00:09:47,810
+Rodopsin هو ال biological molecule اللي بيستعمل
+
+119
+00:09:47,810 --> 00:09:52,810
+لغرض فهم الضوء أو بأصح لغرض استقبال الضوء ..
+
+120
+00:09:52,810 --> 00:09:57,700
+استقبال الضوءطيب، اجوا العلماء قالوا احنا بدنا
+
+121
+00:09:57,700 --> 00:10:03,260
+نشوف اقدم رودوبسين وجد على سطح الأرض، بدنا نبدأ من
+
+122
+00:10:03,260 --> 00:10:08,700
+اقدم رودوبسين استطاعوا العلماء في الحفريات انهم
+
+123
+00:10:08,700 --> 00:10:13,560
+يوصلوله عساس يشوف كيف بساطت هذا ال رودوبسين
+
+124
+00:10:13,830 --> 00:10:17,990
+ويقارنوا بالردوبسين المعقد عند الكائنات العليا أو
+
+125
+00:10:17,990 --> 00:10:22,330
+في خلايا الشبكية بتاعت الكائنات العليا ويشوفوا كيف
+
+126
+00:10:22,330 --> 00:10:28,550
+اتطورت الحياة مقارنة الكائنات الأدنى مثل البكتيريا
+
+127
+00:10:28,550 --> 00:10:33,530
+وما شابه مع الكائنات العليا وعلى رأسها الإنسان
+
+128
+00:10:33,530 --> 00:10:39,740
+Perhaps the earliest form of sensory rhodopsinاسمه
+
+129
+00:10:39,740 --> 00:10:44,140
+bacteriorhodopsin ولمّا بنقول bacteriorhodopsin
+
+130
+00:10:44,140 --> 00:10:49,560
+يعني ال rodopsin الموجود في بعض أنواع البكتيريا
+
+131
+00:10:49,560 --> 00:10:54,020
+هنا الجملة لازم يعني نركز على بعض الكلمات هنا
+
+132
+00:10:54,020 --> 00:10:58,100
+sensory rodopsin معناته ال rodopsin بيقوم بعملية
+
+133
+00:10:58,100 --> 00:11:04,130
+الإحساس بالضوءفهم الضوء، ترجمة الضوء، التفاعل مع
+
+134
+00:11:04,130 --> 00:11:07,230
+الضوء، لما بنقول إحساس بالضوء، طبعا هذا الإحساس
+
+135
+00:11:07,230 --> 00:11:11,590
+يختلف عن إحساسنا إحنا بالضوء، إحساس الجزء الحيوي
+
+136
+00:11:11,590 --> 00:11:16,410
+أو المركب العضوي بالضوء لما يثبت عليه ممكن يشبه
+
+137
+00:11:16,410 --> 00:11:17,250
+إحساس
+
+138
+00:11:19,440 --> 00:11:24,040
+صفيحة المعدن بالضوء لما يسقط عليها الضوء لما بسقط
+
+139
+00:11:24,040 --> 00:11:28,120
+على صفيحة المعدن بينبعث منها إلكترونات زادة شدة
+
+140
+00:11:28,120 --> 00:11:32,580
+الإضاءة بيزيد كمية الإلكترونات المنبعثة إحساس ال
+
+141
+00:11:32,580 --> 00:11:35,500
+bacteriorhodopsin اللي موجود في البكتيريا يعني ال
+
+142
+00:11:35,500 --> 00:11:37,980
+Rodopsin اللي موجود في البكتيريا لما بسقط عليه
+
+143
+00:11:37,980 --> 00:11:42,720
+الضوء أنه بتحدث فيه تفاعلات كيميائية تؤدي إلى
+
+144
+00:11:42,720 --> 00:11:49,120
+استفادة هذه البكتيريا من الضوء في وظائفها الحيوية
+
+145
+00:11:49,360 --> 00:11:54,700
+احساس الإنسان لما الضوء بيسقط على ال rodopsin اللي
+
+146
+00:11:54,700 --> 00:11:59,540
+موجود في خلايا شبكته بيختلف حسب إيش نوع الإضاءة
+
+147
+00:11:59,540 --> 00:12:03,820
+أنا لما بشوف إنسان ممكن أنا أسر لما بشوف مثلا
+
+148
+00:12:03,820 --> 00:12:08,900
+حيوان مفترس ممكن ينتبني نوع من الخوف أو الرعب أو
+
+149
+00:12:08,900 --> 00:12:15,160
+ما شابه لما بشوف مثلاشيء يدعو للفرح بأفرح لما بشوف
+
+150
+00:12:15,160 --> 00:12:20,420
+شيء يدعو بالتالي الإحساسات هو اللي حصل ان ال
+
+151
+00:12:20,420 --> 00:12:24,180
+Rodopsin نفسه صار فيه تفاعل كيميائي هذا التفاعل
+
+152
+00:12:24,180 --> 00:12:29,040
+الكيميائي يرسل كإشارات كهربائية عبر العصب البصري
+
+153
+00:12:29,040 --> 00:12:33,420
+توصل للدماغ الدماغ بحللها وبناء عليه بيصير ردة فعل
+
+154
+00:12:33,420 --> 00:12:38,060
+الإنسان إذا كل كائن حي تعامله مع الضوء وفهمله
+
+155
+00:12:38,060 --> 00:12:41,920
+الضوء وتفاعل ال Rodopsin اللي موجود في خلاياهأو في
+
+156
+00:12:41,920 --> 00:12:47,220
+خلايا الإبصار عنده بيختلف من كائن إلى كائن، اذا
+
+157
+00:12:47,220 --> 00:12:51,200
+perhaps the earliest form of sensory rhodopsin
+
+158
+00:12:51,200 --> 00:12:55,580
+اللي هو ال bacteriorhodopsin is found in primitive
+
+159
+00:12:55,580 --> 00:13:00,020
+purple colored bacterium اسمها Halobacterium
+
+160
+00:13:00,020 --> 00:13:04,530
+halobiumووجدوا أقدم Rhodopsin و أطلقوا عليه
+
+161
+00:13:04,530 --> 00:13:09,430
+bacteriorhodopsin وجدوا في بعض أنواع البكتيريا
+
+162
+00:13:09,430 --> 00:13:16,210
+اللي وجدت في الحفريات هذه لونها purple هي كقرمزي
+
+163
+00:13:16,210 --> 00:13:20,130
+واسمها أو أطلقوا عليها halobacteriumالهالوبكتيريوم
+
+164
+00:13:20,130 --> 00:13:24,390
+هالوبيوم الهالوبكتيريوم هالوبيوم هي بكتيريا وجد
+
+165
+00:13:24,390 --> 00:13:28,790
+فيها أقدم نوع من ال sensory rhodopsin ربما يكون في
+
+166
+00:13:28,790 --> 00:13:33,270
+أشياء أقدم منها ولكن الاكتشافات لحد الآن ان
+
+167
+00:13:33,270 --> 00:13:35,630
+الهالوبكتيريوم هالوبيوم تحتوي على ال
+
+168
+00:13:35,630 --> 00:13:39,310
+bacteriorhodopsin اللي هو أقدم نوع من ال sensory
+
+169
+00:13:39,310 --> 00:13:45,130
+rhodopsin يعني اللي بيحس الضوء وبيفهم على الضوء
+
+170
+00:13:45,130 --> 00:13:51,380
+عفواit is not known how long this organism has
+
+171
+00:13:51,380 --> 00:13:55,340
+inhabited the earth من أمتى ال helobacterium
+
+172
+00:13:55,340 --> 00:14:01,940
+helobium كبكتيريا أو كجسم حي أو ككائن حي من أمتى
+
+173
+00:14:01,940 --> 00:14:05,600
+بدأت تعيش على سطح الأرض هذا الكلام لحد تلان مش
+
+174
+00:14:05,600 --> 00:14:11,490
+معروف ولكن من أزمنة قديمة تقدر بملايين السنينطيب
+
+175
+00:14:11,490 --> 00:14:14,610
+اجوا العلماء يقولوا احنا مش قادرين نحدد امتى
+
+176
+00:14:14,610 --> 00:14:18,770
+الhalobacterium halobium موجودة من امتى على سطح
+
+177
+00:14:18,770 --> 00:14:25,350
+الأرض بس خلينا نشوف خصائصها يمكن نقدر نستنتج يعني
+
+178
+00:14:25,350 --> 00:14:30,330
+وقت تقريبي امتى بدأت تظهر على سطح الأرض أو بمعنى
+
+179
+00:14:30,330 --> 00:14:39,530
+آخر متى خلقت هذه البكتيريا طبعا تقديريا howeverit
+
+180
+00:14:39,530 --> 00:14:43,490
+is preference for anaerobic conditions and a very
+
+181
+00:14:43,490 --> 00:14:47,510
+salty environment may mean it developed at a time
+
+182
+00:14:47,510 --> 00:14:51,690
+when little or no oxygen existed in the atmosphere
+
+183
+00:14:51,690 --> 00:14:55,490
+and the sea contained high salt concentrations
+
+184
+00:14:55,490 --> 00:14:59,990
+العلماء وجدوا هذه البكتيريا فيها صفات أول حاجة
+
+185
+00:14:59,990 --> 00:15:03,990
+أنها anaerobic يعني بتعيش في ظروف لا هوائي يعني مش
+
+186
+00:15:03,990 --> 00:15:10,510
+محتاجة للأكسجين في حياتها، هاي نقطةتاني حاجة أنها
+
+187
+00:15:10,510 --> 00:15:14,970
+بتعيش في بيئة مالحة جدا .. جدا فاتقدروا العلماء
+
+188
+00:15:14,970 --> 00:15:17,870
+طالما أن هذه ال bacteria اللي هي halobacterium ..
+
+189
+00:15:17,870 --> 00:15:21,830
+halobium بتعيش في ظروف لا هوائية يعني مش محتاجة لل
+
+190
+00:15:21,830 --> 00:15:26,370
+oxygen و في نفس الوقت بتعيش في ظروف مالحة جدا
+
+191
+00:15:26,640 --> 00:15:30,820
+معناته البكتيريا هذه ظهرت في الوقت اللي كان مافيش
+
+192
+00:15:30,820 --> 00:15:34,640
+فيه أكسوجين بتاتا أو فيه قليل جدا من الأكسوجين على
+
+193
+00:15:34,640 --> 00:15:40,660
+سطح الأرض و في الغلاف الجوي وأيضا أن البحار كانت
+
+194
+00:15:40,660 --> 00:15:45,820
+تحتوي على كميات أعلى بكثير من الملوحة من زماننا
+
+195
+00:15:45,820 --> 00:15:50,160
+المعاصر طب لو سألنا أنفسنا سؤال أمتى ماكانش فيه
+
+196
+00:15:50,160 --> 00:15:54,410
+أكسوجين؟على سطح الأرض أو كان قليل جدا من ال oxygen
+
+197
+00:15:54,410 --> 00:15:58,270
+لما ماكانش فيه نباتات لأنه النباتات هي المصدر
+
+198
+00:15:58,270 --> 00:16:03,650
+الرئيسي لل oxygen بواسط عملية البناء الضوء اللي هي
+
+199
+00:16:03,650 --> 00:16:08,270
+ال photosynthesis و اللي بينتج عنها كميات ضخمة من
+
+200
+00:16:08,270 --> 00:16:12,230
+ال oxygen .. من ال oxygen فبالتالي .. بالتالي ال
+
+201
+00:16:12,230 --> 00:16:16,150
+halobacterium halobium وجدت في عصور قديمة جدا
+
+202
+00:16:16,150 --> 00:16:20,360
+ساحقة و بعيدةفي .. في .. في الزمن الغابر تقدر
+
+203
+00:16:20,360 --> 00:16:24,720
+بملايين السنين ووجدت في وقت لم يكن هناك أو كان
+
+204
+00:16:24,720 --> 00:16:28,440
+قليل جدا من ال oxygen في الغلاف الجوي وأيضا كانت
+
+205
+00:16:28,440 --> 00:16:32,520
+البحار ملوحتها عالية جدا مقارنة مع ملوحتها في
+
+206
+00:16:32,520 --> 00:16:39,260
+العصر الحالي هاي صورة للhalobacterium halobiumوهاي
+
+207
+00:16:39,260 --> 00:16:43,960
+صورة معقدة للجسم أو لل Rodopsin البكتيريو Rodopsin
+
+208
+00:16:43,960 --> 00:16:49,000
+اللي موجود داخلها و اللي لو سقطت الضوء على ال
+
+209
+00:16:49,000 --> 00:16:51,540
+halobacterium halobium معروف انه الخلايا البكتيريا
+
+210
+00:16:51,540 --> 00:16:55,500
+مكونة من خلية واحدة هذه كائن حي كامل عبارة عن
+
+211
+00:16:55,500 --> 00:17:00,120
+بكتيريا مكون من خلية واحدة و في داخله هذا الجزء
+
+212
+00:17:00,120 --> 00:17:03,220
+المعقد طبعا بالاضافة لبعض الأشياء
+
+213
+00:17:07,800 --> 00:17:11,780
+يعني الأخرى اللي بتساعد الخلية في وظائفها الحيوية
+
+214
+00:17:11,780 --> 00:17:16,900
+إذا هذا ال bacterioprodopsin لما سقط عليه الضوء أو
+
+215
+00:17:16,900 --> 00:17:19,680
+لما .. يعني موجود داخل ال halobacterium halobium
+
+216
+00:17:19,680 --> 00:17:23,100
+موجود داخل هذا كجزء منها لما بسقط عليه الضوء
+
+217
+00:17:23,100 --> 00:17:28,220
+بيتفاعل مع الضوء أو بيعطي رد فعل على الضوء بيخلي
+
+218
+00:17:28,220 --> 00:17:32,140
+الخلية البكتيرية اللي halobacterium halobium بتفهم
+
+219
+00:17:32,140 --> 00:17:38,150
+هذه الإشارات الضوئيةو تستفيد منها في حياتها في
+
+220
+00:17:38,150 --> 00:17:43,410
+حياتها فبالتالي bacteriorhodopsin اللي هو احنا
+
+221
+00:17:43,410 --> 00:17:46,970
+عرضنا صورة تمثيلية له اللي هو هذا الجزء المعقد و
+
+222
+00:17:46,970 --> 00:17:52,950
+هنا رسم تمثيلي مبسط أكتر ال bacteriorhodopsin is a
+
+223
+00:17:52,950 --> 00:17:56,990
+complicated molecule عبارة عن جزء معقد بيحتوي على
+
+224
+00:17:56,990 --> 00:18:02,470
+248 حمض أميني amino acid ال bacteriorhodopsin مكون
+
+225
+00:18:02,470 --> 00:18:07,770
+من جزئينجزء بروتيني .. جزء بروتيني بيسموه الـ
+
+226
+00:18:07,770 --> 00:18:12,590
+obscene portion وجزء آخر بيسموه ال retinal portion
+
+227
+00:18:12,590 --> 00:18:17,190
+ال retinal portion كلمة retinal .. كلمة retina
+
+228
+00:18:17,190 --> 00:18:22,630
+تعني شبكية في علم العيون ال retinal هنا مقصود في
+
+229
+00:18:22,630 --> 00:18:28,850
+أحد أشكال vitamin A إذا ال bacteriorhodopsin .. ال
+
+230
+00:18:28,850 --> 00:18:34,090
+bacteriorhodopsin مكون من جزئينوبسين بورشين عشان
+
+231
+00:18:34,090 --> 00:18:37,890
+هيك بنقول بكتيريو رودوبسين والريتينال بورشين لما
+
+232
+00:18:37,890 --> 00:18:41,410
+بنجمع الوبسين مع الريتينال بطلع عندي ال بكتيريو
+
+233
+00:18:41,410 --> 00:18:45,350
+رودوبسين الوبسين بورشين هو الجزء البروتيني من هذا
+
+234
+00:18:45,350 --> 00:18:49,570
+الجزء المعقد الجزء البروتيني من هذا الجزء المعقد
+
+235
+00:18:49,570 --> 00:18:55,430
+مضافلهأحد أشكال vitamin A بيعطيني كله مع بعض ال
+
+236
+00:18:55,430 --> 00:18:59,570
+bacteriodopsin is a complicated molecule that
+
+237
+00:18:59,570 --> 00:19:05,510
+contains 248 amino acid in the obscene portion
+
+238
+00:19:05,510 --> 00:19:08,650
+يعني ال .. ال protein هو اللي بتكون من الأحماض
+
+239
+00:19:08,650 --> 00:19:12,870
+الأمنية which are linked to one retinal
+
+240
+00:19:12,870 --> 00:19:18,060
+chromophore يعني أنا عندي 248حمض أميني بيشكلولي
+
+241
+00:19:18,060 --> 00:19:23,180
+الأبسين ومربوط معهم retinal chromophore يعني صابغة
+
+242
+00:19:23,180 --> 00:19:29,260
+عبارة عن شكل من أشكال vitamin A طيب، الآن هذا
+
+243
+00:19:29,260 --> 00:19:33,120
+الجزيء المعقد اكتشف في خلية الhalobacterium
+
+244
+00:19:33,120 --> 00:19:36,960
+halobium الآن العلماء سألوا أنفسهم سؤال إيش اللي
+
+245
+00:19:36,960 --> 00:19:40,980
+ضررنا وإيش اللي عرفنا؟إن هذا البكتيريو ردوبسين
+
+246
+00:19:40,980 --> 00:19:46,100
+بتركيب too high فعلا بيتأثر بالضوء، ما هو مجرد
+
+247
+00:19:46,100 --> 00:19:50,660
+إطلاق الكلام إن هذا بيتأثر بالضوء بدون إثباتات
+
+248
+00:19:50,660 --> 00:19:54,780
+يعتبر هذا كلام مرسل لا فائدة منه، أجر العلماء
+
+249
+00:19:54,780 --> 00:19:59,060
+تجاربهذه التجارب اللي هي time-resolved
+
+250
+00:19:59,060 --> 00:20:02,700
+spectroscopic measurements اللي هي القياسات
+
+251
+00:20:02,700 --> 00:20:07,620
+الطيفية المرتبطة بالزمن القياسات الطيفية المرتبطة
+
+252
+00:20:07,620 --> 00:20:12,420
+بالزمن استعملوها العلماء ونتج عنها انه have
+
+253
+00:20:12,420 --> 00:20:14,040
+determined حددوا that
+
+254
+00:20:33,880 --> 00:20:39,270
+التجارب اللي أجروها العلماءبإنهم أسقطوا الضوء على
+
+255
+00:20:39,270 --> 00:20:43,690
+ال bacteriorhodopsin وشافوا إيش التغيرات .. إيش
+
+256
+00:20:43,690 --> 00:20:48,250
+التغيرات اللي بتصير في ال bacteriorhodopsin بمجرد
+
+257
+00:20:48,250 --> 00:20:52,770
+سقوط الضوء عليه عشان نثبت هل هو بتأثر بالضوء ولا
+
+258
+00:20:52,770 --> 00:20:57,770
+لا يتأثر بالضوء قبل ما نقول كيف طريقة تأثره بالضوء
+
+259
+00:20:57,770 --> 00:21:02,670
+بنرجع لتركيبته .. لتركيبته إنه بيتكون من جزءين
+
+260
+00:21:02,920 --> 00:21:06,180
+obscene portion اللي هو الجزء البروتيني اللي هو
+
+261
+00:21:06,180 --> 00:21:11,440
+عبارة عن 248 حمض أميني و retinal portion اللي هو
+
+262
+00:21:11,440 --> 00:21:16,240
+الصبغة المضافة وهي عبارة عن شكل من أشكال vitamin A
+
+263
+00:21:16,240 --> 00:21:22,300
+فوجدوا العلماء أول ما بيسقطوا الضوءوبسرعة خارقة
+
+264
+00:21:22,300 --> 00:21:27,960
+جدا ال retinal portion بتحول من نظير لنظير آخر من
+
+265
+00:21:27,960 --> 00:21:32,420
+.. من نظير ال cis لنظير لترانس ممكن إنسان يقول إيش
+
+266
+00:21:32,420 --> 00:21:35,500
+يعني cis وإيش يعني trans؟ بنذكر في الكيميا
+
+267
+00:21:35,500 --> 00:21:38,660
+العضوية، بنقول هي مركب، هذا خارج عن المحاضرة بس
+
+268
+00:21:38,660 --> 00:21:43,700
+لتوضيح الفكرة هذا cis to butane وهذا trans to
+
+269
+00:21:43,700 --> 00:21:48,600
+butane هم نفس المركب، بس هذا نظير وهذا نظير له،
+
+270
+00:21:48,600 --> 00:21:55,060
+هذا نظير وهذا نظير آخرملاحظين في ال sis isomers ال
+
+271
+00:21:55,060 --> 00:21:59,240
+isomers اللي هو النظير في ال sis isomers المجموعات
+
+272
+00:21:59,240 --> 00:22:02,680
+ال active groups اللي هي مجموعة ال methyl هنا على
+
+273
+00:22:02,680 --> 00:22:06,780
+نفس الناحية على نفس الناحية بينما في ال trans
+
+274
+00:22:06,780 --> 00:22:10,320
+مجموعة methyl هنا و مجموعة methyl هنا الان لما
+
+275
+00:22:10,320 --> 00:22:14,480
+بيكتبوا النظائر بنفس الصيغة الكيميائية بنفس الصيغة
+
+276
+00:22:14,480 --> 00:22:18,440
+الكيميائيةعدد ذرّات الكربون والهيدروجين هي نفسه
+
+277
+00:22:18,440 --> 00:22:22,160
+هنا، هي نفسه هنا، مافي أي فرق، بس الشكل الفراغي في
+
+278
+00:22:22,160 --> 00:22:26,000
+ال-Sys بيكون المجموعات ال active groups بيكون
+
+279
+00:22:26,000 --> 00:22:30,760
+موجودة على أو خلّيني أقول مش ال active groups اللي
+
+280
+00:22:30,760 --> 00:22:34,580
+هو المجموعات المرافقة بتكون على نفس الناحية، بينما
+
+281
+00:22:34,580 --> 00:22:38,860
+هنا المجموعات المرافقة للمركب بتكون على نواحي
+
+282
+00:22:38,860 --> 00:22:42,640
+متقابل أو in opposite direction، واحدة على side،
+
+283
+00:22:42,640 --> 00:22:46,990
+واحدة على side التانيالان ال retinal .. ال retinal
+
+284
+00:22:46,990 --> 00:22:50,990
+هو جزء من ال bacteriorhodopsin و ال obscene هو
+
+285
+00:22:50,990 --> 00:22:54,290
+الجزء التاني، اذا ال obscene زائد retinal بيعطيني
+
+286
+00:22:54,290 --> 00:22:59,130
+ال bacteriorhodopsin أول ما بسقط الضوء .. أول ما
+
+287
+00:22:59,130 --> 00:23:03,970
+بسقط الضوء .. أول شيء بيتغير .. أول شيء بيتغير هو
+
+288
+00:23:03,970 --> 00:23:09,740
+ال retinal portion في سرعة كده تغيره؟في سرعة واحد
+
+289
+00:23:09,740 --> 00:23:13,280
+على عشرة أقصى اتناش أو نقول عشرة أقصى ناقص اتناش
+
+290
+00:23:13,280 --> 00:23:17,840
+من الثانية يعني واحد على مليون مليون جزء من
+
+291
+00:23:17,840 --> 00:23:23,790
+الثانيةيعني في .. في زمن خارق جدا جدا و مجرد صفد
+
+292
+00:23:23,790 --> 00:23:27,350
+الضوء هذا التغيير بيحصل بدون ما نستطيع حتى احنا
+
+293
+00:23:27,350 --> 00:23:32,310
+انه هذا طبعا و في قياسات معينة طب ايش التغير اللي
+
+294
+00:23:32,310 --> 00:23:36,170
+في ال retinal بيحصل؟ انه ال ces isomer نظير ال ces
+
+295
+00:23:36,170 --> 00:23:41,200
+بتحول لنظيرال Trans هل هذه القضية فقط عند سقوط
+
+296
+00:23:41,200 --> 00:23:45,160
+الدقولة بيحصل حاجات تانية؟ أيضا ال obscene portion
+
+297
+00:23:45,160 --> 00:23:48,300
+زي ما ال retinal حصل فيه since ال Trans
+
+298
+00:23:48,300 --> 00:23:53,440
+isomerization وبسرعة خارقة أيضا يتلو بسرعة برضه
+
+299
+00:23:53,440 --> 00:23:57,440
+ليست بسيطةإنه ال obscene portion بيصيرله
+
+300
+00:23:57,440 --> 00:24:02,540
+deprotonation يعني فقدان للبروتون .. فقدان
+
+301
+00:24:02,540 --> 00:24:05,820
+للبروتون، تنسوش إنه ال obscene portion مكون من
+
+302
+00:24:05,820 --> 00:24:11,880
+أحماض أمينية و الحمض يعني لما بيتفاعل مع القاعدة
+
+303
+00:24:11,880 --> 00:24:15,800
+.. لما بيتفاعل مع القاعدة عشان يعطوني الملحالحمب
+
+304
+00:24:15,800 --> 00:24:20,560
+لازم يفقد بروتون من بروتونات الهيدروجين،
+
+305
+00:24:20,560 --> 00:24:24,680
+deprotonation طب ال .. ال Obscene ال deprotonation
+
+306
+00:24:24,680 --> 00:24:30,240
+بتاعهبيصير في سرعة جداش عشرة أص ناقص خمسة من
+
+307
+00:24:30,240 --> 00:24:34,260
+الثانية يعني في واحد على ميت ألف جزء من الثانية
+
+308
+00:24:34,260 --> 00:24:39,900
+يعني بسرعة شاهقة جدا الضوء بيحدث في تغيرات تغيرات
+
+309
+00:24:39,900 --> 00:24:44,340
+في ال option portion و في ال retinal portion بتاعة
+
+310
+00:24:44,340 --> 00:24:47,980
+ال bacteriorhodopsin استدل العلماء من ذلك أن ال
+
+311
+00:24:47,980 --> 00:24:52,740
+bacteriorhodopsin يفهم الضوءويتفاعل مع الضوء وإلا
+
+312
+00:24:52,740 --> 00:24:57,240
+لو لم يكن هذا الكلام صحيح كان بمجرد سقوط الضوء ما
+
+313
+00:24:57,240 --> 00:25:03,580
+حصلش حاجة وضل ال bacteriorhodopsin يعني في حاله
+
+314
+00:25:03,580 --> 00:25:08,540
+الأساسية ما صار عليه أي تغير .. ما صار عليه أي
+
+315
+00:25:08,540 --> 00:25:13,800
+تغير بنتوقف عند هذه النقطة و المرة القادمة بنشوف
+
+316
+00:25:13,800 --> 00:25:19,410
+إيش خصائص ال bacteriorhodopsin و بننتقل لأجزاءأكثر
+
+317
+00:25:19,410 --> 00:25:23,610
+تعقيدا أو كائنات أكثر تعقيدا من البكتيريا ويعطيكم
+
+318
+00:25:23,610 --> 00:25:26,170
+العافية والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/QAMz-r97LWw_raw.json b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/QAMz-r97LWw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..af694abbf82bc8bffa452d5e17a6cd118fbaaa15
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/QAMz-r97LWw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3074, "start": 1.62, "end": 30.74, "text": "بسم الله الرحمن الرحيم وصلنا ل chapter اتنين way اللي بيدرس خصائص الضوء بشكل يعني تفصيلي ان شاء الله تعالى this chapter discusses the characteristics of light and some of the ways these characteristics can be put to clinical use يعني هيدرس هذا الفصل بعض الصفات بتاعة الضوء و can نستفيد من هذه الصفات من الناحية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 4032, 36520, 8315, 5296, 7187, 1975, 2655, 1863, 9957, 636, 13672, 1829, 4724, 25708, 2288, 3794, 16490, 9381, 16373, 9381, 6024, 114, 2407, 38207, 4724, 8592, 28820, 37495, 22653, 6055, 5172, 9381, 1829, 20292, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 341, 7187, 2248, 279, 264, 10891, 295, 1442, 293, 512, 295, 264, 2098, 613, 10891, 393, 312, 829, 281, 9115, 764, 37495, 22653, 8032, 25708, 2288, 3794, 23758, 27188, 36520, 45030, 11242, 31767, 5172, 9307, 39894, 995, 27884, 6024, 114, 2407, 38207, 4032, 393, 8717, 14851, 5172, 25708, 9154, 29538, 31767, 5172, 9307, 9154, 2423, 8315, 5016, 10632], "avg_logprob": -0.08565080083838296, "compression_ratio": 1.7241379310344827, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 1.62, "end": 1.92, "word": "بسم", "probability": 0.90673828125}, {"start": 1.92, "end": 2.12, "word": " الله", "probability": 0.9658203125}, {"start": 2.12, "end": 2.48, "word": " الرحمن", "probability": 0.9596354166666666}, {"start": 2.48, "end": 2.96, "word": " الرحيم", "probability": 0.9949544270833334}, {"start": 2.96, "end": 4.66, "word": " وصلنا", "probability": 0.9122721354166666}, {"start": 4.66, "end": 5.02, "word": " ل", "probability": 0.96875}, {"start": 5.02, "end": 5.56, "word": " chapter", "probability": 0.94921875}, {"start": 5.56, "end": 7.04, "word": " اتنين", "probability": 0.8931884765625}, {"start": 7.04, "end": 8.12, "word": " way", "probability": 0.4775390625}, {"start": 8.12, "end": 8.4, "word": " اللي", "probability": 0.910888671875}, {"start": 8.4, 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فراغي واحد الشعاع الساقط و الشعاع المنكسر و العمود المقام على سطح الانكسار على سطح الانكسار كلها تقع في مستوى فراغي واحد الآن زمان أول ما اكتشفوا الانكسار كانوا يظنوا .. كانوا يظنوا أن theta I", "tokens": [40228, 22653, 7251, 34268, 26890, 8717, 36178, 25124, 1829, 38207, 14739, 28242, 11296, 6055, 4587, 3615, 8978, 3714, 14851, 2407, 7578, 6156, 2288, 5718, 118, 1829, 36764, 24401, 25124, 3615, 45761, 21136, 995, 47432, 4032, 25124, 3615, 45761, 9673, 1863, 4117, 3794, 2288, 4032, 18863, 2304, 23328, 9673, 4587, 10943, 15844, 8608, 9566, 5016, 2423, 7649, 4117, 3794, 9640, 15844, 8608, 9566, 5016, 2423, 7649, 4117, 3794, 9640, 28242, 11296, 6055, 4587, 3615, 8978, 3714, 14851, 2407, 7578, 6156, 2288, 5718, 118, 1829, 36764, 24401, 6024, 48506, 30767, 2304, 7649, 5551, 12610, 19446, 1975, 4117, 2655, 8592, 5172, 14407, 2423, 7649, 4117, 3794, 9640, 25961, 14407, 7251, 19913, 1863, 14407, 4386, 25961, 14407, 7251, 19913, 1863, 14407, 14739, 9725, 286], "avg_logprob": 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new file mode 100644
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--- /dev/null
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@@ -0,0 +1 @@
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"text": "عروضه اكتر بمعنى انه تنوع الموجات عنده اكتر يعني ال timbre ال coherance بتاعه اكتر فبالتالي بنقول كالاتي كل مكان انا عندي انواع الموجات وانواع المقاطع المختلفة اكتر بسميها ده broadband .. broadband", "tokens": [3615, 32887, 11242, 3224, 1975, 4117, 2655, 2288, 4724, 2304, 3615, 1863, 7578, 16472, 3224, 6055, 1863, 45367, 9673, 29245, 9307, 43242, 3224, 1975, 4117, 2655, 2288, 37495, 22653, 2423, 524, 2672, 2423, 26528, 719, 39894, 45761, 3224, 1975, 4117, 2655, 2288, 6156, 3555, 6027, 2655, 6027, 1829, 44945, 39648, 9122, 6027, 9307, 1829, 28242, 3714, 41361, 1975, 8315, 18871, 16254, 16472, 14407, 3615, 9673, 29245, 9307, 4032, 7649, 14407, 3615, 9673, 4587, 41193, 3615, 9673, 46456, 46538, 3660, 1975, 4117, 2655, 2288, 4724, 38251, 1829, 11296, 11778, 3224, 37718, 4386, 37718], "avg_logprob": -0.13230847351012692, "compression_ratio": 1.8166666666666667, "no_speech_prob": 9.894371032714844e-06, "words": [{"start": 722.06, "end": 722.7, "word": "عروضه", "probability": 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narrow band .. narrow band وبالتالي", "tokens": [2407, 4386, 37495, 22653, 3714, 29245, 3660, 6225, 16572, 11242, 3660, 12399, 11933, 1829, 8592, 37495, 22653, 3714, 29245, 3660, 6225, 16572, 11242, 3660, 22807, 37495, 22653, 4386, 37495, 22653, 43242, 3224, 9122, 2304, 10632, 9154, 9673, 29245, 9307, 3714, 46456, 46538, 3660, 8978, 41950, 12610, 9673, 29245, 1829, 4032, 40228, 22653, 4386, 37495, 22653, 4724, 9957, 2655, 46309, 4386, 4724, 1829, 17082, 9566, 1829, 10874, 11622, 38207, 9122, 3555, 13546, 9154, 2423, 8974, 1442, 49374, 15042, 18871, 16254, 5296, 15042, 39894, 30544, 6225, 3215, 3215, 9673, 29245, 9307, 34051, 14739, 14407, 3615, 9673, 29245, 9307, 12174, 20292, 37977, 3714, 29245, 3660, 34051, 6055, 29399, 9957, 4724, 38251, 1829, 3224, 9432, 4116, 4386, 9432, 4116, 46599, 6027, 2655, 6027, 1829], "avg_logprob": -0.10556559917355372, "compression_ratio": 1.9350649350649352, "no_speech_prob": 2.7418136596679688e-06, "words": [{"start": 741.82, "end": 742.3, "word": "و", 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2423, 4386, 2423, 9719, 9122, 33911, 39894, 5016, 31747, 4032, 2423, 5210, 2519, 4724, 36081, 29910, 3555, 29910, 3555, 4724, 8592, 28820, 9429, 37495, 22653, 23758, 28450, 48623, 1442, 23032, 3555, 3615, 995, 3714, 5172, 3224, 20498, 48812, 27842, 995, 4724, 15042, 16472, 3224, 2423, 12688, 2519, 6225, 2304, 2407, 16254, 47356, 23032, 3555, 3615, 995, 31439, 37893, 3714, 1211, 3794, 20498, 39896, 30544, 2423, 12688, 2519, 12750, 4032, 23032, 3555, 3615, 995, 34105, 2423, 5210, 2519, 9429], "avg_logprob": -0.16688144821481607, "compression_ratio": 1.7445887445887447, "no_speech_prob": 1.4901161193847656e-06, "words": [{"start": 23.59, "end": 24.17, "word": "الصرايان", "probability": 0.673876953125}, {"start": 24.17, "end": 24.31, "word": " هي", "probability": 0.60791015625}, {"start": 24.31, "end": 24.67, "word": " اتجاه", "probability": 0.9654541015625}, {"start": 24.67, "end": 25.13, "word": " الصرايان", "probability": 0.9339599609375}, {"start": 25.13, "end": 25.65, "word": " باتجاه", "probability": 0.9346923828125}, {"start": 25.65, "end": 25.93, "word": " ال", "probability": 0.89892578125}, {"start": 25.93, "end": 26.05, "word": " ..", "probability": 0.5244140625}, {"start": 26.05, "end": 26.31, "word": " ال", "probability": 0.77783203125}, {"start": 26.31, "end": 26.69, "word": " mouse", "probability": 0.9140625}, {"start": 26.69, "end": 27.15, "word": " كيف", "probability": 0.4859619140625}, {"start": 27.15, "end": 27.73, "word": " بتحرك", "probability": 0.75927734375}, {"start": 27.73, "end": 28.35, "word": " و", "probability": 0.66015625}, {"start": 28.35, "end": 28.81, "word": " ال", "probability": 0.9765625}, {"start": 28.81, "end": 29.27, "word": " electric", "probability": 0.92822265625}, {"start": 29.27, "end": 29.79, "word": " field", "probability": 0.92041015625}, {"start": 29.79, "end": 30.19, "word": " بيت", "probability": 0.734375}, {"start": 30.19, "end": 30.47, "word": " ذب", "probability": 0.5784912109375}, {"start": 30.47, "end": 30.79, "word": " ذب", "probability": 0.75732421875}, {"start": 30.79, "end": 31.35, "word": " بشكل", "probability": 0.9954427083333334}, {"start": 31.35, "end": 31.87, "word": " vertical", "probability": 0.86865234375}, {"start": 31.87, "end": 32.21, "word": " يعني", "probability": 0.892822265625}, {"start": 32.21, "end": 32.45, "word": " هذا", "probability": 0.8310546875}, {"start": 32.45, "end": 33.17, "word": " vertically", "probability": 0.88916015625}, {"start": 33.17, "end": 33.83, "word": " polarized", "probability": 0.94287109375}, {"start": 33.83, "end": 34.27, "word": " light", "probability": 0.9228515625}, {"start": 34.27, "end": 34.93, "word": " طبعا", "probability": 0.985595703125}, {"start": 34.93, "end": 35.35, "word": " مفهوم", "probability": 0.975830078125}, {"start": 35.35, "end": 35.83, "word": " ضمنا", "probability": 0.8056640625}, {"start": 35.83, "end": 36.13, "word": " بما", "probability": 0.9873046875}, {"start": 36.13, "end": 36.39, "word": " انه", "probability": 0.714599609375}, {"start": 36.39, "end": 36.53, "word": " ال", "probability": 0.9072265625}, {"start": 36.53, "end": 37.13, "word": " magnetic", "probability": 0.9755859375}, {"start": 37.13, "end": 37.85, "word": " field", "probability": 0.94482421875}, {"start": 37.85, "end": 38.41, "word": " عمودي", "probability": 0.9835205078125}, {"start": 38.41, "end": 38.85, "word": " عليه", "probability": 0.96826171875}, {"start": 38.85, "end": 39.25, "word": " طبعا", "probability": 0.9573974609375}, {"start": 39.25, "end": 39.35, "word": " هو", "probability": 0.95556640625}, {"start": 39.35, "end": 39.53, "word": " مش", "probability": 0.99267578125}, {"start": 39.53, "end": 39.89, "word": " ملسوم", "probability": 0.7734375}, {"start": 39.89, "end": 40.25, "word": " هيكون", "probability": 0.875732421875}, {"start": 40.25, "end": 40.37, "word": " ال", "probability": 0.89208984375}, {"start": 40.37, "end": 40.69, "word": " magnetic", "probability": 0.9765625}, {"start": 40.69, "end": 41.23, "word": " field", "probability": 0.93798828125}, {"start": 41.23, "end": 43.21, "word": " horizontal", "probability": 0.5234375}, {"start": 43.21, "end": 44.07, "word": " و", "probability": 0.990234375}, {"start": 44.07, "end": 44.57, "word": " طبعا", "probability": 0.979736328125}, {"start": 44.57, "end": 44.77, "word": " هنا", "probability": 0.98779296875}, {"start": 44.77, "end": 44.99, "word": " ال", "probability": 0.9873046875}, {"start": 44.99, "end": 45.29, "word": " electric", "probability": 0.96337890625}, {"start": 45.29, "end": 45.89, "word": " field", "probability": 0.93994140625}, {"start": 45.89, "end": 47.05, "word": " vertical", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 3, "seek": 5395, "start": 47.75, "end": 53.95, "text": "و يعطيكم العافية اذا vertically polarized light يعطيكم العافية والسلام عليكم ورحمة الله وبركاته", "tokens": [2407, 37495, 9566, 1829, 24793, 18863, 31845, 10632, 1975, 15730, 28450, 48623, 1442, 37495, 9566, 1829, 24793, 18863, 31845, 10632, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.11382378223869535, "compression_ratio": 1.3660714285714286, "no_speech_prob": 0.0, "words": [{"start": 47.75, "end": 48.07, "word": "و", "probability": 0.93212890625}, {"start": 48.07, "end": 48.61, "word": " يعطيكم", "probability": 0.853759765625}, {"start": 48.61, "end": 49.07, "word": " العافية", "probability": 0.9391276041666666}, {"start": 49.07, "end": 49.23, "word": " اذا", "probability": 0.61907958984375}, {"start": 49.23, "end": 49.75, "word": " vertically", "probability": 0.8203125}, {"start": 49.75, "end": 50.57, "word": " polarized", "probability": 0.890625}, {"start": 50.57, "end": 50.93, "word": " light", "probability": 0.91796875}, {"start": 50.93, "end": 51.37, "word": " يعطيكم", "probability": 0.951171875}, {"start": 51.37, "end": 51.69, "word": " العافية", "probability": 0.98046875}, {"start": 51.69, "end": 52.07, "word": " والسلام", "probability": 0.8834635416666666}, {"start": 52.07, "end": 52.51, "word": " عليكم", "probability": 0.917236328125}, {"start": 52.51, "end": 52.97, "word": " ورحمة", "probability": 0.9515380859375}, {"start": 52.97, "end": 53.19, "word": " الله", "probability": 0.98388671875}, {"start": 53.19, "end": 53.95, "word": " وبركاته", "probability": 0.96982421875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 54.195375, "duration_after_vad": 53.136875}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/Xwt0oubjIAY.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/Xwt0oubjIAY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9511ffb99bd9697e2296cbfcc00d6005cad250d2
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/Xwt0oubjIAY.srt
@@ -0,0 +1,1359 @@
+1
+00:00:01,500 --> 00:00:05,740
+بسم الله الرحمن الرحيم بنستكمل محاضرات الـ physical
+
+2
+00:00:05,740 --> 00:00:12,660
+optics ووصلنا لـ superposition of waves أو التداخل
+
+3
+00:00:12,660 --> 00:00:15,960
+الموجي أو التراكب الموجي والمقصود فيه تراكب أو 
+
+4
+00:00:15,960 --> 00:00:22,580
+تداخل موجات الضوء بنذكر في ما مضى من المحاضرات و
+
+5
+00:00:22,580 --> 00:00:28,960
+بنقول احنا في حاجتين رئيسيات أدت إلى هدم النظرية
+
+6
+00:00:28,960 --> 00:00:32,360
+الجسيمية للضوء أو الـ corpuscular theory of light
+
+7
+00:00:32,360 --> 00:00:37,620
+الحاجة الأولى اللي هي ظاهرة الـ .. الـ diffraction،
+
+8
+00:00:37,620 --> 00:00:41,840
+ظاهرة الـ diffraction حيود الضوء عن مساره أثناء
+
+9
+00:00:41,840 --> 00:00:48,260
+عبوره من فتحة من aperture في جدار أو في ورقة أو
+
+10
+00:00:48,260 --> 00:00:51,720
+إلى آخره هي حيود الضوء يعني أنه لا يسير في مسارات
+
+11
+00:00:51,720 --> 00:00:55,480
+مستقيمة، هذه إحدى الحاجتين الحاجة الثانية أن الضوء
+
+12
+00:00:55,480 --> 00:01:00,600
+له سرعة محدودة رغم إنها سرعة شاهقة إلا أنها لا 
+
+13
+00:01:00,600 --> 00:01:05,440
+يمكن أن توصف بأنها سرعة لا نهائية، و هذه اللي يعني
+
+14
+00:01:05,440 --> 00:01:11,820
+بدأ قصتها اللي هو العالم الدنماركي رومر، هدول
+
+15
+00:01:11,820 --> 00:01:16,660
+الحاجتين محدودية سرعته الضوء وظاهرة الـ diffraction
+
+16
+00:01:16,660 --> 00:01:22,040
+خلوا العلماء يبدؤوا يفكروا في موضوع الضوء بأنه
+
+17
+00:01:22,040 --> 00:01:27,340
+عبارة عن موجات وينطبق عليه ما ينطبق على أي شيء
+
+18
+00:01:27,340 --> 00:01:32,060
+طبيعته موجية، ومن ضمن الظواهر اللي بتحدث في الموجات
+
+19
+00:01:32,060 --> 00:01:38,140
+قضية الـ superposition أو التداخل الموجي، مبدأ الـ
+
+20
+00:01:38,140 --> 00:01:41,680
+superposition principle، مبدأ الـ superposition أو 
+
+21
+00:01:41,680 --> 00:01:45,980
+التداخل أو التراكب الموجي states that when two or
+
+22
+00:01:45,980 --> 00:01:50,680
+more waves overlap, their amplitudes will add or
+
+23
+00:01:50,680 --> 00:01:56,490
+cancel، لما بتداخل موجتين فأكثر، بيكون عندي موجة
+
+24
+00:01:56,490 --> 00:02:01,910
+ناتجة هي حصيلة هدول الموجتين، إما بتكون الموجة
+
+25
+00:02:01,910 --> 00:02:06,350
+أكبر من الموجتين وهذا تداخل يعني بي .. بي .. بيضيف
+
+26
+00:02:06,350 --> 00:02:10,390
+موجة لموجة أو بي cancelوا بعضهم، بيلغوا بعضهم
+
+27
+00:02:10,390 --> 00:02:15,830
+البعض حسب كيف هما اتداخلوا، حسب هما .. هما كيف
+
+28
+00:02:15,830 --> 00:02:20,840
+اتداخلوا الوضع السيبراني من اتصالات اتصالات مختلفة
+
+29
+00:02:20,840 --> 00:02:29,010
+يجعلها تغيير حرب التغيير والتغيير والتغيير that in
+
+30
+00:02:29,010 --> 00:02:32,650
+the case of light is much too fast to be observed
+
+31
+00:02:32,650 --> 00:02:36,810
+طيب أول شيء بدنا نقول أنه في عندنا two waves عندنا
+
+32
+00:02:36,810 --> 00:02:42,250
+موجتين ضوئيات بس هدول الموجتين ضوئيات تداخلوا بس
+
+33
+00:02:42,250 --> 00:02:47,370
+مالهمش نفس الـ frequency يعني في موجة منهم طولها
+
+34
+00:02:47,370 --> 00:02:52,790
+الموجي أطول من الموجة الأخرى، إذا في عندي تداخل بين
+
+35
+00:02:52,790 --> 00:02:59,140
+موجتين ضوئيات ذات أطوال موجية مختلفة، إيش اللي هيحدث
+
+36
+00:02:59,140 --> 00:03:05,300
+نتيجة تداخل هدول الموجتين ذوات
+
+37
+00:03:05,300 --> 00:03:10,040
+اللي هو أطوال موجية مختلفة، تداخلهم بيعطيني حاجة
+
+38
+00:03:10,040 --> 00:03:14,580
+بيسميها changing interference pattern، يعني نظام
+
+39
+00:03:14,580 --> 00:03:21,180
+تداخلي متغير بين تقوية الموجة و تضعيفها وجعلها نص
+
+40
+00:03:21,180 --> 00:03:25,040
+نص بين التقوية و التضعيف، وهذا الكلام بيتم بسرعة
+
+41
+00:03:25,040 --> 00:03:29,750
+هائلة جدا، في حالة الموجات الضوئية is much too fast
+
+42
+00:03:29,750 --> 00:03:34,050
+to be observed is much too fast to be observed
+
+43
+00:03:34,050 --> 00:03:37,070
+however the superposition of two waves of
+
+44
+00:03:37,070 --> 00:03:41,570
+identical frequency produces a stable interference
+
+45
+00:03:41,570 --> 00:03:45,510
+pattern، بينما لو في عندي موجتين ضوئيات اللي هم نفس
+
+46
+00:03:45,510 --> 00:03:51,830
+الطول الموجي، التداخل هم مع بعض هيعطيني نظام تداخلي
+
+47
+00:03:51,830 --> 00:03:55,690
+ثابت وليس نظام تداخلي متغير، لما يكون أطولهم
+
+48
+00:03:55,690 --> 00:03:59,310
+الموجية مختلفة بيعطيني changing، لما يكون أطولهم
+
+49
+00:03:59,310 --> 00:04:01,810
+الموجية نفس الطول الموجي بيعطيني stable
+
+50
+00:04:01,810 --> 00:04:06,510
+interference pattern، يعني نظام تداخلي ثابت في
+
+51
+00:04:06,510 --> 00:04:10,170
+الحالة الثانية لأن .. ليش؟ لأن طول الموجة الأولى
+
+52
+00:04:10,170 --> 00:04:13,830
+يساوي طول الموجة الثانية، بينما هنا نظام تداخلي
+
+53
+00:04:13,830 --> 00:04:19,530
+متغير متغير يعني بيقوى و بيضعف نص نص نظام تداخلي
+
+54
+00:04:19,530 --> 00:04:23,070
+متغير بسبب أن طول الموجتين مش identical أو
+
+55
+00:04:23,070 --> 00:04:25,830
+بيختلفوا في الطول الموجي، وطبعا الصور إن شاء الله
+
+56
+00:04:25,830 --> 00:04:31,130
+تعالى هتوضح هذا الموضوع، هاي عندي أنا موجتين ..
+
+57
+00:04:31,130 --> 00:04:37,430
+عندي موجتين اللهم نفس الطول الموجي، طبعا هما تداخلوا
+
+58
+00:04:37,430 --> 00:04:41,030
+يعني إجوا في بعض أو .. أو دخلوا في بعض، دخلوا في
+
+59
+00:04:41,030 --> 00:04:44,610
+بعضهم البعض، تخللوا بعضهم البعض، بس احنا راسمينهم
+
+60
+00:04:44,610 --> 00:04:49,130
+هنا منفصلين، طبعا ممكن انسان يستعجب يعني كيف
+
+61
+00:04:49,130 --> 00:04:52,110
+تداخلوا في بعضهم البعض أو دخلوا في بعضهم البعض أو
+
+62
+00:04:52,110 --> 00:04:56,370
+تخللوا بعضهم البعض، في نقطة مهمة جدا جدا جدا عن
+
+63
+00:04:56,370 --> 00:05:01,870
+الموجات أي شيخ فيزيائي له طبيعة موجية .. له طبيعة
+
+64
+00:05:01,870 --> 00:05:07,460
+موجية، لازم نعرف أن الموجات ليست أجسام، Waves ..
+
+65
+00:05:07,460 --> 00:05:12,950
+waves are not objects، waves are not objects، يعني ..
+
+66
+00:05:12,950 --> 00:05:15,790
+يعني مش أجسام تقول و الله كيف هذا دخل في هذا يعني
+
+67
+00:05:15,790 --> 00:05:18,810
+جسم دخل في جسم، احنا ما بنحكي عن أجسام احنا بنحكي
+
+68
+00:05:18,810 --> 00:05:25,050
+عن موجات، و الموجات اللي هي اهتزازات يعني لشيء معين
+
+69
+00:05:25,050 --> 00:05:31,210
+تمام بين العلو والانحضار، يعني هنا الموجة في قمتها
+
+70
+00:05:31,210 --> 00:05:34,890
+و هنا الموجة في قاع، و هنا الموجة في قاع، هنا
+
+71
+00:05:34,890 --> 00:05:38,570
+الموجة في قمتها، و هنا الموجة .. في قاع، فبالتالي أنا
+
+72
+00:05:38,570 --> 00:05:41,810
+عندي two waves يمكن هم يتداخلوا ويتخللوا بعضهم
+
+73
+00:05:41,810 --> 00:05:45,690
+البعض، وبالتالي عندي التداخل الموجي، طبعا احنا
+
+74
+00:05:45,690 --> 00:05:49,430
+رسمينهم منفصلين عن بعضهم البعض لتوضيح الفكرة، لما
+
+75
+00:05:49,430 --> 00:05:54,530
+بيتداخلوا two waves أول حاجة هم identical يعني لهم
+
+76
+00:05:54,530 --> 00:05:57,910
+نفس الطول الموجي، نفس الـ frequency، نفس التردد،
+
+77
+00:05:57,910 --> 00:06:02,730
+تداخلوا بحيث أن القمة اجت مع القمة والقاع اجت مع
+
+78
+00:06:02,730 --> 00:06:07,070
+القاع، بيكون عند الـ resultant wave الموجة الناتجة
+
+79
+00:06:07,070 --> 00:06:12,050
+عنهم التنتين أن ارتفاعها الـ amplitude بتاعتها
+
+80
+00:06:12,050 --> 00:06:16,530
+يساوي ضعف الـ amplitude بتاعت هدول الموجات، يعني كل
+
+81
+00:06:16,530 --> 00:06:20,110
+واحدة منهم ارتفاعها أو الـ amplitude بتاع الموجة A
+
+82
+00:06:20,110 --> 00:06:24,430
+يقاسي الارتفاع من الـ baseline من الـ baseline سواء
+
+83
+00:06:24,430 --> 00:06:29,550
+علوا أو انخفاضا، يعني جديش جاية من الـ baseline من
+
+84
+00:06:29,550 --> 00:06:33,330
+الخط الأساسي للأسفل أو جديش جاية من الخط الأساسي
+
+85
+00:06:33,590 --> 00:06:37,090
+للأعلى، إذا هذه amplitude للموجة أو هذه amplitude
+
+86
+00:06:37,090 --> 00:06:40,910
+لموجة مماثلة إلها في الطول الموجي، إذا بيكون
+
+87
+00:06:40,910 --> 00:06:46,390
+تداخلهم وفي هذه الحالة بيسميها in phase in phase
+
+88
+00:06:46,390 --> 00:06:50,910
+يعني منطبقين على بعض بنسبة مائة بالمائة، يعني القمة
+
+89
+00:06:50,910 --> 00:06:54,170
+على القمة والقاع على القاع، بيكون عندي الـ
+
+90
+00:06:54,170 --> 00:07:00,010
+resultant wave عبارة عن light wave of twice
+
+91
+00:07:00,010 --> 00:07:06,610
+amplitude، ارتفاعها ضعف ارتفاع الموجتين، الصورة
+
+92
+00:07:06,610 --> 00:07:10,240
+التالية بتوضح نفس الفكرة على الشمال نفس الصورة
+
+93
+00:07:10,240 --> 00:07:14,200
+السابقة اللي هو الجزء الشمال من الرسم، هاي بيوضح
+
+94
+00:07:14,200 --> 00:07:18,520
+نفس الفكرة أي عندي أنا الموجة الأولى اللي أنا بأشر
+
+95
+00:07:18,520 --> 00:07:22,580
+عليها وعندي الموجة الثانية، أول حاجة هم identical
+
+96
+00:07:22,580 --> 00:07:27,140
+frequency اللي هم نفس الطول الموجي و totally in
+
+97
+00:07:27,140 --> 00:07:30,980
+phase، totally in phase، يعني منطبقين على بعض مائة
+
+98
+00:07:30,980 --> 00:07:36,000
+بالمائة يعني متداخلين بحيث القمة تتداخل مع القمة و
+
+99
+00:07:36,000 --> 00:07:40,210
+القاع يتداخل مع القاع، يعني بيسموهم نفس المرحلة ..
+
+100
+00:07:40,210 --> 00:07:44,350
+نفس المرحلة، فبالتالي الـ resultant wave أو الموجة
+
+101
+00:07:44,350 --> 00:07:48,730
+الناتجة بتكون twice the amplitude، ارتفاعها .. ضعف
+
+102
+00:07:48,730 --> 00:07:54,380
+ارتفاع كل من الموجتين .. كل من الموجتين هنا نفس
+
+103
+00:07:54,380 --> 00:07:57,840
+الموجتين ونفس الطول الموجي، الرسم الأعلى هنا اللي
+
+104
+00:07:57,840 --> 00:08:02,240
+بقشر عليها هي موجة إلها طول موجي معين موجة ضوئية و
+
+105
+00:08:02,240 --> 00:08:06,080
+هنا نفس الموجة إلها طول موجي معين، بس التداخل كان
+
+106
+00:08:06,080 --> 00:08:12,950
+بحيث أن القمة تيجي مع القاع والقمة تيجي مع القاع و
+
+107
+00:08:12,950 --> 00:08:16,510
+القاع يجي مع القمة، يعني عكس بعضهم تماما، سعة
+
+108
+00:08:16,510 --> 00:08:21,010
+التداخل فبيلغوا بعضهم البعض وبيكون الناتج ..
+
+109
+00:08:21,010 --> 00:08:24,790
+الموجة الناتجة zero، أنه مافيش موجة، ألغوا بعضهم
+
+110
+00:08:24,790 --> 00:08:30,540
+البعض .. ألغوا بعضهم البعض، أيضا عندي الرسمة الثالثة
+
+111
+00:08:30,540 --> 00:08:34,940
+بس الرسمة الثالثة بتفرج أنه عندي موجتين خلينا نطلع
+
+112
+00:08:34,940 --> 00:08:39,440
+للعرض المكبر عشان توضح الصورة أفضل، عندي الموجة
+
+113
+00:08:39,440 --> 00:08:43,340
+اللي هي مرموز لها باللون الأحمر، لها طول موجي معين
+
+114
+00:08:43,340 --> 00:08:49,460
+والموجة اللي مرسومة باللون الأزرق إلها طول موجي
+
+115
+00:08:49,460 --> 00:08:53,020
+معين، واضح أن الطول الموجي بتاع الموجة الزرقاء
+
+116
+00:08:53,020 --> 00:08:58,700
+يعني أطول قليلا .. أطول قليلا من الطول الموجي بتاع
+
+117
+00:08:58,700 --> 00:09:02,860
+الموجة اللي مرسومة باللون الأحمر، إذا مش .. هدول
+
+118
+00:09:02,860 --> 00:09:06,180
+الموجتين مش the same frequency، الـ frequency
+
+119
+00:09:06,180 --> 00:09:10,720
+بتاعتهم أو التردد بتاعهم بيختلف، حدثوا أنهم تداخلوا
+
+120
+00:09:10,720 --> 00:09:15,320
+هتيجي لحظات معينة .. هتيجي لحظات معينة أن مثلا
+
+121
+00:09:15,320 --> 00:09:20,370
+هنا .. إنلاحظ إيش طبيعة التداخل بين الموجة الحمراء
+
+122
+00:09:20,370 --> 00:09:23,990
+والموجة الزرقاء عند هذا الشريط، عند هذا الشريط ..
+
+123
+00:09:23,990 --> 00:09:27,250
+هذا الشريط تم رسمه عشان يقول في هذه اللحظة عند هذه
+
+124
+00:09:27,250 --> 00:09:31,050
+النقطة من الزمن .. عند هذه النقطة من الزمن كانت
+
+125
+00:09:31,050 --> 00:09:36,610
+الموجة الحمراء في القاع بينما الموجة الزرقاء في
+
+126
+00:09:36,610 --> 00:09:41,990
+القمة .. في القمة، مفروض أنه طالما قاع مع قمة يلغوا
+
+127
+00:09:41,990 --> 00:09:45,610
+بعضهم البعض، وهذا اللي حدث .. وهذا اللي حدث، ممكن
+
+128
+00:09:45,610 --> 00:09:48,590
+إنسان يقول .. طب أنا مش شايف هنا خط مستقيم عشان
+
+129
+00:09:48,590 --> 00:09:52,810
+أعرف إنهم صاروا صفر .. بنقول بسبب أن الـ amplitude
+
+130
+00:09:52,810 --> 00:09:57,510
+بتاع الموجة الحمراء اللي هي في القاع أطول يعني أعلى
+
+131
+00:09:57,510 --> 00:10:01,490
+من الـ amplitude بتاع .. يعني .. يعني الارتفاع
+
+132
+00:10:01,490 --> 00:10:05,570
+الموجي بتاع الموجة الزرقاء أقل من الارتفاع الموجي
+
+133
+00:10:05,570 --> 00:10:08,370
+بتاع الموجة الحمراء، طبعا و الموجة الحمراء في قاع
+
+134
+00:10:08,370 --> 00:10:13,510
+فعشان هي كده الفارق بينهم كان عندي موجة باتجاه أو
+
+135
+00:10:13,510 --> 00:10:17,390
+متجهة يعني في حالة أنها موجودة في حالة القاع
+
+136
+00:10:17,390 --> 00:10:21,330
+فبالتالي الموجة هاي أصغر طبعا من كل من الموجتين، هي
+
+137
+00:10:21,330 --> 00:10:26,930
+حاصل الفرق بينهم إذا جاز التعبير، في لحظة أخرى من
+
+138
+00:10:26,930 --> 00:10:31,330
+الزمن .. في لحظة أخرى من الزمن عند اللي هو الشريط
+
+139
+00:10:31,330 --> 00:10:37,850
+الأزرق بنقول أن الموجة الحمراء والموجة الزرقاء صدف
+
+140
+00:10:37,850 --> 00:10:45,000
+أن هما قاع قمة عفوا مع قمة فكان عندي أنا الموجة أو
+
+141
+00:10:45,000 --> 00:10:50,260
+الموجة المحصلة أقوى من كلا الموجتين، طبعا ممكن تكون
+
+142
+00:10:50,260 --> 00:10:57,700
+twice أو أكثر من .. أو .. أو ضعفهم كمحصلة لهم، في
+
+143
+00:10:57,700 --> 00:11:01,780
+عندي مناطق ثانية بيكون التداخل مش .. مش تماما قمة
+
+144
+00:11:01,780 --> 00:11:08,470
+مع قمة، يعني هنا هنا قاع هنا قاع و هنا عقباله طبعا
+
+145
+00:11:08,470 --> 00:11:12,490
+مش قاع ولا قمة يعني جاي في النص هنا، فبيكون طبعا
+
+146
+00:11:12,490 --> 00:11:16,690
+changing interference pattern، هذا النظام التداخلي
+
+147
+00:11:16,690 --> 00:11:22,090
+أو الموجة الناتجة بتتغير علوا وانخفاضا حسب وين
+
+148
+00:11:22,090 --> 00:11:26,450
+المناطق اللي تداخلت من هذه الموجات، سرعة التغير
+
+149
+00:11:26,450 --> 00:11:30,870
+هائلة جدا، يعني احنا بنقول المدة الزمنية اللي
+
+150
+00:11:30,870 --> 00:11:35,490
+بتتداخل فيها الموجات مرة، مرتين، ثلاث، أربع،
+
+151
+00:11:35,490 --> 00:11:40,820
+خمس، ست، تقريبا و نصف، تداخل .. تداخلت الموجة الحمراء
+
+152
+00:11:40,820 --> 00:11:45,260
+مع الموجة الزرقاء .. الزرقاء تقريبا ست مرات و نصف أو
+
+153
+00:11:45,260 --> 00:11:49,640
+ست مرات في زمن قدره .. في زمن قدره عشر أس ناقص
+
+154
+00:11:49,640 --> 00:11:53,960
+أربع عشرة من الثانية، و ده زمن لا يكاد يذكر أبدا،
+
+155
+00:11:53,960 --> 00:11:58,280
+لا تستطيع العين أن تلاحظ بالعين المجردة أن الضوء
+
+156
+00:11:58,280 --> 00:12:02,460
+يعني صار أقوى أو صار أضعف نتيجة تداخل الموج، وإنما
+
+157
+00:12:02,460 --> 00:12:07,140
+هذا يثبت بالمعامل و التجربة، فتداخل موجتين الملخص
+
+158
+00:12:07,360 --> 00:12:12,100
+تداخل موجتين ما لهمش نفس الـ frequency يعني ما لهمش
+
+159
+00:12:12,100 --> 00:12:15,880
+نفس الطول الموجي، بيختلفوا في الطول الموجي بيعطيني
+
+160
+00:12:15,880 --> 00:12:19,560
+changing interference pattern، هذا changing
+
+161
+00:12:19,560 --> 00:12:24,120
+interference pattern is too fast .. too fast to be
+
+162
+00:12:24,120 --> 00:12:28,340
+observed، يعني سريع جدا لدرجة لا يمكن الإنسان
+
+163
+00:12:28,340 --> 00:12:34,820
+يلاحظه بالعين المجردة، بينما تداخل موجات من نفس من
+
+164
+00:12:34,820 --> 00:12:38,720
+نفس الطول الموجي إذا كانوا totally in phase
+
+165
+00:12:38,720 --> 00:12:43,480
+بيعطوني موجة ناتجة twice ده amplitude ارتفاعها
+
+166
+00:12:43,480 --> 00:12:47,600
+يساوي ضعف ارتفاع كل من الموجتين، ولو كانوا totally
+
+167
+00:12:47,600 --> 00:12:51,020
+out of phase، هنا totally in phase يعني منطبقين
+
+168
+00:12:51,020 --> 00:12:55,600
+تمامًا، totally out of phase، هم يلهم نفس الـ frequency
+
+169
+00:12:55,600 --> 00:13:00,900
+نفس الطول الموجي بس للأسف مختلفين تماما، يعني القمة
+
+170
+00:13:00,900 --> 00:13:06,440
+مع القاع والقمة مع القاع والقاع مع القمة، بالتالي
+
+171
+00:13:06,440 --> 00:13:11,060
+يعني اتجاهاتهم متعاكسة تمامًا، بتكون الـ resultant
+
+172
+00:13:11,060 --> 00:13:16,120
+wave zero، طيب، الآن ممكن انسان يسأل نفسه، طب لو
+
+173
+00:13:16,120 --> 00:13:19,800
+التداخل اللي هم نفس الـ frequency نفس الطول الموجي
+
+174
+00:13:19,800 --> 00:13:25,520
+بس يعني في شيء بين
+
+201
+00:15:27,500 --> 00:15:31,200
+الموجي إذا بمجرد وجود لحظة من الزمن ينطبقوا فيها
+
+202
+00:15:31,200 --> 00:15:34,980
+على بعض من البعض بشكل كامل المفروض يظلوا مترافقين
+
+203
+00:15:34,980 --> 00:15:39,260
+بشكل كامل بدون أي اختلاف لإنهم نفس الطول الموجي بس
+
+204
+00:15:39,260 --> 00:15:43,440
+حقيقة هما مايلهم نفس الطول الموجي الآن في حالة ما
+
+205
+00:15:43,440 --> 00:15:48,640
+يكون عندي الموجات المتداخلة لها نفس الطول الموجي
+
+206
+00:15:48,640 --> 00:15:52,640
+بيكون عندي سيناريو من ثلاث سيناريوهات السيناريو
+
+207
+00:15:52,640 --> 00:15:56,540
+الأول طبعا هدول الموجتين تداخلوا لهما نفس الطول
+
+208
+00:15:56,540 --> 00:16:00,080
+الموجي طبيعي التداخل .. التداخل هما totally in 
+
+209
+00:16:00,080 --> 00:16:05,910
+phase القمة مع القمة والقاع مع القاع هيكون الموجة
+
+210
+00:16:05,910 --> 00:16:09,270
+الناتجة موجة لها twice ال amplitude ارتفاعها
+
+211
+00:16:09,270 --> 00:16:13,690
+يساوي ضعف ارتفاع أي من الموجتين المتداخلتين
+
+212
+00:16:13,690 --> 00:16:18,430
+السيناريو الثاني إنه لهما نفس الطول الموجي نفس
+
+213
+00:16:18,430 --> 00:16:23,870
+الطول الموجي وتداخلوا بحيث أن واحدة منهم قمتها اجتمعت
+
+214
+00:16:23,870 --> 00:16:28,090
+مع قاع الأخرى والقاع اجتمع مع القمة يعني totally out 
+
+215
+00:16:28,090 --> 00:16:31,830
+of phase مختلفات تماما بيكون الموجة الناتجة zero
+
+216
+00:16:31,830 --> 00:16:36,170
+أنه التداخل فيش موجة عندي بسبب تداخلهم يعني ألغوا
+
+217
+00:16:36,170 --> 00:16:40,950
+بعضهم البعض .. ألغوا بعضهم البعض السيناريو
+
+218
+00:16:40,950 --> 00:16:46,470
+الثالث أنه تداخل هدول الموجتين اللي هما نفس الطول
+
+219
+00:16:46,470 --> 00:16:51,030
+الموجي .. نفس الطول الموجي بس تداخلهم ليس totally 
+
+220
+00:16:51,030 --> 00:16:54,590
+in phase وليس totally out of phase يعني هنا قمة
+
+221
+00:16:54,590 --> 00:16:59,630
+الموجة رقم اثنين يعني جاية تقريبا مع منطقة من
+
+222
+00:16:59,630 --> 00:17:05,050
+الموجة لا هي قاع ولا هي قمة فبيكون ال wave الناتجة
+
+223
+00:17:05,050 --> 00:17:09,070
+عندها داخلهم الاثنين جاية بين zero وبين اثنين
+
+224
+00:17:09,070 --> 00:17:12,650
+between zero and twice the amplitude between zero
+
+225
+00:17:12,650 --> 00:17:16,490
+and twice the amplitude the result of two
+
+226
+00:17:16,490 --> 00:17:20,090
+particles striking the same place simultaneously
+
+227
+00:17:20,090 --> 00:17:25,600
+is always additive whereas two overlapping waves
+
+228
+00:17:25,600 --> 00:17:29,480
+may reinforce or cancel each other as just
+
+229
+00:17:29,480 --> 00:17:34,000
+described يعني زي ما وصفنا لو أنا بدأت أضيف two
+
+230
+00:17:34,000 --> 00:17:38,060
+particles لبعضهم البعض يعني two particles جسيمين
+
+231
+00:17:38,060 --> 00:17:43,440
+بدأت أضيفهم لبعضهم البعض النتيجة دائما إضافية جمعية
+
+232
+00:17:43,440 --> 00:17:48,840
+يعني بمعنى آخر أنا جبت ميزان حساس وحطيت على هذا
+
+233
+00:17:48,840 --> 00:17:54,980
+الميزان الحساس يعني ذرة من الرمل وجبت وزنها مثلا
+
+234
+00:17:54,980 --> 00:18:00,400
+عشر gram على سبيل المثال وجبت ذرة أخرى من الرمل
+
+235
+00:18:00,400 --> 00:18:05,180
+أضفتها فوق الميزان الحساس جنبها هيزيد الوزن ما فيش
+
+236
+00:18:05,180 --> 00:18:09,280
+إمكانية أن نقول الذرة الثانية ألغت الذرة الأولى
+
+237
+00:18:09,280 --> 00:18:12,460
+فصار الوزن صفر ما فيش إمكانية ليش؟ لأن هذه أجسام
+
+238
+00:18:12,460 --> 00:18:16,200
+particles إذا في حالة ما أنا بتكلم عن تداخل
+
+239
+00:18:16,200 --> 00:18:20,240
+الأجسام وترافق الأجسام بنحكي دائما عن addition
+
+240
+00:18:20,770 --> 00:18:24,970
+addition يعني إضافة لبعض لبعض الوزن بيزيد الوزن
+
+241
+00:18:24,970 --> 00:18:30,790
+بيزيد بينما التداخل الموجي two overlapping waves
+
+242
+00:18:30,790 --> 00:18:36,690
+may reinforce or cancel each other يعني حسب .. حسب
+
+243
+00:18:36,690 --> 00:18:41,650
+كيف تداخلوا هدول الموجات ممكن يجوا بعضهم وممكن
+
+244
+00:18:41,650 --> 00:18:45,530
+يضعفوا بعضهم وهذه التقوية أو التضعيف ممكن تكون
+
+245
+00:18:45,530 --> 00:18:49,570
+منتظمة إذا two waves إذا الـ two waves لهما نفس
+
+246
+00:18:49,570 --> 00:18:54,250
+الطول الموجي حيكون تداخل منتظم stable بينما لو
+
+247
+00:18:54,250 --> 00:18:57,750
+لهما أطوال موجية مختلفة حيكون في عندي changing
+
+248
+00:18:57,750 --> 00:19:03,970
+interference pattern Interference يعني تداخل نظام
+
+249
+00:19:03,970 --> 00:19:09,330
+تداخلي بين الموجات إما ثابت أو متغير ثابت في حالة
+
+250
+00:19:09,330 --> 00:19:12,850
+ما يكون عندي ال two waves أو أكثر المتداخلة لها
+
+251
+00:19:12,850 --> 00:19:16,970
+نفس الطول الموجي وساعتها يحدث عندي سيناريو من ثلاث
+
+252
+00:19:16,970 --> 00:19:23,970
+سيناريوهات أو هيكون النظام التداخلي متغير متغير و
+
+253
+00:19:23,970 --> 00:19:29,510
+ساعة بسبب أو سبب أنه متغير بين التقوى والتضعيف
+
+254
+00:19:29,510 --> 00:19:33,810
+للموجة الضوئية بسبب أن الأطوال الموجية مختلفة
+
+255
+00:19:33,810 --> 00:19:39,450
+الأطوال الموجية مختلفة طبعا هذه ظاهرة التداخل دل
+
+256
+00:19:39,450 --> 00:19:42,850
+نحكي عنها أن بعض الأشياء البسيطة في حالة ما يكون
+
+257
+00:19:42,850 --> 00:19:48,700
+في عندي two waves two waves لهما نفس الطول الموجي و
+
+258
+00:19:48,700 --> 00:19:53,480
+totally in phase بيصير عندي الموجة الناتجة twice 
+
+259
+00:19:53,480 --> 00:19:56,080
+the amplitude يعني بمعنى إيش؟ twice the amplitude
+
+260
+00:19:56,080 --> 00:19:59,980
+يعني الضوء بيكون أقوى الضوء بيكون أقوى وبالتالي
+
+261
+00:19:59,980 --> 00:20:04,200
+أثره بيكون فيزيائيا أقوى لما احنا بيكون عندي 
+
+262
+00:20:04,200 --> 00:20:10,470
+تداخلت موجتين تداخلت موجتين و totally out of phase
+
+263
+00:20:10,470 --> 00:20:14,670
+الضوء تكاد يكون معدوم لأن الموجة الضوئية ألغت
+
+264
+00:20:14,670 --> 00:20:19,010
+بعضها البعض يعني أنا لو هدول الموجتين تم تسليطهم
+
+265
+00:20:19,010 --> 00:20:23,930
+على جدار .. على جدار وتداخلوا مع بعضهم البعض
+
+266
+00:20:23,930 --> 00:20:28,630
+بالشكل اللي احنا شايفينه اللي هو totally out of
+
+267
+00:20:28,630 --> 00:20:32,510
+phase هلاحظ أن الجدار هذا يكاد يكون معتم بسبب أن
+
+268
+00:20:32,510 --> 00:20:37,330
+هدول الموجتين ألغوا بعضهم البعض الآن لو تم التداخل
+
+269
+00:20:37,330 --> 00:20:40,610
+بشكل لا هو totally in phase ولا هو totally out of
+
+270
+00:20:40,610 --> 00:20:44,870
+phase حسب قد إيش الموجة الناتجة ممكن يكون كمية
+
+271
+00:20:44,870 --> 00:20:49,990
+الإضاءة أو الأثر الضوء على هذا الجدار وهذا الكلام
+
+272
+00:20:49,990 --> 00:20:53,970
+أيضا بينطبق على ال changing interference pattern
+
+273
+00:20:53,970 --> 00:20:57,230
+بس مع ملاحظة أنه في ال changing interference
+
+274
+00:20:57,230 --> 00:21:02,490
+pattern لا يمكن ملاحظة متى صار الضوء أقوى ومتى ضعف
+
+275
+00:21:02,490 --> 00:21:06,970
+الضوء بسبب أن هذا بتغير بسرعة هائلة تقدر بـ 10 أس
+
+276
+00:21:06,970 --> 00:21:13,970
+ناقص 14 من الثانية 10 أس ناقص 14 من الثانية الآن
+
+277
+00:21:13,970 --> 00:21:20,390
+في حالة ما الموجتين يكونوا totally in phase ال
+
+278
+00:21:20,390 --> 00:21:24,430
+interference pattern بتاعهم التداخل بتاعهم أو
+
+279
+00:21:24,430 --> 00:21:28,150
+النظام التداخلي بتاعهم هيقدر لتقوية الموجة الضوئية
+
+280
+00:21:28,150 --> 00:21:30,830
+يعني الموجة الناتجة هتكون twice the amplitude
+
+281
+00:21:30,830 --> 00:21:35,350
+مقارنة مع كل منهم وساعتها الضوء هيقوى بشكل ثابت و
+
+282
+00:21:35,350 --> 00:21:39,050
+بيسموا هذا النوع من التداخل constructive
+
+283
+00:21:39,050 --> 00:21:43,230
+interference يعني التداخل البنائي أضفنا شيء على
+
+284
+00:21:43,230 --> 00:21:46,790
+شيء وأدى إلى زيادته التداخل البنائي أو
+
+285
+00:21:46,790 --> 00:21:49,510
+constructive interference constructive
+
+286
+00:21:49,510 --> 00:21:53,890
+interference يعني بينما في الحالة الثانية اللي
+
+287
+00:21:53,890 --> 00:21:57,610
+إحنا شايفينها ألغوا بعضهم البعض لأنهم totally out
+
+288
+00:21:57,610 --> 00:22:04,500
+of phase وهذا أدى إلى إلغاء موجة الضوء وانعدامها
+
+289
+00:22:04,500 --> 00:22:08,380
+وهذا بيسمى destructive interference destructive
+
+290
+00:22:08,380 --> 00:22:12,640
+يعني هدمي تداخل هدمي يعني الموجتين هدموا بعضهم
+
+291
+00:22:12,640 --> 00:22:17,200
+البعض وألغوا بعضهم البعض وهذا يسمى تداخل هدمي إذا
+
+292
+00:22:17,200 --> 00:22:20,580
+في عندي تداخل بنائي constructive interference
+
+293
+00:22:20,580 --> 00:22:26,050
+وتداخل هدمي destructive interference يعني إيش بناء
+
+294
+00:22:26,050 --> 00:22:29,110
+وإيش هدم؟ يعني هل .. هل هلاقي هنا مثلا أحجار
+
+295
+00:22:29,110 --> 00:22:32,990
+مبنية وهنا أحجار مهدمة؟ لا هنا هلاقي ضوء أقوى في
+
+296
+00:22:32,990 --> 00:22:36,890
+منطقة التداخل هذه يعني لو سلطوا هدول الموجتين على
+
+297
+00:22:36,890 --> 00:22:41,830
+منطقة من جدار .. على منطقة من جدار هلاقي المنطقة
+
+298
+00:22:41,830 --> 00:22:45,270
+اللي سلطوا عليها بسبب أنهم جوا بعضهم البعض هذه
+
+299
+00:22:45,270 --> 00:22:49,610
+المنطقة مضيئة لو في منطقة مجاورة من ال .. من نفس
+
+300
+00:22:49,610 --> 00:22:53,570
+الجدار اللي صار عنده منطقة مضيئة بسبب تداخل بنائي
+
+301
+00:22:53,570 --> 00:22:58,370
+لو في منطقة مجاورة إلا عشان المقارنة طبعا وفي عندي
+
+302
+00:22:58,370 --> 00:23:04,120
+موجتين تداخلوا بشكل هدمي يعني عكس بعض من البعض هلاقي
+
+303
+00:23:04,120 --> 00:23:07,460
+أن المنطقة هيمعتمة إذا .. إذا قورنت بالمنطقة
+
+304
+00:23:07,460 --> 00:23:12,620
+المضيئة هذا الكلام بنحكيه لأنه هيجيله أو .. أو
+
+305
+00:23:12,620 --> 00:23:16,280
+هيصير له لازمة في المحاضرة التالية واللي هنشرح
+
+306
+00:23:16,280 --> 00:23:21,700
+فيها تجربة غاية في الأهمية وهذه التجربة يعني ..
+
+307
+00:23:26,090 --> 00:23:31,770
+تمت في عام ألف وثمانمئة واحد لها علاقة شديدة جدا
+
+308
+00:23:31,770 --> 00:23:34,670
+بالتداخل الموجي وبال constructive و destructive
+
+309
+00:23:34,670 --> 00:23:39,310
+interference طبعا في ألف وثمانمئة واحد العالم
+
+310
+00:23:39,310 --> 00:23:44,850
+اللندني Thomas Young demonstrated that light can
+
+311
+00:23:44,850 --> 00:23:48,550
+produce patterns of cancellation and reinforcement
+
+312
+00:23:48,550 --> 00:23:52,190
+thus providing strong evidence that light is a
+
+313
+00:23:52,190 --> 00:23:56,650
+wave phenomenon طبعا هو أجرى تجربة أثبت في هذه
+
+314
+00:23:56,650 --> 00:24:01,330
+التجربة أن الموجات الضوئية بسبب تداخلها ممكن تقوي
+
+315
+00:24:01,330 --> 00:24:05,430
+بعضها البعض وممكن تلغي بعضها البعض فبالتالي هذا
+
+316
+00:24:05,430 --> 00:24:09,610
+أعطى مجالا لا يدع مجالا للشك أن الضوء عبارة عن
+
+317
+00:24:09,610 --> 00:24:14,590
+موجات وليس جسيمات الضوء عبارة عن موجات وليس جسيمات
+
+318
+00:24:14,590 --> 00:24:18,790
+إذا في عندي ثلاث أشياء لحد الآن من بداية المساقطة على
+
+319
+00:24:18,790 --> 00:24:24,230
+البصريات الفيزيائية لحد اللحظة هذه كل هذه الأشياء
+
+320
+00:24:24,230 --> 00:24:28,970
+الثلاث بتثبت أن الضوء عبارة عن موجات وليس جسيمات
+
+321
+00:24:28,970 --> 00:24:32,590
+الشيء الأول .. الشيء الأول ظاهرة ال diffraction
+
+322
+00:24:33,150 --> 00:24:38,110
+الشيء الثاني أن الضوء سرعته محدودة والشيء الثالث
+
+323
+00:24:38,110 --> 00:24:42,550
+طبيعة التداخل بتاعة الموجات الضوئية وتقوية بعضها
+
+324
+00:24:42,550 --> 00:24:46,210
+البعض وضعف بعضها البعض يعني لو احنا بس الموجات
+
+325
+00:24:46,210 --> 00:24:49,710
+الضوئية عندما تتداخل فقط في معها مجال واحد فقط
+
+326
+00:24:49,710 --> 00:24:53,010
+أنها بتقوي بعضها البعض كنقولنا يمكن تكون جسيمات
+
+327
+00:24:53,010 --> 00:24:57,850
+لأن أي جسم بنضيفه لجسم بيكون الحاصل مجموعهم بينما
+
+328
+00:24:57,850 --> 00:25:01,730
+أي موجة تضاف لموجة ممكن يكون مجموعهم وممكن يكون
+
+329
+00:25:01,730 --> 00:25:05,390
+صفر وممكن يكون بين ذلك وممكن يكون شيء متغير بين
+
+330
+00:25:05,390 --> 00:25:10,510
+القوة والضعف وهذا بيثبت أن الضوء عبارة عن شيء
+
+331
+00:25:10,510 --> 00:25:15,580
+يعني ذو طبيعة موجية وليست جسيمية نتوقف عند هذه
+
+332
+00:25:15,580 --> 00:25:21,200
+النقطة ونبدأ المرة القادمة نحكي عن ال
+
+333
+00:25:21,200 --> 00:25:25,880
+coherence بس خليني ألخص المحاضرة بتاعتنا بنقول
+
+334
+00:25:25,880 --> 00:25:29,880
+superposition of أو superposition of waves التداخل
+
+335
+00:25:29,880 --> 00:25:33,640
+الموجي أو التراكب الموجي في عندي نوعين من التداخل
+
+336
+00:25:33,870 --> 00:25:37,510
+أنه يكون الموجتين of differing frequency ما اللي
+
+337
+00:25:37,510 --> 00:25:42,030
+همش نفس الطول الموجي أو أنه يكون الموجتين of the
+
+338
+00:25:42,030 --> 00:25:46,410
+same frequency إذا كان في تداخل موجتين مختلفتين في
+
+339
+00:25:46,410 --> 00:25:50,190
+الطول الموجي بيكون النتيجة changing interference
+
+340
+00:25:50,190 --> 00:25:54,710
+pattern كيف بنلحظه؟ بنلحظوش حقيقة لسبب أنه متغير
+
+341
+00:25:54,710 --> 00:25:59,690
+بسرعة هائلة بين القوة والضعف والنص نص بسرعة كاد
+
+342
+00:25:59,690 --> 00:26:04,700
+تكون أنه بيتغير .. بيتغير هذا النظام التداخلي أو
+
+343
+00:26:04,700 --> 00:26:10,140
+تتغير حالته كل عشرة أس ناقص أربعة عشر جزء من
+
+344
+00:26:10,140 --> 00:26:14,320
+الثانية إذا سريع جدا لدرجة لا يمكن ملاحظته إذا
+
+345
+00:26:14,320 --> 00:26:17,820
+كانت تداخل السيناريو الثاني أو النوع الثاني من
+
+346
+00:26:17,820 --> 00:26:21,820
+التداخل أنه يكون عندي تداخل لموجتين لهما نفس ال
+
+347
+00:26:21,820 --> 00:26:25,920
+frequency يعني نفس الطول الموجي ساعة أنا في هذا
+
+348
+00:26:25,920 --> 00:26:32,030
+التداخل بميز بين ثلاث سيناريوهات طبعا الثلاث سيعطوني
+
+349
+00:26:32,030 --> 00:26:34,730
+mission changing سيعطوني stable interference
+
+350
+00:26:34,730 --> 00:26:39,290
+pattern نظام تداخلي ثابت هذا النظام التداخلي ثابت
+
+351
+00:26:39,290 --> 00:26:43,070
+حسب الموجتين كيف اتداخلوا في أي وضع والله إذا كان
+
+352
+00:26:43,070 --> 00:26:47,590
+الموجتين totally in phase هتعطيني نتيجة wave of
+
+353
+00:26:47,590 --> 00:26:51,030
+twice amplitude يعني هتكون الموجة الناتجة ارتفاعها
+
+354
+00:26:51,030 --> 00:26:55,610
+ضعف ارتفاع أي من الموجتين المتداخلتين إذا كان
+
+355
+00:26:55,610 --> 00:27:00,170
+السيناريو الثاني إذا كان الموجتين اللي لهما نفس
+
+356
+00:27:00,170 --> 00:27:04,190
+الطول الموجي تداخلوا بحيث أن هما totally out of 
+
+357
+00:27:04,190 --> 00:27:06,890
+phase يعني واحدة في قمتها وواحدة في قاعها هيكون
+
+358
+00:27:06,890 --> 00:27:11,910
+النتيجة zero إنه بيلغوا بعضهم البعض طيب إذا كان ال
+
+359
+00:27:11,910 --> 00:27:15,750
+scenario بين ال scenario الأول والثاني هيعطينا ال
+
+360
+00:27:15,750 --> 00:27:18,850
+scenario الثالث اللي هو waves partially overlap
+
+361
+00:27:18,850 --> 00:27:24,550
+neither completely in nor out of phase يعني لا هما
+
+362
+00:27:24,550 --> 00:27:27,830
+totally in phase ولا هما totally out of phase بين
+
+363
+00:27:27,830 --> 00:27:32,370
+البيينين هيعطيني producing a wave of intermediate
+
+364
+00:27:32,370 --> 00:27:36,770
+amplitude يعني ارتفاع ال wave الناتجة هتكون ارتفاع
+
+365
+00:27:36,770 --> 00:27:41,890
+وسطي بين صفر واثنين بين صفر واثنين ويعطيكم العافية
+
+366
+00:27:41,890 --> 00:27:44,350
+والسلام عليكم ورحمة الله وبركات
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/YDGQovyQIRo_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/YDGQovyQIRo_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9e0f08fcbead10f4c7847c0a4e179c205006a054
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/YDGQovyQIRo_postprocess.srt
@@ -0,0 +1,352 @@
+1
+00:00:01,580 --> 00:00:05,700
+بسم الله الرحمن الرحيم، اليوم هنحكي عن ال
+
+2
+00:00:05,700 --> 00:00:10,000
+scattering of light و .. و تجارب أو simulation
+
+3
+00:00:10,000 --> 00:00:15,080
+توضح هذا الأمر، ضوء الشمس اللي بيصلنا حقيقة بيكون
+
+4
+00:00:15,080 --> 00:00:20,740
+غير مرئي، مش sureيعني صحيح الشمس مبينة يعني منيرة
+
+5
+00:00:20,740 --> 00:00:25,220
+ولكن الضوء .. المسافة منها إلى ال .. ال .. إلى
+
+6
+00:00:25,220 --> 00:00:29,420
+الأرض لا ترى، يعني الضوء لا يرى إلا إذا كان في
+
+7
+00:00:29,420 --> 00:00:34,820
+منطقة فيها dust يعني غبار، ليش؟ لأن هذا الغبار
+
+8
+00:00:34,820 --> 00:00:38,860
+المعلق في الهواء بيعمل scattering of light، هذا
+
+9
+00:00:38,860 --> 00:00:44,010
+بيسموه dust particles أو جسيمات الغباربتساعدنا في
+
+10
+00:00:44,010 --> 00:00:48,790
+رؤية الحزم الضوئية لما بنستخدم عدسة مكبرة بنشوف
+
+11
+00:00:48,790 --> 00:00:53,070
+هذه ال particles اللي بيسموها الجسيمات الغروية أو
+
+12
+00:00:53,070 --> 00:00:59,410
+الغروانية طبعا لأنها معلقة بشكل في الهواء الجوي
+
+13
+00:00:59,410 --> 00:01:02,730
+أيضا لما بنتطلع على الضوء النافذ من بين أوراق
+
+14
+00:01:02,730 --> 00:01:07,880
+الأشجاربنشاهد نفس الظاهرة إنه حزم ضوئية وكأنه
+
+15
+00:01:07,880 --> 00:01:11,580
+الغبار معلق فيها، طبعا الغبار هو اللي بيشتت الحزم
+
+16
+00:01:11,580 --> 00:01:15,980
+الضوئية وبيخلينا .. بيمكننا من أننا نشوفها، نشوف
+
+17
+00:01:15,980 --> 00:01:20,580
+الحزم الضوئية، بنعمل تجربة عبارة عن مصدر قوي للضوء
+
+18
+00:01:20,580 --> 00:01:21,240
+اسمه S
+
+19
+00:01:27,620 --> 00:01:34,560
+بنضخل الضوء في ماء
+
+20
+00:01:34,560 --> 00:01:37,920
+صافي مفيش فيه اي مشكلة مابيصيرش scattering لل
+
+21
+00:01:37,920 --> 00:01:41,950
+light بتظل الحزمة متوازية بندخلها من ماء صافيهو ال
+
+22
+00:01:41,950 --> 00:01:45,810
+.. واسعة شوية و بعدك بنمررها من ال lens هذه ال
+
+23
+00:01:45,810 --> 00:01:48,270
+lens بتعمل focusing مافيش اي scattering ال white
+
+24
+00:01:48,270 --> 00:01:51,710
+light ضال white light .. ضال white light قبل ان
+
+25
+00:01:51,710 --> 00:01:56,210
+نجيب نضيف media تانية بس هذه ال media بداش تكون
+
+26
+00:01:56,210 --> 00:02:01,160
+صافية بدها تكونفيها يعني شوية من المعلق ونحط
+
+27
+00:02:01,160 --> 00:02:04,980
+العنصر كيميائي ال Sodium Thiosulfate أو Sodium
+
+28
+00:02:04,980 --> 00:02:09,340
+Hyposulfate ونضيفله حمض الكبريتيك المركز عشان يصير
+
+29
+00:02:09,340 --> 00:02:15,180
+بعدين في حبيبات الكبريت معلقة، الآن بعد دقيقتين
+
+30
+00:02:15,180 --> 00:02:21,950
+تلاتة بيصير عندىحبيبات الكبريت هذه اللي هتعمل على
+
+31
+00:02:21,950 --> 00:02:25,770
+تشتيت الضوء، بدنا نواجه عند هذه النقطة ونقول طبعا
+
+32
+00:02:25,770 --> 00:02:30,950
+هذه ال microscopic sulfur particles microscopic
+
+33
+00:02:30,950 --> 00:02:33,910
+يعني احنا ما بنشوفهاش بالعين المجردة، هي صغيرة
+
+34
+00:02:33,910 --> 00:02:37,370
+جدا، بس هي بتعمل على تشتيت الضوء، ليه؟ حبيبات
+
+35
+00:02:37,370 --> 00:02:42,530
+الكبريت، النتجة عن تفاعل حمض الكبريتيك المركز مع
+
+36
+00:02:42,530 --> 00:02:47,350
+ال sodium thio sulfateمش موضوعنا الكيميا ولكن
+
+37
+00:02:47,350 --> 00:02:51,770
+موضوعنا أنه زي ما أنتم لاحظين الغالبية العظمة من
+
+38
+00:02:51,770 --> 00:02:57,810
+ال tank اللي بيحتوي أو الوعاء اللي بيحتوي على هذا
+
+39
+00:02:57,810 --> 00:03:02,750
+المعلق بيشتت الضوء الأزرق بكمية أكبر بكتير من
+
+40
+00:03:02,750 --> 00:03:06,250
+تشتيته للألوان التانية فبيبين لون المحلول كأنه
+
+41
+00:03:06,250 --> 00:03:12,260
+أزرقالأزرق بيتشتت الحزمة أو المكوّن للضوء الأبيض
+
+42
+00:03:12,260 --> 00:03:15,580
+أحد مكوناته الضوء الأبيض اللي هو طول الموج الأزرق
+
+43
+00:03:15,580 --> 00:03:19,260
+بتشتت بيخلص بيبدأ تظهر الألوان التانية إذا ملاحظين
+
+44
+00:03:19,260 --> 00:03:23,620
+هنا اللون على برتقالي تقريبا بمع طول المسافة
+
+45
+00:03:23,620 --> 00:03:27,720
+الألوان كلها بتكون تشتتت بيظل عنده الضوء الأحمر
+
+46
+00:03:27,720 --> 00:03:32,560
+واللي هو أنا باستقبله بسبب أن هو الوحيد الأقل
+
+47
+00:03:32,560 --> 00:03:37,510
+تشتتا في ألوانالطفل لأن هو أطولها موجة، نحن عارفين
+
+48
+00:03:37,510 --> 00:03:43,810
+أنه التشتت التعدو له علاقة عكسية مع الطول الموجي،
+
+49
+00:03:43,810 --> 00:03:46,770
+فهذه التجربة بتبين قضية ال scattering of light و
+
+50
+00:03:46,770 --> 00:03:51,470
+علاقتها بالطول الموجي و علاقتها بالطول الموجي زي
+
+51
+00:03:51,470 --> 00:03:58,100
+ما التجربة بتوضع، الآن هنتقل لتفسيربعض الظواهر
+
+52
+00:03:58,100 --> 00:04:02,260
+اللي في حياتنا بتصير ومنها ظاهرة يعني ليش السماء
+
+53
+00:04:02,260 --> 00:04:05,720
+بتكون زرقاء أو ليش السحاب بيكون أبيض أو ليش السماء
+
+54
+00:04:05,720 --> 00:04:10,100
+عند الغروب بتكون مائلة إلى اللون الأحمر بمعنى
+
+55
+00:04:10,100 --> 00:04:16,420
+الشفاءشفق يعني كثير من الظواهر ممكن احنا نفسرها
+
+56
+00:04:16,420 --> 00:04:20,960
+يعني ليش السحاب أبيض؟ ليش السماء زرقاء؟ ليش السماء
+
+57
+00:04:20,960 --> 00:04:25,740
+عند الغروب بتكون مائلة إلى الحمراء؟ مائلة إلى
+
+58
+00:04:25,740 --> 00:04:30,470
+الحمراء فبالتالي هذه القضية بدنا نفسرها الآنالان
+
+59
+00:04:30,470 --> 00:04:34,510
+يحيط بالكورة الأرضية ما يسمى بالـ atmosphere أو
+
+60
+00:04:34,510 --> 00:04:40,150
+الغلاف الجوي واللي في عبارة عن particles عبارة عن
+
+61
+00:04:40,150 --> 00:04:48,330
+بخار الماء وغازات كثيرة بتكون معلقة جزيئاتها فيفي
+
+62
+00:04:48,330 --> 00:04:56,010
+الغلاف الجوي لما بيمر الضوء بتشتت الضوء بواسطة هذه
+
+63
+00:04:56,010 --> 00:05:02,910
+ال particles بتشتت الضوء في هذه ال .. بواسطة هذه
+
+64
+00:05:02,910 --> 00:05:09,630
+الجزيئةالان حسب الان بالنسبة لمرور الضوء من السحب
+
+65
+00:05:09,630 --> 00:05:15,450
+السحب بتشتت أوش السحب هي عبارة عن جثيمات مائية
+
+66
+00:05:15,450 --> 00:05:22,050
+وجثيمات ثلجية يعني ماء متجمد أو ماء حقيقي بتشتت
+
+67
+00:05:22,050 --> 00:05:25,730
+الألوان السابعة بتاعة ألوان الطيف بنفس القدر فكلها
+
+68
+00:05:25,730 --> 00:05:29,850
+اتصل مع بعض هالبعض وبتعطي شعور باللون الأبيض يعني
+
+69
+00:05:29,850 --> 00:05:34,960
+هي بتعمل اتشتيتكل أنواع الأطياف الموجية بنفس القدر
+
+70
+00:05:34,960 --> 00:05:39,700
+فبتعمل على انها نشوف الكل الأطياف مع بعض في مجموعة
+
+71
+00:05:39,700 --> 00:05:43,280
+بتعطي إحساس باللون الأبيض لأن ليش السماء زرقاء
+
+72
+00:05:43,280 --> 00:05:47,580
+السماء زرقاء لأن الضوء الأزرق أو طول الموج الأزرق
+
+73
+00:05:47,580 --> 00:05:52,180
+بتشتتأكتر شيء أكتر من الطول الموجي الأحمر و أكتر
+
+74
+00:05:52,180 --> 00:05:56,460
+عشان هيك السماء بتعطينا شعور باللون أنه فيه blue
+
+75
+00:05:56,460 --> 00:05:59,980
+blue color of the sky لإنه ال blue blue color
+
+76
+00:05:59,980 --> 00:06:03,500
+بتشتت أكتر من أقصر موجتنا طبعا ماننساش أنه ال
+
+77
+00:06:03,500 --> 00:06:08,630
+violet اللي هو البنفسجي أقليعني عيننا صحيح ب ..
+
+78
+00:06:08,630 --> 00:06:12,910
+يعني هو حتى أكتر تشتتا من الأزرق ولكن عيننا مش
+
+79
+00:06:12,910 --> 00:06:17,610
+حساسة كتير لطول البنفسجي، الآن بالنسبة للشمس عند
+
+80
+00:06:17,610 --> 00:06:22,230
+الغروب مالة الشمس هتقطع مسافة في خلال الهواء الجوي
+
+81
+00:06:22,230 --> 00:06:25,430
+أو الغلاف الجوي، مسافة كبيرة جدا، بعكس المسافة
+
+82
+00:06:25,430 --> 00:06:27,790
+اللي بتقطعها في النهار و تكون متعامدة علينا
+
+83
+00:06:28,140 --> 00:06:32,700
+فبالتالي بيكون الضوء الأزرق تشتت كله وتبعثر قبل
+
+84
+00:06:32,700 --> 00:06:36,320
+وصوله إلينا و اللي بتوصل إلينا الموجات الأقل تشتتا
+
+85
+00:06:36,320 --> 00:06:42,180
+عشان هيك احنا بنشوف الشفق بشكل أحمر أو بورتقالي مع
+
+86
+00:06:42,180 --> 00:06:48,600
+أحمر لأن هذه الأطوار الموجية الأقل تشتتا و عند هذا
+
+87
+00:06:48,600 --> 00:06:53,940
+بتنتهي الفيديو و يعطيكم العافية والسلام عليكم
+
+88
+00:06:53,940 --> 00:06:56,200
+ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/_VE01t36gEA.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/_VE01t36gEA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..031de5b0756e04fbfcf5257ad3365e8806b6e061
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/_VE01t36gEA.srt
@@ -0,0 +1,1891 @@
+1
+00:00:01,480 --> 00:00:04,920
+بسم الله الرحمن الرحيم بنكمل مع محاضرات ال
+
+2
+00:00:04,920 --> 00:00:09,900
+physical optics و أيضا بنستمر مع ال image quality
+
+3
+00:00:09,900 --> 00:00:13,640
+.. مع ال image quality واليوم هنحكي عن حاجة اسمها
+
+4
+00:00:13,640 --> 00:00:18,330
+ال modulation transfer function المرة الماضية حكينا
+
+5
+00:00:18,330 --> 00:00:22,190
+عن ال point spread function اليوم هنحكي عن ال
+
+6
+00:00:22,190 --> 00:00:25,270
+modulation transfer function يا ترى إيش هو ال
+
+7
+00:00:25,270 --> 00:00:28,750
+modulation transfer function وإيش علاقته بال
+
+8
+00:00:28,750 --> 00:00:33,190
+image quality بدنا نبدأ بداية بسيطة بنقول بدنا
+
+9
+00:00:33,190 --> 00:00:39,750
+نفترض أن عندنا object ما جسم ما تم تصويره بواسطة
+
+10
+00:00:39,750 --> 00:00:43,790
+two different cameras، يعني استعملنا كاميراتين أو
+
+11
+00:00:43,790 --> 00:00:47,750
+two optical systems، بالأولى التقطنا صورة لهذا ال
+
+12
+00:00:47,750 --> 00:00:51,450
+object، و بالعقل بالكاميرا الثانية التقطنا صورة
+
+13
+00:00:51,450 --> 00:00:54,970
+برضه لنفس ال object من نفس الزاوية وبنفس ظروف
+
+14
+00:00:54,970 --> 00:00:59,410
+الإضاءة assume the photographs are grayscale to
+
+15
+00:00:59,410 --> 00:01:04,070
+simplify discussion بنا نتخيل أن الصورة هي بالأبيض
+
+16
+00:01:04,070 --> 00:01:07,550
+والأسود مش بالألوان في الكاميرتين بس عشان نبسط
+
+17
+00:01:07,550 --> 00:01:12,190
+النقاش إذا في عندنا جسم، عندك كاميرتين two optical
+
+18
+00:01:12,190 --> 00:01:16,690
+systems وقفنا مثلا في زاوية معينة وفي إضاءة معينة
+
+19
+00:01:16,690 --> 00:01:20,550
+بالكاميرا الأولى والتقطنا صورة وبنفس الشروط
+
+20
+00:01:20,550 --> 00:01:24,310
+والظروف التقطنا صورة لنفس ال object بالكاميرا
+
+21
+00:01:24,310 --> 00:01:28,910
+الثانية even when the conditions such as lighting,
+
+22
+00:01:29,350 --> 00:01:32,930
+camera angle and magnification are identical, the
+
+23
+00:01:32,930 --> 00:01:36,390
+two resulting images will differ حتى لو كان عندي
+
+24
+00:01:36,390 --> 00:01:40,890
+ظروف الإضاءة وزاوية الكاميرا و ال magnification
+
+25
+00:01:40,890 --> 00:01:46,210
+كلها موحدة الصورتين لازم يكون بينهم اختلاف لأنهم
+
+26
+00:01:46,210 --> 00:01:50,250
+كل صورة جاية من optical system مختلف فبالتالي
+
+27
+00:01:50,250 --> 00:01:55,330
+which one is better؟ يعني أي من الصورتين أفضل من
+
+28
+00:01:55,330 --> 00:01:58,170
+الثانية صورة الكاميرا الأولى ولا صورة الكاميرا
+
+29
+00:01:58,170 --> 00:02:01,950
+الثانية عشان نقول ال quality أفضل في الصورة الأولى
+
+30
+00:02:01,950 --> 00:02:08,130
+ولا في الصورة الثانية because
+
+31
+00:02:08,130 --> 00:02:11,690
+an image never perfectly duplicates its object the
+
+32
+00:02:11,690 --> 00:02:14,810
+image that comes closest to resembling its object
+
+33
+00:02:14,810 --> 00:02:20,660
+could be considered the better image معروف من الـ
+
+34
+00:02:20,660 --> 00:02:24,260
+geometric optics ومن ال physical optics أنه ما فيش
+
+35
+00:02:24,260 --> 00:02:28,480
+صورة تشبه مائة بالمائة ال object يعني بكل التفاصيل
+
+36
+00:02:28,480 --> 00:02:33,320
+ولكن في المقارنة بين الصور أو بين ال optical
+
+37
+00:02:33,320 --> 00:02:36,920
+systems المختلفة بنقول الصورة اللي بتشبه أكثر ال
+
+38
+00:02:36,920 --> 00:02:40,740
+object بتكون هي الصورة الأعلى في ال quality الصورة
+
+39
+00:02:40,740 --> 00:02:43,980
+اللي بتشبه أكثر ال object هي اللي بتكون أعلى في ال
+
+40
+00:02:43,980 --> 00:02:47,600
+quality عشان هي could be considered the better
+
+41
+00:02:47,600 --> 00:02:52,520
+image it is possible to say that على سبيل المثال
+
+42
+00:02:52,520 --> 00:02:55,880
+ممكن احنا ببساطة نبسط الموضوع كتير نقول one image
+
+43
+00:02:55,880 --> 00:02:58,860
+contains ثمانية وثمانين في المائة of the details
+
+44
+00:02:58,860 --> 00:03:03,460
+in the object and that another image has اثنين
+
+45
+00:03:03,460 --> 00:03:06,960
+وتسعين في المائة هذا مش دقيق مائة في المائة بس ممكن
+
+46
+00:03:06,960 --> 00:03:11,680
+احنا نتجاوزها نقول أنه مثلا الكاميرا الأولى نجلت لي
+
+47
+00:03:11,680 --> 00:03:14,740
+ثمانية وثمانين في المائة من تفاصيل ال object في
+
+48
+00:03:14,740 --> 00:03:24,550
+الصورة الكاميرا الثانية نجلت 92% من التفاصيل بتاعة
+
+49
+00:03:24,550 --> 00:03:29,150
+ال object حطتهم في الصورة هذا مش دقيق تماما but it
+
+50
+00:03:29,150 --> 00:03:32,670
+is possible to come close يعني ممكن احنا نتجاوز
+
+51
+00:03:32,670 --> 00:03:36,210
+نقول .. يعني هذا فبصف عندي أن الكاميرا اللي نجلت
+
+52
+00:03:36,210 --> 00:03:42,050
+92% من التفاصيل ال .. ال image بتاعتها higher
+
+53
+00:03:42,050 --> 00:03:46,250
+quality than the other image higher quality than
+
+54
+00:03:46,250 --> 00:03:51,490
+the other image طيب، الآن بدنا نحكي عن ال image
+
+55
+00:03:51,490 --> 00:03:54,570
+عبارة عن إيش؟ يعني لو قلنا ال image عبارة عن إيش
+
+56
+00:03:54,570 --> 00:03:57,890
+ممكن إنسان يقول من .. من تعريف ال geometric optics
+
+57
+00:03:57,890 --> 00:04:00,970
+هي عبارة عن مجموع ال .. ال point spread function
+
+58
+00:04:00,970 --> 00:04:06,790
+نقوله صحيح بس احنا اليوم هنعرف ال image بتعريف آخر
+
+59
+00:04:06,790 --> 00:04:13,230
+.. بتعريف آخر يشبه تعريف الصوت ولكن مختلف عنه في
+
+60
+00:04:13,230 --> 00:04:16,950
+شيء جوهري just as sound is a mixture of its
+
+61
+00:04:16,950 --> 00:04:21,510
+frequencies So are images. Whereas sound is a
+
+62
+00:04:21,510 --> 00:04:24,770
+mixture of temporal frequencies, images are
+
+63
+00:04:24,770 --> 00:04:28,750
+mixtures of spatial frequencies ما معنى هذا
+
+64
+00:04:28,750 --> 00:04:37,210
+الكلام؟ بنقول الصوت والضوء الصوت والضوء أو الصوت
+
+65
+00:04:37,210 --> 00:04:42,090
+والصورة الصوت والصورة الصورة عبارة أو الصوت عبارة
+
+66
+00:04:42,090 --> 00:04:49,250
+عن خليط من الترددات الترددات في الزمن، خليط من
+
+67
+00:04:49,250 --> 00:04:54,370
+الترددات في الزمن، طيب، والضوء أو الصورة عبارة عن
+
+68
+00:04:54,370 --> 00:04:59,430
+خليط من الترددات الضوئية، من الترددات الضوئية، إذا
+
+69
+00:04:59,430 --> 00:05:04,790
+ال sound ترددات صوتية، والصورة عبارة عن ترددات
+
+70
+00:05:04,790 --> 00:05:08,730
+إضاءية، ترددات إضاءية، وحنشرح هذا الكلام بعد شوية
+
+71
+00:05:08,730 --> 00:05:15,370
+بشكل أكثر تفصيلاً بنعيد بنقول الصوت عبارة عن ترددات
+
+72
+00:05:15,370 --> 00:05:19,050
+والصورة عبارة عن ترددات بس إيش بيختلف في حالة
+
+73
+00:05:19,050 --> 00:05:24,590
+الصوت عن الصورة الترددات هنا صوتية والترددات هنا
+
+74
+00:05:24,590 --> 00:05:30,630
+إضاءية طيب، طب هذا إيش بيقدّم إنهم بيختلفوا في شيء
+
+75
+00:05:30,630 --> 00:05:36,850
+جوهري جدا أن الصوت تردد زماني بينما الضوء تردد
+
+76
+00:05:36,850 --> 00:05:41,740
+مكاني الأمر تعقد، لأ ما تعقد الأمر نشوف المثال
+
+77
+00:05:41,740 --> 00:05:49,860
+على ذلك لما أنا بقول بسم الله الرحمن الرحيم الصوت
+
+78
+00:05:49,860 --> 00:05:54,540
+أو حنجرتي أو الأحبال الصوتية بتتردد عشان تصدر
+
+79
+00:05:54,540 --> 00:05:59,040
+موجات صوتية هذه الموجات الصوتية بتتردد زمانيا، يعني
+
+80
+00:05:59,040 --> 00:06:05,590
+لا يمكن 19 حرفا لا يمكن التسعة عشر حرفا تعني كلمة
+
+81
+00:06:05,590 --> 00:06:08,850
+بسم الله الرحمن الرحيم أسمعهم في نفس اللحظة لازم
+
+82
+00:06:08,850 --> 00:06:12,230
+أسمع حرف ال با في الأول بعدين ال سين في ال ..
+
+83
+00:06:12,230 --> 00:06:16,830
+ياله؟ ياله زمانيا ثم ال ميم ثم الألف ثم ال لام ثم
+
+84
+00:06:16,830 --> 00:06:20,770
+ال .. ال لام ثم ال ه ثم الألف ثم ال لام وهكذا
+
+85
+00:06:20,770 --> 00:06:24,490
+يعني بقدرش أقول ال بسم الله الرحمن الرحيم هدي في
+
+86
+00:06:24,490 --> 00:06:29,810
+نفس اللحظة لازم أقول بسم طب في كلمة بسم لحالها أنا
+
+87
+00:06:29,810 --> 00:06:35,270
+لفظت ال با أولاً في .. في .. في لحظة من الزمن تلتها
+
+88
+00:06:35,270 --> 00:06:40,710
+في لحظة أخرى إذا في تردد زماني تردد زماني للصوت
+
+89
+00:06:40,710 --> 00:06:45,570
+إذا الصوت عبارة عن ترددات وهذه الترددات زمانية
+
+90
+00:06:45,570 --> 00:06:51,110
+زمانية بينما الصورة ترددات مكانية ترددات إضاءية
+
+91
+00:06:51,110 --> 00:06:56,050
+هنا مقطع هنا مقطع آخر اللي هو الفراغ بين الرجل
+
+92
+00:06:56,050 --> 00:06:58,970
+الأول والثاني هنا مقطع ثالث اللي هو الرجل الثاني
+
+93
+00:06:59,320 --> 00:07:03,420
+هنا مقطع آخر، هنا مقطع .. إذا .. إذا في ترددات، في
+
+94
+00:07:03,420 --> 00:07:08,100
+عندي تردد اثنين، يعني هذا حيز، هذا حيز آخر يختلف
+
+95
+00:07:08,100 --> 00:07:12,520
+عنه، هذا حيز ثالث يختلف عنه، أنا بشوف الترددات هي
+
+96
+00:07:12,520 --> 00:07:16,270
+كلها في نفس اللحظة إذا التردد ده مش زماني، أنا
+
+97
+00:07:16,270 --> 00:07:19,730
+بشوفش الرجل الأول، ثم بعد لحظة بشوف الرجل
+
+98
+00:07:19,730 --> 00:07:22,990
+الثاني، ثم بعد لحظة بشوف الرجل الثالث، ثم بعد
+
+99
+00:07:22,990 --> 00:07:26,070
+لحظة بشوف الرجل الرابع أو بشوف الفراغ اللي بين
+
+100
+00:07:26,070 --> 00:07:29,270
+الرجل الثالث والرابع، لأ، أنا كلهم بشوفهم مع بعض،
+
+101
+00:07:29,270 --> 00:07:34,890
+إذا هم مترددين مكانيا، يعني مكانهم مختلف في الفراغ
+
+102
+00:07:35,620 --> 00:07:39,580
+إذا في عندي هنا spatial frequency .. spatial
+
+103
+00:07:39,580 --> 00:07:43,140
+frequency تردد فراغي .. يعني في الفرق .. بس بنشافه
+
+104
+00:07:43,140 --> 00:07:47,700
+في نفس اللحظة .. هنا .. هنا .. بسمعهم مش في نفس
+
+105
+00:07:47,700 --> 00:07:52,020
+اللحظة .. بسمعهم في أزمنة مختلفة .. زمن الباء يسبق
+
+106
+00:07:52,020 --> 00:07:55,680
+زمن السين يسبق زمن الهاء .. وهذا هيك بيختلف الصوت
+
+107
+00:07:55,680 --> 00:08:00,620
+عن الصورة .. إذا just as sound is a mixture of
+
+108
+00:08:00,620 --> 00:08:05,960
+frequencies بالضبط زي ما هو الصوت عبارة عن خليط من
+
+109
+00:08:05,960 --> 00:08:10,140
+الترددات so are images أيضا ال images عبارة عن
+
+110
+00:08:10,140 --> 00:08:13,500
+خليط من الترددات طب إيش بيفرّقوا عن بعض؟ whereas
+
+111
+00:08:13,500 --> 00:08:19,160
+sound is a mixture of temporal frequencies في
+
+112
+00:08:19,160 --> 00:08:23,980
+الوقت اللي أنه الصوت فيه عبارة عن خليط من ترددات
+
+113
+00:08:23,980 --> 00:08:28,080
+زمانية ال images are a mixture of spatial
+
+114
+00:08:28,080 --> 00:08:33,280
+frequency الصورة عبارة .. هي صورة أشخاص عبارة عن
+
+115
+00:08:33,280 --> 00:08:37,460
+خليط من الترددات المكانية، هي تردد اثنين، ثلاثة،
+
+116
+00:08:37,460 --> 00:08:41,660
+أربعة، خمسة، ستة، سبعة، يعني وحدات الصورة بتتردد،
+
+117
+00:08:41,660 --> 00:08:46,340
+يعني عندي كذا جزء من الصورة مختلف عن بعض البعض،
+
+118
+00:08:46,340 --> 00:08:51,610
+طيب an image of single spatial frequency always has
+
+119
+00:08:51,610 --> 00:08:55,730
+the same spatial frequency as the original but
+
+120
+00:08:55,730 --> 00:08:59,170
+with lower contrast هذه جملة مفروض احنا نفهمها
+
+121
+00:08:59,170 --> 00:09:03,170
+تماماً وهي جملة غاية في البساطة بس غاية في
+
+122
+00:09:03,170 --> 00:09:06,910
+الأهمية إيش يعني image of a single spatial
+
+123
+00:09:06,910 --> 00:09:11,390
+frequency always has the same spatial frequency as
+
+124
+00:09:11,390 --> 00:09:16,490
+the original but with lower contrast لما بنقول
+
+125
+00:09:16,490 --> 00:09:23,370
+إنسان أو .. أو فيه object تم تصويره، تردد هذا ال
+
+126
+00:09:23,370 --> 00:09:28,470
+object زي ما هو في الأصل، هينتقل للصورة، بمعنى
+
+127
+00:09:28,470 --> 00:09:33,410
+آخر، هدول الست رجال التقطنا لهم صورة، نفترض إنه
+
+128
+00:09:33,410 --> 00:09:37,050
+هذه مش صورة، هذه ال object الحقيقي، والتقطنا لهم
+
+129
+00:09:37,050 --> 00:09:43,270
+صورة كلهم مع بعض، الصورة هيكون عدد الرجال فيها 6 مش
+
+130
+00:09:43,270 --> 00:09:49,830
+هينقص يصير 5 ولا هيزيد يصير 7 إذا ال frequency ال
+
+131
+00:09:49,830 --> 00:09:53,430
+spatial frequency has the same spatial frequency
+
+132
+00:09:53,430 --> 00:09:58,050
+as the original object ال image ال frequency فيها
+
+133
+00:09:58,050 --> 00:10:02,850
+زي ال object بالضبط عمره ما وقف شخصين أو ثلاثة و
+
+134
+00:10:02,850 --> 00:10:06,470
+اتصوروا ونقصوا في العدد في الصورة أو زادوا في
+
+135
+00:10:06,470 --> 00:10:10,400
+العدد إذا .. إذا عدسة الكاميرا أو عدسة ال optical
+
+136
+00:10:10,400 --> 00:10:16,680
+system جابت أربعة أشخاص جابت أربعة أشخاص فهيطلع في
+
+137
+00:10:16,680 --> 00:10:21,420
+الصورة أربعة أشخاص إذا العدسة التقطت الضوء اللي جاي
+
+138
+00:10:21,420 --> 00:10:25,300
+من عشرة أشخاص فهيطلع في الصورة عشرة أشخاص بالتالي ال
+
+139
+00:10:25,300 --> 00:10:28,800
+frequency هنا لما بنقول single spatial frequency
+
+140
+00:10:28,800 --> 00:10:33,360
+مش مقصود فيها شخص واحد واقف لأ يعني تردد معين تردد
+
+141
+00:10:33,360 --> 00:10:38,600
+معين التردد نفسه بيضل زي ما هو في الصورة طب إيش
+
+142
+00:10:38,600 --> 00:10:43,700
+اللي بيختلف؟ العدد زي ما هو هاي ست أشخاص واقفين
+
+143
+00:10:43,700 --> 00:10:48,440
+صورناهم والتقطنا صورة طلعت في الصورة ست أشخاص، طب
+
+144
+00:10:48,440 --> 00:10:53,240
+إيش اللي بيختلف؟ اللي بيختلف ال contrast التباين
+
+145
+00:10:53,240 --> 00:10:58,900
+الوضوح، وضوح الست أشخاص في الصورة مهما كانت الصورة
+
+146
+00:10:58,900 --> 00:11:03,180
+واضحة، لا يقارب مائة بالمئة، يعني وضوحهم زي وضوح ال
+
+147
+00:11:03,180 --> 00:11:08,420
+object وعشان هيك بنقول أنه مستحيل الصورة تكون مائة
+
+148
+00:11:08,420 --> 00:11:12,980
+بالمئة مطابقة لل object مش معناته أنه العدد هيقل
+
+149
+00:11:12,980 --> 00:11:17,700
+.. مش معناته أنه العدد هيقل ناس تخرجت من الجامعة،
+
+150
+00:11:17,700 --> 00:11:22,340
+خمسة أصدقاء وفي يوم التخرج جاهم بدنا نجتمع نلتقط مع
+
+151
+00:11:22,340 --> 00:11:29,060
+بعضنا صور تذكارية في يعني ساحات الجامعة كذكرى الخمسة
+
+152
+00:11:29,060 --> 00:11:33,840
+أشخاص الأصدقاء لما بيتصوروا بيطلع في الصورة عدد
+
+153
+00:11:33,840 --> 00:11:38,380
+خمسة أشخاص هم نفسهم ما بيصيروش أربعة ولا ثلاثة ولا
+
+154
+00:11:38,380 --> 00:11:41,800
+اثنين ولا واحد وما بيزيدوش يصيروا ستة وسبعة وثمانية
+
+155
+00:11:41,800 --> 00:11:45,740
+وتسعة إذا التردد ال spatial frequency في الصورة
+
+156
+00:11:45,740 --> 00:11:49,400
+هو نفسه اللي في ال object بس مش معناته هيك أن أقول
+
+157
+00:11:49,400 --> 00:11:52,860
+أن الصورة تشبه ال object مائة بالمئة هي تشبه مائة
+
+158
+00:11:52,860 --> 00:11:58,070
+بالمئة بالعدد بس ال contrast هيكون أقل ال contrast
+
+159
+00:11:58,070 --> 00:12:01,750
+هيكون أقل مستحيل ال contrast يكون مائة بالمئة زي
+
+160
+00:12:01,750 --> 00:12:04,690
+ال object مائة بالمئة زي ال object وهذه معنى
+
+161
+00:12:04,690 --> 00:12:08,210
+العبارة أن أن image of single spatial frequency لو
+
+162
+00:12:08,210 --> 00:12:13,780
+عندنا image بتردد معين بتردد معين طبعا هنا سمينا
+
+163
+00:12:13,780 --> 00:12:16,500
+single لأنهم ما بتتغيرش الثلاثة ثلاثة، الأربعة
+
+164
+00:12:16,500 --> 00:12:20,160
+أربعة، العشرة عشرة، المائة مائة، ما بتتغير بين
+
+165
+00:12:20,160 --> 00:12:23,720
+لحظة والأخرى، إذا an image of single spatial
+
+166
+00:12:23,720 --> 00:12:28,380
+frequency always has the same spatial frequency as
+
+167
+00:12:28,380 --> 00:12:32,160
+the original object، بس اللي بيختلف إنها ال image
+
+168
+00:12:32,160 --> 00:12:36,820
+بتكون lower contrast إذا ما قورنت بال object، إذا
+
+169
+00:12:36,820 --> 00:12:42,050
+ما قورنت بال object، يعني هون ثلاثة أشخاص نفرض هدول
+
+170
+00:12:42,050 --> 00:12:46,730
+ال object وهي صورتهم هيكون
+
+171
+00:12:46,730 --> 00:12:51,740
+الصورة فيها نفس ال frequency ثلاثة أشخاص وبينهم
+
+172
+00:12:51,740 --> 00:12:55,480
+فراغين ثلاثة أشخاص وبينهم فراغين إذا ال frequency
+
+173
+00:12:55,480 --> 00:12:59,560
+ما تغيرت ولكن إيش اللي تغير ال contrast هون ال
+
+174
+00:12:59,560 --> 00:13:03,000
+contrast فبالتالي أنا حاولت طبعا أن أجلي ال
+
+175
+00:13:03,000 --> 00:13:06,600
+contrast هون يمكن واضحة في الخلفية بتاعتهم اللي هي
+
+176
+00:13:06,600 --> 00:13:10,380
+الجدار اللي وراهم هون الجدار حاولت أن أعمل أقل
+
+177
+00:13:10,380 --> 00:13:16,000
+contrast بقدر ما ساعدتني ال powerpoint فبالتالي ال
+
+178
+00:13:16,000 --> 00:13:22,570
+contrast بيكون أقل من من ال original object من ال
+
+179
+00:13:22,570 --> 00:13:27,550
+original object هون صورة بتوضح قضية ال frequency وقضية
+
+180
+00:13:27,550 --> 00:13:31,390
+وقضية ال contrast قضية ال frequency وقضية ال
+
+201
+00:14:52,640 --> 00:14:55,920
+higher contrast الـ left هنا higher contrast طيب
+
+202
+00:14:55,920 --> 00:15:00,420
+the left and the right الـ left و الـ right panels have
+
+203
+00:15:00,420 --> 00:15:04,020
+same contrast هنا نفس الـ contrast نفس الـ contrast
+
+204
+00:15:04,020 --> 00:15:09,530
+نفس التباين نفس الوضوح بين الـ light و الـ dark bars
+
+205
+00:15:09,530 --> 00:15:15,090
+but the right has lower frequency lower frequency
+
+206
+00:15:15,090 --> 00:15:19,090
+هنا هنا في اتفاق في الـ contrast بس اختلاف في الـ
+
+207
+00:15:19,090 --> 00:15:23,430
+frequency هنا اتفاق في الـ frequency بس اختلاف في
+
+208
+00:15:23,430 --> 00:15:29,310
+الـ contrast in other words هذا كلام إكمال للجملة
+
+209
+00:15:29,310 --> 00:15:35,400
+المهمة اللي حكيناها بعبارة أخرى، the spatial
+
+210
+00:15:35,400 --> 00:15:38,920
+frequency does not change from the original object
+
+211
+00:15:38,920 --> 00:15:42,740
+to the image، but the contrast does، الـ spatial
+
+212
+00:15:42,740 --> 00:15:48,700
+frequency ما بتتغيرش من الـ object للـ image الـ image
+
+213
+00:15:48,700 --> 00:15:52,200
+بتاعة تلت أشخاص هيكون فيها تلت أشخاص، الـ image
+
+214
+00:15:52,200 --> 00:15:55,620
+بتاعة مائة شخص هيكون فيها مائة شخص، الـ image بتاعة
+
+215
+00:15:55,620 --> 00:15:58,860
+عشر سيارات هيكون فيها عشر سيارات، إذا الـ frequency
+
+216
+00:15:58,860 --> 00:16:02,300
+نفس الـ frequency، مين اللي بتغير؟ الـ contrast،
+
+217
+00:16:02,300 --> 00:16:05,960
+بتغير، بيزيد ولا بينقص؟ لأ، بينقص، دائماً يعتبر الـ
+
+218
+00:16:05,960 --> 00:16:09,320
+object الـ contrast بتاعه الـ object الحقيقي يعتبر
+
+219
+00:16:09,320 --> 00:16:14,060
+standard، يعتبر مائة بالمائة بينما الصورة مهما كانت 
+
+220
+00:16:14,060 --> 00:16:16,980
+واضحة لازم تكون أقل منه ممكن تكون تسعة وتسعين
+
+221
+00:16:16,980 --> 00:16:20,440
+وتسعة من عشرة في المئة من الـ contrast بس بتكونش
+
+222
+00:16:20,440 --> 00:16:24,440
+مائة بالمائة زي الـ object إذا a photograph will
+
+223
+00:16:24,440 --> 00:16:33,980
+always .. always .. will always ..
+
+224
+00:16:33,980 --> 00:16:38,120
+will always have less contrast than the original
+
+225
+00:16:38,120 --> 00:16:38,920
+object
+
+226
+00:16:41,140 --> 00:16:44,860
+عنا original object صورناه بكاميرا ألف و بكاميرا
+
+227
+00:16:44,860 --> 00:16:49,600
+باء الكاميرا ألف أعطتني 
+
+228
+00:16:49,600 --> 00:16:55,740
+92% contrast بينما الكاميرا باء أعطتني 88% contrast
+
+229
+00:16:55,740 --> 00:16:58,960
+مقارنة مع الـ object إذا الكاميرا ألف أفضل إذا الـ
+
+230
+00:16:58,960 --> 00:17:03,680
+كاميرا ألف أفضل إذا one lens might image a single
+
+231
+00:17:03,680 --> 00:17:09,140
+spatial frequency عنا عدسة صورتلي تردد ما لـ object
+
+232
+00:17:10,940 --> 00:17:15,660
+تردد فراغي مال object تمام نفرض أربع أشخاص واقفين
+
+233
+00:17:15,660 --> 00:17:21,500
+ونقلت 92% من الـ contrast يعني التباين في الصورة 92
+
+234
+00:17:21,500 --> 00:17:26,980
+% مقارنة مع الـ object whereas another lens might
+
+235
+00:17:26,980 --> 00:17:32,180
+image the same frequency الـ 88% contrast نفس
+
+236
+00:17:32,180 --> 00:17:36,580
+الكاميرا رقم اتنين صورنا فيها الأربع أشخاص كان في
+
+237
+00:17:36,580 --> 00:17:42,020
+صورتهم فيه تباين 88% مقارنة مع الـ original object
+
+238
+00:17:42,020 --> 00:17:45,200
+إذا الكاميرا ألف هي أفضل من الكاميرا باء أو الـ lens
+
+239
+00:17:45,200 --> 00:17:50,400
+ألف هي أفضل من ناحية quality من الكاميرا أو من الـ
+
+240
+00:17:50,400 --> 00:17:55,080
+lens باء، the ratio of image contrast divided by
+
+241
+00:17:55,080 --> 00:18:01,540
+object contrast اللي هي 88% و 92% في المثال السابق
+
+242
+00:18:01,540 --> 00:18:08,060
+88% و 92% اللي هو نسبة الـ contrast في الـ image على
+
+243
+00:18:08,060 --> 00:18:11,040
+نسبة الـ contrast في الـ object is called the
+
+244
+00:18:11,040 --> 00:18:16,360
+transfer factor ليش بنسميه transfer factor؟
+
+245
+00:18:16,360 --> 00:18:19,460
+because it measures how well the contrast of a
+
+246
+00:18:19,460 --> 00:18:22,500
+single spatial frequency is transferred from the
+
+247
+00:18:22,500 --> 00:18:23,500
+object to the image
+
+248
+00:18:26,830 --> 00:18:32,170
+العدسة الأولى نقلت لي .. نقلت لي من الـ .. الـ
+
+249
+00:18:32,170 --> 00:18:36,510
+contrast بتاع الـ object اللي هو 100% نقلت لي 92% و
+
+250
+00:18:36,510 --> 00:18:40,930
+فقد من الـ contrast 8% إذا بنسميه transfer
+
+251
+00:18:40,930 --> 00:18:44,950
+factor الـ transfer factor هو جداش فيه contrast في
+
+252
+00:18:44,950 --> 00:18:47,610
+الـ image بجسمه على الـ contrast بتاع الـ object اللي
+
+253
+00:18:47,610 --> 00:18:53,730
+هو 100% هي دي نقلت لي 92 من المئة يعني 92 على 100
+
+254
+00:18:53,730 --> 00:18:58,810
+فهي الـ transfer factor بتاعها 92% الكاميرا الثانية
+
+255
+00:18:58,810 --> 00:19:01,570
+أو العدسة الثانية نقلت لي من الـ contrast بتاع الـ
+
+256
+00:19:01,570 --> 00:19:08,160
+object اللي هو 100% نقلت 88% وفقد 12% إذا هذا يسمى
+
+257
+00:19:08,160 --> 00:19:11,400
+للـ transfer factor is called transfer factor اللي
+
+258
+00:19:11,400 --> 00:19:15,760
+هو الـ ratio معدل أو نسبة الـ image contrast في
+
+259
+00:19:15,760 --> 00:19:20,100
+الـ image على الـ object contrast في المقام الـ object
+
+260
+00:19:20,100 --> 00:19:23,790
+contrast المعروف إنه 100 فبالتالي it's called the
+
+261
+00:19:23,790 --> 00:19:28,330
+transfer factor because it measures the how well
+
+262
+00:19:28,330 --> 00:19:31,590
+the contrast يعني كيف اتنقل الـ contrast طبعاً لـ
+
+263
+00:19:31,590 --> 00:19:35,570
+single spatial frequency لتردد ما is transferred
+
+264
+00:19:35,570 --> 00:19:39,250
+from the object to the image طيب، الآن العلماء
+
+265
+00:19:39,250 --> 00:19:43,790
+سألوا أنفسهم سؤال، الآن عندنا عدسة واحدة، ليه
+
+266
+00:19:43,790 --> 00:19:47,570
+العدسة الأولى، هناخدها، بتنقل الـ contrast اتنين
+
+267
+00:19:47,570 --> 00:19:52,350
+وتسعين في المئة لما يكون في عندي تلت أشخاص واقفين
+
+268
+00:19:52,350 --> 00:19:59,710
+هاي
+
+269
+00:19:59,710 --> 00:20:08,970
+عندي شخص بس فلينا نعمل سماكة أكثر تلاتة
+
+270
+00:20:08,970 --> 00:20:13,170
+تمام هاي .. هاي الـ object الـ original object
+
+271
+00:20:20,770 --> 00:20:25,650
+هذه الـ original object تلت أشخاص لما صورناهم
+
+272
+00:20:25,650 --> 00:20:34,410
+بعدسة لما صورناهم بعدسة هذه
+
+273
+00:20:34,410 --> 00:20:35,010
+العدسة
+
+274
+00:20:46,490 --> 00:20:49,530
+تكوينات ليه صورة؟ بغض النظر الصورة مجلوبة، عدلة،
+
+275
+00:20:49,530 --> 00:20:53,070
+هذه مش قضية، هنرسمها عدلة بس لإنه مش موضوعنا
+
+276
+00:20:53,070 --> 00:20:58,790
+Geometric Optics هرسمته متقطع عشان أقول الـ
+
+277
+00:20:58,790 --> 00:21:03,650
+contrast فيها مش 100% طبعا
+
+278
+00:21:03,650 --> 00:21:06,410
+الـ frequency هتظل واحدة الـ frequency الـ
+
+279
+00:21:06,410 --> 00:21:09,590
+magnification ممكن يختلف بس الـ frequency واحدة
+
+280
+00:21:09,590 --> 00:21:12,430
+يعني إننا تلت تلت أشخاص واقفين و تصوروا بعدث
+
+281
+00:21:12,430 --> 00:21:16,230
+الكاميرا و مش هيطلعوا أربع أشخاص طيب في الحالة هاي
+
+282
+00:21:16,230 --> 00:21:23,970
+هنتج 92% نسبة contrast بواسطة العدسة هاي طيب هنضل
+
+283
+00:21:23,970 --> 00:21:29,570
+على نفس العدسة بس إيش اللي هنعمله؟ هنزود الـ
+
+284
+00:21:29,570 --> 00:21:33,690
+frequency بتاعة الـ object هنزود الـ frequency بتاعة
+
+285
+00:21:33,690 --> 00:21:34,350
+الـ object
+
+286
+00:21:37,280 --> 00:21:41,120
+بنخلي هاي شخص اتنين تلاتة أربعة والآن العلماء
+
+287
+00:21:41,120 --> 00:21:43,880
+طلعوا يطرحوا طبعاً حقيقي زيد عندي هنا صار عندي هنا
+
+288
+00:21:43,880 --> 00:21:48,400
+شخص اتنين تلاتة أربعة خمس ست سبعة ثمانية تسعة عشر
+
+289
+00:21:48,400 --> 00:21:53,060
+لذا هدول بدي أزيدهم أيضاً لعشرة طبعا
+
+290
+00:22:07,790 --> 00:22:10,610
+هيكونوا بنفس العدد لأنه نفس الـ frequency
+
+291
+00:22:19,100 --> 00:22:22,800
+وصلنا لعشرة هي أربعة عندي، هنا خمس، ست، سبعة،
+
+292
+00:22:22,800 --> 00:22:27,680
+ثمانية، تسعة، عشر، إذا عشر عشرة وعشر، تمام؟ إذا الـ
+
+293
+00:22:27,680 --> 00:22:31,120
+frequency بتتغيرش في الحالة الأولى لما كانت الـ
+
+294
+00:22:31,120 --> 00:22:35,580
+frequency قليلة التردد قليلة تلت أشخاص كان الـ
+
+295
+00:22:35,580 --> 00:22:39,480
+contrast اللي انتقل في الـ image 92% الآن السؤال
+
+296
+00:22:39,480 --> 00:22:43,780
+اللي طرحه العلماء على أنفسهم يا ترى لو زادت الـ
+
+297
+00:22:43,780 --> 00:22:47,940
+frequency بتاعة الـ object كانوا شخصين بدهم يتصوروا
+
+298
+00:22:47,940 --> 00:22:52,300
+في حفل تخرج والتقاطنا لهم أول صورة، هذه الصورة
+
+299
+00:22:52,300 --> 00:22:57,640
+اللي التقطناها لهم للشخصين فيها contrast 92%، بعدين
+
+300
+00:22:57,640 --> 00:23:00,280
+أتوا زملائهم التحقوا فيهم وقالوا بنا نتصور معاكم
+
+301
+00:23:00,280 --> 00:23:04,180
+زملائهم عشرة أو اثنين عشرة ه يطلع عند الـ
+
+302
+00:23:04,180 --> 00:23:06,940
+frequency هنا اثنا عشر هنا اثنا عشر، فالـ frequency ما فيش
+
+303
+00:23:06,940 --> 00:23:10,760
+فيها تغيير، نفس اللي التقط، نفس أعداد الترددات
+
+304
+00:23:10,760 --> 00:23:14,040
+هيكون نفس الأعداد، بس يا ترى هل الـ contrast هيضل
+
+305
+00:23:14,040 --> 00:23:21,320
+92% ولا هيتغير؟ وجدوا العلماء بالتجارب، بالبرهان
+
+306
+00:23:21,320 --> 00:23:25,440
+والتجربة، أنه كل ما زادت الـ frequency الـ contrast
+
+307
+00:23:25,440 --> 00:23:30,800
+بينقص يعني كان 92% لما كان 3 أشخاص نسبة الـ contrast
+
+308
+00:23:30,800 --> 00:23:35,560
+في الـ image لما صار 12 شخص أو 10 أشخاص هينقص عن 92%
+
+309
+00:23:35,560 --> 00:23:40,800
+ممكن يصير 90 أو 88 مثلاً لو صاروا 100 شخص بينقص
+
+310
+00:23:40,800 --> 00:23:45,180
+أكثر، إذا كل ما زادت الـ frequency نسبة قدرة العدسة
+
+311
+00:23:45,180 --> 00:23:49,540
+على نقل الـ contrast لـ transfer factor بيصير أقل،
+
+312
+00:23:49,540 --> 00:23:53,720
+بيصير أقل فبالتالي هذه القضية ضرورية إنه في علاقة
+
+313
+00:23:53,720 --> 00:23:58,780
+عكسية بين زيادة الـ frequency وقلة نقل الـ contrast
+
+314
+00:23:58,780 --> 00:24:04,700
+بواسطة العدسة الـ transfer factor it changes as the
+
+315
+00:24:04,700 --> 00:24:08,220
+spatial frequency it changes الـ transfer factor it
+
+316
+00:24:08,220 --> 00:24:11,760
+changes as the spatial frequency it changes كل ما
+
+317
+00:24:11,760 --> 00:24:15,600
+زادت الـ spatial frequency التردد الفراغي، عدد
+
+318
+00:24:15,600 --> 00:24:19,720
+العناصر في الـ object كل ما زاد هيضل .. أيضاً هيزيد
+
+319
+00:24:19,720 --> 00:24:22,800
+عدد العناصر في الـ image هيضلوا نفس الشيء أنه عندي
+
+320
+00:24:22,800 --> 00:24:25,880
+عشر عناصر في الـ object هيكون فيه عشر عناصر في الـ
+
+321
+00:24:25,880 --> 00:24:29,620
+image مية عنصر في الـ object أيضاً هيكون مية عنصر
+
+322
+00:24:29,620 --> 00:24:34,180
+بس بأقل contrast يعني كل ما زادت الـ frequency بينقص
+
+323
+00:24:34,180 --> 00:24:40,500
+قدرة العدسة أي optical system بتنقص قدرته على أنه
+
+324
+00:24:40,500 --> 00:24:44,120
+ينقل الـ contrast أنه ينقل الـ contrast وهذه قاعدة
+
+325
+00:24:44,120 --> 00:24:47,780
+عامة اللي احنا حكينا عنها الآن the transfer factor
+
+326
+00:24:47,780 --> 00:24:52,980
+decreases as spatial frequency increases أجوا
+
+327
+00:24:52,980 --> 00:25:00,420
+العلماء قالوا احنا بدنا نعمل رسم بياني graph وفي
+
+328
+00:25:00,420 --> 00:25:03,860
+الـ vertical axis في الـ y axis بتاعة هذا الرسم
+
+329
+00:25:03,860 --> 00:25:09,160
+البياني بدنا نحط لـ transfer factor قدرة العدسة على
+
+330
+00:25:09,160 --> 00:25:16,120
+نقل الـ contrast وفي الإحداثي الصيني أو الـ X في الـ Y
+
+331
+00:25:16,120 --> 00:25:21,120
+الـ transfer factor وفي الـ X اللي هو الـ spatial
+
+332
+00:25:21,120 --> 00:25:27,380
+frequency a graph plotting transfer factor on the
+
+333
+00:25:27,380 --> 00:25:31,220
+vertical axis
+
+334
+00:25:32,270 --> 00:25:36,030
+versus مقابل الـ spatial frequency التردد الفراغي
+
+335
+00:25:36,030 --> 00:25:40,170
+للعناصر on the horizontal axis هذا الـ graph أو هذا
+
+336
+00:25:40,170 --> 00:25:43,690
+الرسم البياني بيسموه modulation transfer function
+
+337
+00:25:43,690 --> 00:25:52,530
+modulation transfer function MTF إذا modulation
+
+338
+00:25:52,530 --> 00:25:56,810
+transfer factor هو الرسم البياني أو الخط البياني
+
+339
+00:25:56,810 --> 00:26:04,910
+اللي بيبين العلاقة بين transfer factor مع التردد،
+
+340
+00:26:04,910 --> 00:26:11,110
+مع التردد وهنشوف رسم بياني يوضح هذه العلاقة،
+
+341
+00:26:11,110 --> 00:26:16,480
+modulation is another word for contrast يعني بقدر
+
+342
+00:26:16,480 --> 00:26:22,020
+أقول modulation transfer function أو contrast
+
+343
+00:26:22,020 --> 00:26:25,600
+transfer function contrast transfer function يعني
+
+344
+00:26:25,600 --> 00:26:31,200
+جداش قدرة العدسة على نقل الـ contrast جداش قدرة
+
+345
+00:26:31,200 --> 00:26:34,280
+العدسة على نقل الـ contrast يا ترى هذه القدرة بتاعة
+
+346
+00:26:34,280 --> 00:26:38,650
+العدسة على نقل الـ contrast ثابتة ولا بتتغير بتتغير
+
+347
+00:26:38,650 --> 00:26:42,530
+الـ frequency؟ طبعا هي بتتغير بتتغير الـ frequency
+
+348
+00:26:42,530 --> 00:26:46,970
+بتتغير بتتغير الـ frequency طبعا قبل ما نكمل بدنا
+
+349
+00:26:46,970 --> 00:26:52,460
+نيجي لأ احنا مثلاً بنقول لما احنا بنصور أشخاص عديدين
+
+350
+00:26:52,460 --> 00:26:56,580
+يعني التردد high high frequency صورتهم بيكون فيها
+
+351
+00:26:56,580 --> 00:27:01,820
+contrast أقل مما لو احنا صورنا عدد أقل من الأشخاص
+
+352
+00:27:01,820 --> 00:27:04,920
+يعني التردد قليل بيكون higher contrast حدود
+
+353
+00:27:04,920 --> 00:27:09,240
+الرجلين في الصورة أوضح من الحدود طبعاً هذه بس مثال
+
+354
+00:27:09,530 --> 00:27:12,210
+يوضحني هذه الصورة مبروزة و هذه الصورة مبروزة،
+
+355
+00:27:12,210 --> 00:27:16,950
+القصد أن هنا الحدود أوضح، التباين أوضح، فهنا
+
+356
+00:27:16,950 --> 00:27:20,530
+التباين أقل وضوحاً، بس لتقريب المفهوم، ليش أقل
+
+357
+00:27:20,530 --> 00:27:24,030
+وضوحاً، مع أن هدول تصوروا، و هدول تصوروا بنفس
+
+358
+00:27:24,030 --> 00:27:28,610
+الكاميرا، بنفس ظروف الإضاءة، بنفس زاوية التصوير،
+
+359
+00:27:28,610 --> 00:27:33,820
+إلى آخره، طبعاً، لأن هدول التردد أو العناصر متكررة
+
+360
+00:27:33,820 --> 00:27:37,760
+أقل يعني التردد low low frequency بيكون high
+
+361
+00:27:37,760 --> 00:27:41,440
+contrast high frequency بيكون low contrast لنفس
+
+362
+00:27:41,440 --> 00:27:45,520
+العدسة يعني قدرة العدسة على نقل الـ contrast بتنقص
+
+363
+00:27:45,520 --> 00:27:49,320
+كل ما زادت الـ frequency كل ما زادت الـ frequency
+
+364
+00:27:50,610 --> 00:27:54,590
+فهذه هي المقصود إنه الـ transfer factor بينقص كل ما
+
+365
+00:27:54,590 --> 00:27:57,910
+زادت الـ special frequency العلاقة اللي بتربط الـ
+
+366
+00:27:57,910 --> 00:28:00,770
+transfer factor بالـ special frequency هي علاقة
+
+367
+00:28:00,770 --> 00:28:06,170
+عكسية يعني ممثلة بخط بياني أو برسم بياني هو الـ
+
+368
+00:28:06,170 --> 00:28:09,190
+modulation transfer function أو الـ contrast
+
+369
+00:28:09,190 --> 00:28:15,520
+transfer function واللي هنشوفها بعد شوية هي عند الـ
+
+370
+00:28:15,520 --> 00:28:18,560
+modulation transfer function أو الـ contrast
+
+371
+00:28:18,560 --> 00:28:23,460
+transfer function على الـ .. هنا الـ transfer
+
+372
+00:28:23,460 --> 00:28:27,660
+function نفسها جداش قدرة العدسة على أنها تنقل من
+
+373
+00:28:27,660 --> 00:28:32,200
+الـ contrast اللي في الـ object قدرتها 50% 40% 60%
+
+374
+00:28:32,200 --> 00:28:35,140
+أنها تنقل يعني لو صورنا object الـ contrast بتاعه
+
+375
+00:28:35,140 --> 00:28:40,030
+هيكون 100% الـ object هو الـ standard بعدسة بتنقل
+
+376
+00:28:40,030 --> 00:28:43,210
+خمسين في المئة لما الـ special frequency يكون اثنين
+
+377
+00:28:43,210 --> 00:28:46,070
+و بتنقل أربعين في المئة لما يزيد الـ special
+
+378
+00:28:46,070 --> 00:28:49,810
+frequency يعني مثلاً لو احنا طلعنا على الرسم المك
+
+401
+00:30:35,680 --> 00:30:39,320
+بتنخفض 20% من ال contrast اللي موجود في ال object
+
+402
+00:30:39,320 --> 00:30:42,900
+من ال object؟ ال object اللي هي ال lines هذه هذه
+
+403
+00:30:42,900 --> 00:30:47,820
+ال lines صورناها بالكاميرا A يعني .. يعني خلينا
+
+404
+00:30:47,820 --> 00:30:50,080
+احنا نرجع لو قلنا احنا I and D
+
+405
+00:30:57,900 --> 00:31:03,980
+بدنا نخفي، بس بدنا نحافظ على أنه هعندي one
+
+406
+00:31:03,980 --> 00:31:09,060
+أو الأفضل أنه
+
+407
+00:31:09,060 --> 00:31:18,960
+نأخذ الجزء هذا من الصورة و أنقله عند ال ..
+
+408
+00:31:18,960 --> 00:31:21,300
+هننقله لما عليه بعض الإجراءات
+
+409
+00:31:32,970 --> 00:31:37,210
+انعيد بس .. واحد اثنين .. واحد اثنين .. هاي جزئين
+
+410
+00:31:37,210 --> 00:31:43,190
+.. هاي ثلاثة .. هاي أربعة .. هاي خمسة .. هاي ستة
+
+411
+00:31:43,190 --> 00:31:48,650
+عند السودة هاي انعيد
+
+412
+00:31:48,650 --> 00:31:52,550
+.. واحد اثنين .. واحد اثنين .. هاي اثنتين .. واحد
+
+413
+00:31:52,550 --> 00:31:55,910
+اثنين .. واحد اثنين .. هاي أربعة .. واحد اثنين ..
+
+414
+00:31:55,910 --> 00:32:01,570
+واحد اثنين .. هذا الستة تمام نفرض هذه ال object
+
+415
+00:32:05,660 --> 00:32:14,060
+ممتد على تردد واحد ملي كل واحد ملي من الجسم فيه
+
+416
+00:32:14,060 --> 00:32:18,740
+تردد بالشكل هذا يعني
+
+417
+00:32:18,740 --> 00:32:22,480
+هذا ال object بدنا نصوره الآن بالكاميرا A وبدنا
+
+418
+00:32:22,480 --> 00:32:28,100
+نصوره بالكاميرا B وبدنا نصوره بالكاميرا C لو قلنا
+
+419
+00:32:28,100 --> 00:32:32,420
+جداش ال frequency عدينا ال frequency طلعت عندي 6
+
+420
+00:32:37,720 --> 00:32:41,660
+إذا ال frequency عندي ستة في ال millimeter ستة
+
+421
+00:32:41,660 --> 00:32:45,500
+إيش؟ ستة pairs .. ستة pairs line pairs يعني أبيض
+
+422
+00:32:45,500 --> 00:32:48,940
+مع أسود .. هذا one pair .. هذا one pair .. هاي
+
+423
+00:32:48,940 --> 00:32:51,380
+كمان one pair .. هاي اثنين .. هاي كمان one pair ..
+
+424
+00:32:51,380 --> 00:32:54,160
+هاي ثلاثة .. هاي كمان one pair أربعة .. هاي كمان
+
+425
+00:32:54,160 --> 00:32:58,040
+one pair خمسة و كمان one pair ستة .. line pairs
+
+426
+00:32:58,040 --> 00:33:00,600
+بال millimeter هاي ستة .. عند هذه .. عند هذا
+
+427
+00:33:00,600 --> 00:33:04,840
+التردد طبعًا في أجسام ثانية أقل ترددا وفي أجسام
+
+428
+00:33:04,840 --> 00:33:12,460
+ثانية أكثر ترددا بس احنا بدنا نقول عند تردد 6 line
+
+429
+00:33:12,460 --> 00:33:16,640
+pairs في الmillimeter ال camera A انخفضت لما صورنا
+
+430
+00:33:16,640 --> 00:33:19,820
+فيها هذا ال object انخفضت من ال contrast بتاعه 80%
+
+431
+00:33:20,600 --> 00:33:26,820
+بينما الكاميرا B على نفس التردد انخفضت 60% بينما
+
+432
+00:33:26,820 --> 00:33:34,240
+الكاميرا C انخفضت 20% أفضل كاميرا A وأسوأ كاميرا C و
+
+433
+00:33:34,240 --> 00:33:39,640
+A جاية في النص بينهم اللي هي B فبالتالي كل ما كان
+
+434
+00:33:39,640 --> 00:33:43,920
+ال modulation transfer function يعني مش منحني كثير
+
+435
+00:33:43,920 --> 00:33:48,160
+للأسفل حسب الرسم كل مكان أفضل .. إيه؟ ليش مش منحني
+
+436
+00:33:48,160 --> 00:33:51,600
+كثير للأسفل؟ لأنه كل ما زاد التردد في الثلاث
+
+437
+00:33:51,600 --> 00:33:54,220
+كاميرات .. في الثلاث كاميرات أو الثلاث optical
+
+438
+00:33:54,220 --> 00:33:57,770
+system بينخفض transfer function بيقل ال transfer
+
+439
+00:33:57,770 --> 00:34:03,030
+function يعني عند .. عند تردد أربعين عند تردد أربع
+
+440
+00:34:03,030 --> 00:34:07,290
+line pairs لـ ال millimeter ال camera A انخفضت لـ
+
+441
+00:34:07,290 --> 00:34:10,270
+تسعين في المئة ال camera B تقريبًا انخفضت خمسة و
+
+442
+00:34:10,270 --> 00:34:14,350
+ثمانين في المئة و ال camera C تقريبًا انخفضت خمسة و
+
+443
+00:34:14,350 --> 00:34:18,720
+ستين في المئة عـ جبال .. عـ جبال أربعة طبعًا لما بيزيد
+
+444
+00:34:18,720 --> 00:34:22,780
+التردد بيقل قدرة الكاميرات الثلاث على النقل بس
+
+445
+00:34:22,780 --> 00:34:27,860
+بتظهر A أفضل من B وC لو زاد التردد أكثر عن ثمانية
+
+446
+00:34:27,860 --> 00:34:32,850
+pairs أو عند 8 line pairs بالmillimeter الكاميرا A
+
+447
+00:34:32,850 --> 00:34:38,450
+بتنخفض 60% الكاميرا B بتنخفض تقريبًا 45% والكاميرا C
+
+448
+00:34:38,450 --> 00:34:44,770
+بتنخفض تقريبًا 35 أو 38% عـ جبلها فبالتالي هذه وسيلة
+
+449
+00:34:44,770 --> 00:34:50,570
+للمقارنة بين العدسات أو ال optical system المختلفة
+
+450
+00:34:50,570 --> 00:34:54,650
+إذا every lens has unique modulation transfer
+
+451
+00:34:54,650 --> 00:34:59,280
+function كل lens لها منحنى خاص فيها منحنى خاص فيه،
+
+452
+00:34:59,280 --> 00:35:02,760
+إذا every lens has unique modulation transfer
+
+453
+00:35:02,760 --> 00:35:06,260
+function and by comparing the modulation transfer
+
+454
+00:35:06,260 --> 00:35:09,600
+function of lenses it is possible to determine
+
+455
+00:35:09,600 --> 00:35:13,060
+which lens is better for an intended purpose، لو
+
+456
+00:35:13,060 --> 00:35:19,390
+واحد طلب مني أن أقارن بين A وB وC بده يشتري واحدة
+
+457
+00:35:19,390 --> 00:35:23,970
+من الثلاث كاميرات لغرض العمل أو ما شبه، هقوله
+
+458
+00:35:23,970 --> 00:35:27,790
+الكاميرا A هي الأفضل لأنها ال modulation transfer
+
+459
+00:35:27,790 --> 00:35:31,210
+function بتاعها أفضل، إيش يعني أفضل؟ يعني قدرتها
+
+460
+00:35:31,210 --> 00:35:34,990
+على نقل ال contrast مهما زادت التردادات ال special
+
+461
+00:35:34,990 --> 00:35:38,230
+frequency بتكون أفضل من غيرها من الثلاث من
+
+462
+00:35:38,230 --> 00:35:42,430
+الكاميرتين الباقيتين، فهذه القضية ضروري تكون واضحة
+
+463
+00:35:43,600 --> 00:35:46,240
+Like the point spread function اللي حكينا عنها
+
+464
+00:35:46,240 --> 00:35:48,780
+المرة الماضية في المحاضرات، the modulation
+
+465
+00:35:48,780 --> 00:35:52,320
+transfer function completely describes the imaging
+
+466
+00:35:52,320 --> 00:35:56,450
+properties of lens يعني زي ما ال point spread
+
+467
+00:35:56,450 --> 00:36:03,270
+function حددت حدود يعني صور النقاط بتاعة ال object
+
+468
+00:36:03,270 --> 00:36:08,230
+وحددت كل صورة كيف تعرجها وكيف مساحتها لكل نقطة في
+
+469
+00:36:08,230 --> 00:36:12,250
+ال object ال modulation transfer function بحدد ليه
+
+470
+00:36:12,250 --> 00:36:16,770
+قد إيش انخفض من ال contrast من ال object لـ ال image
+
+471
+00:36:16,770 --> 00:36:20,210
+إذا the modulation transfer function completely
+
+472
+00:36:20,210 --> 00:36:27,390
+describes the imaging الشيء الوحيد هو أن الشيء
+
+473
+00:36:27,390 --> 00:36:33,490
+يتعامل مع الشيء يتعامل مع الشيء يتعامل مع الشيء
+
+474
+00:36:33,490 --> 00:36:38,770
+يتعامل مع الشيء يتعامل مع الشيء يتعامل مع الشيء
+
+475
+00:36:38,770 --> 00:36:43,430
+يتعامل مع الشيء يتعامل مع الشيء يتعامل مع الشيء
+
+476
+00:36:43,430 --> 00:36:45,130
+يتعامل مع الشيء
+
+477
+00:36:48,280 --> 00:36:52,420
+يعني ال point spread function حسبناها و ممكن
+
+478
+00:36:52,420 --> 00:36:56,480
+نستنتج منها استنتاج بدون إجراء تجارب ال modulation
+
+479
+00:36:56,480 --> 00:36:59,560
+ال transfer function يقول هذه العدسة هتقدر تنقلي
+
+480
+00:36:59,560 --> 00:37:04,620
+مثلًا سبعين في المئة عند تردد كذا و هتنقلي مثلًا
+
+481
+00:37:04,620 --> 00:37:08,060
+خمسين في المئة عند تردد كذا و هكذا طبعًا يعني ممكن
+
+482
+00:37:08,060 --> 00:37:12,000
+يستنتج استنتاج من ال point spread function بواسطة
+
+483
+00:37:12,000 --> 00:37:15,520
+الـ Fourier transfer mathematics وهذا يعني خارج
+
+484
+00:37:15,520 --> 00:37:20,740
+نطاق الموضوع بتاعنا والناس اللي بيشتغلوا يعني في
+
+485
+00:37:20,740 --> 00:37:24,680
+علم الرياضيات بيستطيعوا أنهم يوصلوا لهذه القضية
+
+486
+00:37:24,680 --> 00:37:28,800
+طبعًا further details of this process are beyond
+
+487
+00:37:28,800 --> 00:37:31,760
+the scope of this discussion يعني مش داخلة في ال
+
+488
+00:37:31,760 --> 00:37:35,520
+geometric أو ال physical optics آخر حاجة بنحكيها
+
+489
+00:37:35,520 --> 00:37:40,870
+اليوم بنقول إن انسان أجرى على عينه مثلًا اليمين عملية
+
+490
+00:37:40,870 --> 00:37:46,430
+الليزك بدنا نشوف كيف بتحسن ال modulation transfer
+
+491
+00:37:46,430 --> 00:37:49,830
+function قدرة العين، ما هي العين optical system
+
+492
+00:37:49,830 --> 00:37:55,050
+العين قبل الليزك optical system وبعد الليزك
+
+493
+00:37:55,050 --> 00:37:58,610
+optical system بختلف عنه في الخصائص يعني بختلف عنه
+
+494
+00:37:58,610 --> 00:38:05,090
+في الجودة جاب للليزك هي pre-ليزك المربعات السوداء
+
+495
+00:38:05,090 --> 00:38:09,940
+اللي مشار إليها بالسهم الأصفر قدرة أو ال modulation
+
+496
+00:38:09,940 --> 00:38:14,720
+transfer function بتاعة العيان سيئة عند تردد 12
+
+497
+00:38:14,720 --> 00:38:21,680
+دورة 12 cycle لكل degree في الفراغ عند تردد 12
+
+498
+00:38:21,680 --> 00:38:25,660
+قدرتها 2 من 10 يعني 20% أنها تنخفض من ال contrast
+
+499
+00:38:25,660 --> 00:38:30,360
+بتاعة ال object اللي بتطلع عليه طيب بعد ال Lasik
+
+500
+00:38:30,360 --> 00:38:37,530
+post Lasik الدوائر عند تردد 12 أصبح تنخفض بدل 20%
+
+501
+00:38:37,530 --> 00:38:40,990
+أصبح تنخفض في ال image اللي هتطبع على ال retina
+
+502
+00:38:40,990 --> 00:38:49,250
+80% تحسنت من 20%Contrast لـ 80% Contrast هذه الـ
+
+503
+00:38:49,250 --> 00:38:51,710
+image .. هذه الـ image اللي سقطت على الشبكية جاب
+
+504
+00:38:51,710 --> 00:38:54,730
+العملية اللازق لهذا الإنسان أو لهذا العين لهذا الـ
+
+505
+00:38:54,730 --> 00:38:58,550
+optical system لأنه التردد ال .. تاع ال object
+
+506
+00:38:58,550 --> 00:39:03,350
+اللي بتطلع عليه العين تردده في الفراغ 12 cycles
+
+507
+00:39:03,350 --> 00:39:09,090
+لكل degree من الفراغ لكل زاوية one degree كان
+
+508
+00:39:09,090 --> 00:39:12,190
+الانخفاض 20% من ال contrast اللي موجود في ال object
+
+509
+00:39:13,900 --> 00:39:19,580
+طيب، الآن بعد ال Lasik أصبح ثمانين في المئة بنفس
+
+510
+00:39:19,580 --> 00:39:24,920
+التردد فبالتالي ال .. ال refractive procedures أو
+
+511
+00:39:24,920 --> 00:39:28,580
+عمليات ال laser vision correction بتساهم كثير في
+
+512
+00:39:28,580 --> 00:39:32,360
+تحسين ال contrast أو عملية نقل ال contrast من ال
+
+513
+00:39:32,360 --> 00:39:38,000
+object لـ ال image هيك احنا بنكون انتهينا من مادة ال
+
+514
+00:39:38,000 --> 00:39:40,840
+physical optics ويعطيكم العافية والسلام عليكم
+
+515
+00:39:40,840 --> 00:39:42,680
+ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/aLorsNBiAsc_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/aLorsNBiAsc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b0cceedca8dbfd080dbd99c04f38167b56e3bcf8
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/aLorsNBiAsc_postprocess.srt
@@ -0,0 +1,1300 @@
+1
+00:00:01,530 --> 00:00:05,410
+بسم الله الرحمن الرحيم بنستكمل محاضرات ال physical
+
+2
+00:00:05,410 --> 00:00:12,050
+optics واتوقفنا عند موضوع اللي هي صفات أو خصائص ال
+
+3
+00:00:12,050 --> 00:00:17,270
+laser بنقول contrary to common belief lasers are
+
+4
+00:00:17,270 --> 00:00:20,850
+not very efficient light sources بعض الناس بي ..
+
+5
+00:00:20,850 --> 00:00:24,610
+بيعتقد أنه ال laser light هو عبارة عن efficient
+
+6
+00:00:24,610 --> 00:00:30,370
+source بمعنى أنه الفعلية أو ال .. ال .. الكفاءة
+
+7
+00:00:30,740 --> 00:00:38,160
+بتاعت ال laser light يعني إيه بتستاهل كمية الطاقة
+
+8
+00:00:38,160 --> 00:00:43,320
+المنفقة أو المصروفة على إنتاج هذا ال laser لما
+
+9
+00:00:43,320 --> 00:00:49,040
+بنقول كفاءة الضوء يعني جدش أنا يعني بذلتمصادر طاقة
+
+10
+00:00:49,040 --> 00:00:53,560
+عشان أحصل على هذا الضوء والله إذا الإضاءة أو كمية
+
+11
+00:00:53,560 --> 00:00:57,240
+الإضاءة اللي باخدها من هذا الضوء أو من هذا المصدر
+
+12
+00:00:57,240 --> 00:01:04,980
+اللي أنا بذلت فيه صور أخرى من الطاقة إذا كان يعني
+
+13
+00:01:04,980 --> 00:01:10,650
+..كمية الإضاءة يعني كافية فساعتها بقول انا والله
+
+14
+00:01:10,650 --> 00:01:14,490
+efficient light source مثال على ذلك بنقول لو احنا
+
+15
+00:01:14,490 --> 00:01:20,430
+جبنا مسباح كهربائي ويعني زودناه بكمية من الكهربا
+
+16
+00:01:20,430 --> 00:01:25,830
+عالية وبالنهاية ما أعطاني إضاءة كما يجب ساعتها
+
+17
+00:01:25,830 --> 00:01:29,050
+بنقول مش efficient light source يعني الكفاءة
+
+18
+00:01:29,050 --> 00:01:36,770
+بتاعته مش المرجوه مش المرجوهال laser light مش very
+
+19
+00:01:36,770 --> 00:01:42,250
+efficient light sources compared with the amount
+
+20
+00:01:42,250 --> 00:01:45,690
+of energy required to power a laser يعني أنا عشان
+
+21
+00:01:45,690 --> 00:01:53,110
+أنتجكمية laser بدي كمية من الطاقة عالية كتير عشان
+
+22
+00:01:53,110 --> 00:01:57,410
+أنتج قليل من ضوء ال laser إذا ال laser لا يعتبر
+
+23
+00:01:57,410 --> 00:02:01,130
+efficient light source compared with the amount of
+
+24
+00:02:01,130 --> 00:02:04,810
+energy required to power a laser the amount of
+
+25
+00:02:04,810 --> 00:02:10,590
+energy produced is modest فبالتالي لما أنا بد أحصل
+
+26
+00:02:10,590 --> 00:02:18,360
+على ضوء ال laserبدي أستخدم طاقة أخرى بكمية عالية
+
+27
+00:02:18,360 --> 00:02:22,800
+عشان أقدر أحصل على القليل من ال laser عشان أقدر
+
+28
+00:02:22,800 --> 00:02:27,040
+أحصل على القليل من طاقة ال laser the light
+
+29
+00:02:27,040 --> 00:02:29,660
+produced however has unique and useful
+
+30
+00:02:29,660 --> 00:02:33,000
+characteristics طيب مدام هيك يعني احنا اشي الفايدة
+
+31
+00:02:33,000 --> 00:02:39,250
+من ..إنتاج ال laser أو ضوء ال laser لأن ضوء ال
+
+32
+00:02:39,250 --> 00:02:44,110
+laser فيه صفات فريدة من نوعها لا تتوفر في مصادر
+
+33
+00:02:44,110 --> 00:02:48,410
+الضوء الأخرى فهذه الصفات احنا بدنا يعني نستعرضها
+
+34
+00:02:48,410 --> 00:02:54,010
+الآن laser light has very narrow bandwidth بمعنى
+
+35
+00:02:54,010 --> 00:02:58,090
+nearly single color or wholly monochromatic أول
+
+36
+00:02:58,090 --> 00:03:03,760
+صفة من صفات ال laser أنه ال bandwidth بتاعتهسيقشنز
+
+37
+00:03:03,760 --> 00:03:10,040
+دعاته very narrow band width بمعنى أنه في الأطوال
+
+38
+00:03:10,040 --> 00:03:14,420
+الموجية الموجودة في ضوء الليزر يعني قريبة من بعضها
+
+39
+00:03:14,420 --> 00:03:18,480
+لبعض أو تكاد تكون لون واحد فبالتالي narrow band مش
+
+40
+00:03:18,480 --> 00:03:23,660
+broad band هذه نقطة هذه النقطة بينتج عنها أنه في
+
+41
+00:03:23,660 --> 00:03:29,400
+عندي high temporal coherence الترابط الزماني بتاع
+
+42
+00:03:29,400 --> 00:03:36,570
+الموجات عالي بمعنى آخرإنه ال sections أيضا طويلة
+
+43
+00:03:36,570 --> 00:03:39,970
+.. ال sections طويلة في ال wave train زي ما حكينا
+
+44
+00:03:39,970 --> 00:03:46,010
+في المحاضرات السابقة .. في المحاضرات السابقة هنا
+
+45
+00:03:46,010 --> 00:03:52,340
+ناخد مثالهاي ال white light العادي، طبعا فيه
+
+46
+00:03:52,340 --> 00:03:56,880
+بيسموه polychromatic light، polychromatic light
+
+47
+00:03:56,880 --> 00:03:59,800
+يعني فيه أكتر من أطوا الموجية بتعطي شعور بألوان
+
+48
+00:03:59,800 --> 00:04:03,780
+مختلفة، هنا monochromatic light source بس مش laser
+
+49
+00:04:04,740 --> 00:04:08,940
+هنا ال laser light source هو monochromatic أيضا بس
+
+50
+00:04:08,940 --> 00:04:16,040
+يعني مترابطة الموجات مع بعضها البعض و in-phase و
+
+51
+00:04:16,040 --> 00:04:20,380
+in-phase هذه مقارنة بين أنواع مختلفة من مصادر
+
+52
+00:04:20,380 --> 00:04:25,120
+الضوء هنا أيضا أنواع مختلفة من ال laser light
+
+53
+00:04:25,120 --> 00:04:29,120
+color بناء على ال active medium الموجودة في الجهاز
+
+54
+00:04:29,120 --> 00:04:33,280
+ال active mediumاللي موجودة في جهاز الليزر، إذا
+
+55
+00:04:33,280 --> 00:04:36,560
+الليزر لاقيت أول صفة إنه monochromatic،
+
+56
+00:04:36,560 --> 00:04:40,220
+monochromatic يعني تقريبا في single frequency أو
+
+57
+00:04:40,220 --> 00:04:44,800
+single color، و ال bandwidth بتاعه very narrow،
+
+58
+00:04:44,800 --> 00:04:49,000
+very narrow ال
+
+59
+00:04:49,000 --> 00:04:54,030
+coherence link is relatively longAbout half the
+
+60
+00:04:54,030 --> 00:04:57,070
+length of the resonator cavity اللي هو الـ cavity
+
+61
+00:04:57,070 --> 00:05:00,530
+بتاع الليزر تقريبا ال coherence length بتاع عضو
+
+62
+00:05:00,530 --> 00:05:06,950
+الليزر تقريبا يكاد يصل إلى نصف طول ال cavity لنصف
+
+63
+00:05:06,950 --> 00:05:11,150
+طول ال cavity يعني تقريبا عدة سنتمتراتلما بنقول
+
+64
+00:05:11,150 --> 00:05:14,830
+بدنا نقارنه بال coherance length تاع ضوء الشمس
+
+65
+00:05:14,830 --> 00:05:19,530
+اللي هو يعاد تقريبا من .. من واحد لاتنين micron كل
+
+66
+00:05:19,530 --> 00:05:23,410
+section في ضوء الشمس واحد لاتنين micron لما
+
+67
+00:05:23,410 --> 00:05:29,610
+نقارنها باتنين او تلاتة صنطة اللي تقريبا في فرق
+
+68
+00:05:29,610 --> 00:05:33,830
+كبير جدافى الطول فى فرج كبير جدا فى الطول لإن
+
+69
+00:05:33,830 --> 00:05:38,370
+الصنط الواحد عشرة ملي والملي الواحد الف مايكرون
+
+70
+00:05:38,370 --> 00:05:42,390
+فالصنط الواحد بيصير عشر تلاف مايكرون فبالتالي ال
+
+71
+00:05:42,390 --> 00:05:46,250
+coherance length بتاع ال laser light أطول بكثير من
+
+72
+00:05:46,250 --> 00:05:51,330
+ال coherance length بتاع اللى هو الضوء العادي أو
+
+73
+00:05:51,330 --> 00:05:56,040
+ضوء الشمسLasers are the most intense source of
+
+74
+00:05:56,040 --> 00:06:01,180
+monochromatic light available أقوى مصدر للضوء أو
+
+75
+00:06:01,180 --> 00:06:04,960
+أشد مصدر للضوء لل monochromatic light هو ضوء ال
+
+76
+00:06:04,960 --> 00:06:08,520
+laser يعني هنا ضوء ال laser أو الضوء العادي
+
+77
+00:06:08,520 --> 00:06:13,020
+monochromatic وهنا ضوء ال laser أيضا monochromatic
+
+78
+00:06:13,020 --> 00:06:21,000
+أشد مصدر أو أشد طريقة للحصول على ال ..على اللي هو
+
+79
+00:06:21,000 --> 00:06:25,300
+monochromatic light هو إن هي استعمل ال laser، إذا
+
+80
+00:06:25,300 --> 00:06:29,000
+lasers are the most intense sources of
+
+81
+00:06:29,000 --> 00:06:32,880
+monochromatic light availableAlthough the total
+
+82
+00:06:32,880 --> 00:06:37,700
+energy in laser light may be slight، الكمية الكلية
+
+83
+00:06:37,700 --> 00:06:41,540
+لطاقة ال laser ممكن تكون طائلة جدا، بس إلها ميزة
+
+84
+00:06:41,540 --> 00:06:45,480
+إنه it can be focused on very small area، وهذا
+
+85
+00:06:45,480 --> 00:06:49,500
+اللي بيفرق ال monochromatic light source العادي عن
+
+86
+00:06:49,500 --> 00:06:53,300
+ال monochromatic طبعا أو عن ال laser lightإحنا الـ
+
+87
+00:06:53,300 --> 00:06:56,300
+monochromatic light source صعب إن أنا أعمله
+
+88
+00:06:56,300 --> 00:06:59,440
+focusing على area صغيرة ممكن الإنسان يقول أنا ممكن
+
+89
+00:06:59,440 --> 00:07:05,460
+أعمل pen hole ويعني أخلي الضوء يعني على مساحة
+
+90
+00:07:05,460 --> 00:07:10,340
+صغيرة مظبوط ولكن ال diffraction أيضا هيفرد المساحة
+
+91
+00:07:10,340 --> 00:07:14,600
+هي نقطة بس ال laser light المساحة اللي .. اللي ..
+
+92
+00:07:14,600 --> 00:07:18,060
+اللي ممكن أركز فيها ممكن تكون غاية في الصغر زي ما
+
+93
+00:07:18,060 --> 00:07:23,760
+هنشوف بعد شوية .. زي ما هنشوف بعد شوية إذاوالتطبيق
+
+94
+00:07:23,760 --> 00:07:26,100
+الوضعي في الوضع الوضعي في الوضع الوضع الوضع الوضع
+
+95
+00:07:26,100 --> 00:07:34,920
+الوضع الوضع الوضع الوضع الوضع الوضعفي حاجة اسمها
+
+96
+00:07:34,920 --> 00:07:39,080
+ال energy الطاقة في حاجة اسمها energy density
+
+97
+00:07:39,080 --> 00:07:43,180
+كثافة الطاقة ايش هي ال energy density اللي هي
+
+98
+00:07:43,180 --> 00:07:46,440
+كثافة الطاقة يعني ال energy per square centimeter
+
+99
+00:07:46,440 --> 00:07:50,880
+يعني كل centimeter من النسيج اللي انا موجه عليه ال
+
+100
+00:07:50,880 --> 00:07:54,860
+laser او اللي موجه عليه ضوء عادي قداش وصله كمية
+
+101
+00:07:54,860 --> 00:07:58,060
+الطاقة فهذه بيسموها ال energy density اللي هي
+
+102
+00:07:58,320 --> 00:08:03,420
+الطاقة لكل centimeter مربع
+
+103
+00:08:03,420 --> 00:08:07,080
+من المنطقة اللي أنا موجه عليها ال laser طبعا ال
+
+104
+00:08:07,080 --> 00:08:11,440
+energy density فيه لها مصطلح وسموه ال radiance
+
+105
+00:08:11,440 --> 00:08:16,320
+التشعيع يعني جداش انا وصلت اشعة من ضوء ال laser او
+
+106
+00:08:16,320 --> 00:08:22,220
+من اي ضوء اخرجداش انا وصلت لكل centimeter مربع من
+
+107
+00:08:22,220 --> 00:08:26,120
+المادة او من النسيج اللي انا بدأ اوجه عليه ال
+
+108
+00:08:26,120 --> 00:08:29,760
+laser التشعيع فبالتالي ال radiance اللي هو ال
+
+109
+00:08:29,760 --> 00:08:33,500
+energy density طب عمكن الإنسان يقول طب ماهيش الفرق
+
+110
+00:08:33,500 --> 00:08:36,360
+بين ال energy و ال energy density ما كل واحد لأ
+
+111
+00:08:36,360 --> 00:08:42,780
+انا عندى مثلا طاقة ميت جول ميت جول وزعتها على مائة
+
+112
+00:08:42,780 --> 00:08:49,860
+متر مربع مائة متر مربعكل متر هيصلوا تقريبا جول من
+
+113
+00:08:49,860 --> 00:08:54,660
+طاقة الضوء، من طاقة الضوء، طيب المائة جول بزعتها
+
+114
+00:08:54,660 --> 00:08:58,860
+على متر واحد، اذا هذا المتر هيصلوا مائة جول، مائة
+
+115
+00:08:58,860 --> 00:09:02,340
+ضعف، فبالتالي الطاقة هي واحدة، ولكن ال energy
+
+116
+00:09:02,340 --> 00:09:06,740
+density، ال energy density اختلفت، يعني قداش بيصل
+
+117
+00:09:07,240 --> 00:09:11,940
+من الطاقة لكل سنتمتر مربع أو بنسميها مش energy
+
+118
+00:09:11,940 --> 00:09:15,460
+density اللي هي مصطلح آخر ال radiance أو التشعيع
+
+119
+00:09:15,460 --> 00:09:19,820
+بمعنى كده وصلت كمية الإشعاعات تاعة ال laser أو
+
+120
+00:09:19,820 --> 00:09:27,000
+كمية الضوء تاعة ال laser لكل سنتمترمن النسيج اللي
+
+121
+00:09:27,000 --> 00:09:30,820
+انا موجه ال laser عليه هنا في رسمة بتوضح هذه
+
+122
+00:09:30,820 --> 00:09:37,260
+القضية قضية ال irradiance يعني انا عندي مساحة عندي
+
+123
+00:09:37,260 --> 00:09:41,280
+مساحة ال irradiance هي عندي انا centimeter مربع
+
+124
+00:09:41,280 --> 00:09:46,000
+مرسوم باللون الأحمرقداش طاقة وصل لهذا ال
+
+125
+00:09:46,000 --> 00:09:48,560
+centimeter المربع هذا اللي بيسموه ال irradiance
+
+126
+00:09:48,560 --> 00:09:52,560
+طبعا ال irradiance في منه direct irradiance وفي
+
+127
+00:09:52,560 --> 00:09:55,540
+عندى diffuse irradiance وفي reflected irradiance
+
+128
+00:09:55,540 --> 00:09:59,880
+يعني مثلا ضوء الشمس لما بيجي على المساحة هاي بشكل
+
+129
+00:09:59,880 --> 00:10:06,160
+مباشر بيسموه direct irradianceبتشتت بواسطة السحاب
+
+130
+00:10:06,160 --> 00:10:10,160
+أو أي شيء آخر بيسموه diffuse irradiance طب ضوء
+
+131
+00:10:10,160 --> 00:10:15,840
+الشمس سقط على أسطح عاكسة وانعكس باتجاه هذه المساحة
+
+132
+00:10:15,840 --> 00:10:19,540
+أيضا، هذا بيسموه reflected irradianceالمهم بغض
+
+133
+00:10:19,540 --> 00:10:23,740
+النظر عن نوع ال irradiance عن نوع التشعيع جداش وصل
+
+134
+00:10:23,740 --> 00:10:27,840
+كمية الطاقة لهذه المساحة لهذه النسيج او لهذه
+
+135
+00:10:27,840 --> 00:10:32,400
+القطعة هذا بيسموه ال irradiance بيسموه ال
+
+136
+00:10:32,400 --> 00:10:36,960
+irradiance او التشعيع او ال energy density لان كله
+
+137
+00:10:36,960 --> 00:10:43,920
+هيصل لمساحة معينة فبالتالي انا بقدر اخلي ال laser
+
+138
+00:10:43,920 --> 00:10:50,390
+light رغم ان طاقته slightslight يعني قليلة بقدر
+
+139
+00:10:50,390 --> 00:10:54,110
+أركز على مساحة قليلة جدا فأحصل على ال radiance
+
+140
+00:10:54,110 --> 00:10:58,190
+عالي فأحصل على ال radiance عالي يعني كثافة الطاقة
+
+141
+00:10:58,190 --> 00:11:02,790
+عالية جدا كثافة الطاقة عالية جدا وهذه من ضمن
+
+142
+00:11:02,790 --> 00:11:08,020
+الصفات بتاعة ال laserفي صفة تالتة ان ال laser
+
+143
+00:11:08,020 --> 00:11:12,940
+light is also highly directional يعني يمكن توجيهه
+
+144
+00:11:12,940 --> 00:11:18,500
+بشكل يعني ممتاز جدا وما بتشتتش مني and depending
+
+145
+00:11:18,500 --> 00:11:22,160
+on the design of the resonator may also be
+
+146
+00:11:22,160 --> 00:11:26,260
+polarized طبعا ال laser عبارة عن light بالنهاية
+
+147
+00:11:26,670 --> 00:11:30,550
+عبارة عن light و ال light إله electric field و إله
+
+148
+00:11:30,550 --> 00:11:35,010
+magnetic field ال electric field بتاعه ممكن يكون
+
+149
+00:11:35,010 --> 00:11:40,270
+بتغير بشكل عشوائي و هذا بيسموه randomly polarized
+
+150
+00:11:40,270 --> 00:11:44,550
+light أو بي .. بي .. بيتخذ اتجاه منتظم بيسموه
+
+151
+00:11:44,550 --> 00:11:48,400
+linearly polarized lightضوء الليزر ممكن يكون
+
+152
+00:11:48,400 --> 00:11:53,380
+randomly polarized وممكن يكون linearly polarized
+
+153
+00:11:53,380 --> 00:11:58,820
+بناء على تصميم ال resonator cavity أو اللي هو ال
+
+154
+00:11:58,820 --> 00:12:03,060
+laser cavity يعني ممكن يكون polarized بس بغض النظر
+
+155
+00:12:03,060 --> 00:12:08,380
+سواء polarized أو randomly polarized الصفة التالتة
+
+156
+00:12:08,380 --> 00:12:12,080
+في ال laser light انه highly directional ..highly
+
+157
+00:12:12,080 --> 00:12:14,500
+directional وبالتالي
+
+158
+00:12:17,280 --> 00:12:21,980
+يعني ممكن توجيهه في الاتجاه اللي بدنا إياه بدون ما
+
+159
+00:12:21,980 --> 00:12:26,340
+يتشدد منها إذا نرجع بس للصفات عشان نذكر فيها أول
+
+160
+00:12:26,340 --> 00:12:32,200
+صفة أنه monochromatic أول صفة أنه monochromatic
+
+161
+00:12:32,200 --> 00:12:39,140
+طبعا و تاني صفة أنه ال coherence link بتاعه طويل
+
+162
+00:12:39,140 --> 00:12:44,660
+relatively long coherence linkتالت .. تالت صفة إنه
+
+163
+00:12:44,660 --> 00:12:48,580
+بقدر أحصل بالليزر على high energy density، high ال
+
+164
+00:12:48,580 --> 00:12:52,120
+radiance، ليش؟ لأنه بقدر أعمله focusing on very
+
+165
+00:12:52,120 --> 00:12:55,940
+small area، إذن هذه الصفة التالتة الصفة الرابعة
+
+166
+00:12:55,940 --> 00:13:01,250
+إنه highly directionalhighly directional and may
+
+167
+00:13:01,250 --> 00:13:05,170
+be polarized may be polarized بنا على التصميم بتاع
+
+168
+00:13:05,170 --> 00:13:10,030
+اللي هو ال laser cavity بطريقة معينة ممكن احنا
+
+169
+00:13:10,030 --> 00:13:11,970
+نحصل على highly directional
+
+170
+00:13:16,200 --> 00:13:20,720
+أو احنا هو highly directional بس ممكن نحصل على
+
+171
+00:13:20,720 --> 00:13:24,640
+polarized laser light، polarized laser light فهذه
+
+172
+00:13:24,640 --> 00:13:27,840
+القضية ضرورية احنا نكون عارفينها، هذه الصفة
+
+173
+00:13:27,840 --> 00:13:32,960
+الرابعةالان طريقة عمل ال laser في طريقتين لعمل ال
+
+174
+00:13:32,960 --> 00:13:38,600
+laser ممكن تكون continuous laser أو pulsed laser
+
+175
+00:13:38,600 --> 00:13:41,760
+إيش يعني continuous laser أو pulsed laser نروح
+
+176
+00:13:41,760 --> 00:13:46,360
+للرسمة اللي بتوضح القضية هنا عندي continuous wave
+
+177
+00:13:46,360 --> 00:13:50,680
+laser beam و هنا pulsed laser beam عندي جهاز
+
+178
+00:13:50,680 --> 00:13:51,880
+بيشتغل على ال continuous
+
+179
+00:13:54,480 --> 00:14:00,260
+Wave أول ما بضغط على الذر بتاع ال laser عشان يبدأ
+
+180
+00:14:00,260 --> 00:14:04,960
+ال laser يعني بالإنتاج أو يبدأ خط ال laser أو ضوء
+
+181
+00:14:04,960 --> 00:14:10,860
+ال laser بالظهور ال laser طالما أنا ضغطه شغل .. هو
+
+182
+00:14:10,860 --> 00:14:14,240
+شغل ال output يعني ال laser اللي بطلع عندي من
+
+183
+00:14:14,240 --> 00:14:19,740
+الجهازبيضلوا شغال بدون انقطع طيب في عندي نوع اخر
+
+184
+00:14:19,740 --> 00:14:24,040
+او طريقة اخرى بيكون انا لما بدغط انا ضابط بس ال
+
+185
+00:14:24,040 --> 00:14:29,080
+laser بيطلع على دفعات يعني هنا طلع ال laser هنا
+
+186
+00:14:29,080 --> 00:14:33,380
+توقف هنا طلعت نبضة تانية من ال laser او دفقة تانية
+
+187
+00:14:33,380 --> 00:14:37,160
+او دفعة تانية من ال laser هنا توقف هنا طلعت دفعة
+
+188
+00:14:37,160 --> 00:14:41,140
+تالتة لو أخدت المتوسط بتاع ال power القدرة بتاعة
+
+189
+00:14:41,140 --> 00:14:45,700
+ال laser هيطلع نفس ال issueلما انت او احنا ب .. ب
+
+190
+00:14:45,700 --> 00:14:49,280
+.. ب .. بن .. بناخد على ال time .. على ال time ال
+
+191
+00:14:49,280 --> 00:14:53,780
+average .. ال average قدرة ال laser .. متوسط قدرة
+
+192
+00:14:53,780 --> 00:14:58,900
+ال laser لما بنقارنها مع الزمنhigh وhigh نفس الأشي
+
+193
+00:14:58,900 --> 00:15:03,600
+طب ليش أنا بدي أطلع بشكل دفعات لأنه عشان يحققلي
+
+194
+00:15:03,600 --> 00:15:07,940
+يعني power أو قدرة عالية جدا في الفترة اللي بيكون
+
+195
+00:15:07,940 --> 00:15:10,780
+فيها ال laser شغال في الفترة اللي بيكون فيها ال
+
+196
+00:15:10,780 --> 00:15:15,360
+laser شغال طبعا ال continuous laser إله استخدامات
+
+197
+00:15:15,360 --> 00:15:19,740
+و ال pulsed laser إله استخدامات إذا lasers may
+
+198
+00:15:19,740 --> 00:15:23,840
+operate ممكن ال lasers تعمل بشكل continuouslyزي
+
+199
+00:15:23,840 --> 00:15:27,100
+الـ Argon Laser Photococculation هذا نوع من الليزر
+
+200
+00:15:27,100 --> 00:15:32,700
+احنا يعني بنعالج فيه الشبكية أو اعتلال الشبكية
+
+201
+00:15:32,700 --> 00:15:37,880
+السكري أو ممكن أنواع تانية من الليزر مابتشتغلش
+
+202
+00:15:37,880 --> 00:15:41,780
+بشكل continuous بتشتغل بشكل pulses على نبضات يعني
+
+203
+00:15:41,780 --> 00:15:46,440
+الليزر بيتدفق من جهاز الليزر بشكل دفعات في الفترة
+
+204
+00:15:46,440 --> 00:15:50,180
+بين الدفعات مافيشش ليزر بيكون قوة الليزر أو قدرة
+
+205
+00:15:50,180 --> 00:15:55,520
+الليزر أو ال output صفرإذا في أنواع تانية من ال
+
+206
+00:15:55,520 --> 00:15:59,680
+laser زي ال yag laser اللي بنستخدمه برضه في شيء
+
+207
+00:15:59,680 --> 00:16:04,680
+معين هنحكيه في وقته طيب كيف .. كيف الأجهزة ال
+
+208
+00:16:04,680 --> 00:16:12,400
+laser بتتحول من continuous mode ل pulse mode فاحنا
+
+209
+00:16:12,400 --> 00:16:18,100
+بس قبل ما نحكي هذا القضية بدنا نوضح الفكرة بشكل ال
+
+210
+00:16:18,100 --> 00:16:20,140
+simulation اللي عرضنا يعني
+
+211
+00:16:22,970 --> 00:16:27,830
+that مرة نروح لـ simulation بتاع ال laser
+
+212
+00:17:06,180 --> 00:17:10,420
+عشان نشرح بس فكرة ال continuous laser و اش بيفرج
+
+213
+00:17:10,420 --> 00:17:14,120
+عنه
+
+214
+00:17:14,120 --> 00:17:22,800
+الان احنا ممكن نعطي ال laser اذا شايفين ال laser
+
+215
+00:17:22,800 --> 00:17:28,630
+بطلع بشكل مستمربشكل مستمر في ال pulse laser بطلع
+
+216
+00:17:28,630 --> 00:17:32,470
+عبارة عن دفقات دفقات و بتوقف دفقات و بتوقف
+
+217
+00:17:32,470 --> 00:17:37,030
+فبالتالي هنفرض
+
+218
+00:17:37,030 --> 00:17:43,350
+طلعة الجرعة الأولى هاي الجرعة التانية هاي الجرعة
+
+219
+00:17:43,350 --> 00:17:50,070
+التالتة هاي الجرعة الرابعة من ال laser طبعا بينهم
+
+220
+00:17:50,070 --> 00:17:54,850
+مسافات زمانية قليلة جداهي هيك بيفرق ال laser ال
+
+221
+00:17:54,850 --> 00:18:00,910
+continuous laser عن ال ال pulsed laser لنرجع بس
+
+222
+00:18:00,910 --> 00:18:05,710
+نمثل ال continuoushigh continuous laser بتدفق بشكل
+
+223
+00:18:05,710 --> 00:18:09,110
+مستمر بمجرد ما نسمح لل laser أنه يخرج من ال laser
+
+224
+00:18:09,110 --> 00:18:14,670
+cavity بينما في ال pulsed laser بيطلع على دفعات
+
+225
+00:18:14,670 --> 00:18:18,910
+بين الدفعات في المسافات الزمنية بين الدفعات مافي
+
+226
+00:18:18,910 --> 00:18:23,390
+أبدا أي laser مافي أبدا أي laser نشوف هذه القضية
+
+227
+00:18:23,390 --> 00:18:29,510
+نقول هاي هنا عندي طلعت دفعة بعدين طلعت دفعة تانية
+
+228
+00:18:32,530 --> 00:18:36,970
+بعدين طلعت دفعة تالتة و هكذا .. طبعا المسافات ال
+
+229
+00:18:36,970 --> 00:18:40,990
+.. ال .. ال .. ال .. البينية بين الدفعة و التانية
+
+230
+00:18:40,990 --> 00:18:47,190
+بتكون يعني قليلة جدا .. قليلة جدا .. اذا بالنسبة ل
+
+231
+00:18:47,190 --> 00:18:51,810
+.. ال laser ممكن يكون continuous .. continuous
+
+232
+00:18:53,830 --> 00:18:59,770
+continuous laser أو pulsed laser أو بشكل pulses زي
+
+233
+00:18:59,770 --> 00:19:03,410
+ما الرسم البياني اللي قبل شوية عرضناه بيوضح هذه
+
+234
+00:19:03,410 --> 00:19:07,350
+القضية هذا continuous laser ال laser output ثابت
+
+235
+00:19:07,350 --> 00:19:13,150
+بمجرد ما فتحناالليزر كافيتى أو ضغطنا على الزر بيظل
+
+236
+00:19:13,150 --> 00:19:18,430
+لغاية ما يعني نترك اللى هو الزر بتاع الليزر
+
+237
+00:19:18,430 --> 00:19:22,490
+وبالتالي بتكون خلصت العملية في الفترة هاى طول ما
+
+238
+00:19:22,490 --> 00:19:26,130
+انا ضغط على الزر و الليزر شغال اما في ال pulse
+
+239
+00:19:26,130 --> 00:19:29,830
+mode في ال pulse mode انا ضغط على الزر بس الليزر
+
+240
+00:19:29,830 --> 00:19:34,010
+بيطلع على دفقات او جرعاتفي الفترة بين الجرعة
+
+241
+00:19:34,010 --> 00:19:36,550
+الأولى والتانية مافيش laser أبدا في الفترة بين
+
+242
+00:19:36,550 --> 00:19:39,010
+الجرعة التانية والتالتة مافيش laser أبدا طبعا هذه
+
+243
+00:19:39,010 --> 00:19:43,410
+المسافات الزمنية قليلة جدا جدا أجزاء لا تكاد تذكر
+
+244
+00:19:43,410 --> 00:19:50,110
+من الثانية أجزاء لا تكاد تذكر من الثانية طبعا كل
+
+245
+00:19:50,110 --> 00:19:53,850
+نوع من الأنواع بيستخدم أو له استخدامات معينة هذا
+
+246
+00:19:53,850 --> 00:19:57,910
+بنستخدمه في العين وهذا أيضا بنستخدم استخدامات أخرى
+
+247
+00:19:57,910 --> 00:20:01,730
+أيضا في العينهنا بنكوي فيه الشبكية في عملية
+
+248
+00:20:01,730 --> 00:20:05,510
+بنسميها laser photococculation وهذا هنحكي عنها ان
+
+249
+00:20:05,510 --> 00:20:09,710
+شاء الله تعالى في حينها والياج لازر هذه بنعمل فتحة
+
+250
+00:20:09,710 --> 00:20:14,610
+في ال posterior capsule بتاعة ال lens بعد عملية
+
+251
+00:20:14,610 --> 00:20:20,180
+الميه البيضةكيف احصل على ال pulse laser انه احول
+
+252
+00:20:20,180 --> 00:20:24,600
+ال laser من continuous اخليه بشكل pulses يطلع او
+
+253
+00:20:24,600 --> 00:20:28,740
+نبضات في عندي طريقتين في عندي اول طريقة بيسموها
+
+254
+00:20:28,740 --> 00:20:33,820
+mode locking و
+
+255
+00:20:33,820 --> 00:20:38,740
+الطريقة
+
+256
+00:20:38,740 --> 00:20:44,100
+التانية بيسموها cue switchingEQ switching و mode
+
+257
+00:20:44,100 --> 00:20:47,980
+locking هتقول الطريقتين are two common methods of
+
+258
+00:20:47,980 --> 00:20:52,380
+producing a pulsed output، the details of such
+
+259
+00:20:52,380 --> 00:20:55,100
+methods are beyond the scope of this text وحقيقة
+
+260
+00:20:55,100 --> 00:20:58,840
+هذه شغلة إلها علاقة بالفيزيا أكتر ما إلها علاقة في
+
+261
+00:20:58,840 --> 00:21:02,640
+البصريات، إحنا اللي بدنا نعرفه إنه في عندي
+
+262
+00:21:02,640 --> 00:21:05,460
+continuous laser وفي عندي pulsed laser وفي عندي
+
+263
+00:21:05,460 --> 00:21:06,300
+pulsed laser
+
+264
+00:21:09,100 --> 00:21:12,800
+power is the amount of energy delivered in a given
+
+265
+00:21:12,800 --> 00:21:21,060
+time period طيب الطاقة بتاعت الضوء لما أجسمها على
+
+266
+00:21:21,060 --> 00:21:24,360
+.. على الزمن بتعطيني القدرة، الطاقة على الزمن
+
+267
+00:21:24,360 --> 00:21:29,900
+بتعطيني القدرة، إذا القدرة قدرة هي عبارة عن كمية
+
+268
+00:21:29,900 --> 00:21:36,390
+الطاقة اللي تم إعطاها في وحدة الزمنالوات قدرة تقاس
+
+269
+00:21:36,390 --> 00:21:40,390
+بالوات الوات اللي هو وحدة قياس القدرة is one joule
+
+270
+00:21:40,390 --> 00:21:44,550
+of energy delivered over one second الوات يساوي
+
+271
+00:21:44,550 --> 00:21:47,670
+واحد joule على واحد ثانية واحد joule على واحد
+
+272
+00:21:47,670 --> 00:21:52,090
+ثانية وكاني بقول انا لو في عندي مصباح كهربائي
+
+273
+00:21:52,090 --> 00:21:57,250
+قدرته واحد واتقدرته واحد واط مش مائة واط ولا سبتين
+
+274
+00:21:57,250 --> 00:22:01,250
+واط ولا تلاتين واط قدرته واحد واط اذا هذا المصباح
+
+275
+00:22:01,250 --> 00:22:06,250
+الكهربائي بيعطيني طاقة كهربائية مقدارها واحد جول
+
+276
+00:22:06,250 --> 00:22:10,610
+كل ثانية واحد جول كل ثانية لو عندي مصباح كهربائي
+
+277
+00:22:10,610 --> 00:22:15,390
+قدرته مائة واط يعني بيعطيني مية جول في كل ثانية
+
+278
+00:22:15,390 --> 00:22:21,770
+طيب انا بدأ أجيب طاقة مقدارها واحد جولو اعطيها مش
+
+279
+00:22:21,770 --> 00:22:26,410
+فى ثانية اعطيها فى nano ثانية فى nano ثانية
+
+280
+00:22:26,410 --> 00:22:32,370
+هتعطينى قدرة مقدارها مليار واط بليون واط بنشوف هذه
+
+281
+00:22:32,370 --> 00:22:37,050
+المعادلة كيف بنقول one joule over one second يساوي
+
+282
+00:22:37,050 --> 00:22:41,570
+one wattبينما الـ Joule هذا لما اعطيه في .. في ..
+
+283
+00:22:41,570 --> 00:22:46,210
+في .. في مسافة زمانية عبارة عن واحد nano second ال
+
+284
+00:22:46,210 --> 00:22:50,610
+nano second واحد على مليار يعني عشرة أس ناقص تسعة
+
+285
+00:22:50,610 --> 00:22:55,530
+من الثانيةلما الواحد جول بجسمه على عشرة أس ناقص
+
+286
+00:22:55,530 --> 00:22:59,750
+تسعة من الثانية بيعطيني طبعا عشرة أس ناقص تسعة في
+
+287
+00:22:59,750 --> 00:23:03,790
+المقام لما بتطلع في ال bus بتصير عشرة أس تسعة watt
+
+288
+00:23:03,790 --> 00:23:08,150
+إذا عشرة أس تسعة يعني ألف مليون watt يعني مليار
+
+289
+00:23:08,150 --> 00:23:13,730
+watt هو نفس الجول لما أنا بذلته في ثانية واحدة
+
+290
+00:23:13,730 --> 00:23:17,130
+أعطاني واحد watt لما أنا بذلته في nano second
+
+291
+00:23:18,140 --> 00:23:22,760
+أعطاني مليار وط يعني قدرة هائلة للغاية لا تقارن مع
+
+292
+00:23:22,760 --> 00:23:27,240
+انه كمية الطاقة وهنا سر الاستفادة من ال laser ال
+
+293
+00:23:27,240 --> 00:23:30,620
+laser مش سيئ أي ضوء عادي ال laser بقدر انا اعطيه
+
+294
+00:23:30,620 --> 00:23:33,720
+في nano second بقدر اعطيه في micro second بقدر
+
+295
+00:23:33,720 --> 00:23:39,240
+اعطيه في وقت من الزمن قليل جدا جدا جدا يمكن للجهاز
+
+296
+00:23:39,240 --> 00:23:44,450
+انه يتحكم فيه يمكن للجهاز انه يتحكم فيهPulsing is
+
+297
+00:23:44,450 --> 00:23:47,750
+a way of increasing the power of a lasers output
+
+298
+00:23:47,750 --> 00:23:51,870
+by delivering a modest amount of energy over a
+
+299
+00:23:51,870 --> 00:23:56,390
+very short time period قضية ان انتاج ال pulse
+
+300
+00:23:56,390 --> 00:24:03,670
+laser هو طريقة للحصول على قدرة عالية جدا، كيف؟
+
+301
+00:24:03,670 --> 00:24:10,170
+كيف؟ هنا الزمن، من هنا لهنا، نفرض انه مثلا واحد من
+
+302
+00:24:10,170 --> 00:24:14,840
+عشرة ثانيةالواحد من العشرة ثانية بس انا في ال
+
+303
+00:24:14,840 --> 00:24:17,780
+pulse mode انا باعطي في الواحد nano second او في
+
+304
+00:24:17,780 --> 00:24:21,640
+العشرة nano second باعطي جرعة هيكون قدرتها عالية
+
+305
+00:24:21,640 --> 00:24:26,600
+جداالـ output power القدرة عالية جدا و بخلي مسافات
+
+306
+00:24:26,600 --> 00:24:29,320
+زمانية باعطيش فيها ال laser بدل ما اوزع ال laser
+
+307
+00:24:29,320 --> 00:24:33,160
+بشكل continuous على كل الزمن ابداعي فبالتالي ال
+
+308
+00:24:33,160 --> 00:24:38,900
+pulsing عبارة عن طريقة لزيادة ال power لزيادة
+
+309
+00:24:38,900 --> 00:24:44,380
+القدرة بتاعة ال laser output بتاعة ال laser المنتج
+
+310
+00:24:44,850 --> 00:24:49,130
+كيف بدنا نزيد القدرة by delivering modest amount
+
+311
+00:24:49,130 --> 00:24:53,090
+of energy بإنه نعطي كمية ضائلة من الطاقة ضائلة مش
+
+312
+00:24:53,090 --> 00:24:57,290
+كتيرة بس كيف بدنا نزيد القدرة ان هذه الطاقة
+
+313
+00:24:57,290 --> 00:25:00,650
+الضائلة اللي انا اعطيتها بتعطيها over a very short
+
+314
+00:25:00,650 --> 00:25:05,470
+time period لأنه لما بنقول ان معادلة القدرة معادلة
+
+315
+00:25:05,470 --> 00:25:10,610
+القدرة ان اقسم الطاقة على الزمن فكل ما صغر الزمن
+
+316
+00:25:10,610 --> 00:25:15,010
+القدرة بتعلى كتير وهي عندي واحد جولأعطيته في ثانية
+
+317
+00:25:15,010 --> 00:25:18,430
+أعطاني واحد وط، بس نفس ال jewel .. نفس ال jewel
+
+318
+00:25:18,430 --> 00:25:22,790
+أعطيته في nano ثانية أعطاني مليار وط، يعني في فرق
+
+319
+00:25:22,790 --> 00:25:27,150
+بين واحد وط ومليار وط، اللي هو المليار وط أكتر من
+
+320
+00:25:27,150 --> 00:25:32,040
+الواحد وط بمليار مرةمليار مرة بتنتهي المحاضرة عند
+
+321
+00:25:32,040 --> 00:25:35,860
+هذه النقطة و المرة القادمة ان شاء الله تعالى هنشوف
+
+322
+00:25:35,860 --> 00:25:39,200
+ال light tissue interaction يعني تأثير ال light
+
+323
+00:25:39,200 --> 00:25:43,180
+اللي بنقصد فيه ال laser light تأثيره على الأنسجة
+
+324
+00:25:43,180 --> 00:25:47,100
+الحيوية و بنقصد فيها أنسجة العين و يعطيكم العافية
+
+325
+00:25:47,100 --> 00:25:49,880
+والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/cXuZwortwt8.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/cXuZwortwt8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c690b183c3fa8e399b2b71c7912d27e7bf9e46b3
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/cXuZwortwt8.srt
@@ -0,0 +1,1862 @@
+1
+00:00:01,750 --> 00:00:05,830
+بسم الله الرحمن الرحيم بنواصل محاضرات الـ physical
+
+2
+00:00:05,830 --> 00:00:11,070
+optics واتوقفنا عند ظاهرة تسمى الـ fluorescence 
+
+3
+00:00:11,070 --> 00:00:15,210
+الـ fluorescence عبارة عن ظاهرة فيزيائية هي عبارة عن
+
+4
+00:00:15,210 --> 00:00:19,130
+إيش؟ بنقول when an electron absorbs a photon and
+
+5
+00:00:19,130 --> 00:00:22,900
+jumps to a higher energy level. Usually it quickly 
+
+6
+00:00:22,900 --> 00:00:27,120
+drops back to its original level and emits a
+
+7
+00:00:27,120 --> 00:00:31,600
+photon identical in frequency to the one it 
+
+8
+00:00:31,600 --> 00:00:37,000
+absorbed. الآن لما في إلكترون بيمتص فوتون، يعني ده
+
+9
+00:00:37,000 --> 00:00:41,980
+بيمتص حصة من الطاقة، نرجع لرسمة توضح هذه القضية
+
+10
+00:00:48,160 --> 00:00:52,400
+بنقول لما في عندنا إلكترون يكتسب حصة من الطاقة،
+
+11
+00:00:52,400 --> 00:00:57,660
+يكتسب فوتون، صعد لـ energy level معين، عادة اللي
+
+12
+00:00:57,660 --> 00:01:01,060
+بيحصل إن هذا الإلكترون اللي امتص طاقة وطلع لمدار
+
+13
+00:01:01,060 --> 00:01:05,000
+أعلى في الطاقة، الطاقة نفسها اللي امتصها هيفقدها
+
+14
+00:01:05,680 --> 00:01:10,740
+وهينزل للمدار الأصلي بتاعه للمسكن الأصلي بتاعه
+
+15
+00:01:10,740 --> 00:01:15,980
+نفرض إن طاقة الفوتون اللي جاي 2 جول أدت لأن هذا
+
+16
+00:01:15,980 --> 00:01:19,980
+الإلكترون اللي موجود في المستوى رقم 2 صعد بالـ2
+
+17
+00:01:19,980 --> 00:01:24,140
+جول اللي أضيف إليه صعد للمدار رقم 6 على سبيل
+
+18
+00:01:24,140 --> 00:01:30,650
+المثال عادة بعد فترة قليلة جدا بيفقد الـ2 جول بشكل
+
+19
+00:01:30,650 --> 00:01:35,830
+فوتون وبينزل للمسكن الأصلي له، إذا هو لما اكتسب
+
+20
+00:01:35,830 --> 00:01:40,310
+اكتسب اثنين جول ولما فقد فقد اثنين جول، الفوتون
+
+21
+00:01:40,310 --> 00:01:46,100
+اللي جاء أعطى طاقته للإلكترون طبعا الفوتون هو حصة
+
+22
+00:01:46,100 --> 00:01:50,540
+من الطاقة، bucket of energy أعطى طاقته للإلكترون و
+
+23
+00:01:50,540 --> 00:01:55,280
+أدى لصعوده للمدار رقم 6 على سبيل المثال فقد نفس
+
+24
+00:01:55,280 --> 00:01:58,540
+الفوتون ليش نفس الفوتون؟ لأن نفس الحصة اللي جاءت هي
+
+25
+00:01:58,540 --> 00:02:02,990
+نفس الحصة اللي غادرت، نفس الفوتون اللي جاء هو نفس
+
+26
+00:02:02,990 --> 00:02:06,770
+الفوتون اللي غادر، بمعنى ترددهم واحد، كمية الطاقة
+
+27
+00:02:06,770 --> 00:02:10,030
+اللي جاءت هي كمية الطاقة اللي غادرت، فبالتالي زي ما
+
+28
+00:02:10,030 --> 00:02:15,310
+صعد من اثنين لستة هينزل من ستة لاثنين، طب نفرض أنه
+
+29
+00:02:15,310 --> 00:02:19,590
+في عندي حصة طاقة مثلا نصف جول أدت لصعوده من اثنين
+
+30
+00:02:19,590 --> 00:02:25,050
+لثلاثة هيفقد النص جول وينزل من ثلاثة لاثنين
+
+31
+00:02:25,050 --> 00:02:31,730
+فالفوتون اللي اكتسبه هو نفس الفوتون اللي يعني فقده،
+
+32
+00:02:31,730 --> 00:02:35,250
+اللي هم نفس الطاقة، يعني اللي هم نفس التردد ونفس
+
+33
+00:02:35,250 --> 00:02:38,630
+الطول الموجي، هدف الطبيعي، يعني أنا جاية احنا
+
+34
+00:02:38,630 --> 00:02:45,730
+بنحكي عن الأمور الطبيعية فيها شيء يعني مختلف قليلا
+
+35
+00:02:45,730 --> 00:02:49,810
+بيؤدي للظاهرة اللي احنا بصددها اليوم، however 
+
+36
+00:02:49,810 --> 00:02:55,370
+atoms of some elements have two energy levels that 
+
+37
+00:02:55,370 --> 00:02:59,590
+are close together. نشوف المنظر التالي، بنقول هي أن
+
+38
+00:02:59,590 --> 00:03:06,070
+مثلا ذرة، نموذج لذرة، هي مستوى من مستويات
+
+39
+00:03:06,070 --> 00:03:12,890
+الطاقة اللي هو المستوى يعني الأول، المستوى الثاني
+
+40
+00:03:12,890 --> 00:03:16,890
+المستوى الثالث، المستوى الثالث هنا مرتبينهم واحد
+
+41
+00:03:16,890 --> 00:03:20,970
+اثنين ثلاثة حسب مقدار الطاقة هو هذا الأعلى طاقة
+
+42
+00:03:20,970 --> 00:03:26,090
+أدنى منه طاقة، أدنى جدا في الطاقة ترتيبه رقم ثلاثة
+
+43
+00:03:26,090 --> 00:03:29,690
+في الطاقة بس هو الأقرب للنواة، هو الأقرب للنواة
+
+44
+00:03:29,690 --> 00:03:34,010
+بنقول إلكترون كان بيمشي في المدار اللي سميناه رقم 
+
+45
+00:03:34,010 --> 00:03:39,810
+ثلاثة، جاءت حصة من الطاقة أدت لصعوده مدارين مرة
+
+46
+00:03:39,810 --> 00:03:42,910
+واحدة يعني ما .. ما صعد للمدار الثالث .. الثاني
+
+47
+00:03:42,910 --> 00:03:47,610
+صعد للمدار رقم .. الرمز له الرقم واحد، لذَن هو
+
+48
+00:03:47,610 --> 00:03:52,310
+قفز عبر مدارين، ليش؟ لأن هذه الذرة أو هذا العنصر
+
+49
+00:03:52,310 --> 00:03:56,950
+فيه مدارين متقاربين، يعني أول شرط من شروط ظاهرة الـ
+
+50
+00:03:56,950 --> 00:04:00,330
+fluorescence أن يكون بعض العنصر اللي .. اللي
+
+51
+00:04:00,330 --> 00:04:04,310
+بيتمتع بخاصية الـ fluorescence هذه الـ elements have
+
+52
+00:04:04,310 --> 00:04:07,710
+two energy levels that are close together، زي ما
+
+53
+00:04:07,710 --> 00:04:11,770
+الرسم عندي أنا بيوضح، يعني المدار هذا والمدار هذا
+
+54
+00:04:11,770 --> 00:04:14,890
+قريبين من بعض في الطاقة، لو قلنا طاقة المدار هذا
+
+55
+00:04:14,890 --> 00:04:19,290
+اثنين جول وهذا تسعة جول، هذا هيكون مثلا عشرة جول
+
+56
+00:04:19,290 --> 00:04:24,150
+قريبين من بعض في .. في .. في الطاقة، قريبين من بعض في
+
+57
+00:04:24,150 --> 00:04:30,610
+الـ spacing بتاعنا، الآن في إلكترون بيدور في المدار
+
+58
+00:04:30,610 --> 00:04:34,770
+اللي قلنا طاقته اثنين جول، هذا الإلكترون ضروري
+
+59
+00:04:34,770 --> 00:04:37,990
+تكون طاقته أيضا اثنين جول عشان يكون مناسبة أنه
+
+60
+00:04:37,990 --> 00:04:44,510
+يدور في هذا المدار، طيب جاء له ثمانية جول مرة واحدة
+
+61
+00:04:44,510 --> 00:04:49,430
+أصبح طاقته مش اثنين جول، أصبح طاقته عشرة جول فهذا
+
+62
+00:04:49,430 --> 00:04:53,070
+المدار طاقته تسعة جول وهذا المدار عشرة جول، فهيقفز
+
+63
+00:04:53,780 --> 00:04:57,920
+مرة واحدة هيطلع من المدار هذا للمدار الآخر للمدار
+
+64
+00:04:57,920 --> 00:05:03,000
+الآخر لأنه أصبح طاقته تناسب طاقة المدار الآخر، طيب
+
+65
+00:05:03,000 --> 00:05:07,680
+اللي بيحصل احنا الإلكترونات زي ما هي بتحب ترجع
+
+66
+00:05:07,680 --> 00:05:13,440
+لمداراتها الأصلية ومساكنها الأصلية، بس هو رجوعه
+
+67
+00:05:13,440 --> 00:05:16,860
+هيكون مش مرة واحدة زي ما المثال اللي احنا ضربناه
+
+68
+00:05:16,860 --> 00:05:23,680
+قبل شوية، مش مرة واحدة، ليس مرة واحدة، إنه طلع من
+
+69
+00:05:23,680 --> 00:05:27,160
+اثنين لستة، حيرجع من ستة لاثنين، أو طلع من اثنين
+
+70
+00:05:27,160 --> 00:05:30,940
+لثلاثة حيرجع لاثنين مرة واحدة، أو طلع مثلا من اثنين
+
+71
+00:05:30,940 --> 00:05:36,940
+لخمسة، حينزل من خمسة لاثنين دفعة واحدة، لأ، العناصر
+
+72
+00:05:36,940 --> 00:05:41,680
+اللي فيها ظاهرة الـ fluorescence اللي بيصير فيها
+
+73
+00:05:41,680 --> 00:05:46,480
+إنه أول شيء في عندي مدارين متقاربين، الإلكترون بيصعد
+
+74
+00:05:46,480 --> 00:05:50,520
+من مدار أدنى في الطاقة للمدار الأعلى قافزا عبر
+
+75
+00:05:50,520 --> 00:05:54,120
+المدار اللي أقل منه شوية والقريب منه في الطاقة
+
+76
+00:05:54,120 --> 00:05:59,460
+هدف الإلكترون الآن في النزول بده ينزل بالتدريج مش مرة
+
+77
+00:05:59,460 --> 00:06:04,580
+واحدة، هينزل هو أصبح طاقته عشرة جول هيفقد حصة من
+
+78
+00:06:04,580 --> 00:06:08,840
+الطاقة مقدارها واحد جول، مقدارها واحد جول احنا
+
+79
+00:06:08,840 --> 00:06:13,330
+خلينا على أساس الأمور تظل يعني واضحة، بنقول
+
+80
+00:06:13,330 --> 00:06:28,150
+كالتالي، المدار الأخير عشرة جول والمدار
+
+81
+00:06:28,150 --> 00:06:32,770
+اللي قريب منه في مستوى الطاقة في كمية الطاقة تسعة 
+
+82
+00:06:32,770 --> 00:06:33,350
+جول
+
+83
+00:06:50,620 --> 00:06:59,780
+والمستوى الأدنى اثنين جول، هذه 
+
+84
+00:06:59,780 --> 00:07:04,040
+الأرقام افتراضية وليست حقيقية بس لتقريب المفهوم
+
+85
+00:07:04,040 --> 00:07:09,390
+لتقريب المفهوم إذا عندي مدار اثنين جول، عندي مدار
+
+86
+00:07:09,390 --> 00:07:12,430
+اللي بعده تسعة جول، اللي بعده عشرة جول، هدول
+
+87
+00:07:12,430 --> 00:07:15,650
+المدارين قريبين من بعض في الطاقة فعشان هيك لما
+
+88
+00:07:15,650 --> 00:07:19,390
+بيرسموا .. لما بيرسموا على الورق الـ spacing بينهم
+
+89
+00:07:19,390 --> 00:07:23,110
+قريب، بينما لما بيفرجوا عن مدار آخر في الطاقة فرق
+
+90
+00:07:23,110 --> 00:07:27,830
+كبير، بيكون الـ spacing بينه وبينهم أكبر، جاءت .. جاءت
+
+91
+00:07:27,830 --> 00:07:33,790
+فوتون حصة من الطاقة للإلكترون اللي هنا، جاءت حصة 
+
+92
+00:07:33,790 --> 00:07:38,150
+من الطاقة كده مقدار هذه الحصة ثمانية جول
+
+93
+00:07:46,790 --> 00:07:53,570
+هذا الفوتون يحمل طاقة أو هو عبارة عن حصة من الطاقة
+
+94
+00:07:53,570 --> 00:07:57,210
+مقدارها ثمانية جول اكتسبها الإلكترون اللي طاقته 
+
+95
+00:07:57,210 --> 00:08:01,050
+اثنين جول، أصبح طاقته عشرة جول، مش هينفع يدور في
+
+96
+00:08:01,050 --> 00:08:04,590
+المدار التالي، لأ بده يقفز عبر مدار، هيعدي المدار
+
+97
+00:08:04,590 --> 00:08:08,270
+اللي طاقته تسعة جول ويصير في المدار العشرة جول
+
+98
+00:08:08,270 --> 00:08:11,810
+الآن احنا قلنا الإلكترون أصبح الآن هذا الإلكترون
+
+99
+00:08:11,810 --> 00:08:17,430
+اللي اكتسب طاقة الفوتون أصبح في المدار الأخير اللي
+
+100
+00:08:17,430 --> 00:08:22,070
+هو الأعلى طاقة، بيحب يرجع لمسكنه الأصلي بس مش هيرجع
+
+101
+00:08:22,070 --> 00:08:28,050
+مرة واحدة هيفقد حصة قليلة من الطاقة مقدارها واحد
+
+102
+00:08:28,050 --> 00:08:34,150
+جول، طاقة قليلة مقدارها واحد جول، طاقته أصبحت عشرة 
+
+103
+00:08:34,150 --> 00:08:39,120
+جول بس هيفقد من العشرة جول 1 جول، هذه هيفقدها بشكل
+
+104
+00:08:39,120 --> 00:08:43,700
+حصة من الطاقة، طاقة قليلة جدا، جاية أو الفوتون اللي
+
+105
+00:08:43,700 --> 00:08:47,220
+هيفقدها أو الحصة اللي فقدها في الـ infrared region
+
+106
+00:08:47,220 --> 00:08:55,990
+مش هنشوفه، مش هنشوفه، إذا الـ infrared فوتون اللي
+
+107
+00:08:55,990 --> 00:08:59,830
+انفقد طاقته واحد جول، طاقة قليلة، مش في الـ range،
+
+108
+00:08:59,830 --> 00:09:03,770
+اللي ما range طيب، لسه طاقة الـ electron لما هبط
+
+109
+00:09:03,770 --> 00:09:09,030
+الهبوط الأول، أصبح طاقته تسعة جول، بينما لسه 
+
+110
+00:09:09,030 --> 00:09:12,730
+ما رجعش لمسكنه الأصلي، هيروح فاقد الحصة الثانية من
+
+111
+00:09:12,730 --> 00:09:18,230
+الطاقة، اللي هي كمية أكبر، هيفقد سبعة جول، سبعة
+
+112
+00:09:18,230 --> 00:09:18,710
+جول
+
+113
+00:09:22,610 --> 00:09:29,510
+هذه هيفقدها بشكل فوتون، فوتون له تردد معين، طيب،
+
+114
+00:09:29,510 --> 00:09:35,130
+الآن أنا عندي فوتون جاء وغادر بعده فوتونين
+
+115
+00:09:35,130 --> 00:09:39,430
+بالتدريج، الفوتون اللي جاء طاقته ثمانية جول، ثمانية
+
+116
+00:09:39,430 --> 00:09:42,970
+جول، الفوتون الأول اللي غادر أو الحصة الأولى من
+
+117
+00:09:42,970 --> 00:09:46,330
+الطاقة اللي غادرت وفقدها الإلكترون وهبط من المدار
+
+118
+00:09:46,330 --> 00:09:51,820
+الأخير للي قبله طاقتها واحد جول، الفوتون الثاني اللي 
+
+119
+00:09:51,820 --> 00:09:55,000
+رجع الـ electron لمداره الأصلي ولمسكنه الأصلي
+
+120
+00:09:55,000 --> 00:09:59,380
+طاقته سبعة جول، أي الثلاثة فوتونات هو الأعلى في
+
+121
+00:09:59,380 --> 00:10:04,360
+الطاقة، الأعلى في الطاقة هو اللي جاء ثمانية جول 
+
+122
+00:10:04,360 --> 00:10:08,880
+طاقته، فبالتالي هذا الفوتون تردده هيكون أعلى من
+
+123
+00:10:08,880 --> 00:10:13,940
+تردد الفوتونين اللي هو هذا الفوتون وهذا الفوتون
+
+124
+00:10:13,940 --> 00:10:18,640
+الفوتونات هي حصص من الطاقة، هذه الحصص من الطاقة قد
+
+125
+00:10:18,640 --> 00:10:23,740
+تكون مرئية وقد تكون غير مرئية، هذا له طاقة معينة هي
+
+126
+00:10:23,740 --> 00:10:28,550
+الأعلى في الثلاثة، هو جاء اكتسبه الإلكترون، تردده
+
+127
+00:10:28,550 --> 00:10:34,050
+مناسب للتردد مثلا الأزرق، الأزرق، الضوء المرئي في
+
+128
+00:10:34,050 --> 00:10:39,570
+الـ range بتاع التردد الأزرق، إله طاقة ثمانية جول، الآن
+
+129
+00:10:39,570 --> 00:10:45,110
+صعد الـ electron من المدار الأدنى للمدار الأعلى على
+
+130
+00:10:45,110 --> 00:10:49,150
+الإطلاق في الرسم اللي إحنا شايفينه، الآن الثمانية
+
+131
+00:10:49,150 --> 00:10:52,290
+جول هيعود يفقدهم عشان يرجع لمسكنه الأصلي بس
+
+132
+00:10:52,290 --> 00:10:57,630
+هيفقدهم بالتدريج، أول هيفقد واحد جول بشكل فوتون
+
+133
+00:10:57,630 --> 00:11:01,830
+طاقته واحد جول، يعني طاقته ضعيفة جدا إذا قورنت
+
+134
+00:11:01,830 --> 00:11:07,170
+بطاقة الفوتون المكتسب، الفوتون المكتسب ضعيفة جدا،
+
+135
+00:11:07,170 --> 00:11:10,410
+قليلة جدا الطاقة، إذا التردد قليل، هيجي في الـ
+
+136
+00:11:10,410 --> 00:11:15,870
+infrared region يعني هيكون طاقة غير مرئية، فقدت،
+
+137
+00:11:15,870 --> 00:11:19,630
+مقدارها واحد جول، طوله الموجي جاي في الـ infrared
+
+138
+00:11:19,630 --> 00:11:23,670
+وهذه لن تراها، لن تراها العين المجردة، طيب، ظل
+
+139
+00:11:23,670 --> 00:11:27,610
+عندي سبعة جول، بدنا نفقدهم، هيفقدهم الإلكترون
+
+140
+00:11:27,610 --> 00:11:32,190
+السبعة جول عشان يفقدها في المرحلة التالية عشان يرجع
+
+141
+00:11:32,190 --> 00:11:37,850
+لمسكِنه الأصلي، هيفقدهم بشكل فوتون أو حصة من الطاقة
+
+142
+00:11:37,850 --> 00:11:42,770
+مقدارها سبعة جول، طيب، بدنا نقارن الفوتون الأخير
+
+143
+00:11:43,600 --> 00:11:47,980
+اللي فقد اللي هو مقدار الطاقة وسبعة جول بالفوتون
+
+144
+00:11:47,980 --> 00:11:52,640
+المكتسب، مين أكثر منهم في الطاقة؟ اللي أكثر في
+
+145
+00:11:52,640 --> 00:11:55,760
+الطاقة اللي هو المكتسب ثمانية جول، والأقل في 
+
+146
+00:11:55,760 --> 00:11:59,500
+الطاقة، احنا ننسى الفوتون الـ infrared خلاص فقدناه وما 
+
+147
+00:11:59,500 --> 00:12:04,060
+شوفناهوش، بدنا نقارن بين الفوتون المكتسب و
+
+148
+00:12:04,060 --> 00:12:09,760
+الفوتون المرئي اللي فقد اللي هو سبعة جول، مين أكثر
+
+149
+00:12:09,760 --> 00:12:16,130
+في الطاقة؟ اللي هو المكتسب، المكتسب جاء في التردد
+
+150
+00:12:16,130 --> 00:12:21,410
+الأزرق في الـ blue light region، طب هنا طاقته أقل
+
+151
+00:12:21,410 --> 00:12:26,550
+إذا تردده أقل، إذا طول الموجة أطول شوية، هيجي في الـ
+
+152
+00:12:26,550 --> 00:12:30,010
+green في الـ green، يعني الفوتون هذا اللي مفقود
+
+153
+00:12:30,010 --> 00:12:35,520
+طاقته أقل من الفوتون المكتسب، طاقته أقل من الفوتون 
+
+154
+00:12:35,520 --> 00:12:39,620
+المكتسب، وطالما طاقته أقل من الفوتون المكتسب، إذا
+
+155
+00:12:39,620 --> 00:12:43,520
+تردده أقل، لأن الطاقة والتردد الـ frequency
+
+156
+00:12:43,520 --> 00:12:47,560
+يتناسبان طرديا مع بعضهما البعض، فإذا كان هذا تردده
+
+157
+00:12:47,560 --> 00:12:52,440
+في الأزرق هذا هيكون تردده في موجات أطول قليلا زي
+
+158
+00:12:52,440 --> 00:12:56,600
+اللي هو الـ green light
+
+159
+00:12:59,450 --> 00:13:03,610
+هذه الظاهرة تسمى الـ fluorescence، هذه الظاهرة تسمى
+
+160
+00:13:03,610 --> 00:13:08,930
+الـ fluorescence، يعني بالعربي ممكن نسميها ظاهرة
+
+161
+00:13:08,930 --> 00:13:12,930
+التفلور، ظاهرة التفلور، إيش يعني ظاهرة التفلور؟
+
+162
+00:13:12,930 --> 00:13:19,510
+يعني إحنا بنعمل stimulation بطول موجي معين زي الطول
+
+163
+00:13:19,510 --> 00:13:27,870
+الموجي الأزرق وبناخد إشعاع أو ضوء آخر بتردد آخر من
+
+164
+00:13:27,870 --> 00:13:31,370
+هذه المادة أو من هذه الذرة، الذرة احنا عملنا
+
+165
+00:13:31,370 --> 00:13:36,820
+stimulation للإلكترونات بتاعتها بإضاءة معينة ..
+
+166
+00:13:36,820 --> 00:13:41,440
+بإضاءة معينة اللي هي الطول الموجي الأزرق وأشعاتنا
+
+167
+00:13:41,440 --> 00:13:46,620
+إضاءة الطول الموجي الأخضر، نشوف المنظر التالي
+
+168
+00:13:46,620 --> 00:13:54,790
+كاستخدام في .. في موضوع طب العيون، احنا المادة .. 
+
+169
+00:13:54,790 --> 00:13:59,430
+المادة اللي بنحطها وبنقطرها في العين تسمى
+
+170
+00:13:59,430 --> 00:14:02,570
+fluorescein من .. من .. من أصل اسمها من ظاهرة الـ
+
+171
+00:14:02,570 --> 00:14:05,630
+fluorescence، مادة الـ fluorescein sodium .. الـ 
+
+172
+00:14:05,630 --> 00:14:11,590
+fluorescein sodium، لو نطلع على
+
+201
+00:16:20,490 --> 00:16:23,830
+الأزرق، تشايفين الضوء الأزرق؟ العين مضوية بالضوء
+
+202
+00:16:23,830 --> 00:16:28,850
+الأزرق، إيش اللي صار؟ المناطق اللي أخدت fluorescein
+
+203
+00:16:28,850 --> 00:16:35,140
+أو تشربت هذه المادة، هذه المادة أصبحت المادة مركزة 
+
+204
+00:16:35,140 --> 00:16:39,260
+فيها بشكل كويس، إجت ضوء الأزرق عمل stimulation
+
+205
+00:16:39,260 --> 00:16:44,040
+لذرات الفلوريسين، لما عمل stimulation لذرات
+
+206
+00:16:44,040 --> 00:16:47,380
+الفلوريسين بالضوء الأزرق بالتردد الأزرق يعني
+
+207
+00:16:47,380 --> 00:16:52,320
+اكتسبت فوتون طاقته عالية شوية، صعدت الإلكترونات في
+
+208
+00:16:52,320 --> 00:16:57,740
+هذه الذرات إلى مدارات أعلى، قافزة عبر المدار التالي
+
+209
+00:16:57,740 --> 00:17:04,020
+الآن فقدت على التوالي، وبشكل لحظي بمجرد ما تبتصعد
+
+210
+00:17:04,020 --> 00:17:10,020
+بترجع فورا، بس ترجعه بيكون أنه بتنزل للمدار اللي
+
+211
+00:17:10,020 --> 00:17:13,540
+أدنى قليلا، بتفقد infrared photon، هذا ال infrared 
+
+212
+00:17:13,540 --> 00:17:16,900
+photon احنا مش هنشوفه لأنه لا يراه لأنه في ال
+
+213
+00:17:16,900 --> 00:17:23,180
+range الغير مرئي، و بتفقد بعده مباشرة photon باللون
+
+214
+00:17:23,180 --> 00:17:27,020
+الأخضر، باللون الأخضر ليش photon باللون الأخضر لأن
+
+215
+00:17:27,020 --> 00:17:31,870
+طاقته طاقته أقل من الفوتون المكتسب، الفوتون المكتسب
+
+216
+00:17:31,870 --> 00:17:35,270
+جاي في ال range الأزرق، فطاقة هذا الفوتون التالي
+
+217
+00:17:35,270 --> 00:17:40,390
+المرئي بالنسبة لنا أقل، فبالتالي هيكون في التردد أو
+
+218
+00:17:40,390 --> 00:17:44,630
+في ال green light region، في ال green light region
+
+219
+00:17:44,630 --> 00:17:48,310
+فهذه هي الظاهرة تسمى ظاهرة ال fluorescence، ظاهرة
+
+220
+00:17:48,310 --> 00:17:54,790
+ال fluorescence، ضوين مادة أو منطقة فيها مادة
+
+221
+00:17:54,790 --> 00:18:03,290
+كيميائية بتتمدع بظاهر ال fluorescence، ضوينها ب high
+
+222
+00:18:03,290 --> 00:18:08,800
+energy photon اللي هو الضوء الأزرق أشععتلي أو ردتلي
+
+223
+00:18:08,800 --> 00:18:13,980
+أو عكستلي lower energy photon، lower energy photon
+
+224
+00:18:13,980 --> 00:18:18,460
+فوتون أقل منه في الطاقة، طب ليش؟ لأنه قبل ما أشع
+
+225
+00:18:18,460 --> 00:18:22,480
+هذا lower energy photon أشعت كمية ضئيلة من الطاقة
+
+226
+00:18:22,480 --> 00:18:26,540
+بشكل ال infrared الغير مرئي، طيب، الآن إيش
+
+227
+00:18:26,540 --> 00:18:31,400
+الاستفادة العملية من هذه القضية؟ استفادات حقيقية في
+
+228
+00:18:31,400 --> 00:18:35,840
+مجال طب العيون لا تكاد تحصى ولا تعد، احنا المنظر
+
+229
+00:18:35,840 --> 00:18:39,440
+اللي شايفينه هذا جرح في قرانية العين، لما قرانية
+
+230
+00:18:39,440 --> 00:18:44,620
+العين بيصير فيها جرح يعني في مكان من القرنية عشان
+
+231
+00:18:44,620 --> 00:18:47,840
+نعرف حدود الجريح، و هل هو كبير ولا صغير أو كده
+
+232
+00:18:47,840 --> 00:18:52,440
+المنطقة اللي فيها الجريح عادة بيتتشبع أو بتمتص
+
+233
+00:18:52,440 --> 00:18:56,160
+مادة الفلوريسين، طيب لما بنضوي ضوء الأزرق، شايفين
+
+234
+00:18:56,160 --> 00:19:00,060
+الأماكن اللي مش مجروحة عادة ما أخدت فلوريسين
+
+235
+00:19:00,060 --> 00:19:03,800
+ما امتصت مادة الفلوريسين فعشان هيك ظاهرة ال
+
+236
+00:19:03,800 --> 00:19:09,230
+fluorescence هتكون مركزة في المنطقة اللي فيها الجرح
+
+237
+00:19:09,230 --> 00:19:11,670
+و احنا هنشوف الجرح باللون هذا اللي احنا شايفينه
+
+238
+00:19:11,670 --> 00:19:15,730
+اللون اللون الأخضر، بس بشرط انه نضوي .. نضوي أو
+
+239
+00:19:15,730 --> 00:19:19,410
+نعمل stimulation لمادة الفلوريسين بالضوء الأزرق
+
+240
+00:19:19,410 --> 00:19:22,750
+اذا ال corneal abrasion .. ال corneal abrasion انا
+
+241
+00:19:22,750 --> 00:19:27,210
+بقدر اعرفه بواسطة مادة الفلوريسين و اللي هي بتشتغل
+
+242
+00:19:27,210 --> 00:19:32,220
+بظاهرة ال fluorescence .. ال fluorescence هي
+
+243
+00:19:32,220 --> 00:19:38,520
+الفلوريسين قبل ما انا .. قبل ما انا يعني احط عليه
+
+244
+00:19:38,520 --> 00:19:42,920
+او اضيق عليه بال .. أو اكسبه طاقة اللي هو ال blue
+
+245
+00:19:42,920 --> 00:19:45,980
+light، طاقة ال blue light، When a photon is
+
+246
+00:19:45,980 --> 00:19:50,200
+absorbed, the electron jumps to the highest energy
+
+247
+00:19:50,200 --> 00:19:53,900
+level، Instead of dropping back to the original
+
+248
+00:19:53,900 --> 00:19:57,280
+level, however, the electron transitions to the
+
+249
+00:19:57,280 --> 00:20:01,360
+slightly lower level and emits non-visible energy,
+
+250
+00:20:01,480 --> 00:20:05,100
+infrared, next it drops to the initial energy
+
+251
+00:20:05,100 --> 00:20:09,060
+level and emits a photon، يعني بدل ما يرجع مرة
+
+252
+00:20:09,060 --> 00:20:14,980
+واحدة لمسكنه الأصلي، هو قفز للمدار الأعلى، نتيجة
+
+253
+00:20:14,980 --> 00:20:18,640
+اكتسابه طاقة .. طاقة الفوتون الأزرق .. طاقة
+
+254
+00:20:18,640 --> 00:20:22,560
+الفوتون الأزرق، بدل ما يرجع مرة واحدة ويفقد فوتون
+
+255
+00:20:22,560 --> 00:20:27,170
+أزرق، لأ بيرجع بالتدريج، بيفقد فوتون صغير الطاقة في
+
+256
+00:20:27,170 --> 00:20:30,490
+الـ infrared region، بعدين بيكمل بيفقد ما تبقى من
+
+257
+00:20:30,490 --> 00:20:33,870
+الطاقة واللي هي هتكون ما تبقى أقل من الطاقة
+
+258
+00:20:33,870 --> 00:20:37,470
+المكتسبة، الطاقة المكتسبة ثمانية جول، وما تبقى بعد
+
+259
+00:20:37,470 --> 00:20:41,950
+ما فقد ال infrared photon سبعة جول، إذا السبعة جول
+
+260
+00:20:41,950 --> 00:20:45,370
+أقل من التمانية جول، فإذا قلنا التمانية جول اللي
+
+261
+00:20:45,370 --> 00:20:49,470
+اكتسبها طاقتها وترددها بيجي في ال range الأزرق
+
+262
+00:20:49,470 --> 00:20:54,030
+هيكون هذا الطاقة أقل، فالتردد أقل، فالطول الموجي
+
+263
+00:20:54,030 --> 00:20:57,570
+أطول شوية، هيكون في ال range الأخضر، في ال range
+
+264
+00:20:57,570 --> 00:21:01,810
+الأخضر، فبالتالي هذه القضية بدأت تكون واضحة، اذا
+
+265
+00:21:01,810 --> 00:21:05,450
+next it drops to the initial energy level and
+
+266
+00:21:05,450 --> 00:21:10,380
+emits photon، the photon emitted .. الفوتون اللي صدر
+
+267
+00:21:10,380 --> 00:21:14,100
+أو اللي أشعع is still visible، أيضا في ال range
+
+268
+00:21:14,100 --> 00:21:17,840
+المرئي، في ال range المرئي، but has .. but has less
+
+269
+00:21:17,840 --> 00:21:21,580
+energy than the absorbed photon and therefore
+
+270
+00:21:21,580 --> 00:21:25,720
+lower frequency، تردده أقل، هذه الظاهرة called
+
+271
+00:21:25,720 --> 00:21:29,940
+fluorescence، occurs only، و بنقول only، و بنأكد على
+
+272
+00:21:29,940 --> 00:21:33,570
+only، هذه ظاهرة ال fluorescence تحدث فقط in
+
+273
+00:21:33,570 --> 00:21:37,230
+materials possessing close spacing between energy
+
+274
+00:21:37,230 --> 00:21:45,190
+levels، يعني لو لجيت ذرة، لو
+
+275
+00:21:45,190 --> 00:21:49,610
+لجينا ذرة ما فيش close spacing between energy
+
+276
+00:21:49,610 --> 00:21:55,130
+levels، يعني المسافات متساوية ومتباعدة في الطاقة
+
+277
+00:21:55,130 --> 00:21:59,690
+ساعتها مش هيتم ظاهرة ال fluorescence، ضروري يكون
+
+278
+00:21:59,690 --> 00:22:05,400
+عندي يعني مثلا هنابين N2 و N3 المسافة بعيدة، بين
+
+279
+00:22:05,400 --> 00:22:12,000
+N3 و N4 المسافة بعيدة، بين N4 و N5 المسافة بعيدة،
+
+280
+00:22:12,000 --> 00:22:16,180
+بس بين .. بين N5 و N6 المسافة قريبة، إذا الطاقة
+
+281
+00:22:16,180 --> 00:22:20,740
+قريبة، الطاقة قريبة، يعني بنفع لما بكون في عندي
+
+282
+00:22:20,740 --> 00:22:26,510
+مواد فيها .. فيها مدارين متقاربين في الذرات في
+
+283
+00:22:26,510 --> 00:22:30,870
+الطاقة بينفع انها يعني تكون fluorescent material،
+
+284
+00:22:30,870 --> 00:22:34,750
+fluorescent material، اذا ضروري جدا نفهم ان ظاهرة
+
+285
+00:22:34,750 --> 00:22:40,450
+ال fluorescence بتحدث فقط only in materials
+
+286
+00:22:40,450 --> 00:22:45,010
+possessing تملك .. materials تملك a close spacing
+
+287
+00:22:45,010 --> 00:22:49,250
+between energy levels، the essential feature is
+
+288
+00:22:49,250 --> 00:22:53,550
+that the emitted photon has a lower frequency and
+
+289
+00:22:53,550 --> 00:22:56,410
+therefore a different color from that of the
+
+290
+00:22:56,410 --> 00:23:00,690
+stimulating photon، القضية كلها كظاهرة كظاهرة هي
+
+291
+00:23:00,690 --> 00:23:06,000
+عبارة عن إيش؟ أن ال photon اللي تم إشعاعه طاقته أقل
+
+292
+00:23:06,000 --> 00:23:11,220
+وبالتالي تردده أقل من ال stimulating photon اللي
+
+293
+00:23:11,220 --> 00:23:15,160
+إيجا وحفز، وبالتالي طالما ال frequency بتاعته
+
+294
+00:23:15,160 --> 00:23:20,440
+بتختلف ف ال color بتاعه بيختلف، وهذه هي ظاهرة اللي
+
+295
+00:23:20,440 --> 00:23:24,820
+هو ال fluorescence، the clinical utility of this
+
+296
+00:23:24,820 --> 00:23:29,820
+phenomenon اللي هي هتناقش بعد قليل، derives from
+
+297
+00:23:29,820 --> 00:23:32,440
+the difference in frequency between the absorbed
+
+298
+00:23:32,440 --> 00:23:37,340
+and emitted photons، الاستفادة الاستفادة من هذه
+
+299
+00:23:37,340 --> 00:23:40,340
+الظاهرة، ظاهرة ال fluorescence و اللي هنقشها الآن
+
+300
+00:23:40,340 --> 00:23:46,040
+هي استفادة متعددة و تكمن .. تكمن أو .. أو سر
+
+301
+00:23:46,040 --> 00:23:50,300
+الاستفادة من هذه الظاهرة أنه في عندي فرق في ال
+
+302
+00:23:50,300 --> 00:23:53,280
+frequency بين ال absorbed photon و ال emitted
+
+303
+00:23:53,280 --> 00:23:57,020
+photon، ال absorbed photon هيكون blue، ال emitted
+
+304
+00:23:57,020 --> 00:24:00,860
+photon هيكون green، و نشوف كيف احنا بنستفيد ..
+
+305
+00:24:00,860 --> 00:24:03,960
+بنستفيد منه في .. بالذات في مجال طب العيون في
+
+306
+00:24:03,960 --> 00:24:08,350
+حاجات كتيرة، هنضرب أمثلة على ذلك، بنقول fluorescence
+
+307
+00:24:08,350 --> 00:24:11,950
+is the basis of fluorescein angiography، هي أول
+
+308
+00:24:11,950 --> 00:24:16,650
+حاجة، macular autofluorescence and the C-DEL test
+
+309
+00:24:16,650 --> 00:24:20,190
+بدنا نفهم إيش هذه التلت استفادات، طبعا في استفادات
+
+310
+00:24:20,190 --> 00:24:24,130
+أكثر بكثير في مجال طب العيون من مجرد هذه القضية،
+
+311
+00:24:24,130 --> 00:24:27,830
+الاستفادة الأولى اللي هي ال fluorescein
+
+312
+00:24:27,830 --> 00:24:31,790
+angiography، يعني angio معناها وعاء دموي،
+
+313
+00:24:31,790 --> 00:24:36,150
+angiography تصوير الأوعية الدموية باستخدام مادة
+
+314
+00:24:36,150 --> 00:24:40,230
+الفلوريسين، يعني باستخدام ظاهرة الفلوريسين، ظاهرة
+
+315
+00:24:40,230 --> 00:24:43,790
+الفلوريسين، أي أوعية دموية اللي هنصورها، الأوعية
+
+316
+00:24:43,790 --> 00:24:48,610
+الدموية بتاعة الشبكية، نشوف المنظر هذا، المنظر هذا
+
+317
+00:24:48,610 --> 00:24:55,590
+حقيقة، هاي أول شيء، الصورة بتبدو في بعد ال
+
+318
+00:24:55,590 --> 00:24:59,350
+fluorescein angiography، هاي الشبكية، هاي العصب
+
+319
+00:24:59,350 --> 00:25:03,430
+البصري، خارجة منه الأوعية الدموية، الأوعية الدموية
+
+320
+00:25:03,430 --> 00:25:08,130
+مليانة بمادة ال fluorescein، طبعا الكمبيوتر بيعملها
+
+321
+00:25:08,130 --> 00:25:12,910
+بالشكل هذا بحيث أنه تبين أسود و أبيض .. أسود و
+
+322
+00:25:12,910 --> 00:25:16,850
+أبيض .. اذا هذه الصورة النهائية معالجة من قبل
+
+323
+00:25:16,850 --> 00:25:21,650
+الكمبيوتر، طبعا لو احنا حابينا نعرف الشبكية لونها
+
+324
+00:25:21,650 --> 00:25:30,890
+في الوضع الطبيعي كيف، احنا بنقول retina
+
+325
+00:25:41,410 --> 00:25:45,370
+هي صورة الرجل هنا مثلا في الوضع الطبيعي، هاي اللون
+
+326
+00:25:45,370 --> 00:25:48,470
+الطبيعي للvisuals، طبعا مليانة بال blood ال red
+
+327
+00:25:48,470 --> 00:25:54,590
+color وهي الصورة بتاعة الشبكية، هاي الفوفيا، هاي
+
+328
+00:25:54,590 --> 00:25:58,570
+منطقة الفوفيا،
+
+329
+00:25:58,570 --> 00:26:02,610
+هادي ال .. الماكولا اللي هي الفوفيا، طبعا الماكولا
+
+330
+00:26:02,610 --> 00:26:06,530
+اللي بيلاحظ أنه في عندي هنا لون، هاي هنا اللي هو
+
+331
+00:26:06,530 --> 00:26:11,060
+اللون الأصفر، عشان كده بيسموها ماكولا لوتية البقعة
+
+332
+00:26:11,060 --> 00:26:14,280
+الصفراء، هاي العصب البصري، هاي الأوعية الدموية ال
+
+333
+00:26:14,280 --> 00:26:18,200
+retinal arteries and retinal veins، فبالتالي هاي
+
+334
+00:26:18,200 --> 00:26:22,500
+المنظر الطبيعي للعين،
+
+335
+00:26:22,500 --> 00:26:26,580
+الآن احنا ليش بنحقق المادة لفلوريسين عشان تتركز في
+
+336
+00:26:26,580 --> 00:26:29,780
+الأوعية الدموية؟ ليش بدنا تتركز في الأوعية
+
+337
+00:26:29,780 --> 00:26:34,740
+الدموية؟ لأن لو في رشوحات أو إفرازات بتفرزها
+
+338
+00:26:34,740 --> 00:26:38,420
+الأوعية الدموية، زي في اعتلال الشبكية السكري اللي
+
+339
+00:26:38,420 --> 00:26:42,040
+بيخرب الأوعية الدموية إلى آخرين، بنقدر بمواسطة ال
+
+340
+00:26:42,040 --> 00:26:45,540
+fluorescein أنه نعمل fluorescein أنجيографي، تصوير
+
+341
+00:26:45,540 --> 00:26:49,060
+للأوعية الدموية باستعمال مادة ال fluorescein، طيب،
+
+342
+00:26:49,060 --> 00:26:54,960
+الآن بدنا نفهم إيش الفكرة أو كيف احنا عملناها، كيف
+
+343
+00:26:54,960 --> 00:26:58,840
+احنا عملناها، بدنا احنا نصغر الصورة هاي على الآخر
+
+344
+00:27:00,980 --> 00:27:06,240
+و نحاول نكبر هذه الصورة شوية عشان تتضح الأمور، الآن
+
+345
+00:27:06,240 --> 00:27:12,960
+المريض بده يتحقق مادة الفلوريسين عنده في الوريد، هذه
+
+346
+00:27:12,960 --> 00:27:17,430
+المادة اللي هي مادة الفلوريسين برتقالية اللون، طبعا
+
+347
+00:27:17,430 --> 00:27:20,990
+هنا أغمق من البرتقالي لأنه تركيزه أعلى .. تركيزه
+
+348
+00:27:20,990 --> 00:27:26,030
+أعلى، فبالتالي بيسري مع دم المريض بيصل لأوعيات
+
+349
+00:27:26,030 --> 00:27:30,230
+الشبكية، طيب وصل لأوعيات الشبكية وصار يسري في
+
+350
+00:27:30,230 --> 00:27:35,050
+الأوعياء بتاعة شبكية العين، بنروح احنا بنصدر من
+
+351
+00:27:35,050 --> 00:27:39,710
+جهاز التصوير ضوء أبيض، هذا الضوء الأبيض بنمرره عبر
+
+352
+00:27:39,710 --> 00:27:44,490
+blue filter، بلو فيلتر، بسمح للضوء الأزرق فقط يمر
+
+353
+00:27:44,490 --> 00:27:48,810
+باجي الأطوار الموجية بيمنعه، أصبح عنده الآن الموجه
+
+354
+00:27:48,810 --> 00:27:52,990
+لعين المريض اللي حققناه في دمه مادة الفلوريسين،
+
+355
+00:27:52,990 --> 00:27:57,570
+حققناها، أصبح موجه باتجاه عينه فقط، الضوء الأزرق،
+
+356
+00:27:57,570 --> 00:28:02,990
+طيب، الضوء الأزرق هذا هيعمل stimulation لكل
+
+357
+00:28:02,990 --> 00:28:08,450
+الشبكية مش بس للأوعية الدموية، لكل الشبكية، نفرض إجت
+
+358
+00:28:08,450 --> 00:28:12,730
+في المنطقة high اللي أنا بأشر عليها، إجت .. إجت ضوء
+
+359
+00:28:12,730 --> 00:28:15,970
+الأزرق، هينعكس ما فيش .. المنطقة high خالية من
+
+360
+00:28:15,970 --> 00:28:19,930
+الأوعية الدموية، فبالتالي هينعكس مرة تانية، بده يخرج
+
+361
+00:28:19,930 --> 00:28:24,010
+من العين، اصطدم في .. في جدار، اصطدم في ال internal
+
+362
+00:28:24,010 --> 00:28:28,410
+limiting membrane، و بده يرجع يرتد تاني، طيب في
+
+363
+00:28:28,410 --> 00:28:34,670
+مناطق تانية اللي هي مملوءة .. مملوءة بالفلوريسين زي
+
+364
+00:28:34,670 --> 00:28:38,690
+الأوعية الدموية، ولو اتخيلنا أنه الفلوريسين ايضا
+
+365
+00:28:38,690 --> 00:28:42,510
+بيسيل من .. من رشوحات أو من مسامات، يعني نتيجة أنه
+
+366
+00:28:42,510 --> 00:28:46,230
+الوعاء الدموي تالف بسبب السكر، واتجمع الفلوريسين
+
+367
+00:28:46,230 --> 00:28:49,730
+في منطقة ما، غير المنظر اللي احنا شايفينه ايضا
+
+368
+00:28:49,730 --> 00:28:52,850
+هيكون في عندي كمية فلوريسين مثلا في المنطقة هاي
+
+369
+00:28:52,850 --> 00:28:55,550
+هنا ما فيش فلوريسين بالمرة، الأوعية الدموية فيها
+
+370
+00:28:55,550 --> 00:28:59,410
+فلوريسين، مادة الفلوريسين لما تضاء بال .. بال ..
+
+371
+00:28:59,410 --> 00:29:02,870
+بالضوء الأزرق هتحصل معاها ظاهرة ال fluorescence
+
+372
+00:29:02,870 --> 00:29:07,470
+هتصعد الذرات لمستويات أعلى من الطاقة، هترجع
+
+373
+00:29:07,470 --> 00:29:10,850
+لمستوياتها الأصلية بس بالتدريج، هتفقد أول اشي
+
+374
+00:29:10
+
+401
+00:30:55,300 --> 00:31:00,500
+المناطق اللي وجد فيها مادة فلوريسين وبالتالي
+
+402
+00:31:00,500 --> 00:31:04,960
+هتطبع الصورة على جهاز الكمبيوتر ويحولها للون اللي
+
+403
+00:31:04,960 --> 00:31:09,620
+احنا شايفينه .. هيحولها للون اللي احنا شايفينه
+
+404
+00:31:09,620 --> 00:31:14,220
+هذه الصورة طبعا صورة
+
+405
+00:31:14,220 --> 00:31:15,800
+طبيعية مافيش فيها مشكلة
+
+406
+00:31:20,380 --> 00:31:26,320
+يعني لا يوجد أي مشاكل لو احنا روحنا نشوف ال
+
+407
+00:31:26,320 --> 00:31:44,700
+fluorescent angiography لل
+
+408
+00:31:44,700 --> 00:31:47,040
+choroidal neovascular membrane
+
+409
+00:31:56,590 --> 00:32:01,550
+هي مثلا عندي مناطق تجمع فيها الفلوريسين .. نشوف
+
+410
+00:32:01,550 --> 00:32:04,270
+الصورة .. هاي الفلوريسين هيبين .. طبعا الكمبيوتر
+
+411
+00:32:04,270 --> 00:32:10,450
+هيحول الصورة لأبيض و أسود ..
+
+412
+00:32:10,450 --> 00:32:14,910
+هاي عندي صورة واضحة جدا .. هاي هنا في منطقة .. من
+
+413
+00:32:14,910 --> 00:32:20,200
+الإشعاع الفلوريسيني .. الـ fluorescent يعني نتيجة
+
+414
+00:32:20,200 --> 00:32:23,320
+تجمع الفلوريسين، وعنده ها دي choroidal neovascular
+
+415
+00:32:23,320 --> 00:32:26,960
+membrane، هاي عندي مرة تانية، ها دي في منطقة
+
+416
+00:32:26,960 --> 00:32:30,180
+الفوفيا، ها دي أوعية دموية نشأت تحت الفوفيا في
+
+417
+00:32:30,180 --> 00:32:33,300
+الـ choroid، هاي هنا كمان صورة واضحة جدا، فيها
+
+418
+00:32:33,300 --> 00:32:39,380
+leakage، سيلان لمادة الفلوريسين بشكل واضح فهذه كلها
+
+419
+00:32:39,380 --> 00:32:44,480
+بتساعدني أعرف ايش الخلل و اتخذ الخطوات اللازمة
+
+420
+00:32:44,480 --> 00:32:47,700
+للعلاج فإذا أول استفادة من ظاهرة الـ fluorescence
+
+421
+00:32:47,700 --> 00:32:52,000
+هي الـ fluorescein angiography الاستفادة الثانية الـ
+
+422
+00:32:52,000 --> 00:32:55,080
+macular autofluorescenceالـ macular
+
+423
+00:32:55,080 --> 00:32:58,740
+autofluorescence الصورة هذه اللي احنا شايفينها هي
+
+424
+00:32:58,740 --> 00:33:01,700
+عبارة عن ظاهرة الـ fluorescence بدون ما أحقن مادة
+
+425
+00:33:01,700 --> 00:33:04,960
+الـ fluorescein أحيانا بيكون عندي بعض الرشوحات اللي
+
+426
+00:33:04,960 --> 00:33:08,560
+ما بتحتاجش .. اللي ما بتحتاجش عندي أني أحقن
+
+427
+00:33:08,560 --> 00:33:12,040
+fluorescein عشان أشوفها هذه الرشوحات طبعا في أمراض
+
+428
+00:33:12,040 --> 00:33:16,640
+معينة .. في أمراض معينة ما بتحتاجش أني أحقن
+
+429
+00:33:16,640 --> 00:33:20,750
+fluorescein لأن مكونات هذه الإفرازات بتاعة الشبكية
+
+430
+00:33:20,750 --> 00:33:25,810
+بتكون عندي فيها مواد تتمتع بظاهرة الـ fluorescence
+
+431
+00:33:25,810 --> 00:33:29,430
+بس يكفي أعمل stimulation بالـ blue light بالـ blue
+
+432
+00:33:29,430 --> 00:33:34,730
+light و هتحكسلي المنظر اللي أنا يعني بقى أبحث عنه
+
+433
+00:33:34,730 --> 00:33:37,730
+اللي بقى أبحث عنه الـ macular autofluorescence الـ
+
+434
+00:33:37,730 --> 00:33:43,010
+macular autofluorescence طيب ثالث شيء الـ Seidel
+
+435
+00:33:43,010 --> 00:33:46,910
+testأيضا بستخدم ظاهرة الـ fluorescein أو الـ
+
+436
+00:33:46,910 --> 00:33:50,270
+fluorescence في ما يسمى الـ Seidel test عبارة عن
+
+437
+00:33:50,270 --> 00:33:53,570
+ايش الـ Seidel test؟ الـ Seidel test لما بيكون في
+
+438
+00:33:53,570 --> 00:33:58,370
+عندي جرح في القرنية عشان أعرف الجرح نافذ ولا مش 
+
+439
+00:33:58,370 --> 00:34:05,600
+نافذ يعني اخترق أوصار فيه نفاذ للجرح من سطح القرنية
+
+440
+00:34:05,600 --> 00:34:09,320
+للـ anterior chamber يعني فتحة العين بشكل كامل
+
+441
+00:34:09,320 --> 00:34:15,000
+بمعنى أن سائل العين الـ aqueous بيطلع و بيسيل عبر هذا
+
+442
+00:34:15,000 --> 00:34:18,520
+الجرح أحيانا بالعين المجردة أنا ما أقدرش أعرف هذه
+
+443
+00:34:18,520 --> 00:34:23,020
+القضية فبستخدم مادة الفلوريسين بحطها على طرف
+
+444
+00:34:23,020 --> 00:34:28,610
+الجرح الخارجي تمام و بضوي الـ blue light و بقى أضغط
+
+445
+00:34:28,610 --> 00:34:32,070
+ضغط خفيف جدا على العين و أحيانا ما بلزمش الضغط هذا
+
+446
+00:34:32,070 --> 00:34:36,350
+إذا كان في الجرح بيسيل هادي المية اللي هي تحت الـ
+
+447
+00:34:36,350 --> 00:34:38,810
+aqueous اللي جاية من جوا من الـ anterior chamber
+
+448
+00:34:40,530 --> 00:34:44,550
+بيتخفف مادة الفلوريسين ف الـ green light زي ما
+
+449
+00:34:44,550 --> 00:34:47,590
+انتوا شايفينه هذا هذي اللي هو السائل اللي طالع و
+
+450
+00:34:47,590 --> 00:34:51,930
+بي تسرب جاعد بي تسرب لبرا العين فلما بيكون عندي
+
+451
+00:34:51,930 --> 00:34:57,230
+الـ aqueous بيطلع لبرا جاعد بياخد شوية شوية من مادة
+
+452
+00:34:57,230 --> 00:35:00,590
+الفلوريسين اللي أنا حاطيتها على سطح الجرح عند فوهة
+
+453
+00:35:00,590 --> 00:35:03,790
+الجرح بياخد شوية شوية و شايفين اللون الأخضر طب أنا
+
+454
+00:35:03,790 --> 00:35:08,000
+ضاوي أزرقاللون الأخضر معناته هذا السائل حمل كمية
+
+455
+00:35:08,000 --> 00:35:13,000
+من الفلوريسين و خففها و بالتالي أصبحت بتظهر عندي
+
+456
+00:35:13,000 --> 00:35:17,520
+الفلوريسين بشكل اللون الأخضر وهذا هنشوفه بشكل إن
+
+457
+00:35:17,520 --> 00:35:25,470
+شاء الله فيديو طبعا في .. ليه؟ التجارب اللي مرفقة
+
+458
+00:35:25,470 --> 00:35:29,730
+في المودل in Seidel test the high concentration of
+
+459
+00:35:29,730 --> 00:35:33,090
+fluorescein prevents fluorescence from occurring
+
+460
+00:35:33,090 --> 00:35:36,610
+يعني لما بكون عندي التركيز عالي يعني نفرض أن
+
+461
+00:35:36,610 --> 00:35:40,470
+الجرح غير نافذ و سطح العين سليم و حطيت كمية من الـ
+
+462
+00:35:40,470 --> 00:35:44,290
+fluorescein عدد ذرات الـ fluorescein كثير جدا لدرجة
+
+463
+00:35:44,290 --> 00:35:48,580
+أن الـ blue light مش كافي إنه يعني يعملها stimulation
+
+464
+00:35:48,580 --> 00:35:53,840
+لكل ذراتها فبالتالي .. فبالتالي مش هشوف ظاهرة الـ
+
+465
+00:35:53,840 --> 00:35:56,860
+fluorescence بينما لو عندي جرح نافذ و الـ aqueous
+
+466
+00:35:56,860 --> 00:36:00,300
+قاعد بيطلع و بيخففلي في مادة الـ fluorescein شايفين
+
+467
+00:36:00,300 --> 00:36:04,900
+هنا فوهة الجرح بس اللون الأخضر ملاحظ هنا في السائل
+
+468
+00:36:04,900 --> 00:36:08,900
+اللي بيسيل بعيدا عن الجرح هو بيسيل من الجرح بياخد
+
+469
+00:36:08,900 --> 00:36:12,320
+قليل من ذرات الـ fluorescein بيوزعها في السائل و
+
+470
+00:36:12,320 --> 00:36:16,800
+بالتالي .. و بالتالي بيسير الـ blue light كافي إنه
+
+471
+00:36:16,800 --> 00:36:21,060
+يعملها stimulation و تعكس لضوء أخضر، و تعكس لضوء
+
+472
+00:36:21,060 --> 00:36:24,740
+أخضر فيما يسمى بظاهرة الـ fluorescence، إذا in the
+
+473
+00:36:24,740 --> 00:36:27,880
+Seidel test the high concentration of fluorescein
+
+474
+00:36:27,880 --> 00:36:31,220
+prevents fluorescence from occurring، بيمنع ظاهرة
+
+475
+00:36:31,220 --> 00:36:34,280
+الـ fluorescence من إنها تحدث إذا كان تركيز الـ
+
+476
+00:36:34,280 --> 00:36:37,320
+fluorescein عالي كثير only when the fluorescein is
+
+477
+00:36:37,320 --> 00:36:40,940
+sufficiently dilute لما يصير تخفيف و dilution
+
+478
+00:36:40,940 --> 00:36:44,660
+تخفيف بماء يعني هنا بنقصد فيه بالـ aqueous humor
+
+479
+00:36:44,660 --> 00:36:48,120
+because of aqueous leaking from a lesion اللي هو
+
+480
+00:36:48,120 --> 00:36:52,720
+من الجرح is fluorescence seen لما بتتم تخفيفه الـ
+
+481
+00:36:52,720 --> 00:36:55,960
+fluorescein بواسطة السائل اللي طالع من جواة العين
+
+482
+00:36:55,960 --> 00:36:59,340
+عبر الجرح ساعتها ظهرت الـ fluorescence يمكن احنا
+
+483
+00:36:59,340 --> 00:37:05,690
+يعني نشاهدها الآن هذا بالنسبة لطب العيون، بالنسبة لـ
+
+484
+00:37:05,690 --> 00:37:08,970
+الـ gas discharge tube اللي حكينا عنها المرة
+
+485
+00:37:08,970 --> 00:37:11,770
+الماضية common fluorescent lights are gas
+
+486
+00:37:11,770 --> 00:37:16,250
+discharge tubes containing mercury vapor، يعني
+
+487
+00:37:16,250 --> 00:37:19,890
+ممكن أنا أشوف ظاهرة الـ fluorescence، ظاهرة الـ
+
+488
+00:37:19,890 --> 00:37:23,850
+fluorescence في الـ gas discharge tube و بالذات في
+
+489
+00:37:23,850 --> 00:37:26,530
+الـ gas discharge tubes اللي بتحتوي على بخار
+
+490
+00:37:26,530 --> 00:37:30,850
+الزئبق على بخار الزئبق the discrete mercury
+
+491
+00:37:30,850 --> 00:37:34,730
+spectrum is converted to continuous spectrum by
+
+492
+00:37:34,730 --> 00:37:37,370
+coating the inside of the glass tube with
+
+493
+00:37:37,370 --> 00:37:40,710
+fluorescent materials from which the light sources
+
+494
+00:37:40,710 --> 00:37:46,420
+gets its name طيب احنا عاد الـ mercury spectrum
+
+495
+00:37:46,420 --> 00:37:49,940
+عبارة عن spectrum discrete يعني لونه محدد الـ
+
+496
+00:37:49,940 --> 00:37:54,940
+mercury spectrum لونه محدد بس اللي .. اللي بيصير
+
+497
+00:37:54,940 --> 00:38:02,720
+أنه هاي الـ gas discharge tube نفرض و فيها ذرات ..
+
+498
+00:38:02,720 --> 00:38:07,360
+فيها ذرات اللي هي الـ mercury اللي .. اللي هي ذرات
+
+499
+00:38:07,360 --> 00:38:08,380
+بخار الذئبق
+
+500
+00:38:18,590 --> 00:38:26,310
+زرّاية بخار الذئبق اللي
+
+501
+00:38:26,310 --> 00:38:27,770
+باللون الأسود بتشاهدوها
+
+502
+00:38:38,050 --> 00:38:41,550
+هذه هتعطيني discrete mercury spectrum .. discrete
+
+503
+00:38:41,550 --> 00:38:44,610
+mercury spectrum يعني visible light ب range معين
+
+504
+00:38:44,610 --> 00:38:48,270
+.. بدنا نحاوله .. بدنا نحوله لـ continuous
+
+505
+00:38:48,270 --> 00:38:53,890
+spectrum يعني طيف متصل بيطلع جدار الأنبوبة
+
+506
+00:38:53,890 --> 00:38:58,190
+الزجاجية اللي هي الـ gas discharge tube بمواد فيها
+
+507
+00:38:58,190 --> 00:39:03,390
+ظاهرة الـ fluorescence بمواد يعني .. الها مدارات
+
+508
+00:39:03,390 --> 00:39:07,050
+متقاربة from which this light source gets its name
+
+509
+00:39:07,050 --> 00:39:10,670
+بأبطل أسميها gas discharge .. mercury gas
+
+510
+00:39:10,670 --> 00:39:14,710
+discharge tube أو لمبة البخار الذئبكي، لأ بسميها
+
+511
+00:39:14,710 --> 00:39:17,790
+fluorescent lamp بسميها fluorescent lamp لأنها
+
+512
+00:39:17,790 --> 00:39:21,650
+مطلية من الداخل .. مطلية من الداخل بـ fluorescent
+
+513
+00:39:21,650 --> 00:39:24,410
+material مش شرط أنه الـ fluorescent sodium اللي
+
+514
+00:39:24,410 --> 00:39:27,420
+حكينا عنه في هذه المحاضرة، لكن في إنه fluorescent
+
+515
+00:39:27,420 --> 00:39:30,480
+materials كثيرة، احنا قلنا الـ fluorescent material
+
+516
+00:39:30,480 --> 00:39:34,360
+هي أي material فيها عندها مدارين متقاربين عشان
+
+517
+00:39:34,360 --> 00:39:38,100
+تقدر تتمتع بظاهرة الـ fluorescence، ليه
+
+518
+00:39:38,100 --> 00:39:41,140
+fluorescence؟ حتى نتوقف عن ظاهرة أخرى هي الـ
+
+519
+00:39:41,140 --> 00:39:44,200
+phosphorescence ويعطيكم العافية والسلام عليكم
+
+520
+00:39:44,200 --> 00:39:45,920
+ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/cXuZwortwt8_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/cXuZwortwt8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7faf06489a6e2dc9fa2e07b94c453da89a3b52a2
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/cXuZwortwt8_postprocess.srt
@@ -0,0 +1,2080 @@
+1
+00:00:01,750 --> 00:00:05,830
+بسم الله الرحمن الرحيم بنواصل محاضرات ال physical
+
+2
+00:00:05,830 --> 00:00:11,070
+optics واتوقفنا عند ظاهرة تسمى ال fluorescence ال
+
+3
+00:00:11,070 --> 00:00:15,210
+fluorescence عبارة عن ظاهرة فيزيائية هي عبارة عن
+
+4
+00:00:15,210 --> 00:00:19,130
+إيش؟ بنقول when an electron absorbs a photon and
+
+5
+00:00:19,130 --> 00:00:22,900
+jumps to a higher energy levelUsually it quickly
+
+6
+00:00:22,900 --> 00:00:27,120
+drops back to its original level and emits a
+
+7
+00:00:27,120 --> 00:00:31,600
+photon identical in frequency to the one it
+
+8
+00:00:31,600 --> 00:00:37,000
+absorbed.الآن لما في إلكترون بيمتص فوتون، يعني ده
+
+9
+00:00:37,000 --> 00:00:41,980
+بيمتص حصة من الطاقة، نرجع لرسمة توضح هذه القضية
+
+10
+00:00:48,160 --> 00:00:52,400
+بنقول لما في عندنا إلكترون إيجاله حصة من الطاقة،
+
+11
+00:00:52,400 --> 00:00:57,660
+إيجاله فوتون، صعد ل energy level معين، عادة اللي
+
+12
+00:00:57,660 --> 00:01:01,060
+بيحصل إن هذا الإلكترون اللي امتص طاقة و طلع لمدار
+
+13
+00:01:01,060 --> 00:01:05,000
+أعلى في الطاقة، الطاقة نفسها اللي امتصها هيفقدها
+
+14
+00:01:05,680 --> 00:01:10,740
+وهينزل للمدار الأصلي بتاعه للمسكن الأصلي بتاعه
+
+15
+00:01:10,740 --> 00:01:15,980
+نفرض إن طاقة الفوتون اللي جاي 2 جول هدت إن هذا
+
+16
+00:01:15,980 --> 00:01:19,980
+الإلكترون اللي موجود في المستوى رقم 2 صعد بالـ2
+
+17
+00:01:19,980 --> 00:01:24,140
+جول اللي أضيفه إليه صعد للمدار رقم 6 على سبيل
+
+18
+00:01:24,140 --> 00:01:30,650
+المثال عادة بعد فترة قليلة جدا بيفقد الـ2 جولبشكل
+
+19
+00:01:30,650 --> 00:01:35,830
+فوتون وبينزل للمسكن الأصلي له، إذا هو لما اكتسب
+
+20
+00:01:35,830 --> 00:01:40,310
+اكتسب اتنين جول و لما فقد فقد اتنين جول، الفوتون
+
+21
+00:01:40,310 --> 00:01:46,100
+اللي اجاو أعطى طاقته للإلكترون طبعا الفوتون هو حصة
+
+22
+00:01:46,100 --> 00:01:50,540
+من الطاقة bucket of energy أعطى طاقته للإلكترون و
+
+23
+00:01:50,540 --> 00:01:55,280
+أدى لصعوده للمدار رقم 6 على سبيل المثال فقد نفس
+
+24
+00:01:55,280 --> 00:01:58,540
+الفوتون ليش نفس الفوتون لأن نفس الحصة اللى إجت هي
+
+25
+00:01:58,540 --> 00:02:02,990
+نفس الحصة اللى غادرت نفس الفوتوناللي جاء هو نفس
+
+26
+00:02:02,990 --> 00:02:06,770
+الفوتون اللي غادر بمعنى ترددهم واحد كمية الطاقة
+
+27
+00:02:06,770 --> 00:02:10,030
+اللي اجت هي كمية الطاقة اللي غادرت فبالتالي زي ما
+
+28
+00:02:10,030 --> 00:02:15,310
+صعد من اتنين لستةهينزل من ستة لاتنين طب نفرض انه
+
+29
+00:02:15,310 --> 00:02:19,590
+في عندي حص الطاقة مثلا نصف جول قدت لصعوده من اتنين
+
+30
+00:02:19,590 --> 00:02:25,050
+لتلاتة هيفقد النص جول وينزل من تلاتة لاتنين
+
+31
+00:02:25,050 --> 00:02:31,730
+فالفوتون اللي اكتسبه هو نفس الفوتون اللي يعني فقده
+
+32
+00:02:31,730 --> 00:02:35,250
+اللي هم نفس الطاقة يعني اللي هم نفس التردد ونفس
+
+33
+00:02:35,250 --> 00:02:38,630
+الطول الموجودة هدف الطبيعي يعني انا جاية احنا
+
+34
+00:02:38,630 --> 00:02:45,730
+بنحكي عن الأمور الطبيعيةفيها شيء يعني مختلف قليلا
+
+35
+00:02:45,730 --> 00:02:49,810
+بيقدّي للظاهرة اللي احنا بصددها اليوم however
+
+36
+00:02:49,810 --> 00:02:55,370
+atoms of some elements have two energy levels that
+
+37
+00:02:55,370 --> 00:02:59,590
+are close together نشوف المنظر التالي، بنقول هي أن
+
+38
+00:02:59,590 --> 00:03:06,070
+مثلا ذرّمة، نموذج لذرّمة هي مستوى من مستويات
+
+39
+00:03:06,070 --> 00:03:12,890
+الطاقة اللي هو المستوى يعني الأولالمستوى التاني
+
+40
+00:03:12,890 --> 00:03:16,890
+المستوى التالت المستوى التالت هنا مرتبينهم واحد
+
+41
+00:03:16,890 --> 00:03:20,970
+اتنين تلاتة حسب مقدار الطاقة هو هذا الاعلى طاقة
+
+42
+00:03:20,970 --> 00:03:26,090
+ادنى منه طاقة ادنى جدا فى الطاقة ترتيبه رقم تلاتة
+
+43
+00:03:26,090 --> 00:03:29,690
+فى الطاقة بس هو الاقرب للنواة هو الاقرب للنواة
+
+44
+00:03:29,690 --> 00:03:34,010
+بنقول electron كان بيمشي فى المدار اللى سمناه رقم
+
+45
+00:03:34,010 --> 00:03:39,810
+تلاتةأجته حصة من الطاقة أدت لصعوده مدارين مرة
+
+46
+00:03:39,810 --> 00:03:42,910
+واحدة يعني ما .. ما صعد للمدار التالت .. التاني
+
+47
+00:03:42,910 --> 00:03:47,610
+صعد للمدار الرقم .. الرمزين له الرقم واحد، لذن هو
+
+48
+00:03:47,610 --> 00:03:52,310
+قفز عبر مدارين، ليش؟ لأن هذه الذرة أو هذا العنصر
+
+49
+00:03:52,310 --> 00:03:56,950
+في مدارين متقاربين، يعني أول شرط من شروط ظاهرة ال
+
+50
+00:03:56,950 --> 00:04:00,330
+fluorescence أن يكون بعض العنصر اللي .. اللي
+
+51
+00:04:00,330 --> 00:04:04,310
+بيتمتع بخاصية ال fluorescence هذه ال elementshave
+
+52
+00:04:04,310 --> 00:04:07,710
+two energy levels that are close together زي ما
+
+53
+00:04:07,710 --> 00:04:11,770
+الرسم عندي أنا بتودع، يعني المدار هذا والمدار هذا
+
+54
+00:04:11,770 --> 00:04:14,890
+جراب من بعض في الطاقة، لو قلنا طاقة المدار هذا
+
+55
+00:04:14,890 --> 00:04:19,290
+اتنين جول وهذا تسعة جول، هذا هيكون مثلا عشرة جول
+
+56
+00:04:19,290 --> 00:04:24,150
+جراب من بعض في .. في .. في الطاقة، جراب من بعض في
+
+57
+00:04:24,150 --> 00:04:30,610
+ال spacing بتاعنا، الآن في electron بيدورفى المدار
+
+58
+00:04:30,610 --> 00:04:34,770
+اللى قولنا طاقته اتنين جول هذا الالكترون ضرورى
+
+59
+00:04:34,770 --> 00:04:37,990
+تكون طاقته ايضا اتنين جول عشان يكون مناسبة انه
+
+60
+00:04:37,990 --> 00:04:44,510
+يدور فى هذا المدار طيب اجاله تمانية جول مرة واحدة
+
+61
+00:04:44,510 --> 00:04:49,430
+اصبح طاقته مش اتنين جول اصبح طاقته عشرة جول فهذا
+
+62
+00:04:49,430 --> 00:04:53,070
+المدار طاقته تسعة جول وهذا المدار عشرة جول فهيقفز
+
+63
+00:04:53,780 --> 00:04:57,920
+مرة واحدة هيطلع من المدار هذا للمدار الأخر للمدار
+
+64
+00:04:57,920 --> 00:05:03,000
+الأخر لأنه أصبح طاقته تناسب طاقة المدار الأخر طيب
+
+65
+00:05:03,000 --> 00:05:07,680
+اللي بيحصل احنا الإلكترونات زي ما هي بتحب ترجع
+
+66
+00:05:07,680 --> 00:05:13,440
+لمداراتها الأصلية ومساكنها الأصلية بس هو رجوعه
+
+67
+00:05:13,440 --> 00:05:16,860
+هيكون مش مرة واحدة زي ما المثال اللي احنا ضربناه
+
+68
+00:05:16,860 --> 00:05:23,680
+قبل شوية مش مرة واحدة ليس مرة واحدةإنه طلع من
+
+69
+00:05:23,680 --> 00:05:27,160
+اتنين لستة حيرجع من ستة لاتنين أو طلع من اتنين
+
+70
+00:05:27,160 --> 00:05:30,940
+لتلاتة حيرجع لاتنين مرة واحدة أو طلع مثلا من اتنين
+
+71
+00:05:30,940 --> 00:05:36,940
+لخمسة حينزل من خمسة لاتنين دفعة واحدة، لأ العناصر
+
+72
+00:05:36,940 --> 00:05:41,680
+اللي فيها ظاهرة ال fluorescence اللي بيصير فيها
+
+73
+00:05:41,680 --> 00:05:46,480
+إنه أول شيء في عندي مدارين متقاربينالإلكترون بيصعد
+
+74
+00:05:46,480 --> 00:05:50,520
+من مدار أدنى في الطاقة للمدار الأعلى قافزا عبر
+
+75
+00:05:50,520 --> 00:05:54,120
+المدار اللي أقل منه شوية و الجريب منه في الطاقة
+
+76
+00:05:54,120 --> 00:05:59,460
+هدف السعود الان في النزول بده ينزل بالتدريج مش مرة
+
+77
+00:05:59,460 --> 00:06:04,580
+واحدة هينزل هو أصبح طاقته عشرة جول هيفقد حصة من
+
+78
+00:06:04,580 --> 00:06:08,840
+الطاقة مقدارها واحد جول مقدارها واحد جول احنا
+
+79
+00:06:08,840 --> 00:06:13,330
+خلينا على أساس الأمور تظلها يعني واضحةبنقول
+
+80
+00:06:13,330 --> 00:06:28,150
+كالهاتي المدار الأخير عشرة جول والمدار
+
+81
+00:06:28,150 --> 00:06:32,770
+اللي قريب منه في مستوى الطاقة في كمية الطاقة تسعة
+
+82
+00:06:32,770 --> 00:06:33,350
+جول
+
+83
+00:06:50,620 --> 00:06:59,780
+والمستوى الأدنى اتنين جول هذه
+
+84
+00:06:59,780 --> 00:07:04,040
+الأرقام افتراضية وليست حقيقية بس لتقريب المفهوم
+
+85
+00:07:04,040 --> 00:07:09,390
+لتقريب المفهوم اذا عندي مدرع اتنين جولعندي مدار
+
+86
+00:07:09,390 --> 00:07:12,430
+اللي بعده تسعة جول اللي بعده عشرة جول هدوله
+
+87
+00:07:12,430 --> 00:07:15,650
+المدارين متقاربين من بعض في الطاقة فعشان هيك لما
+
+88
+00:07:15,650 --> 00:07:19,390
+بيرسموا .. لما بيرسموا على الورق ال spacing بينهم
+
+89
+00:07:19,390 --> 00:07:23,110
+قريب بينما لما بيفرجوا عن مدار آخر في الطاقة فرق
+
+90
+00:07:23,110 --> 00:07:27,830
+كبير بيكون ال spacing بينه وبينهم اكبر اجت .. اجت
+
+91
+00:07:27,830 --> 00:07:33,790
+فوتون حصة من الطاقة للإلكترون اللي هنا اجاله حصة
+
+92
+00:07:33,790 --> 00:07:38,150
+من الطاقة كدهش مقدار هذه الحصة تمانية جول
+
+93
+00:07:46,790 --> 00:07:53,570
+هذا الفوتون يحمل طاقة او هو عبارة عن حصة من الطاقة
+
+94
+00:07:53,570 --> 00:07:57,210
+مقدارها تمانية جول اكتسبها الالكترون اللي طاقته
+
+95
+00:07:57,210 --> 00:08:01,050
+اتنين جول اصبح طاقته عشرة جول مش هينفع يدور في
+
+96
+00:08:01,050 --> 00:08:04,590
+المدار التالي لأ بده يقفز عبر مدار هيعدي المدار
+
+97
+00:08:04,590 --> 00:08:08,270
+اللي طاقته تسعة جول ويصير فيه المدار العشرة جول
+
+98
+00:08:08,270 --> 00:08:11,810
+الان احنا قولنا الالكترون اصبح الان هذا الالكترون
+
+99
+00:08:11,810 --> 00:08:17,430
+اللي اكتسب طاقة الفوتون اصبحفي المدار الأخير اللي
+
+100
+00:08:17,430 --> 00:08:22,070
+هو الأعلى طاقة بيحب يرجع لمسكنه الأصلي بس مش هيرجع
+
+101
+00:08:22,070 --> 00:08:28,050
+مرة واحدة هيفقد حصة قليلة من الطاقة مقدارها واحد
+
+102
+00:08:28,050 --> 00:08:34,150
+جول طاقة قليلة مقدارها واحد جول طاقته أصبحت عشرة
+
+103
+00:08:34,150 --> 00:08:39,120
+جول بس هيفقد من العشرة جول1 جول هذه هيفقدها بشكل
+
+104
+00:08:39,120 --> 00:08:43,700
+حصة من الطاقة طاقة قليلة جدا جاية او الفوتون اللى
+
+105
+00:08:43,700 --> 00:08:47,220
+هيفقدها او الحصة اللى فقدها فى ال infrared region
+
+106
+00:08:47,220 --> 00:08:55,990
+مش هنشوفه مش هنشوفه اذا ال infrared فوتوناللي
+
+107
+00:08:55,990 --> 00:08:59,830
+انفقد طاقته واحد جول، طاقة قليلة، مش في ال range،
+
+108
+00:08:59,830 --> 00:09:03,770
+اللي ما range طيب، لسه طاقة ال electrode لما هبط
+
+109
+00:09:03,770 --> 00:09:09,030
+الهبوط الأول، أصبح طاقته تسعة جول، بينما لسه
+
+110
+00:09:09,030 --> 00:09:12,730
+مارجعش لمسكنه الأصلي، هيروح فاقد الحصة التانية من
+
+111
+00:09:12,730 --> 00:09:18,230
+الطاقة، اللي هي كمية أكبر، هيفقد سبعة جول، سبعة
+
+112
+00:09:18,230 --> 00:09:18,710
+جول
+
+113
+00:09:22,610 --> 00:09:29,510
+هذه هيفقدها بشكل فوتون فوتون له تردد معين طيب،
+
+114
+00:09:29,510 --> 00:09:35,130
+الان انا عندى فوتون اجى وغادر بعده فوتونين
+
+115
+00:09:35,130 --> 00:09:39,430
+بالتدريج الفوتون اللى اجى طاقته تمانية جول تمانية
+
+116
+00:09:39,430 --> 00:09:42,970
+جول الفوتون الاول اللى غادر او الحصة الاولى من
+
+117
+00:09:42,970 --> 00:09:46,330
+الطاقة اللى غادرت وفقدها الالكترون وهبط من المدار
+
+118
+00:09:46,330 --> 00:09:51,820
+الأخير للي قبله طاقتها واحد جول الفوتون التانىاللي
+
+119
+00:09:51,820 --> 00:09:55,000
+رجع ال electron لمداره الأصلي و لمسكهم الأصلي
+
+120
+00:09:55,000 --> 00:09:59,380
+طاقته سبعة جولة، أي التلت فوتونات هو الأعلى في
+
+121
+00:09:59,380 --> 00:10:04,360
+الطاقة، الأعلى في الطاقة هواللي اجا تمانية جول
+
+122
+00:10:04,360 --> 00:10:08,880
+طاقته فبالتالي هذا الفوتون تردده هيكون أعلى من
+
+123
+00:10:08,880 --> 00:10:13,940
+تردد الفوتونين اللي هو هذا الفوتون وهذا الفوتون
+
+124
+00:10:13,940 --> 00:10:18,640
+الفوتونات هي حصص من الطاقة هذه الحصص من الطاقة قد
+
+125
+00:10:18,640 --> 00:10:23,740
+تكون مرئية وقد تكون غير مرئية هذا له طاقة معينة هي
+
+126
+00:10:23,740 --> 00:10:28,550
+الأعلى في التلاتة هو جاي اكتسبوا الالكترونتردده
+
+127
+00:10:28,550 --> 00:10:34,050
+مناسب للتردد مثلا الأزرق، الأزرق، الضوء المرئي في
+
+128
+00:10:34,050 --> 00:10:39,570
+ال range بتاع التردد الأزرق، إله طاقة تمنيجه، الآن
+
+129
+00:10:39,570 --> 00:10:45,110
+صعد ال electron من المدار الأدنى للمدار الأعلى على
+
+130
+00:10:45,110 --> 00:10:49,150
+الإطلاق في الرسم اللي إحنا شايفينهالان التمانية
+
+131
+00:10:49,150 --> 00:10:52,290
+جول هيعود يفقدهم عشان يرجع لمسكنه الأصلي بس
+
+132
+00:10:52,290 --> 00:10:57,630
+هيفقدهم بالتدريج أول هيفقد واحد جول بشكل فوتون
+
+133
+00:10:57,630 --> 00:11:01,830
+طاقته واحد جول يعني طاقته ضعيفة جدا إذا ما قُرنت
+
+134
+00:11:01,830 --> 00:11:07,170
+بطاقة الفوتون المكتسب، الفوتون المكتسب ضعيفة جدا،
+
+135
+00:11:07,170 --> 00:11:10,410
+قليلة جدا الطاقة، إذا التردد قليل هييجي في ال
+
+136
+00:11:10,410 --> 00:11:15,870
+infrared region يعني هيكون طاقة غير مرئية فقدت،
+
+137
+00:11:15,870 --> 00:11:19,630
+مقدارها واحد جولطولها الموجي جاي في ال infrared
+
+138
+00:11:19,630 --> 00:11:23,670
+وهذه لن تراها، لن تراها العين المجردة طيب، ضال
+
+139
+00:11:23,670 --> 00:11:27,610
+عندي سبعة جول، بدنا نفقدهم، هيفقدهم الإلكترون
+
+140
+00:11:27,610 --> 00:11:32,190
+السبعة جول عشان يفقي في المرحلة التالية عشان يرجع
+
+141
+00:11:32,190 --> 00:11:37,850
+لمسكنه الأصلي، هيفقدهم بشكل فوتون أو حصة من الطاقة
+
+142
+00:11:37,850 --> 00:11:42,770
+مقدارها سبعة جول طيب، بدنا نقارن الفوتون الأخير
+
+143
+00:11:43,600 --> 00:11:47,980
+اللي فقد اللي هو مقدار الطاقة و سبعة جول بالفوتون
+
+144
+00:11:47,980 --> 00:11:52,640
+المكتسب مين أكتر منهم في الطاقة اللي أكتر في
+
+145
+00:11:52,640 --> 00:11:55,760
+الطاقة اللي هو المكتسب تمانية جول و الأقل في
+
+146
+00:11:55,760 --> 00:11:59,500
+الطاقة احنا ننسى الفوتون ال infrared خلاص فقدناه و
+
+147
+00:11:59,500 --> 00:12:04,060
+ماشوفناهوش بدنا نقارن بين الفوتون المكتسب و
+
+148
+00:12:04,060 --> 00:12:09,760
+الفوتون المرئي اللي فقد اللي هو سبعة جول مين أكتر
+
+149
+00:12:09,760 --> 00:12:16,130
+في الطاقةاللي هو المكتسب المكتسب جاي في التردد
+
+150
+00:12:16,130 --> 00:12:21,410
+الأزرق في ال blue light region طب هنا طاقته أقل
+
+151
+00:12:21,410 --> 00:12:26,550
+إذا تردده أقل إذا طول الموج أطول شوية هيجي في ال
+
+152
+00:12:26,550 --> 00:12:30,010
+green في ال green يعني الفوتون هذا اللي مفقود
+
+153
+00:12:30,010 --> 00:12:35,520
+طاقته أقل من الفوتون المكتسبطاقته أقل من الفوتون
+
+154
+00:12:35,520 --> 00:12:39,620
+المكتسب وطالما طاقته أقل من الفوتون المكتسب إذا
+
+155
+00:12:39,620 --> 00:12:43,520
+تردده أقل لأن الطاقة و التردد ال frequency
+
+156
+00:12:43,520 --> 00:12:47,560
+بتناسبوا ترضيا مع بعضهم البعض فإذا كان هذا تردده
+
+157
+00:12:47,560 --> 00:12:52,440
+في الأزرق هذا هيكون تردده في موجات أطول قليلا زي
+
+158
+00:12:52,440 --> 00:12:56,600
+اللي هو ال green light
+
+159
+00:12:59,450 --> 00:13:03,610
+هذه الظاهرة تسمى ال fluorescence، هذه الظاهرة تسمى
+
+160
+00:13:03,610 --> 00:13:08,930
+ال fluorescence يعني بالعربي ممكن نسميها ظاهرة
+
+161
+00:13:08,930 --> 00:13:12,930
+التفلور، ظاهرة التفلور، إيش يعني ظاهرة التفلور؟
+
+162
+00:13:12,930 --> 00:13:19,510
+يعني إحنا بنعمل stimulation طول موجي معينزي الطول
+
+163
+00:13:19,510 --> 00:13:27,870
+الموجي الأزرق وبناخد إشعاع أو ضوء آخر بتردد آخر من
+
+164
+00:13:27,870 --> 00:13:31,370
+هذه المادة أو من هذه الذرع الذرع احنا عملنا
+
+165
+00:13:31,370 --> 00:13:36,820
+stimulation للإلكترونات بتاعهاب .. بإضاءة معينة ..
+
+166
+00:13:36,820 --> 00:13:41,440
+بإضاءة معينة اللي هي الطول الموجي الأزرق وأشعاتنا
+
+167
+00:13:41,440 --> 00:13:46,620
+إضاءة الطول الموجي الأخضر نشوف المنظر التالي
+
+168
+00:13:46,620 --> 00:13:54,790
+كاستخدام في .. في موضوع طب العيوناحنا المادة ..
+
+169
+00:13:54,790 --> 00:13:59,430
+المادة اللي بنحطها و بنقطرها في العين تسمى
+
+170
+00:13:59,430 --> 00:14:02,570
+fluorescein من .. من .. من أحدث اسمها من ظاهرة ال
+
+171
+00:14:02,570 --> 00:14:05,630
+fluorescence مادة ال fluorescein sodium .. ال
+
+172
+00:14:05,630 --> 00:14:11,590
+fluorescein sodium لو نطلع على منظر مكبر، هاي قطرة
+
+173
+00:14:12,420 --> 00:14:17,340
+تحتوي على سائل لفلوريسين صوديوم وهذه شرائح او
+
+174
+00:14:17,340 --> 00:14:24,620
+استربات او ورق يعني طرفه عبارة عن ورقة يعني مشبعة
+
+175
+00:14:24,620 --> 00:14:29,460
+بالفلوريسين صوديوم بنبللها بسائل معين غالبا بنج
+
+176
+00:14:29,460 --> 00:14:33,180
+موضع وهي بنحطها على سطح الكونجانكتايفا على سطح
+
+177
+00:14:33,180 --> 00:14:39,960
+الآن بعد هيك طبعا إذا ملاحظين لون المادة برتقالي
+
+178
+00:14:40,720 --> 00:14:45,640
+لما بنحطها على سطح العين ايضا بتضالها برتقالية زي
+
+179
+00:14:45,640 --> 00:14:49,560
+المنظر اللي انتوا شايفينه هذا المنظر بعد ما حطينا
+
+180
+00:14:49,560 --> 00:14:53,920
+بعد ما جطرنا جطرة ال fluorescein اللي هي هاي او ال
+
+181
+00:14:53,920 --> 00:14:57,920
+strip بتاع ال fluorescein اللي احنا شايفينه سواء
+
+182
+00:14:57,920 --> 00:15:03,920
+استعملت هذه مع نقطة locale أو بنج موضع مع نقطة بنج
+
+183
+00:15:03,920 --> 00:15:08,420
+موضع او استعملته جاهز بشكل قطرة المنظر الأول هيكون
+
+184
+00:15:08,420 --> 00:15:12,300
+عندى هنابس مش هي كظاهرة ال fluorescence هو هذه
+
+185
+00:15:12,300 --> 00:15:17,200
+مادة ال fluorescein هي مادة .. مادة فيها في ذراتها
+
+186
+00:15:17,200 --> 00:15:20,840
+مدارين متقاربين و احنا قلنا شرط عشان يحدث ال
+
+187
+00:15:20,840 --> 00:15:25,480
+fluorescence انه اضوب لون و اخد لون تاني عشان يحدث
+
+188
+00:15:25,480 --> 00:15:29,520
+لازم تكون العنصر المستعمل .. العنصر المستعمل في
+
+189
+00:15:29,520 --> 00:15:34,550
+ذراته في .. في ذراته في مدارين متقاربينالان احنا
+
+190
+00:15:34,550 --> 00:15:38,630
+قطرنا الفلوريسين اش هنعمل؟ هنروح نعمل stimulation
+
+191
+00:15:38,630 --> 00:15:41,970
+لمادة الفلوريسين هذه اللي تبدو باللون الأصفر او
+
+192
+00:15:41,970 --> 00:15:46,410
+البردقالي هنعملها stimulation ب high energy photon
+
+193
+00:15:46,410 --> 00:15:50,290
+high energy photon يعني ضوء أزرق لأنه في الضوء
+
+194
+00:15:50,290 --> 00:15:54,870
+المرئي في الضوء المرئي الفوتونات الأعلى طاقتها هي
+
+195
+00:15:54,870 --> 00:15:57,990
+الأزرق أعلى من الأخضر وأعلى من الأصفر وأعلى من
+
+196
+00:15:57,990 --> 00:16:01,430
+الأحمر لأنه ترددها أعلى بما أنه ترددها أعلى معناه
+
+197
+00:16:01,430 --> 00:16:08,750
+طاقتها أعلىاحنا ضوينا .. ضوينا على قرانية العين أو
+
+198
+00:16:08,750 --> 00:16:12,970
+على سطح العين كقرانية مع ال conjunctiva ضوينا
+
+199
+00:16:12,970 --> 00:16:16,170
+المفروض أن اللون هذا اللي اللي لاجينا اللي هو
+
+200
+00:16:16,170 --> 00:16:20,490
+اللون الطبيعي للمادة بس لما احنا ضوينا بالضوء
+
+201
+00:16:20,490 --> 00:16:23,830
+الأزرق، تشايفين الضوء الأزرق؟ العين مضوية بالضوء
+
+202
+00:16:23,830 --> 00:16:28,850
+الأزرق، إيش اللي صار؟ المناطق اللي أخدت fluoresin
+
+203
+00:16:28,850 --> 00:16:35,140
+أو تشربت هذه المادةهذه المادة أصبحت المادة مركزة
+
+204
+00:16:35,140 --> 00:16:39,260
+فيها بشكل كويس إجت ضوء الأزرق عمل stimulation
+
+205
+00:16:39,260 --> 00:16:44,040
+لذرات الفلوريسين لما عمل stimulation لذرات
+
+206
+00:16:44,040 --> 00:16:47,380
+الفلوريسين بالضوء الأزرق بالتردد الأزرق يعني
+
+207
+00:16:47,380 --> 00:16:52,320
+اكتسبت فوتون طاقته عالية شوية صعدت الإلكترونات في
+
+208
+00:16:52,320 --> 00:16:57,740
+هذه الذرات إلى مدارات أعلى قافزة عبر المدار التالي
+
+209
+00:16:57,740 --> 00:17:04,020
+الآن فقدت على التواليوبشكل لحظي بمجرد ماتبتصعد
+
+210
+00:17:04,020 --> 00:17:10,020
+بترجع فورا بس ترجعه بيكون انه بتنزل للمدار اللي
+
+211
+00:17:10,020 --> 00:17:13,540
+أدنى قليلا بتفقد infrared photon هذا ال infrared
+
+212
+00:17:13,540 --> 00:17:16,900
+photon احنا مش هنشوفه لأنه لا يراه لأنه في ال
+
+213
+00:17:16,900 --> 00:17:23,180
+range الغير مرئي و بتفقد بعده مباشرة photon باللون
+
+214
+00:17:23,180 --> 00:17:27,020
+الأخضر باللون الأخضر ليش photon باللون الأخضر لأن
+
+215
+00:17:27,020 --> 00:17:31,870
+طاقتهطاقته أقل من الفوتون المكتسب الفوتون المكتسب
+
+216
+00:17:31,870 --> 00:17:35,270
+جاي في ال range الأزرق فطاقت هذا الفوتون التالي
+
+217
+00:17:35,270 --> 00:17:40,390
+المرئي بالنسبة لنا أقل فبالتالي هيكون في التردد أو
+
+218
+00:17:40,390 --> 00:17:44,630
+في ال green light region في ال green light region
+
+219
+00:17:44,630 --> 00:17:48,310
+فهذه هي الظاهرة تسمى ظاهرة ال fluorescence ظاهرة
+
+220
+00:17:48,310 --> 00:17:54,790
+ال fluorescence ضوين مادة أو منطقة فيها مادة
+
+221
+00:17:54,790 --> 00:18:03,290
+كيميائيةبتتمدع بظاهر ال fluorescence ضوينها ب high
+
+222
+00:18:03,290 --> 00:18:08,800
+energy photon اللي هو الضوء الأزرقأشععتلي أو ردتلي
+
+223
+00:18:08,800 --> 00:18:13,980
+أو عكستلي lower energy photon lower energy photon
+
+224
+00:18:13,980 --> 00:18:18,460
+فوتون أقل منه في الطاقة طب ليش؟ لأنه قبل ما اشع
+
+225
+00:18:18,460 --> 00:18:22,480
+هذا lower energy photon أشعت كمية ضئيلة من الطاقة
+
+226
+00:18:22,480 --> 00:18:26,540
+بشكل ال infrared الغير مرئي طيب، الآن إيش
+
+227
+00:18:26,540 --> 00:18:31,400
+الاستفادة العملية من هذه القضية؟ استفادات حقيقة في
+
+228
+00:18:31,400 --> 00:18:35,840
+مجال طب العيون لا تكاد تحصى ولا تعاداحنا المنظر
+
+229
+00:18:35,840 --> 00:18:39,440
+اللي شايفينه هذا جرح في قرانية العين لما قرانية
+
+230
+00:18:39,440 --> 00:18:44,620
+العين بيصير فيها جرحيعني في مكان من القرنية عشان
+
+231
+00:18:44,620 --> 00:18:47,840
+نعرف حدود الجريح و هل هو كبير ولا صغير او كده
+
+232
+00:18:47,840 --> 00:18:52,440
+المنطقة اللي فيها الجريح عادة بيتتشبع او بتمتص
+
+233
+00:18:52,440 --> 00:18:56,160
+مادة الفلوريسين طيب لما بنضوط ضوء الأزرق شايفين
+
+234
+00:18:56,160 --> 00:19:00,060
+الأماكن اللي مش مجروحة عادة ما أخدت فلوريسين
+
+235
+00:19:00,060 --> 00:19:03,800
+مامتصت مادة الفلوريسين فعشان هيك ظاهرة ال
+
+236
+00:19:03,800 --> 00:19:09,230
+fluorescence هتكون مركزةفي المنطقة اللي فيها الجرح
+
+237
+00:19:09,230 --> 00:19:11,670
+و احنا هنشوف الجرح باللون هذا اللي احنا شايفينه
+
+238
+00:19:11,670 --> 00:19:15,730
+اللون اللون الأخضر بس بشرط انه نضوي .. نضوي او
+
+239
+00:19:15,730 --> 00:19:19,410
+نعمل stimulation لمادة الفلوريسين بالضوء الأزرق
+
+240
+00:19:19,410 --> 00:19:22,750
+اذا ال corneal abrasion .. ال corneal abrasion انا
+
+241
+00:19:22,750 --> 00:19:27,210
+بقدر اعرفه بواسطة مادة الفلوريسين و اللي هي بتشتغل
+
+242
+00:19:27,210 --> 00:19:32,220
+بظاهرة ال fluorescence .. ال fluorescenceهي
+
+243
+00:19:32,220 --> 00:19:38,520
+الفلوريسين قبل ما انا .. قبل ما انا يعني احط عليه
+
+244
+00:19:38,520 --> 00:19:42,920
+او اضيق عليه بال .. او اكسبه طاقة اللي هو ال blue
+
+245
+00:19:42,920 --> 00:19:45,980
+light، طاقة ال blue light When a photon is
+
+246
+00:19:45,980 --> 00:19:50,200
+absorbed, the electron jumps to the highest energy
+
+247
+00:19:50,200 --> 00:19:53,900
+levelInstead of dropping back to the original
+
+248
+00:19:53,900 --> 00:19:57,280
+level, however, the electron transitions to the
+
+249
+00:19:57,280 --> 00:20:01,360
+slightly lower level and emits non-visible energy,
+
+250
+00:20:01,480 --> 00:20:05,100
+infrared, next it drops to the initial energy
+
+251
+00:20:05,100 --> 00:20:09,060
+level and emits a photon يعني بدل ما يرجع مرة
+
+252
+00:20:09,060 --> 00:20:14,980
+واحدةلمسكنه الأصلي هو قفز للمدار الأعلى، نتيجة
+
+253
+00:20:14,980 --> 00:20:18,640
+اكتسابه طاقة .. طاقة الفوتون الأزرق .. طاقة
+
+254
+00:20:18,640 --> 00:20:22,560
+الفوتون الأزرق بدل ما يرجع مرة واحدة ويفقد فوتون
+
+255
+00:20:22,560 --> 00:20:27,170
+أزرق، لأ بيرجع بالتدريج، بيفقد فوتون صغير الطاقةفي
+
+256
+00:20:27,170 --> 00:20:30,490
+الـ infrared region بعدين بيكمل بيفقد ما تبقى من
+
+257
+00:20:30,490 --> 00:20:33,870
+الطاقة واللي هي هتكون ما تبقى أقل من الطاقة
+
+258
+00:20:33,870 --> 00:20:37,470
+المكتسبة الطاقة المكتسبة تمانية جول وما تبقى بعد
+
+259
+00:20:37,470 --> 00:20:41,950
+ما فقد ال infrared photon سبعة جول إذا السبعة جول
+
+260
+00:20:41,950 --> 00:20:45,370
+أقل من التمانية جول فإذا قلنا التمانية جول اللي
+
+261
+00:20:45,370 --> 00:20:49,470
+اكتسبها طاقتها وترددها بيجي في ال range الأزرق
+
+262
+00:20:49,470 --> 00:20:54,030
+هيكون هذا الطاقة أقل فالتردد أقل فالطول الموجي
+
+263
+00:20:54,030 --> 00:20:57,570
+أطول شوية هيكون في ال range الأخضرفي ال range
+
+264
+00:20:57,570 --> 00:21:01,810
+الأخضر فبالتالي هذه القضية بدأت تكون واضحة اذا
+
+265
+00:21:01,810 --> 00:21:05,450
+next it drops to the initial energy level and
+
+266
+00:21:05,450 --> 00:21:10,380
+emits photonthe photon emitted .. الفوتون اللي صدر
+
+267
+00:21:10,380 --> 00:21:14,100
+أو اللي أشعع is still visible أيضا في ال range
+
+268
+00:21:14,100 --> 00:21:17,840
+المرئي في ال range المرئي but has .. but has less
+
+269
+00:21:17,840 --> 00:21:21,580
+energy than the absorbed photon and therefore
+
+270
+00:21:21,580 --> 00:21:25,720
+lower frequency تردده أقل هذه الظاهرة called
+
+271
+00:21:25,720 --> 00:21:29,940
+fluorescence occurs only و بنقول only و بنأكد على
+
+272
+00:21:29,940 --> 00:21:33,570
+only هذه ظاهرة ال fluorescence تحدث فقطin
+
+273
+00:21:33,570 --> 00:21:37,230
+materials possessing close spacing between energy
+
+274
+00:21:37,230 --> 00:21:45,190
+levels يعني لو لجيت ذرة لو
+
+275
+00:21:45,190 --> 00:21:49,610
+لجينا ذرة مافيش close spacing between energy
+
+276
+00:21:49,610 --> 00:21:55,130
+levels يعني المسافات متساوية ومتباعدة في الطاقة
+
+277
+00:21:55,130 --> 00:21:59,690
+ساعتها مش هيتم ظاهرة ال fluorescence ضروري يكون
+
+278
+00:21:59,690 --> 00:22:05,400
+عندي يعني مثلا هنابين N2 و N3 المسافة بعيدة، بين
+
+279
+00:22:05,400 --> 00:22:12,000
+N3 و N4 المسافة بعيدة، بين N4 و N5 المسافة بعيدة،
+
+280
+00:22:12,000 --> 00:22:16,180
+بس بين .. بين N5 و N6 المسافة قريبة، اذا الطاقة
+
+281
+00:22:16,180 --> 00:22:20,740
+قريبة، الطاقة قريبة، يعني بنفع لما بكون في عندي
+
+282
+00:22:20,740 --> 00:22:26,510
+موادفيها .. فيها مدارين متقاربين في الذرات في
+
+283
+00:22:26,510 --> 00:22:30,870
+الطاقة بينفع انها يعني تكون fluorescent material،
+
+284
+00:22:30,870 --> 00:22:34,750
+fluorescent material، اذا ضروري جدا نفهم ان ظاهرة
+
+285
+00:22:34,750 --> 00:22:40,450
+ال fluorescence بتحدث فقط only inmaterials
+
+286
+00:22:40,450 --> 00:22:45,010
+possessing تملك ..materials تملك a close spacing
+
+287
+00:22:45,010 --> 00:22:49,250
+between energy levels the essential feature is
+
+288
+00:22:49,250 --> 00:22:53,550
+that the emitted photon has a lower frequency and
+
+289
+00:22:53,550 --> 00:22:56,410
+therefore a different color from that of the
+
+290
+00:22:56,410 --> 00:23:00,690
+stimulating photon القضية كلها كظاهرة كظاهرة هي
+
+291
+00:23:00,690 --> 00:23:06,000
+عبارة عن إيش؟ إن ال photon اللي تم إشعاعهطاقته أقل
+
+292
+00:23:06,000 --> 00:23:11,220
+وبالتالي تردده أقل من ال stimulating photon اللي
+
+293
+00:23:11,220 --> 00:23:15,160
+إيجا وحفز وبالتالي طالما ال frequency بتاعته
+
+294
+00:23:15,160 --> 00:23:20,440
+بتختلف ف ال color بتاعه بيختلف وهذه هي ظاهرة اللي
+
+295
+00:23:20,440 --> 00:23:24,820
+هو ال fluorescence the clinical utility of this
+
+296
+00:23:24,820 --> 00:23:29,820
+phenomenon اللي هي هتناقش بعد قليل derives from
+
+297
+00:23:29,820 --> 00:23:32,440
+the difference in frequency between the absorbed
+
+298
+00:23:32,440 --> 00:23:37,340
+and emitted photonsالاستفادةالاستفادة من هذه
+
+299
+00:23:37,340 --> 00:23:40,340
+الظاهرة، ظاهرة ال fluorescence و اللي هنقشها الآن
+
+300
+00:23:40,340 --> 00:23:46,040
+هي استفادة متعددة و تكمن .. تكمن أو .. أو سر
+
+301
+00:23:46,040 --> 00:23:50,300
+الاستفادة من هذه الظاهرة أنه في عندي فرق في ال
+
+302
+00:23:50,300 --> 00:23:53,280
+frequency بين ال absorbed photon و ال emitted
+
+303
+00:23:53,280 --> 00:23:57,020
+photon ال absorbed photon هيكون blue، ال emitted
+
+304
+00:23:57,020 --> 00:24:00,860
+photon هيكون green و نشوف كيف احنا بنستفيد ..
+
+305
+00:24:00,860 --> 00:24:03,960
+بنستفيد منه في .. بالذات في مجال طب العيون في
+
+306
+00:24:03,960 --> 00:24:08,350
+حاجات كتيرةهنضرب أمثلة على ذلك، بنقول fluorescence
+
+307
+00:24:08,350 --> 00:24:11,950
+is the basis of fluorescein angiography، هي أول
+
+308
+00:24:11,950 --> 00:24:16,650
+حاجة، macular autofluorescence and the C-DEL test
+
+309
+00:24:16,650 --> 00:24:20,190
+بدنا نفهم إيش هذه التلت استفادات، طبعا في استفادات
+
+310
+00:24:20,190 --> 00:24:24,130
+أكتر بكتير في مجال طب العيون من مجرد هذه القضية،
+
+311
+00:24:24,130 --> 00:24:27,830
+الاستفادة الأولى اللي هي ال fluorescein
+
+312
+00:24:27,830 --> 00:24:31,790
+angiographyيعني angio معناها وعاء دموي،
+
+313
+00:24:31,790 --> 00:24:36,150
+angiography تصوير الأوعية الدموية باستخدام مادة
+
+314
+00:24:36,150 --> 00:24:40,230
+الفلوريسين، يعني باستخدام ظاهرة الفلوريسين، ظاهرة
+
+315
+00:24:40,230 --> 00:24:43,790
+الفلوريسينأي أوعية دموية اللي هنصورها، الأوعية
+
+316
+00:24:43,790 --> 00:24:48,610
+الدموية بتاعة الشبكية، نشوف المنظر هذا، المنظر هذا
+
+317
+00:24:48,610 --> 00:24:55,590
+حقيقة، هاي أول شيء الصورة بتبدو في بعد ال
+
+318
+00:24:55,590 --> 00:24:59,350
+fluorescein angiography، هاي الشبكية، هاي العصب
+
+319
+00:24:59,350 --> 00:25:03,430
+البصري، خارجة منه الأوعية الدموية، الأوعية الدموية
+
+320
+00:25:03,430 --> 00:25:08,130
+مليانة بمادة ال fluoresceinطبعا الكمبيوتر بيعملها
+
+321
+00:25:08,130 --> 00:25:12,910
+بالشكل هذا بحيث انه تبين أسود و أبيض .. أسود و
+
+322
+00:25:12,910 --> 00:25:16,850
+أبيض .. اذا هذه الصورة النهائية معالجة من قبل
+
+323
+00:25:16,850 --> 00:25:21,650
+الكمبيوتر طبعا لو احنا حابينا نعرف الشبكية لونها
+
+324
+00:25:21,650 --> 00:25:30,890
+في الوضع الطبيعي كيف احنا بنقول retina
+
+325
+00:25:41,410 --> 00:25:45,370
+هي صورة الرجل هنا مثلا في الوضع الطبيعي، هاي اللون
+
+326
+00:25:45,370 --> 00:25:48,470
+الطبيعي للvisuals طبعا مليانة بال blood ال red
+
+327
+00:25:48,470 --> 00:25:54,590
+color وهي الصورة بتاعة الشبكية، هاي الفوفيا، هاي
+
+328
+00:25:54,590 --> 00:25:58,570
+منطقة الفوفيا،
+
+329
+00:25:58,570 --> 00:26:02,610
+هادي ال .. الماكولا اللي هي الفوفيا، طبعا الماكولا
+
+330
+00:26:02,610 --> 00:26:06,530
+اللي بيلاحظ أنه في عندي هنا لون، هاي هنا اللي هو
+
+331
+00:26:06,530 --> 00:26:11,060
+اللون الأصفر، عشان كده بيسموها ماكولا لوتيةالبقعة
+
+332
+00:26:11,060 --> 00:26:14,280
+الصفراء، هاي العصب البصري، هاي الأوعية الدموية ال
+
+333
+00:26:14,280 --> 00:26:18,200
+retinal arteries and retinal veins فبالتالي هاي
+
+334
+00:26:18,200 --> 00:26:22,500
+المنظر الطبيعي للعين،
+
+335
+00:26:22,500 --> 00:26:26,580
+الآن احنا ليش بنحق المادة لفلوريسين عشان تتركز في
+
+336
+00:26:26,580 --> 00:26:29,780
+الأوعية الدموية؟ ليش بدنا تتركز في الأوعية
+
+337
+00:26:29,780 --> 00:26:34,740
+الدموية؟ لأن لو في رشوحاتأو إفرازات بتفرزها
+
+338
+00:26:34,740 --> 00:26:38,420
+الأوعية الدموية زي في اعتلال الشبكية السكري اللي
+
+339
+00:26:38,420 --> 00:26:42,040
+بيخرب الأوعية الدموية إلى آخرين بنقدر بمواسطة ال
+
+340
+00:26:42,040 --> 00:26:45,540
+fluorescein أنه نعمل fluorescein أنجيографي تصوير
+
+341
+00:26:45,540 --> 00:26:49,060
+للأوعية الدموية باستعمال مادة ال fluorescein طيب،
+
+342
+00:26:49,060 --> 00:26:54,960
+الآن بدنا نفهم إيش الفكرة أو كيف احنا عملناها كيف
+
+343
+00:26:54,960 --> 00:26:58,840
+احنا عملناها بدنا احنا نصغر الصورة هاي على الآخر
+
+344
+00:27:00,980 --> 00:27:06,240
+وانحاول نكبر هذه الصورة شوية عشان تتضح الأمور الآن
+
+345
+00:27:06,240 --> 00:27:12,960
+المريض بده تحقق مادة الفلوريسين عنده في الوريد هذه
+
+346
+00:27:12,960 --> 00:27:17,430
+المادة اللي هي مادة الفلوريسين بورتقالية اللونطبعا
+
+347
+00:27:17,430 --> 00:27:20,990
+هنا أغمج من البرتقالي لأنه تركيزه أعلى .. تركيزه
+
+348
+00:27:20,990 --> 00:27:26,030
+أعلى فبالتالي بيسري مع دم المريض بيصل لأوعيات
+
+349
+00:27:26,030 --> 00:27:30,230
+الشبكية طيب وصل لأوعيات الشبكية وصار يسري في
+
+350
+00:27:30,230 --> 00:27:35,050
+الأوعياء بتاعة شبكية العين بنروح احنا بنصدر من
+
+351
+00:27:35,050 --> 00:27:39,710
+جهاز التصوير ضوء أبيض هذا الضوء الأبيض بنمرره عبر
+
+352
+00:27:39,710 --> 00:27:44,490
+blue filterبلوفرد لتر بسمح للضوء الأزرق فقط يمر
+
+353
+00:27:44,490 --> 00:27:48,810
+بجيط الأطوار الموجية بيمنعه أصبح عنده الآن الموجه
+
+354
+00:27:48,810 --> 00:27:52,990
+لعين المريض اللي حققناه في دمه مادة الفلوريسين
+
+355
+00:27:52,990 --> 00:27:57,570
+حققناها أصبح موجه باتجاه عينه فقط الضوء الأزرق
+
+356
+00:27:57,570 --> 00:28:02,990
+طيب، الضوء الأزرق هذا هيعمل stimulation لكل
+
+357
+00:28:02,990 --> 00:28:08,450
+الشبكية مش بس للأوعية الدموية، لكل الشبكيةنفرض إجت
+
+358
+00:28:08,450 --> 00:28:12,730
+في المنطقة high اللي أنا بأشر عليها إجت .. إجت ضوء
+
+359
+00:28:12,730 --> 00:28:15,970
+الأزرق هينعكس مافيش .. المنطقة high خالية من
+
+360
+00:28:15,970 --> 00:28:19,930
+الأوعية الدموية فبالتالي هينعكس مرة تانية بده يخرج
+
+361
+00:28:19,930 --> 00:28:24,010
+من العين أصطدم في .. في جدار أصطدم في ال internal
+
+362
+00:28:24,010 --> 00:28:28,410
+limiting membrane و بده يرجع يرتد تاني طيب في
+
+363
+00:28:28,410 --> 00:28:34,670
+مناطق تانية اللي هي مملوقة .. مملوقة بالفلوريسينزي
+
+364
+00:28:34,670 --> 00:28:38,690
+الأوعية الدموية و لو اتخيلنا انه الفلوريسين ايضا
+
+365
+00:28:38,690 --> 00:28:42,510
+بيسيل من .. من رشوحات او من مسامات يعني نتيجة انه
+
+366
+00:28:42,510 --> 00:28:46,230
+الوعاء الدموي تالف بسبب السكر و اتجمع الفلوريسين
+
+367
+00:28:46,230 --> 00:28:49,730
+في منطقة ما غير المنظر اللي احنا شايفينه ايضا
+
+368
+00:28:49,730 --> 00:28:52,850
+هيكون في عندى كمية فلوريسين مثلا في المنطقة هاي
+
+369
+00:28:52,850 --> 00:28:55,550
+هنا مافيش فلوريسين بالمرة الأوعية الدموية فيها
+
+370
+00:28:55,550 --> 00:28:59,410
+فلوريسين مادة الفلوريسين لما تضاء بال .. بال ..
+
+371
+00:28:59,410 --> 00:29:02,870
+بالضوء الأزرق هتحصل معاها ظاهرة ال fluorescence
+
+372
+00:29:02,870 --> 00:29:07,470
+هتصعدالذرات لمستويات اعلى من الطاقة هترجع
+
+373
+00:29:07,470 --> 00:29:10,850
+لمستوياتها الأصلية بس بالتدريج هتفقد اول اشي
+
+374
+00:29:10,850 --> 00:29:13,870
+Infrared و بعد هيك هتفقد ل Green ل Green احنا
+
+375
+00:29:13,870 --> 00:29:18,910
+هيرتدلنا فالانسان ال .. ال .. الضوء ال .. ال ..
+
+376
+00:29:18,910 --> 00:29:22,110
+الخارج من العين عبارة عن ضوء أزرق، من وين اجت
+
+377
+00:29:22,110 --> 00:29:25,530
+الضوء الأزرق استضامه في مناطق من الشبكية لا يوجد
+
+378
+00:29:25,530 --> 00:29:28,820
+فيها Fluorescentلا يوجد فيها مادة لفلوريسين
+
+379
+00:29:28,820 --> 00:29:33,500
+فبالتالي هينعكس زي ما هو أزرق مش هتحدث ظاهرة
+
+380
+00:29:33,500 --> 00:29:37,080
+التفلور أو ال fluorescence لأنه الضوء الأزرق اللي
+
+381
+00:29:37,080 --> 00:29:41,140
+دخل العين جزء منه اجع مناطق فيها fluorescein
+
+382
+00:29:41,140 --> 00:29:45,240
+والجزء الآخر اجع مناطق مافيهاش fluorescein إذا ال
+
+383
+00:29:45,240 --> 00:29:48,960
+.. ال .. الضوء المرتد هيكون خليط من الضوء الأزرق
+
+384
+00:29:48,960 --> 00:29:52,040
+هذا اللي راجع من مناطق الضوء الأزرق راجع من مناطق
+
+385
+00:29:52,040 --> 00:29:55,360
+ليس فيها fluorescein فهو اجع أزرق و رجع أزرق
+
+386
+00:29:55,360 --> 00:29:59,050
+ماتغير إشي عليهوالضوء الأخضر اللي طلع من العين هو
+
+387
+00:29:59,050 --> 00:30:03,770
+ايه؟ ضوء .. هو عبارة عن ضوء أزرق حفظ .. حفظ مناطق
+
+388
+00:30:03,770 --> 00:30:07,030
+فيها fluorescein فيها مادة ال fluorescein حدثت
+
+389
+00:30:07,030 --> 00:30:10,630
+ظاهرة التفلور أو ال fluorescence ال .. الضوء اللي
+
+390
+00:30:10,630 --> 00:30:14,610
+.. اللي اكتسب أزرق اللي أشيع أخضر فهيكون عندي خليط
+
+391
+00:30:14,610 --> 00:30:18,210
+من الضوء الأزرق و الضوء الأخضر طب هل أنا معنى أدرس
+
+392
+00:30:18,210 --> 00:30:22,110
+المناطق اللي ماحدثتش فيها ظاهرة التفلور؟لأ أنا
+
+393
+00:30:22,110 --> 00:30:25,970
+بالعكس معني أدرس المناطق اللي حدثت فيها ظاهرة ال
+
+394
+00:30:25,970 --> 00:30:29,830
+fluorescence عشان أشوفها الأوعية الدموية سليمة ولا
+
+395
+00:30:29,830 --> 00:30:34,130
+مش سليمة فهيكون في طريق الضوء العائد من العين ال
+
+396
+00:30:34,130 --> 00:30:37,630
+green filter هيمنع الضوء الأزرق لأن الضوء الأزرق
+
+397
+00:30:37,630 --> 00:30:42,030
+زي ما قلنا انعكس من مناطق ليس فيها أو لا يوجد فيها
+
+398
+00:30:42,030 --> 00:30:46,390
+fluorescein يعني مناطق ماليهاش علاقة في الصورة و
+
+399
+00:30:46,390 --> 00:30:51,620
+هينفذ فقط .. ينفذ فقطالضوء الأزرق .. الأخضر عفواً
+
+400
+00:30:51,620 --> 00:30:55,300
+اللي .. اللي انعكس نتيجة ظاهرة التفلور يعني من
+
+401
+00:30:55,300 --> 00:31:00,500
+المناطق اللي وجد فيها مادة لفلوريسين وبالتالي
+
+402
+00:31:00,500 --> 00:31:04,960
+هتطبع الصورة على جهاز الكمبيوتر ويحولها لللون اللي
+
+403
+00:31:04,960 --> 00:31:09,620
+احنا شايفينه .. هيحولها لللون اللي احنا شايفينه
+
+404
+00:31:09,620 --> 00:31:14,220
+هذه الصورة طبعا صورة
+
+405
+00:31:14,220 --> 00:31:15,800
+طبيعية مافيش فيها مشكلة
+
+406
+00:31:20,380 --> 00:31:26,320
+يعني لا يوجد أي مشاكل لو احنا روحنا نشوف ال
+
+407
+00:31:26,320 --> 00:31:44,700
+fluorescent angiography لل
+
+408
+00:31:44,700 --> 00:31:47,040
+choroidal neovascular membrane
+
+409
+00:31:56,590 --> 00:32:01,550
+هي مثلا عندي مناطق تجمع فيها الفلوريسين .. نشوف
+
+410
+00:32:01,550 --> 00:32:04,270
+الصورة .. هاي الفلوريسين هيبين .. طبعا الكمبيوتر
+
+411
+00:32:04,270 --> 00:32:10,450
+هيحول الصورة لأبيض و أسود ..
+
+412
+00:32:10,450 --> 00:32:14,910
+هاي عندي صورة واضحة جدا .. هاي هنا في منطقة .. من
+
+413
+00:32:14,910 --> 00:32:20,200
+الإشعاع الفلوريسيني .. ال fluorescentيعني نتيجة
+
+414
+00:32:20,200 --> 00:32:23,320
+تجمع الفلوريسين، وعنده ها دي choroidal neovascular
+
+415
+00:32:23,320 --> 00:32:26,960
+membrane، هاي عندي مرة تانية، ها دي في منطقة
+
+416
+00:32:26,960 --> 00:32:30,180
+الفوفيا، ها دي أوعية دموية نشأت تحت الفوفيا في
+
+417
+00:32:30,180 --> 00:32:33,300
+الكورويد، هاي هنا كمان صورة واضحة جدا، فيها
+
+418
+00:32:33,300 --> 00:32:39,380
+leakage، سيلان لمادة الفلوريسينبشكل واضح فهذه كلها
+
+419
+00:32:39,380 --> 00:32:44,480
+بتساعدني اعرف ايش الخلل و اتفض الخطوات اللازمة
+
+420
+00:32:44,480 --> 00:32:47,700
+للعلاج فإذا أول استفادة من ظاهرة ال fluorescence
+
+421
+00:32:47,700 --> 00:32:52,000
+هي ال fluorescein angiography الاستفادة التانية ال
+
+422
+00:32:52,000 --> 00:32:55,080
+macular autofluorescenceال macular
+
+423
+00:32:55,080 --> 00:32:58,740
+autofluorescence الصورة هذه اللي احنا شايفينها هي
+
+424
+00:32:58,740 --> 00:33:01,700
+عبارة عن ظاهرة ال fluorescence بدون ما أحقن مادة
+
+425
+00:33:01,700 --> 00:33:04,960
+ال fluorescein أحيانا بيكون عندي بعض الرشوحات اللي
+
+426
+00:33:04,960 --> 00:33:08,560
+مابتحتاجش .. اللي مابتحتاجش عندي أني أحقن
+
+427
+00:33:08,560 --> 00:33:12,040
+fluorescein عشان أشوفها هذه الرشوحات طبعا في أمراض
+
+428
+00:33:12,040 --> 00:33:16,640
+معينة .. في أمراض معينة مابتحتاجش أني أحقن
+
+429
+00:33:16,640 --> 00:33:20,750
+fluorescein لأنهمكونات هذه الإفرازات بتاعة الشبكية
+
+430
+00:33:20,750 --> 00:33:25,810
+بتكون عندى فيها مواد تتمتع بظاهرة ال fluorescence
+
+431
+00:33:25,810 --> 00:33:29,430
+بس يكفي أعمل stimulation بال blue light بال blue
+
+432
+00:33:29,430 --> 00:33:34,730
+light و هتحكسلي المنظر اللى أنا يعني بقى أبحث عنه
+
+433
+00:33:34,730 --> 00:33:37,730
+اللى بقى أبحث عنه ال macular autofluorescence ال
+
+434
+00:33:37,730 --> 00:33:43,010
+macular autofluorescence طيب تالت شىء ال seedle
+
+435
+00:33:43,010 --> 00:33:46,910
+testأيضا بستخدم ظاهرة ال fluorescein أو ال
+
+436
+00:33:46,910 --> 00:33:50,270
+fluorescence في ما يسمى ال seedle test عبارة عن
+
+437
+00:33:50,270 --> 00:33:53,570
+إيش ال seedle test؟ ال seedle test لما بيكون في
+
+438
+00:33:53,570 --> 00:33:58,370
+عندي جرح في القرنية عشان أعرف الجرح نافذ ولا مش
+
+439
+00:33:58,370 --> 00:34:05,600
+نافذ يعني اخترقوصار فيه نفاذ للجريح من سطح القرنية
+
+440
+00:34:05,600 --> 00:34:09,320
+لل anterior chamber يعني فتحت العين بشكل كامل
+
+441
+00:34:09,320 --> 00:34:15,000
+بمعنى أن سائل العين الأكواس بيطلع و بيسيل عبر هذا
+
+442
+00:34:15,000 --> 00:34:18,520
+الجريح أحيانا بالعين المجردة أنا مابقدرش أعرف هذه
+
+443
+00:34:18,520 --> 00:34:23,020
+القضية فبستخدم مادة الفلوريسين بحطها على طرف
+
+444
+00:34:23,020 --> 00:34:28,610
+الجريح الخارجي تمام و بضوي الضوء الأزرقو بقى أضغط
+
+445
+00:34:28,610 --> 00:34:32,070
+ضغط خفيف جدا على العين و أحيانا بلزمش الضغط هذا
+
+446
+00:34:32,070 --> 00:34:36,350
+إذا كان في الجارح بيسيل هادي الميه اللي هي تحت ال
+
+447
+00:34:36,350 --> 00:34:38,810
+aqueous اللي جاية من جوا من ال anterior chamber
+
+448
+00:34:40,530 --> 00:34:44,550
+بيتخفف مادة الفلوريسين ف ال green light زي ما
+
+449
+00:34:44,550 --> 00:34:47,590
+انتوا شايفينه هذا هذي اللي هو السائل اللي طالع و
+
+450
+00:34:47,590 --> 00:34:51,930
+بي seal جاعد بي seal لبرا العين فلما بيكون عندي
+
+451
+00:34:51,930 --> 00:34:57,230
+الأكواس بيطلع لبرا جاعد بياخد شوية شوية من مادة
+
+452
+00:34:57,230 --> 00:35:00,590
+الفلوريسين اللي أنا حاطيتها على سطح الجرح عند فوهة
+
+453
+00:35:00,590 --> 00:35:03,790
+الجرح بياخد شوية شوية و شايفين اللون الأخضر طب أنا
+
+454
+00:35:03,790 --> 00:35:08,000
+ضاوي أزرقاللون الأخضر معناته هذا السائل حمل كمية
+
+455
+00:35:08,000 --> 00:35:13,000
+من الفلوريسين وخففها وبالتالي أصبحت بتظهر عندى
+
+456
+00:35:13,000 --> 00:35:17,520
+الفلوريسين بشكل اللون الأخضر وهذا هنشوفه بشكل ان
+
+457
+00:35:17,520 --> 00:35:25,470
+شاء الله فيديو طبعا في .. ليه؟التجارب اللي مرفقة
+
+458
+00:35:25,470 --> 00:35:29,730
+في المودل in seed test the high concentration of
+
+459
+00:35:29,730 --> 00:35:33,090
+fluorescein prevents fluorescence from occurring
+
+460
+00:35:33,090 --> 00:35:36,610
+يعني لما بكون عندي التركيز عالي يعني نفرض ان
+
+461
+00:35:36,610 --> 00:35:40,470
+الجروح غير نافذ و سطح العين سليم و حطيت كمية من ال
+
+462
+00:35:40,470 --> 00:35:44,290
+fluorescein عدد ذرات ال fluorescein كتير جدا لدرجة
+
+463
+00:35:44,290 --> 00:35:48,580
+ان الضوء الأزرق مش كافي انهيعني يعملها stimulation
+
+464
+00:35:48,580 --> 00:35:53,840
+لكل ذراتها فبالتالي .. فبالتالي مش هشوف ظاهرة ال
+
+465
+00:35:53,840 --> 00:35:56,860
+fluorescence بينما لو عندي جروح نافذ و ال aqueous
+
+466
+00:35:56,860 --> 00:36:00,300
+قاعد بيطلع و بيخففلي في مادة ال fluorescein شايفين
+
+467
+00:36:00,300 --> 00:36:04,900
+هنا فوهت الجرح بس اللون الأخضر ملاحظ هنا في السائل
+
+468
+00:36:04,900 --> 00:36:08,900
+اللي بيسيل بعيدا عن الجرح هو بيسيل من الجرح بياخد
+
+469
+00:36:08,900 --> 00:36:12,320
+قليل من ذرات ال fluorescein بيوزعها في السائل و
+
+470
+00:36:12,320 --> 00:36:16,800
+بالتالي .. و بالتالي بيسير الضوء الأزرقكافي إنه
+
+471
+00:36:16,800 --> 00:36:21,060
+يعملها stimulation وتعكس لضوء أخضر، وتعكس لضوء
+
+472
+00:36:21,060 --> 00:36:24,740
+أخضر فيما يسمى بظاهرات ال fluorescence، إذا in the
+
+473
+00:36:24,740 --> 00:36:27,880
+C-delta test the high concentration of fluorescein
+
+474
+00:36:27,880 --> 00:36:31,220
+prevents fluorescence from occurring، بيمنع ظاهرة
+
+475
+00:36:31,220 --> 00:36:34,280
+ال fluorescence من إنها تحدث إذا كان تركيز ال
+
+476
+00:36:34,280 --> 00:36:37,320
+fluorescein عالي كتيرonly when the fluorescein is
+
+477
+00:36:37,320 --> 00:36:40,940
+sufficiently dilute لما يصير تخفيف و dilution
+
+478
+00:36:40,940 --> 00:36:44,660
+تخفيف بماء يعني هنا بنقصد فيه بال aqueous humor
+
+479
+00:36:44,660 --> 00:36:48,120
+because of aqueous leaking from a lesion اللي هو
+
+480
+00:36:48,120 --> 00:36:52,720
+من الجرح is fluorescence seen لما بتتم تخفيفه ال
+
+481
+00:36:52,720 --> 00:36:55,960
+fluorescein بواسطة السائل اللي طالع من جواة العين
+
+482
+00:36:55,960 --> 00:36:59,340
+عبر الجرح ساعتها ظهرت ال fluorescence يمكن احنا
+
+483
+00:36:59,340 --> 00:37:05,690
+يعني نشاهدهاالان هذا بالنسبة لطب العيون، بالنسبة ل
+
+484
+00:37:05,690 --> 00:37:08,970
+ال gas discharge tube اللي حكينا عنها المرة
+
+485
+00:37:08,970 --> 00:37:11,770
+الماضية common fluorescent lights are gas
+
+486
+00:37:11,770 --> 00:37:16,250
+discharge tubes containing mercury vapor، يعني
+
+487
+00:37:16,250 --> 00:37:19,890
+ممكن انا اشوف ظاهرة ال fluorescence، ظاهرة ال
+
+488
+00:37:19,890 --> 00:37:23,850
+fluorescenceفي الـ gas discharge tube و بالذات في
+
+489
+00:37:23,850 --> 00:37:26,530
+الـ gas discharge tubes اللي بتحتوي على بخار
+
+490
+00:37:26,530 --> 00:37:30,850
+الزئبق على بخار الزئبق the discrete mercury
+
+491
+00:37:30,850 --> 00:37:34,730
+spectrum is converted to continuous spectrum by
+
+492
+00:37:34,730 --> 00:37:37,370
+coating the inside of the glass tube with
+
+493
+00:37:37,370 --> 00:37:40,710
+fluorescent materials from which the light sources
+
+494
+00:37:40,710 --> 00:37:46,420
+gets its name طيب احنا عادال mercury spectrum
+
+495
+00:37:46,420 --> 00:37:49,940
+عبارة عن spectrum discrete يعني لونه محدد ال
+
+496
+00:37:49,940 --> 00:37:54,940
+mercury spectrum لونه محدد بس اللي .. اللي بيصير
+
+497
+00:37:54,940 --> 00:38:02,720
+انه هاي ال gas discharge tube نفرض و فيها ذرات ..
+
+498
+00:38:02,720 --> 00:38:07,360
+فيها ذرات اللي هي ال mercury اللي .. اللي هي ذرات
+
+499
+00:38:07,360 --> 00:38:08,380
+بخار الذئبق
+
+500
+00:38:18,590 --> 00:38:26,310
+زرّاية بخار الذئبق اللي
+
+501
+00:38:26,310 --> 00:38:27,770
+باللون الأسود بتشاهدوها
+
+502
+00:38:38,050 --> 00:38:41,550
+هذه هتعطيني discrete mercury spectrum .. discrete
+
+503
+00:38:41,550 --> 00:38:44,610
+mercury spectrum يعني visible light ب range معين
+
+504
+00:38:44,610 --> 00:38:48,270
+.. بدنا نحاوله .. بدنا نحاوله ل continuous
+
+505
+00:38:48,270 --> 00:38:53,890
+spectrum يعني طيف متصل بيطلع جدار الأنبوبة
+
+506
+00:38:53,890 --> 00:38:58,190
+الزجاجية اللي هي ال gas discharge tube بموادفيها
+
+507
+00:38:58,190 --> 00:39:03,390
+ظاهرة ال fluorescence بمواد يعني .. الها مدارات
+
+508
+00:39:03,390 --> 00:39:07,050
+متقاربة from which this light source gets its name
+
+509
+00:39:07,050 --> 00:39:10,670
+بابطل أسميها gas discharge .. mercury gas
+
+510
+00:39:10,670 --> 00:39:14,710
+discharge tube أو لمبة البخار الذئبك، لأ بسميها
+
+511
+00:39:14,710 --> 00:39:17,790
+fluorescent lamp بسميها fluorescent lamp لأنها
+
+512
+00:39:17,790 --> 00:39:21,650
+مطلية من الداخل .. مطلية من الداخل ب fluorescent
+
+513
+00:39:21,650 --> 00:39:24,410
+material مش شرط أنه ال fluorescent sodium اللي
+
+514
+00:39:24,410 --> 00:39:27,420
+حكينا عنهفي هذه المحاضرة، لكن في إنه fluorescent
+
+515
+00:39:27,420 --> 00:39:30,480
+materials كتيرة، احنا قلنا ال fluorescent material
+
+516
+00:39:30,480 --> 00:39:34,360
+هي أي material فيها عندها مدارين متقاربين عشان
+
+517
+00:39:34,360 --> 00:39:38,100
+تقدر تتمتع بظاهرة ال fluorescence، ليه
+
+518
+00:39:38,100 --> 00:39:41,140
+fluorescence؟ حتى نتوقف عن ظاهرة أخرى هي ال
+
+519
+00:39:41,140 --> 00:39:44,200
+phosphorescence ويعطيكم العافية والسلام عليكم
+
+520
+00:39:44,200 --> 00:39:45,920
+ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/d4HD03npCUs_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/d4HD03npCUs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d7ec44107d585c56632e21479f6940288b483750
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/d4HD03npCUs_postprocess.srt
@@ -0,0 +1,2308 @@
+1
+00:00:01,690 --> 00:00:04,530
+بسم الله الرحمن الرحيم بنواصل مع محاضرات ال
+
+2
+00:00:04,530 --> 00:00:08,750
+physical optics و المرة الماضية حكينا عن ال image
+
+3
+00:00:08,750 --> 00:00:15,070
+quality و بنستكمل الحديث عنها اليوم قلنا عشان ندرس
+
+4
+00:00:15,070 --> 00:00:19,330
+ال image quality وجودتها وقداش هي بتشبه ال object
+
+5
+00:00:19,330 --> 00:00:22,990
+لازم ندرس ال point spread functionالـ point spread
+
+6
+00:00:22,990 --> 00:00:26,970
+function بتحكم فيها شغلات كتيرة بس أهم حاجتين هي
+
+7
+00:00:26,970 --> 00:00:30,610
+ال aberrations و ال diffraction فعشان ندرس هدول
+
+8
+00:00:30,610 --> 00:00:37,610
+الحاجتين اللي هم أهم محددات أو أهم الخصائص اللي
+
+9
+00:00:37,610 --> 00:00:42,430
+بيأثروا على حجم و شكل ال point spread function هم
+
+10
+00:00:42,430 --> 00:00:45,050
+ال aberration و ال diffraction عشان ندرس ال point
+
+11
+00:00:45,050 --> 00:00:48,610
+spread function لازم ندرس كل واحدة منهم على حدة و
+
+12
+00:00:48,610 --> 00:00:55,250
+أيضا حكينا ان ال aberrationالها علاقة ما بالشكل
+
+13
+00:00:55,250 --> 00:00:58,270
+بتاع ال point في ال spread function والتعريج بتاع
+
+14
+00:00:58,270 --> 00:01:01,950
+الخريطة بتاعت ال point spread function وال
+
+15
+00:01:01,950 --> 00:01:05,010
+diffraction اللي علاقة بمساحة ال point spread
+
+16
+00:01:05,010 --> 00:01:11,210
+function يعني بشكل او باخر بمعنى اخر هي عندي انا
+
+17
+00:01:11,210 --> 00:01:13,910
+ال point spread function اللي لها مساحة معينة
+
+18
+00:01:13,910 --> 00:01:16,730
+سببها ال diffraction لو ال diffraction اكتر هيكون
+
+19
+00:01:16,730 --> 00:01:23,310
+المساحة اكبر وايضا فيها تعريج في سطحهامسئولة عنه
+
+20
+00:01:23,310 --> 00:01:26,210
+ال aberration اللي عملت ليها هذا ال optical system
+
+21
+00:01:26,210 --> 00:01:27,210
+او هذه ال lens
+
+22
+00:01:52,110 --> 00:01:54,410
+Sir George Irey calculated the point spread
+
+23
+00:01:54,410 --> 00:01:58,710
+function for an axial object point imaged by an
+
+24
+00:01:58,710 --> 00:02:02,230
+aberration-free optical system with circular
+
+25
+00:02:02,230 --> 00:02:07,870
+aperture stop الآن الـ Sir George Irey أو العلم
+
+26
+00:02:07,870 --> 00:02:11,730
+George Irey بدأ بدراسة الـ diffraction عشان يدرس
+
+27
+00:02:11,730 --> 00:02:16,350
+الـ diffraction بده يحيد ال aberrationفجاب حاجة
+
+28
+00:02:16,350 --> 00:02:20,670
+اسمها aberration-free optical system aberration
+
+29
+00:02:20,670 --> 00:02:24,330
+-free optical system with circular aperture stop
+
+30
+00:02:24,330 --> 00:02:29,610
+يعني هذا ال system في فتحة بينفذ منها الضوء هذه
+
+31
+00:02:29,610 --> 00:02:33,670
+الفتحة دائرية طبعا ال system اللي استخدموا بيعملش
+
+32
+00:02:33,670 --> 00:02:36,890
+أي نوع من ال aberration فبيسموه aberration-free
+
+33
+00:02:36,890 --> 00:02:41,590
+optical system ال pinhole ممكنبشكل ما نعتبره
+
+34
+00:02:41,590 --> 00:02:45,290
+operation free optical system لأنه إذا متذكرين في
+
+35
+00:02:45,290 --> 00:02:49,010
+ال geometric optics ال .. ال .. ال pin hole بيعمل
+
+36
+00:02:49,010 --> 00:02:52,110
+إيه ب layer circle و بيعملش point spread function
+
+37
+00:02:52,110 --> 00:02:59,310
+يعني الصورة عنده حدود ه دائريةأو إذا كانوا النقطة
+
+38
+00:02:59,310 --> 00:03:02,050
+اللي احنا بدنا ندرس صورتها النقطة اللي في ال
+
+39
+00:03:02,050 --> 00:03:05,890
+object of axis يعني جاية بعيد عن ال optical axis
+
+40
+00:03:05,890 --> 00:03:10,750
+بتعمل ب layer ellipse بس مابتعمليش point spread
+
+41
+00:03:10,750 --> 00:03:14,890
+function إذا السير جورج آيري استخدم aberration
+
+42
+00:03:14,890 --> 00:03:17,570
+free optical system بمعنى إنه استخدم optical
+
+43
+00:03:17,570 --> 00:03:21,840
+system مافي aberration بتاعةوإنما هيعمللي هذا ال
+
+44
+00:03:21,840 --> 00:03:25,520
+optical system diffraction و هنجيس هذا ال
+
+45
+00:03:25,520 --> 00:03:30,120
+diffraction و نشوف إيش طبيعته و إيش علاقته بال
+
+46
+00:03:30,120 --> 00:03:34,880
+image equalityإذا هذا ال optical system aberration
+
+47
+00:03:34,880 --> 00:03:38,940
+free و في نفس الوقت في .. في هذا ال system في
+
+48
+00:03:38,940 --> 00:03:42,560
+circular aperture stop يعني فتحة دائرية يمكن
+
+49
+00:03:42,560 --> 00:03:46,540
+التحكم في مساحتها أو في ال diameter تاعة عشان نشوف
+
+50
+00:03:46,540 --> 00:03:50,460
+الضوء يعني اللي بينفذ منها كيف هيعمل ليه
+
+51
+00:03:50,460 --> 00:03:55,320
+diffractionايضا ايري جورج ايري استخدم temporal
+
+52
+00:03:55,320 --> 00:03:59,100
+coherent
+
+53
+00:03:59,100 --> 00:04:02,600
+light زي ضوء الليزر ايضا point spread function
+
+54
+00:04:02,600 --> 00:04:09,360
+contain interference rings زي ما هنشوف بالشكل
+
+55
+00:04:09,360 --> 00:04:12,640
+التالي بنقول كالقاتل هاي عندي انا simulation
+
+56
+00:04:15,590 --> 00:04:20,290
+optical system aberration free وفي فتحة صغيرة في
+
+57
+00:04:20,290 --> 00:04:24,390
+النص و هنا لوحة التلقى عشان اشوف الصورة تعت الضوء
+
+58
+00:04:24,390 --> 00:04:28,590
+اللي انا باستهتم طبعا ال diameter هنا ال diameter
+
+59
+00:04:28,590 --> 00:04:34,790
+هنا اربعة من مية ملي متر و بستطيع انا اكبره اذا
+
+60
+00:04:34,790 --> 00:04:41,250
+ملاحظين بيكبر جاعد ال diameter بتاع الفتحة بيكبر
+
+61
+00:04:41,250 --> 00:04:47,870
+اكتر و ممكن اصغرههذه الفتحة اللي منها الضوء هينفر
+
+62
+00:04:47,870 --> 00:04:53,130
+اللي هو سموها circular stop
+
+63
+00:04:56,710 --> 00:05:00,670
+circular aperture stop يعني فتحة دائرية بس يعني
+
+64
+00:05:00,670 --> 00:05:05,530
+بتشكل زي فيها حاجز بيصغر لغاية ما يغلق وممكن يكبر
+
+65
+00:05:05,530 --> 00:05:09,550
+يعني ممكن تحكم في الفتحة الدائرية وفي عندى ايضا
+
+66
+00:05:09,550 --> 00:05:13,350
+ورقة التلقي او ال screen اللى انا بتلقى عليه عشان
+
+67
+00:05:13,350 --> 00:05:18,050
+اشوف ال result لما احنا بنسلط ضوء ال laser بظهر
+
+68
+00:05:18,050 --> 00:05:21,830
+هذا ال butter نتيجة ال diffraction ونتيجة ال
+
+69
+00:05:21,830 --> 00:05:27,420
+interference في عندى بقعة مضيقةبشكل disk قرص يعني
+
+70
+00:05:27,420 --> 00:05:31,780
+إضاءته عالية بعدين في منطقة يعني dark بعدين في
+
+71
+00:05:31,780 --> 00:05:36,500
+إضاءة ring بس أقل إضاءة من ال central disk بعدين
+
+72
+00:05:36,500 --> 00:05:40,100
+darkness نتيجة التداخل هنا constructive
+
+73
+00:05:40,100 --> 00:05:43,100
+interference هنا destructive هنا constructive هنا
+
+74
+00:05:43,100 --> 00:05:48,080
+destructive وهكذا وهكذا فبالتالي هذه القضية بدها
+
+75
+00:05:48,080 --> 00:05:54,310
+تكون واضحة الآنهذا الـ central disk أصبح يسمى ايري
+
+76
+00:05:54,310 --> 00:06:00,310
+ديسك ايري ديسك تمام فبالتالي هذا هو المنظر او هذا
+
+77
+00:06:00,310 --> 00:06:03,930
+هو ال diffraction اللي بيحدث لما الضوء ينفذ من
+
+78
+00:06:03,930 --> 00:06:09,650
+فتحة في حاجز فتحة في حاجز يا ترى حجم الفتحة بيأثر
+
+79
+00:06:09,650 --> 00:06:15,090
+على هذا الصورة ولا بيأثرش بعد شوية هنشوف و الطول
+
+80
+00:06:15,090 --> 00:06:19,430
+الموجي بيأثر ولا ما بيأثرش ايضا هنشوف اذا هذه
+
+81
+00:06:19,430 --> 00:06:20,010
+القضية
+
+82
+00:06:24,850 --> 00:06:28,750
+عيري ايضا اعتقدت ان الوضع كان موجودًا في الوضع
+
+83
+00:06:28,750 --> 00:06:34,890
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+84
+00:06:34,890 --> 00:06:37,590
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+85
+00:06:37,590 --> 00:06:38,210
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+86
+00:06:38,210 --> 00:06:38,450
+الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع
+
+87
+00:06:38,450 --> 00:06:42,860
+الوضع الوضع الوضع الوضعcentral brightest spot
+
+88
+00:06:42,860 --> 00:06:47,420
+اسمها الـ iry disk surrounded by larger rings زي
+
+89
+00:06:47,420 --> 00:06:52,080
+ما الصورة عندى هنا بتوضح هنا صورة مختصرة لل
+
+90
+00:06:52,080 --> 00:06:55,220
+simulation اللى عرضناها قبل شوية هاد ال central
+
+91
+00:06:55,220 --> 00:07:01,900
+area او ال central disk بيسموه ال iry diskمحاط ب
+
+92
+00:07:01,900 --> 00:07:05,780
+rings من ال darkness و ال brightness أو من الإضاءة
+
+93
+00:07:05,780 --> 00:07:09,780
+و الظلام، هاي هنا ال ring مضيق، هذا مظلم، اللي
+
+94
+00:07:09,780 --> 00:07:13,460
+بعده مظلم، هنا مضيق و هكذا و ممكن هاد ال rings
+
+95
+00:07:13,460 --> 00:07:18,380
+يكون لعدد يعني ضخم، حسب طبيعة ال diffraction اللي
+
+96
+00:07:18,380 --> 00:07:23,580
+صار و حسب ال aperture اللي احنا
+
+97
+00:07:23,580 --> 00:07:28,260
+استخدمناها، قداش ال diameter بتاعها
+
+98
+00:07:29,450 --> 00:07:33,730
+most of the energy is in the central discs, so the
+
+99
+00:07:33,730 --> 00:07:38,170
+outer rings are usually ignored يعني بمعنى أخر
+
+100
+00:07:39,470 --> 00:07:43,930
+الطاقة تحت الضوء اللي صدر من مصدره، من النقطة اللي
+
+101
+00:07:43,930 --> 00:07:48,150
+صدر منها، لو فرضنا النقطة A هي ال object، معظم
+
+102
+00:07:48,150 --> 00:07:51,390
+الطاقة اللي صدرت أو الطاقة الأشعة الضوئية، طاقة
+
+103
+00:07:51,390 --> 00:07:54,310
+الأشعة الضوئية معظمها مركزة في ال central disk
+
+104
+00:07:54,310 --> 00:07:58,750
+عشان هيك إذا ملاحظين ال central disk أوضح ما يكون،
+
+105
+00:07:58,750 --> 00:08:04,010
+و بعدين إذا جينا نتحدث عن مضوح ال light rings
+
+106
+00:08:05,580 --> 00:08:09,900
+الحلقات المضيقة بيكون مقارنة مع ال central disk
+
+107
+00:08:09,900 --> 00:08:15,180
+تعتبر إضاءتها خفيفة كتير وبالتالي ممكن إهمال كمية
+
+108
+00:08:15,180 --> 00:08:18,760
+الطاقة يعني ممكن نعتبر إن الصورة فقط هي .. يعني
+
+109
+00:08:18,760 --> 00:08:24,200
+هذا كله يهمل ولكن صورة النقطة هي هذه البقعة
+
+110
+00:08:24,200 --> 00:08:27,340
+المضيقة البقعة الدائرية اللي بيسموها ال iron disk
+
+111
+00:08:27,340 --> 00:08:31,000
+واللي نتجت عن ال diffraction طبعا طالما عندي
+
+112
+00:08:32,280 --> 00:08:35,340
+Aberration free مافيش aberration بالمرة عشان هيك
+
+113
+00:08:35,340 --> 00:08:39,100
+مافيش تعريج هذه الصورة، هنتظر ال ايري ديسك هو صورة
+
+114
+00:08:39,100 --> 00:08:44,260
+النقطة اللي في ال object طبعا مافيش تعريج فيها، بس
+
+115
+00:08:44,260 --> 00:08:46,760
+فيه diffraction، ليش فيه diffraction؟ لأن حجمها
+
+116
+00:08:46,760 --> 00:08:50,840
+أكبر بكتير من النقطة، حجمها أكبر بكتير من النقطة،
+
+117
+00:08:50,840 --> 00:08:55,060
+و هنشوف المعادلة اللي بتحسب ليه الحجم، اذا most of
+
+118
+00:08:55,060 --> 00:08:58,580
+the energy in the central diskSo the outer rings
+
+119
+00:08:58,580 --> 00:09:01,880
+are usually ignored، بنحمل الـ outer rings The
+
+120
+00:09:01,880 --> 00:09:05,420
+diameter of the iridisc is determined according to
+
+121
+00:09:05,420 --> 00:09:09,420
+the equation في معادلة عشان أقدر أوصل ليديش ال
+
+122
+00:09:09,420 --> 00:09:12,900
+diameter تاع ال iridisc، ليديش ال diameter تاع ال
+
+123
+00:09:12,900 --> 00:09:17,320
+iridisc كيف أحسب ال diameter قطره؟ في معادلة،
+
+124
+00:09:17,320 --> 00:09:21,700
+المعادلة بتنص على أنه ال diameter تاع ال iridisc
+
+125
+00:09:21,700 --> 00:09:28,720
+يساويتقريبا يساوي 2.44% في lambda اللي هي طول
+
+126
+00:09:28,720 --> 00:09:34,360
+الموج إلى الموجة اللي .. اللي ساقطة في F في البعد
+
+127
+00:09:34,360 --> 00:09:39,240
+البؤري لل optical system على D ال diameter بتاع
+
+128
+00:09:39,240 --> 00:09:44,120
+الفتحة بتاعة ال optical system او ال circular
+
+129
+00:09:44,120 --> 00:09:47,880
+aperture أسطور بمعنى آخر لو أجينا احنا نكتبها
+
+130
+00:09:47,880 --> 00:09:52,840
+كتابة عشان تكون الأمور أوضحبنقول ال ايري ديسك
+
+131
+00:09:52,840 --> 00:09:59,660
+ديامتر ايري ديسك ديامتر يساوي اتنين
+
+132
+00:09:59,660 --> 00:10:04,620
+صحيح و اربعة و اربعين من مية ضرب لامبدا اللي هو
+
+133
+00:10:04,620 --> 00:10:05,500
+الطول الموجي
+
+134
+00:10:52,500 --> 00:11:16,240
+Lambda اللي هو الطول الموجي Lambda
+
+135
+00:11:16,240 --> 00:11:21,340
+الطول الموجيضرب الـ focal lengths أو البعد البُقري
+
+136
+00:11:21,340 --> 00:11:29,400
+للـ optical system على طبعا
+
+137
+00:11:29,400 --> 00:11:40,440
+هنا ضرب نميز علامات الضرب بس بلون آخر مقسوما
+
+138
+00:11:40,440 --> 00:11:41,040
+كله على
+
+139
+00:11:53,230 --> 00:11:59,610
+هذا هو المعادلة اللي انا بقدر اجيب فيها ايري ديسك
+
+140
+00:11:59,610 --> 00:12:00,390
+ديامتر
+
+141
+00:12:08,310 --> 00:12:13,710
+بنعيد ال iridisk diameter 42% من 100 في lambda طول
+
+142
+00:12:13,710 --> 00:12:16,970
+الموج اللي ساقط أو اللي صادر من ال object في البعد
+
+143
+00:12:16,970 --> 00:12:19,650
+البقري لل optical system على ال diameter بتاع
+
+144
+00:12:19,650 --> 00:12:25,310
+الفتحة اللي هيمر منها اللي
+
+145
+00:12:25,310 --> 00:12:30,770
+هو الضوء طيب معناته هذه 42% ثابت في المعادلة
+
+146
+00:12:30,770 --> 00:12:35,830
+بمترايرش الرقم هذاالطول الموجي موجود في البصد و ال
+
+147
+00:12:35,830 --> 00:12:42,030
+focal length موجود في البصد بمعنى آخر كل ما زاد
+
+148
+00:12:42,030 --> 00:12:46,510
+الطول الموجي كل
+
+149
+00:12:46,510 --> 00:12:51,510
+ما كان ال iridisc diameter القطر بتاعه أكبر كل ما
+
+150
+00:12:51,510 --> 00:12:55,950
+زاد ال focal length كل ما ال iridisc diameter كل
+
+151
+00:12:55,950 --> 00:13:00,220
+ما كان أكبركل ما زاد الـ Diameter بتاع الفتحة اللي
+
+152
+00:13:00,220 --> 00:13:03,460
+هينفذ منها الضوء كل ما جال لأنه هذه بتزيد في
+
+153
+00:13:03,460 --> 00:13:08,640
+المقام معناته هتجل الكيمية الكلية اذا زيادة الطول
+
+154
+00:13:08,640 --> 00:13:13,960
+الموجي بتكبر لل Iridisc Diameterوزيادة ال focal
+
+155
+00:13:13,960 --> 00:13:17,520
+length بتاع ال optical system بيكبر ال iridisc
+
+156
+00:13:17,520 --> 00:13:22,580
+diameter وزيادة ال diameter بتاع الفتحة اللي هينفذ
+
+157
+00:13:22,580 --> 00:13:26,140
+منها الضوء اللي بيسموها ال exit pupil ال exit
+
+158
+00:13:26,140 --> 00:13:29,960
+pupil بيجلل ال iridisc diameter زي ما هنشوف في ال
+
+159
+00:13:29,960 --> 00:13:33,180
+simulation الآن بدنا نشوف موضوع الطول الموجي هل
+
+160
+00:13:33,180 --> 00:13:38,310
+بيأثر على ال iridisc diameter ولا لأهنا احنا
+
+161
+00:13:38,310 --> 00:13:43,130
+مستخدمين الطول الموجي ال green بدنا نزود باتجاه
+
+162
+00:13:43,130 --> 00:13:46,910
+هاي ال wavelength بدنا نزودها باتجاه ال red ونشوف
+
+163
+00:13:46,910 --> 00:13:50,770
+ال iridisk diameter هنا ننتبه للنقطة هاي ايش هيحصل
+
+164
+00:13:50,770 --> 00:13:57,010
+معاه، هيزيد ولا هيجل؟ اذا الحجم جاعت بيزيد القطر
+
+165
+00:13:57,010 --> 00:14:01,090
+.. القطر تاع ال iridisk diameter أصبح كبير أصبح
+
+166
+00:14:01,090 --> 00:14:04,770
+أكبر فبالتالي هذه القضية ضرورة تكون واضحة لنا،
+
+167
+00:14:04,770 --> 00:14:11,710
+الآن لو زغرناأذن كل ما جلت طول الموجي كل ما الـ
+
+168
+00:14:11,710 --> 00:14:17,490
+iridisc diameter صغر كل ما ال iridisc diameter صغر
+
+169
+00:14:17,490 --> 00:14:20,150
+ننتبه للcourse هذا اللي هو ال iridisc diameter و
+
+170
+00:14:20,150 --> 00:14:23,430
+نهمل ال rings هذه لأن الطاقة اللي فيها قليلة جدا
+
+171
+00:14:23,430 --> 00:14:27,810
+لدرجة أنه يمكن اهملها واعتبار صورة المطة هي عبارة
+
+172
+00:14:27,810 --> 00:14:31,910
+عن ال iridisc لحاله فبالتالي لما بيكون عندي ال
+
+173
+00:14:31,910 --> 00:14:35,770
+wavelengths طولها قليل بيكون ال iridisc diameter
+
+174
+00:14:35,770 --> 00:14:42,460
+صغيرو لما بيكبر طول الموجة بيزيد
+
+175
+00:14:42,460 --> 00:14:47,100
+ال diameter القطر بتاعه بيكبر فبالتالي هذه ال
+
+176
+00:14:47,100 --> 00:14:50,760
+diameter بيكبر طيب هذه نقطة النقطة التانية
+
+177
+00:14:53,430 --> 00:14:57,770
+النقطة التانية بدنا نخلي ال IRI او الطول الموجي
+
+178
+00:14:57,770 --> 00:15:02,390
+ثابت بس بدنا نتحكم في ال Exit Pupil ال Exit Pupil
+
+179
+00:15:02,390 --> 00:15:09,470
+ال Exit Pupil اللي هي ال D هاي اللي هي Diameter لل
+
+180
+00:15:09,470 --> 00:15:12,370
+Exit Pupil اللي هي الفتحة اللي بيخرج منها الضوء او
+
+181
+00:15:12,370 --> 00:15:17,870
+ال circular aperture stop لما بنزود الفتحة هل
+
+182
+00:15:17,870 --> 00:15:21,190
+بيصغر ال IRI disk Diameter ولا لأ خلينا نشوف مع
+
+183
+00:15:21,190 --> 00:15:26,920
+بعضهي الفتحة بدنا احنا نبدأ نزودها و نتطلع هنا مع
+
+184
+00:15:26,920 --> 00:15:30,120
+بعض كيف الـ IRIDISC Diameter بيصغر ولا بيكبر لما
+
+185
+00:15:30,120 --> 00:15:35,300
+بنزود الفتحة ال IRIDISC Diameter بيصغر بيصغر بيصغر
+
+186
+00:15:35,300 --> 00:15:40,480
+يا كل ما زادت الفتحة كبرا كل ما كان ال diffraction
+
+187
+00:15:40,480 --> 00:15:45,680
+أقلهذا الـ Iredisk Diameter أو الـ Iredisk مع الـ
+
+188
+00:15:45,680 --> 00:15:48,740
+Rings اللي حواليها، ده عبارة عن Diffraction
+
+189
+00:15:48,740 --> 00:15:52,540
+Pattern عبارة عن Diffraction Pattern بيتم مع الـ
+
+190
+00:15:52,540 --> 00:15:55,540
+Diffraction Interference فإذا كانوا Constructive
+
+191
+00:15:55,540 --> 00:15:58,860
+بيعطيني Light Rings وإذا كانوا Destructive بيعطيني
+
+192
+00:15:58,860 --> 00:16:02,360
+Dark Rings فبالتالي، احنا قلنا هدولة كلهم، هنهملهم
+
+193
+00:16:02,360 --> 00:16:06,180
+و هنركز على ال Iredisk Diameter ونعتبره هو الصورة
+
+194
+00:16:06,180 --> 00:16:10,830
+كل ما ال Exitشايفين تقريبا الفتحة مش ظاهرة الان
+
+195
+00:16:10,830 --> 00:16:14,910
+لما انا ب .. اجي بكبر بدت تظهر الفتحة ناخد بالنا
+
+196
+00:16:14,910 --> 00:16:20,790
+من النقطة high بدت تكبر عفوا الفتحة وبالتالي لغاية
+
+197
+00:16:20,790 --> 00:16:24,850
+ما نوصل ل 4 من 10 ملي متر لغاية ما نوصل ل 4 من 10
+
+198
+00:16:24,850 --> 00:16:28,470
+ملي متر هذه حجم الفتحة simulation بيقولي انها كبرت
+
+199
+00:16:28,470 --> 00:16:33,870
+كتير فالhighly disk diameter صغر كتير اذا .. لما
+
+200
+00:16:33,870 --> 00:16:40,990
+..بنصغره أكتر بنصغر الطول الموجية بنصغر الطول
+
+201
+00:16:40,990 --> 00:16:45,530
+الموجية أكاد يختفي ال iridisc diameter الآن السؤال
+
+202
+00:16:45,530 --> 00:16:48,950
+اللي بيطرح نفسه احنا إيش محتاجين عشان الصورة تكون
+
+203
+00:16:48,950 --> 00:16:52,310
+ال quality بتاعتها عالية ال iridisc diameter يكون
+
+204
+00:16:52,310 --> 00:16:56,590
+كبير ولا يكون صغير كل مكان ال iridisc diameter
+
+205
+00:16:56,590 --> 00:17:00,670
+أصغر كل مكان أفضل ليش لأن اعتبرنا احنا ال iridisc
+
+206
+00:17:00,670 --> 00:17:04,960
+diameter ان هو صورة النقطةفمحتاجين أن صورة النقطة
+
+207
+00:17:04,960 --> 00:17:10,040
+تكون صغيرة إلى أبعد حد ممكن عشان تصير تشبه النقطة
+
+208
+00:17:10,040 --> 00:17:14,580
+نفسها يعني صدر عندي من نقطة مضيقة فكل ما كان احنا
+
+209
+00:17:14,580 --> 00:17:17,580
+بندرس الآن زي ما حكينا الـ diffraction مش ال
+
+210
+00:17:17,580 --> 00:17:20,660
+aberration مش ال aberration واستعملنا optical
+
+211
+00:17:20,660 --> 00:17:24,520
+system aberration free aberration free يعني
+
+212
+00:17:24,520 --> 00:17:27,900
+مابيعمليش أي نوع من التعريج في السطح فبالتالي
+
+213
+00:17:29,740 --> 00:17:33,460
+الصورة بتكون دائرية بس انا محتاج ان هذه الصورة
+
+214
+00:17:33,460 --> 00:17:37,240
+تكون اصغر ما يكون ليش لان اذا كانت اصغر ما يكون
+
+215
+00:17:37,240 --> 00:17:40,860
+تداخلها مع صور النقاط المجاورة هيكون اقل فبالتالي
+
+216
+00:17:40,860 --> 00:17:45,100
+هتكون ال details اوضح والتفاصيل اوضح اذا الاول
+
+217
+00:17:45,100 --> 00:17:49,680
+شغلة في ال diffraction اذا بدنا ندرسه يعني على حده
+
+218
+00:17:49,680 --> 00:17:53,820
+بنقول ال iridisc diameter اللي هو عبارة عن ال
+
+219
+00:17:53,820 --> 00:17:57,450
+point spread functionهو نفسه ال point spread
+
+220
+00:17:57,450 --> 00:18:00,450
+function ما نتخيلش ان ال point spread function
+
+221
+00:18:00,450 --> 00:18:03,290
+لازم تكون معرجة زي ما الصورة الأولانية اللي
+
+222
+00:18:03,290 --> 00:18:06,730
+عرضناها في المحاضرة السابقة بتقول يعني ما نتخيل
+
+223
+00:18:06,730 --> 00:18:10,150
+انه ضروري تكون ال point spread function دائما
+
+224
+00:18:10,150 --> 00:18:15,940
+متعرجةزي الأشكال هاي ولكن احنا لان ليش مش متعرجة
+
+225
+00:18:15,940 --> 00:18:20,100
+لأنه فيش aberration احنا قلنا اللي في عندي حاجتين
+
+226
+00:18:20,100 --> 00:18:22,720
+مهمات جدا في ال point spread function طبعا في
+
+227
+00:18:22,720 --> 00:18:26,940
+أشياء كتيرة ولكن أهم حاجتين ال diffraction و ال
+
+228
+00:18:26,940 --> 00:18:30,410
+aberrationاستخدمنا aberration free optical system
+
+229
+00:18:30,410 --> 00:18:33,150
+يعني optical system مايعطينيش اي نوع من ال
+
+230
+00:18:33,150 --> 00:18:36,750
+aberration بس بيعطيني diffraction بمعنى ان صورة
+
+231
+00:18:36,750 --> 00:18:40,050
+النقطة بتتوسع و بتفرد لإن ال diffraction هو
+
+232
+00:18:40,050 --> 00:18:44,170
+divergence of light لما يعدي من فتحة في جدار لما
+
+233
+00:18:44,170 --> 00:18:48,620
+يعدي من فتحة في جدار فبالتالياحنا بندرس الـ
+
+234
+00:18:48,620 --> 00:18:51,460
+diffraction إذا في هذا ال optical system اللي هو
+
+235
+00:18:51,460 --> 00:18:54,900
+aberration free ال point spread function عبارة عن
+
+236
+00:18:54,900 --> 00:18:59,080
+circle بدون تعريج طبعا قلنا هدول ال rings احنا
+
+237
+00:18:59,080 --> 00:19:03,260
+بنهملهم لأن كمية الطاقة الضوئية فيهم لا تكاد تذكر
+
+238
+00:19:03,260 --> 00:19:07,180
+فبالتالي ال point spread function عندي هي ال
+
+239
+00:19:07,180 --> 00:19:10,800
+iridisc diameter طيب الآن ال iridisc diameter من
+
+240
+00:19:10,800 --> 00:19:14,950
+مصلحتنا أنه يكون أصغر ولا يكون أكبرطيب لأ من
+
+241
+00:19:14,950 --> 00:19:18,390
+مصلحتنا انه يكون أصغر عشان ان هذا الـ Iredisk
+
+242
+00:19:18,390 --> 00:19:22,390
+Diameter هو صورة النقطة اللي إجا منها الضوء لو
+
+243
+00:19:22,390 --> 00:19:26,930
+النقطة هي A هذا بيكون A شرطة من كل مكان أصغر كل
+
+244
+00:19:26,930 --> 00:19:30,470
+مكان تداخله مع ال Iredisk Diameters من أو ال point
+
+245
+00:19:30,470 --> 00:19:33,770
+spread functions بتاعة النقاط التانية بيكون أقل
+
+246
+00:19:33,770 --> 00:19:38,730
+فبتكون الصورة أجود فبتكون الصورة أجود اذا عشان انا
+
+247
+00:19:38,730 --> 00:19:44,210
+أصغر ال Iredisk Diameterبدي استعمل حاجات ال focal
+
+248
+00:19:44,210 --> 00:19:47,130
+length بتاع ال optical system عادة ما بنقدرش نغيره
+
+249
+00:19:47,130 --> 00:19:50,310
+كيف مثلا نقول احنا مثلا بعض ال optical system
+
+250
+00:19:50,310 --> 00:19:54,890
+العين مثلا عين الإنسان بنقدرش نغير البعد البقري
+
+251
+00:19:54,890 --> 00:19:58,540
+بتاعها لأنه إلها قوة معينةالطول الموجي اللي ساقط
+
+252
+00:19:58,540 --> 00:20:04,200
+علينا برضه في كل منظر بنشوفه يعتبر طول موجي ساقط
+
+253
+00:20:04,200 --> 00:20:07,920
+يعني ثابت يعني ضوء الغرفة مش كل شوية مثلا مش كل
+
+254
+00:20:07,920 --> 00:20:11,500
+ثانية هروح نبدل المصباح الكهربائي بحيث مرة يعطيني
+
+255
+00:20:11,500 --> 00:20:15,480
+blue wavelength و مرة green wavelength و مرة كذا
+
+256
+00:20:15,480 --> 00:20:19,140
+لأ فبالتالي lambda دائما ثابتة و ال focal length
+
+257
+00:20:19,140 --> 00:20:24,740
+ثابت و هذا المقدار في المعادلة رقم ثابت فبالتالي
+
+258
+00:20:24,740 --> 00:20:28,710
+الحاجة الوحيدة اللي ممكن احنااللي هنتحكم فيها هي
+
+259
+00:20:28,710 --> 00:20:32,270
+ال diameter بتاع ال aperture اللي بدي ينفذ منها
+
+260
+00:20:32,270 --> 00:20:36,270
+الضوء بمعنى ال diameter بتاع الفتحة اللي في ال
+
+261
+00:20:36,270 --> 00:20:40,750
+optical system طيب لو أجينا نحكي عن العينبنقول
+
+262
+00:20:40,750 --> 00:20:44,030
+كالقادة هل في في ال optical system بتاع العين
+
+263
+00:20:44,030 --> 00:20:48,170
+فاتحة بالجواب نعم هي ال pupil هي ال pupil بعض
+
+264
+00:20:48,170 --> 00:20:51,490
+الناس بيكون ال pupil عنده واسع وبعض الناس بيكون
+
+265
+00:20:51,490 --> 00:20:56,370
+عنده ال pupil مش واسع فبالتالي بدنا نشوف هل هذا
+
+266
+00:20:56,370 --> 00:20:59,010
+بيأثر على ال diffraction ولا مابيأثرش على ال
+
+267
+00:20:59,010 --> 00:21:09,090
+diffraction بنقول dilated and undilated
+
+268
+00:21:13,760 --> 00:21:18,320
+Pupils الان مثلا هذا المنظر هي عندي undilated
+
+269
+00:21:18,320 --> 00:21:22,860
+pupil normal sized pupil وهذا ال pupil واسع هذا ال
+
+270
+00:21:22,860 --> 00:21:27,200
+pupil واسع كل ما كان ال diameter هنا القطر طبعا
+
+271
+00:21:27,200 --> 00:21:31,840
+هيكون اكبر هنا القطر هيكون اقل تاع ال pupil تاع ال
+
+272
+00:21:31,840 --> 00:21:35,240
+pupil او تاع ال exit pupil ممكن انسان يقول ما
+
+273
+00:21:35,240 --> 00:21:39,020
+الفرق بين ال pupil و ال exit pupil ال exit pupil
+
+274
+00:21:39,020 --> 00:21:44,000
+احنا الصورةالصورة احنا اللي شايفينه هنا مش ال
+
+275
+00:21:44,000 --> 00:21:46,900
+pupil حقيقة صورة ال pupil لأنه احنا بنشوف ال pupil
+
+276
+00:21:46,900 --> 00:21:52,280
+من خلال من خلال القرانية ما بنشوفه مجرد في الهواء
+
+277
+00:21:52,280 --> 00:21:55,920
+يعني ما بنرفع القرانية و بنتطلع على حجمه الحقيقي و
+
+278
+00:21:55,920 --> 00:21:59,500
+طبعا ال exit pupil هذا ال pupil اللي احنا شايفينه
+
+279
+00:21:59,500 --> 00:22:04,860
+أكبر من حجمه بمرة و شوي تقريبا بمرة و 14% لأنه
+
+280
+00:22:04,860 --> 00:22:07,640
+بيصير magnification نتيجة انه فيه القرانية اللي
+
+281
+00:22:07,640 --> 00:22:11,690
+هيتعتبر optical system يعني الضوء سقط علىالـ Iris
+
+282
+00:22:11,690 --> 00:22:15,010
+و الـ Pupil اللي هي فتحة في الـ Iris و انعكس
+
+283
+00:22:15,010 --> 00:22:18,810
+باتجاه عيوننا للخارج و هو منعكس بده يمر عبر
+
+284
+00:22:18,810 --> 00:22:24,250
+القرنية فهتعمله شوية magnification فالـ Exept
+
+285
+00:22:24,250 --> 00:22:26,750
+pupil أيه هو ما أفضل بالنسبة لموضوع الـ
+
+286
+00:22:26,750 --> 00:22:31,770
+diffraction و ال-iridisc هل انه يكون ال pupil ال
+
+287
+00:22:31,770 --> 00:22:35,170
+diameter بتاعه أوسع ولا ال diameter بتاعه أديج
+
+288
+00:22:35,170 --> 00:22:41,300
+طالما ان ال diameter بتاع ال Exept pupilموجود في
+
+289
+00:22:41,300 --> 00:22:45,720
+المقام، إذا كل ما كبر هذه الرقم كل ما كان الـPupil
+
+290
+00:22:45,720 --> 00:22:49,780
+أوسع كل ما كان الـIridisc Diameter أصغر نرجع
+
+291
+00:22:49,780 --> 00:22:53,980
+للـSimulation بنقول بدنا نفرض هذه الفتحة هذه
+
+292
+00:22:53,980 --> 00:22:57,840
+الفتحة أن الـOptical System، هذه الـOptical System
+
+293
+00:22:58,890 --> 00:23:05,570
+وإن ورقة التلقها هي ال retina وهذا ال pupil وهي
+
+294
+00:23:05,570 --> 00:23:10,130
+الضوء الساقط و اللي داخل العين هيدخل من القرنية
+
+295
+00:23:10,130 --> 00:23:13,070
+بعدين عبر ال pupil على ال crystalline lens بعدين
+
+296
+00:23:13,070 --> 00:23:18,070
+هيتم تتلقي من الشبكية لما بيكون ال pupil أوسع
+
+297
+00:23:18,070 --> 00:23:22,390
+نتطلع مع بعض ال eye ال disc diameter جاعت بيصغر
+
+298
+00:23:22,940 --> 00:23:26,860
+وقلنا احنا معنيين انه يكون اصغر، اذا كل ما زاد ..
+
+299
+00:23:26,860 --> 00:23:32,000
+كل ما زاد الـ pupillary diameter كل ما توسع البقب
+
+300
+00:23:32,000 --> 00:23:35,320
+كل ما كان افضل لموضوع الـ diffraction كل ما كان
+
+301
+00:23:35,320 --> 00:23:38,800
+افضل لموضوع الـ diffraction، ليش؟ لأن ساعتها الـ
+
+302
+00:23:38,800 --> 00:23:44,040
+iridisc diameter بيصير اصغر وكل ما صار ال pupil
+
+303
+00:23:44,040 --> 00:23:49,480
+meioticيعني .. يعني منقبض يعني بيصغر حجمه كل ما
+
+304
+00:23:49,480 --> 00:23:52,580
+زاد الـ iridisc diameter معناته الـ diffraction
+
+305
+00:23:52,580 --> 00:23:58,360
+بيزيد اذا لـ pupil الواسع اقل diffraction لـ pupil
+
+306
+00:23:58,360 --> 00:24:02,420
+الديك اكتر diffraction اكتر diffraction ال
+
+307
+00:24:02,420 --> 00:24:07,400
+undilated and undilated pupils undiffraction
+
+308
+00:24:09,290 --> 00:24:13,270
+نحاول نشوف إذا كان في صورة بتوضح هذا الكلام مع أنه
+
+309
+00:24:13,270 --> 00:24:17,610
+ال simulation بيوضح جدا ال simulation بيوضح جدا
+
+310
+00:24:17,610 --> 00:24:24,830
+هذه القضية هنا effect of pupil size on point
+
+311
+00:24:24,830 --> 00:24:29,710
+spread function for typical human eye هنا كل ما
+
+312
+00:24:29,710 --> 00:24:35,130
+كان ال pupil size أصغريمكن الصورة هنا مش واضحة
+
+313
+00:24:35,130 --> 00:24:41,010
+بشكل سليم ولكن كل ما كان ال pupil size أصغر كل ما
+
+314
+00:24:41,010 --> 00:24:44,190
+كان ال diffraction أكتر كل ما كان ال diffraction
+
+315
+00:24:44,190 --> 00:24:48,310
+أكتر طبعا هذا الصورة يعني ما بتجيب الأثر تاع ال
+
+316
+00:24:48,310 --> 00:24:50,990
+diffraction لوحده وإنما ال diffraction مع ال
+
+317
+00:24:50,990 --> 00:24:54,090
+aberration واحنا اتفجنا أن ال aberration لسه مش
+
+318
+00:24:54,090 --> 00:24:59,570
+معاد دراستها الآن مش معاد دراستها الآن المهم أن ال
+
+319
+00:24:59,570 --> 00:25:00,790
+simulation عندى هنا
+
+320
+00:25:03,780 --> 00:25:08,480
+برضه الصورة مش كتير واضحة .. مش كتير واضحة
+
+321
+00:25:08,480 --> 00:25:13,680
+فبالتالي يعني
+
+322
+00:25:13,680 --> 00:25:17,160
+يمكن لو أخدنا هذه الصورة و اقطعنا منها جزء اللي
+
+323
+00:25:17,160 --> 00:25:19,860
+اتوضحلنا القضية و كبرناها
+
+324
+00:25:46,140 --> 00:25:51,720
+هنا لو قلنا واحد ملي متر pupil ال pupil diameter
+
+325
+00:25:51,720 --> 00:26:00,500
+نكبر اكتر ال
+
+326
+00:26:00,500 --> 00:26:01,400
+pupil diameter
+
+327
+00:26:05,950 --> 00:26:08,490
+لما بيكون واحد millimeter بيكون ال diffraction او
+
+328
+00:26:08,490 --> 00:26:11,330
+ال iridisc diameter بالشكل هذا لما بيصير ال pube
+
+329
+00:26:11,330 --> 00:26:15,230
+الاتنين millimeter يعني بتضاعف في القطر بتاعه
+
+330
+00:26:15,230 --> 00:26:19,050
+بيبدأ يصغر ال diffraction بس عندنا هنا كل ما صغر
+
+331
+00:26:19,050 --> 00:26:21,670
+ال diffraction ال aberration بتزيد وهذا موضوع
+
+332
+00:26:21,670 --> 00:26:27,740
+هنحكي عنه في حينه اذا كل ما زادالقطر تاع ال pupil
+
+333
+00:26:27,740 --> 00:26:32,460
+يعني ال diameter تاع ال exit pupil كل ما كانت
+
+334
+00:26:32,460 --> 00:26:35,180
+diffraction pattern بيجل يعني هنا ال iridisc
+
+335
+00:26:35,180 --> 00:26:40,920
+diameter واضح انه له حجم معين كبير لما كبر حجم
+
+336
+00:26:40,920 --> 00:26:45,620
+البقبه بدأ يصغر ال diameter تاع ال iridisc
+
+337
+00:26:45,620 --> 00:26:49,780
+diameter هنا لما بكبر .. ننتبه هنا ال iridisc
+
+338
+00:26:49,780 --> 00:26:56,000
+diameter لما بكبر الحجمببدأ يصغر الـ IRY DISC
+
+339
+00:26:56,000 --> 00:26:59,380
+DIAMETER حجم الفتحة و هنا طبعا كل مكان البيوب
+
+340
+00:26:59,380 --> 00:27:07,020
+الأوسع كل مكان أفضل طيب الان بدنا نوصل لقضية
+
+341
+00:27:11,250 --> 00:27:15,390
+for an eye ليه optical system with تلاتة ملي متر
+
+342
+00:27:15,390 --> 00:27:19,470
+diameter pupil the point spread function diameter
+
+343
+00:27:19,470 --> 00:27:25,310
+is approximately ستة مايكرو متر يعني لو عندي عين
+
+344
+00:27:25,310 --> 00:27:32,150
+قطر ال pupil فيها تلاتة ملي بروح أنا بعوضعن الـ
+
+345
+00:27:32,150 --> 00:27:35,650
+Diameter هذا بتلاتة ملي و ال focal length حسب ال
+
+346
+00:27:35,650 --> 00:27:40,390
+focal length هذه العين و Lambda حسب الضوء الساقط و
+
+347
+00:27:40,390 --> 00:27:45,990
+الطول الموجي إذا لما أجروا العلماء الحسابات ل
+
+348
+00:27:45,990 --> 00:27:51,110
+pupil تلاتة ملي قطره طلع ال Iridisk Diameter اللي
+
+349
+00:27:51,110 --> 00:27:53,910
+هي ال point split function Diameter بتاعها ستة
+
+350
+00:27:53,910 --> 00:27:59,860
+مايكرو متر طيب إذا ساعتهاقطر هذا الـ Iridisk
+
+351
+00:27:59,860 --> 00:28:03,380
+Diameter لما الـ Cube اللي بيكون تلاتة ملي متر
+
+352
+00:28:03,380 --> 00:28:07,820
+بيكون قطر الـ Iridisk Diameter ستة مايكرو متر طيب
+
+353
+00:28:07,820 --> 00:28:12,360
+ستة مايكرو متر هيسقط ع الشبكية جدش هيغطي مساحة من
+
+354
+00:28:12,360 --> 00:28:18,340
+الشبكية هيغطي مساحة تشمل سبعة photoreceptors سبعة
+
+355
+00:28:18,340 --> 00:28:21,660
+photoreceptors زي ده مقطع عرضي في ال outer segment
+
+356
+00:28:21,660 --> 00:28:28,130
+بتاع ال photoreceptorsهيسقط عليها و يغطي مساحة
+
+357
+00:28:28,130 --> 00:28:35,190
+منها تعادل مساحة سبعة من ال outer segments بتاع ال
+
+358
+00:28:35,190 --> 00:28:36,190
+photo receptors
+
+359
+00:29:08,100 --> 00:29:12,480
+أذا مساحة الـ Iridescent Diameter اللي هو 6 مايكرو
+
+360
+00:29:12,480 --> 00:29:16,720
+أو القطر بتاعه 6 مايكرو حيشمل لو أخدنا هنا العين
+
+361
+00:29:16,720 --> 00:29:27,380
+هاي كرسيم تمثيلي حيشمل سبعة
+
+362
+00:29:27,380 --> 00:29:28,620
+photoreceptors
+
+363
+00:29:49,830 --> 00:29:55,090
+هيك تقريبا سبعة، واحد، اتنين، تلاتة، اربعة، خمسة،
+
+364
+00:29:55,090 --> 00:30:00,450
+ستة، سبعة، هيك تمانية يعني مساحة هذا الرسم مكبر
+
+365
+00:30:00,450 --> 00:30:05,730
+جدا لل photo receptors فبالتاليبس ليه مجرد اي ضاحل
+
+366
+00:30:05,730 --> 00:30:09,590
+هذا؟ اذا الـ Iredisk Diameter هيقطره هو هيغطي سبعة
+
+367
+00:30:09,590 --> 00:30:13,770
+من ال outer segments بتاع ال photo receptor هنا في
+
+368
+00:30:13,770 --> 00:30:16,690
+مقطع عرض بيوضح القضية هاي هاي ال photo receptors
+
+369
+00:30:16,690 --> 00:30:21,070
+لما أخدنا cross section مغطي سبع photo receptors
+
+370
+00:30:21,070 --> 00:30:24,710
+ال Iredisk Diameter اللي احنا شايفينه اذا صورة
+
+371
+00:30:24,710 --> 00:30:28,210
+نقطة واحدة غطت على سبعة photo receptors يعني
+
+372
+00:30:28,210 --> 00:30:32,660
+استقبلوها سبعة photo receptors اذا for an eyewith
+
+373
+00:30:32,660 --> 00:30:36,860
+3 mm diameter pupil the point spread function
+
+374
+00:30:36,860 --> 00:30:40,200
+diameter اللي هي الـ IRIDISC Diameter is
+
+375
+00:30:40,200 --> 00:30:44,300
+approximately 6 micrometer encompassing تشمل the
+
+376
+00:30:44,300 --> 00:30:48,180
+outer segments of roughly 7 photoreceptors as
+
+377
+00:30:48,180 --> 00:30:51,380
+noted زي ما احنا شرحنا قبل شوية the IRIDISC
+
+378
+00:30:51,380 --> 00:30:55,320
+Diameter is the point spread function produced
+
+379
+00:30:55,320 --> 00:30:59,040
+solely by diffraction IRIDISC Diameter اللي احنا
+
+380
+00:30:59,040 --> 00:31:00,200
+شايفينه في المنظر
+
+381
+00:31:02,760 --> 00:31:06,400
+هو عبارة عن ال point spread function الناتجة فقط
+
+382
+00:31:06,400 --> 00:31:10,620
+عن ال diffraction عن ال diffraction produced
+
+383
+00:31:10,620 --> 00:31:14,540
+solely فقط by diffraction و ال no aberration are
+
+384
+00:31:14,540 --> 00:31:17,840
+present لما مايكونش عندي aberration بالمرة ال
+
+385
+00:31:17,840 --> 00:31:20,540
+point spread function هي عبارة عن ال iridisc
+
+386
+00:31:20,540 --> 00:31:24,380
+diameterبالتالي، يمكن تخطيط الـ Point Spread
+
+387
+00:31:24,380 --> 00:31:29,640
+Function باستخدام فقط ثلاث قوانين من الجيومتريك
+
+388
+00:31:29,640 --> 00:31:33,220
+الأبطيكيين تمامًا بدلا من الـ diffraction إذا أحنا
+
+389
+00:31:33,220 --> 00:31:39,160
+بدنا نهمل الـ diffraction لأنه مش مهمساعتها بواسطة
+
+390
+00:31:39,160 --> 00:31:43,780
+تلت قوانين تحت الـ Geometric Optics اللي هي قانون
+
+391
+00:31:43,780 --> 00:31:47,060
+الصرايان المستقيم وقانون الـ Reflection وقانون الـ
+
+392
+00:31:47,060 --> 00:31:49,880
+Refraction اللي واسه نلزله طب كيف هي كساعتها
+
+393
+00:31:49,880 --> 00:31:53,020
+نستخدمهم عشان نحسب الـ Point Spread Function؟
+
+394
+00:31:53,020 --> 00:31:57,600
+بنقول كالاتي ال object مثلا ارتفاعه عشرة صنطةو
+
+395
+00:31:57,600 --> 00:32:00,600
+استخدمنا القوانين هذه و طلع عندى ال image مثلا
+
+396
+00:32:00,600 --> 00:32:04,940
+ارتفاعها عشرين صنطي يعني مكبره مرتين اذا كل شيء في
+
+397
+00:32:04,940 --> 00:32:09,620
+ال object كبر مرتين طب لو مكبره عشر مرات معناته كل
+
+398
+00:32:09,620 --> 00:32:13,500
+شيء في ال image اكبر من مثله في ال object عشر مرات
+
+399
+00:32:13,500 --> 00:32:16,840
+وبالتالي هيك احنا بنحسب ال point spread function
+
+400
+00:32:16,840 --> 00:32:20,180
+طبعا هذا من باب التبسيط بس اذا كانت ال diffraction
+
+401
+00:32:20,180 --> 00:32:24,800
+عندى مهم لازم احسب اول حاجة ال iridisc diameter
+
+402
+00:32:25,030 --> 00:32:29,430
+عشان أحسب الـ diffraction إيش أثره على مساحة ال
+
+403
+00:32:29,430 --> 00:32:32,550
+point spread function وإذا كمان بدي أحسب ال
+
+404
+00:32:32,550 --> 00:32:36,210
+aberration بأنتقل لحساب ال aberration اللي بتأثر
+
+405
+00:32:36,210 --> 00:32:39,610
+على تعريج ال point spread function هذه المحاضرة
+
+406
+00:32:39,610 --> 00:32:45,050
+كانت علشان أو قبل من هذا لازم نخلص as a rule
+
+407
+00:32:45,050 --> 00:32:50,090
+diffraction decreases as pupil size increases طيب
+
+408
+00:32:50,090 --> 00:32:55,990
+هنا ال diffraction بيقلكل ما زودت ال pupil size
+
+409
+00:32:55,990 --> 00:32:58,990
+هاي ال pupil size قاعد بيزيد ال diffraction بيقل
+
+410
+00:32:58,990 --> 00:33:02,310
+ال iridisc بيصغر فبدي يعني ال diffraction ممكن
+
+411
+00:33:02,310 --> 00:33:05,470
+نقول طب هذه عددها زاد ال rings هذه ال rings طاقتها
+
+412
+00:33:05,470 --> 00:33:09,730
+مهمة لأنها قليلة جدا الطاقة غالبيتها العظمة مركزة
+
+413
+00:33:09,730 --> 00:33:13,510
+في ال iridisc فيعتبر هو الصورة بتاعة النقطة كل ما
+
+414
+00:33:13,510 --> 00:33:18,660
+زاد ال pupilكل ما جل ال diffraction ممكن الإنسان
+
+415
+00:33:18,660 --> 00:33:23,100
+يقول ماشي okay معناته احنا بنجيب الناس كلهم و
+
+416
+00:33:23,100 --> 00:33:27,880
+بنجدر اللي هم جدر التوسيع عشان يعني يجل ال
+
+417
+00:33:27,880 --> 00:33:28,920
+diffraction عندهم
+
+418
+00:33:42,740 --> 00:33:47,680
+بنجطر للناس كلهم عشان ال diffraction يجل و بالتالي
+
+419
+00:33:47,680 --> 00:33:51,460
+أحسن إنه نعملهم توسيع للبقبو عشان يكون حجم ال
+
+420
+00:33:51,460 --> 00:33:54,340
+iridisc ال diameter صغير وبالتالي الصورة ال
+
+421
+00:33:54,340 --> 00:33:59,080
+quality بتاعتها تكون أعلى .. بنقول هذا الكلام صحيح
+
+422
+00:33:59,080 --> 00:34:02,740
+بيجل ال diffraction بس بيزيد شغلة تانية اللي هي ال
+
+423
+00:34:02,740 --> 00:34:07,030
+aberration يعني صحيح بيصغرالايري ديسك ال diameter
+
+424
+00:34:07,030 --> 00:34:11,650
+بس يصير متعرج كتير وبالتالي هذا أيضا بشوش على وضوح
+
+425
+00:34:11,650 --> 00:34:15,230
+الصورة، اذا ال dilatation مش حل، ال dilatation مش
+
+426
+00:34:15,230 --> 00:34:19,470
+حل، اذا as a rule diffraction decreases as the
+
+427
+00:34:19,470 --> 00:34:23,790
+pupil size increases، كل ما زاد ال pupil size كل
+
+428
+00:34:23,790 --> 00:34:27,790
+ما زاد حجم البقبق القطر بتاعه كل ما توسع البقبق ال
+
+429
+00:34:27,790 --> 00:34:32,250
+diffraction بيقلبس ال aberration increase as the
+
+430
+00:34:32,250 --> 00:34:37,170
+pupil size increases يعني كل ما زاد ال pupillary
+
+431
+00:34:37,170 --> 00:34:44,470
+size كل ما زاد حجم البقبه بيقل ال diffraction
+
+432
+00:34:44,470 --> 00:34:51,130
+بتزيد ال aberration طيب لما بنصفر حجم البقبه ال
+
+433
+00:34:51,130 --> 00:34:54,690
+aberration بتقل و ال diffraction بيزيد خلينا هذه
+
+434
+00:34:54,690 --> 00:34:57,830
+نكتبها عشان ما ننسهاش بنقول كالقاتل
+
+435
+00:35:05,680 --> 00:35:10,720
+بنقول هنا الـ
+
+436
+00:35:10,720 --> 00:35:18,360
+diffraction هنا
+
+437
+00:35:18,360 --> 00:35:26,680
+خلّيني أقول dilated pupil وهنا
+
+438
+00:35:26,680 --> 00:35:28,660
+بنقول undilated pupil
+
+439
+00:35:50,900 --> 00:35:56,520
+وهنا هنقول aberration
+
+440
+00:35:56,520 --> 00:36:02,660
+وهنا
+
+441
+00:36:02,660 --> 00:36:15,100
+هنقول diffraction
+
+442
+00:36:38,680 --> 00:36:52,780
+طبعا هنا في ال
+
+443
+00:36:52,780 --> 00:36:58,120
+dilated pupil ال aberration بتزيد في ال undilated
+
+444
+00:36:58,120 --> 00:37:02,520
+pupil ال direction بيزيد ال diffraction عفوا ال
+
+445
+00:37:02,520 --> 00:37:03,520
+diffraction بيزيد
+
+446
+00:37:18,210 --> 00:37:25,070
+في ال dilated pupil ال diffraction بيجل وفي ال
+
+447
+00:37:25,070 --> 00:37:30,250
+aberration وفي ال undilated pupil ال aberrations
+
+448
+00:37:30,250 --> 00:37:39,890
+بتجل يعني خلف خلاف تماما وسعت البقبق صحيح جللت ال
+
+449
+00:37:39,890 --> 00:37:42,890
+aberration .. جللت ال diffraction اسف بس زوّت ال
+
+450
+00:37:42,890 --> 00:37:47,020
+aberrationيعني مساعة الـ iridisc صغيرة بس تعريجه
+
+451
+00:37:47,020 --> 00:37:51,200
+صار كتير طيب الآن الـ undilated pupil جللنا ال
+
+452
+00:37:51,200 --> 00:37:54,160
+diffraction بس زاد ال aberration إذا بنفعش أوسع
+
+453
+00:37:54,160 --> 00:37:59,200
+كتير أو بنفعش أضيق كتير البوب بنفعش أوسع كتير أو
+
+454
+00:37:59,200 --> 00:38:03,980
+بنفعش أضيق كتير إذا as a rule diffraction
+
+455
+00:38:03,980 --> 00:38:08,400
+decreases as pupil size increases but aberration
+
+456
+00:38:08,400 --> 00:38:14,070
+increase as pupil size increaseالان if the
+
+457
+00:38:14,070 --> 00:38:18,550
+geometric point spread function value is much
+
+458
+00:38:18,550 --> 00:38:22,910
+larger than the iridisc diameter then aberration
+
+459
+00:38:22,910 --> 00:38:27,290
+dominate and diffraction can be ignored إذا حسبت
+
+460
+00:38:27,290 --> 00:38:31,550
+ال aberration بطريق ال geometric principles ال
+
+461
+00:38:31,550 --> 00:38:35,710
+exact ray tracingوحددت حدودها ولاجيت ان الـ
+
+462
+00:38:35,710 --> 00:38:39,790
+geometric point spread function أكبر من ال iridisc
+
+463
+00:38:39,790 --> 00:38:43,710
+diameter معناته ال aberration ال aberration هي
+
+464
+00:38:43,710 --> 00:38:46,810
+الأساس في ال point spread function و ال
+
+465
+00:38:46,810 --> 00:38:53,610
+diffraction can be ignored طيب بمعنى أخر هاي
+
+466
+00:38:53,610 --> 00:38:59,690
+أنا عندى optical system اللي هو العين و دخل الضوء
+
+467
+00:38:59,690 --> 00:39:04,830
+في العين عشان يكون صورةالصورة متعرجة صورة نقطة
+
+468
+00:39:04,830 --> 00:39:09,630
+مضيقة واحدة متعرجة حسبنا ال iridisc diameter حسب
+
+469
+00:39:09,630 --> 00:39:15,610
+المعادل اللي قبل شوية أخدناها حسبناها مثلا طلعت
+
+470
+00:39:15,610 --> 00:39:20,250
+سبعة مايكرو سبعة مايكرو متر ال iridisc diameter
+
+471
+00:39:20,250 --> 00:39:24,070
+لحالي حسبنا ال point spread function ال geometric
+
+472
+00:39:24,070 --> 00:39:28,270
+point spread function لقنا
+
+473
+00:39:29,450 --> 00:39:33,150
+الـ Geometric Point Spread Function أكبر من 7
+
+474
+00:39:33,150 --> 00:39:36,050
+مايكرون، إذا الـ Geometric Point Spread Function
+
+475
+00:39:36,050 --> 00:39:41,350
+أو الـ aberration بمعنى آخر أهم وأكتر من الـ
+
+476
+00:39:41,350 --> 00:39:45,000
+diffraction في تحديد جودة الصورةو الـ diffraction
+
+477
+00:39:45,000 --> 00:39:48,840
+بقدر أهمله لأن هو أصغر من .. لو أخينا بمعنى أخر ال
+
+478
+00:39:48,840 --> 00:39:52,120
+diffraction موجود أو مش موجود في هذه الحالة لو
+
+479
+00:39:52,120 --> 00:39:54,320
+شيلنا ال diffraction ما هي ال geometric point
+
+480
+00:39:54,320 --> 00:39:58,860
+split function قطرها أكبر أو هي larger than the
+
+481
+00:39:58,860 --> 00:40:04,630
+iridisc diameter طيب إذا المثال الآخرهذا الـ point
+
+482
+00:40:04,630 --> 00:40:08,510
+spread function أصغر من الـ iridisc diameter
+
+483
+00:40:08,510 --> 00:40:14,370
+ساعتها الـ diffraction هو الأهم و لو ماكانش حتى
+
+484
+00:40:14,370 --> 00:40:18,430
+فيه تعريج في سطح الصورة ال aberration حتى لو
+
+485
+00:40:18,430 --> 00:40:21,190
+أهملناها ال aberration بيظل ال point spread
+
+486
+00:40:21,190 --> 00:40:24,990
+function اللي بتحكم فيها ال diffraction عشان توضح
+
+487
+00:40:24,990 --> 00:40:31,290
+الأمور هذه بشكل لا لبس فيه بنقولهي عندي أربع صور
+
+488
+00:40:31,290 --> 00:40:36,270
+لأربع .. لنفس النقطة أربع صور لنفس النقطة بنقول
+
+489
+00:40:36,270 --> 00:40:41,210
+كالقادة هذه الصورة الـ ideal إن النقطة صورتها نقطة
+
+490
+00:40:41,210 --> 00:40:46,910
+عندنا نقطة A مش راسمها أنا عندنا نقطة A لو عندي
+
+491
+00:40:46,910 --> 00:40:51,230
+optical system يعطي صورة إلها عبارة عن نقطة يعني
+
+492
+00:40:51,230 --> 00:40:53,750
+بالمرة مافيش aberrations و بالمرة مافيش
+
+493
+00:40:53,750 --> 00:40:57,090
+diffraction هيكون شكل الصورة النقطة A عبارة عن
+
+494
+00:40:57,090 --> 00:41:01,240
+نقطة اللي أنا بأشر عليها طيبلو استخدمنا optical
+
+495
+00:41:01,240 --> 00:41:05,360
+system آخر هذا ال optical system aberration free
+
+496
+00:41:05,360 --> 00:41:08,740
+مافيش فيه أي aberration بس بيعمللي diffraction
+
+497
+00:41:08,740 --> 00:41:14,020
+محترم هيكون صورة النقطة A عبارة عن iridisc مافيش
+
+498
+00:41:14,020 --> 00:41:18,500
+فيه تعريش صحيح بس واسع إله حجم معين يشغل حيز من
+
+499
+00:41:18,500 --> 00:41:23,140
+المساحة إذا هذه صورة للنقطة A هذه صورة ideal لا
+
+500
+00:41:23,140 --> 00:41:26,520
+فيها aberration ولا فيها diffraction هذه الصورة
+
+501
+00:41:28,170 --> 00:41:32,110
+مافيهاش aberration بس فيها a lot of diffraction a
+
+502
+00:41:32,110 --> 00:41:34,870
+lot of diffraction نشوف ال simulation مرة تانية
+
+503
+00:41:34,870 --> 00:41:39,910
+الصورة انه
+
+504
+00:41:39,910 --> 00:41:44,490
+مافيش aberration نحمل ال rings زي ما قولنا هاي هي
+
+505
+00:41:44,490 --> 00:41:48,440
+صورة النقطة Aكمية الـ diffraction كبيرة، ليش؟
+
+506
+00:41:48,440 --> 00:41:53,080
+القرص كبير، القرص كبير، يعني إذا أخدنا مقياس رسم
+
+507
+00:41:53,080 --> 00:41:55,900
+هنا عشرة ملي، يعني هي اللي بيطلع لها تقريبا ال
+
+508
+00:41:55,900 --> 00:42:00,320
+size هنا تقريبا عشرين ملي تقريبا أو خلينا نقول
+
+509
+00:42:00,320 --> 00:42:03,960
+خمستاشر أو سبعتاشر ملي القطر بتاع ال iridisc وهذا
+
+510
+00:42:03,960 --> 00:42:07,920
+يعتبر يعني مساحة كبيرة، إذا هذه صورة النقطة إيه؟
+
+511
+00:42:07,920 --> 00:42:12,520
+هنا بنقول أنه مافيش aberration بس في عندي a lot of
+
+512
+00:42:12,520 --> 00:42:17,380
+diffractionالسيناريو التالت ممكن استخدم optical
+
+513
+00:42:17,380 --> 00:42:22,360
+system يعطيني a lot of aberration بس بدون
+
+514
+00:42:22,360 --> 00:42:26,260
+diffraction الحجم ال point spread function صغير
+
+515
+00:42:26,260 --> 00:42:30,760
+كتير يقترب من أنه يكون نقطة يقترب بنقول .. بنقول
+
+516
+00:42:30,760 --> 00:42:35,020
+بس متعرج كتير .. متعرج كتير لو طلعنا لرسمة مكبرة
+
+517
+00:42:35,770 --> 00:42:39,410
+متعرج كتير، طبعا هي بتكون أصغر من هيك، بنقول no
+
+518
+00:42:39,410 --> 00:42:43,030
+diffraction، ماانتشرش الضوء، ماتوسعش الضوء، بس a
+
+519
+00:42:43,030 --> 00:42:54,610
+lot of aberration السيناريو الرابع والأخير انه
+
+520
+00:42:54,610 --> 00:42:58,830
+صورة فيها diffraction كتير فردت على مساحة كبيرةو
+
+521
+00:42:58,830 --> 00:43:02,250
+فيها aberration كتير، اذا a lot of aberration and
+
+522
+00:43:02,250 --> 00:43:05,470
+diffraction فهيكون .. هذا أسوأ optical system في
+
+523
+00:43:05,470 --> 00:43:10,110
+الأربع وهذا أحسن optical system أعطاني ال image
+
+524
+00:43:10,110 --> 00:43:16,410
+اللي هي ال ideal اللي احنا بنتمناها طبعا هنا مش ..
+
+525
+00:43:16,410 --> 00:43:20,710
+مش جيد انه يكون ال diffraction هندي كتير و هنا مش
+
+526
+00:43:20,710 --> 00:43:24,690
+جيد انه يكون ال aberration كتير طيب، ايش أفضل؟
+
+527
+00:43:27,070 --> 00:43:32,330
+ما هو أفضل صورة ممكن يعمل إياها optical system لما
+
+528
+00:43:32,330 --> 00:43:37,130
+يكون في توازن بين كمية ال diffraction وكمية ال
+
+529
+00:43:37,130 --> 00:43:40,790
+aberration يعني احنا قلنا ان ال ideal هذا مستحيل
+
+530
+00:43:40,790 --> 00:43:45,370
+طبعا في الوقت الحالي ان نصله بس كل ما كان في توازن
+
+531
+00:43:45,370 --> 00:43:48,690
+بين ال aberration و ال diffraction بيكون هذا ال
+
+532
+00:43:48,690 --> 00:43:52,110
+optimal for that optical system if values of the
+
+533
+00:43:52,110 --> 00:43:55,510
+geometric point spread function اللي هي بتحدد لل
+
+534
+00:43:55,510 --> 00:43:59,180
+aberrationand iridisc diameter اللي هي اللي بيحدد
+
+535
+00:43:59,180 --> 00:44:03,060
+للـ diffraction are about the same then image
+
+536
+00:44:03,060 --> 00:44:06,480
+quality is probably close to optimal for that
+
+537
+00:44:06,480 --> 00:44:11,020
+optical system ساعتها بنقول هذه لما بتتساوى أو
+
+538
+00:44:11,020 --> 00:44:14,320
+بيصيروا تقريبا نفس الشيء ال geometric point spread
+
+539
+00:44:14,320 --> 00:44:21,160
+function بمعنى آخر التعريج في سطح الصورة التعريج
+
+540
+00:44:21,160 --> 00:44:28,060
+في سطح الصورةبيكون إله كمية معينة و مساحة سطح
+
+541
+00:44:28,060 --> 00:44:31,540
+الصورة إله كمية معينة و تقريبا متوازنين مع بعض من
+
+542
+00:44:31,540 --> 00:44:35,480
+بعض أو تقريبا بيساو بعض من بعض و نقول بس هنا عند
+
+543
+00:44:35,480 --> 00:44:38,800
+هذه النقطة هذا أفضل صورة ممكن يعطينيها هذا ال
+
+544
+00:44:38,800 --> 00:44:42,060
+optical system طبعا ممكن optical systems تانية
+
+545
+00:44:42,060 --> 00:44:45,420
+تعطيني صورة أفضل من ذلك ولكن ال aberration لما
+
+546
+00:44:45,420 --> 00:44:49,560
+يكون عند ال diffraction كتير و ال aberration كتير
+
+547
+00:44:49,560 --> 00:44:54,130
+هذه صورة سيئةطيب هنا ايضا صورة مش .. مش optimal مش
+
+548
+00:44:54,130 --> 00:44:56,910
+optimal ليش؟ لأنه في كتير aberration بس مافيش
+
+549
+00:44:56,910 --> 00:45:02,050
+diffraction طيب هنا برضه صورة مش .. مش مقبولة ليش؟
+
+550
+00:45:02,050 --> 00:45:05,230
+لأنه مافيش aberration صحيح وهذا ممتاز بس في عندي a
+
+551
+00:45:05,230 --> 00:45:09,150
+lot of diffraction يعني انا مابديش واحد يجل وواحد
+
+552
+00:45:09,150 --> 00:45:13,010
+يزيد بد التانين يتوازنوا مع بعضهم ساعتها هيعطيني
+
+553
+00:45:13,010 --> 00:45:16,570
+ال optical image اللي هي احنا شايفينها فيها تعريج
+
+554
+00:45:17,400 --> 00:45:24,400
+بس التعريج قليل انا رمزتله باللون الأزرق الغامق بس
+
+555
+00:45:24,400 --> 00:45:29,620
+هذا يعني احنا لو احنا جينا نكبره عشان يظهر التعريج
+
+556
+00:45:29,620 --> 00:45:35,800
+معانا هذا التعريج طبعاحدود الصورة حدود الصورة هي
+
+557
+00:45:35,800 --> 00:45:39,140
+الأزراج الفاتح هذه المناطق بالأزراج الغامق مش
+
+558
+00:45:39,140 --> 00:45:43,280
+موجودة الصورة في ذلك المكان وإنما في تعليج قليل في
+
+559
+00:45:43,280 --> 00:45:50,400
+السطح تاع صورة النقطة ومساحتهايعني مقبولة جدا يعني
+
+560
+00:45:50,400 --> 00:45:53,340
+مش كتير الـ diffraction اللي فيها مش كتير فهذه
+
+561
+00:45:53,340 --> 00:45:56,540
+ساعتها بنقول ال optimal image لذلك ال optical
+
+562
+00:45:56,540 --> 00:45:59,640
+system طبعا other optical system ممكن يعطينا
+
+563
+00:45:59,640 --> 00:46:04,160
+images أفضل أو أسوأ حسب إيش الخصائص بتاع هذا ال
+
+564
+00:46:04,160 --> 00:46:08,720
+optical system إذا عشان نوصل ل optimal quality بده
+
+565
+00:46:08,720 --> 00:46:12,400
+يكون كمية ال geometric point spread function اللي
+
+566
+00:46:12,400 --> 00:46:15,760
+هي المقصود فيها ال aberrations مناسبة لكمية ال
+
+567
+00:46:15,760 --> 00:46:19,400
+diffractionطبعا لو كان هذه صفر وهذه صفر يعني
+
+568
+00:46:19,400 --> 00:46:22,620
+اعطتني الصورة ال ideal بكون ممتاز جدا بس مش قادر
+
+569
+00:46:22,620 --> 00:46:26,880
+اوصل لل ideal مش اختار optical system يعطيني
+
+570
+00:46:26,880 --> 00:46:29,740
+diffraction كتير بدون aberration او يعطيني
+
+571
+00:46:29,740 --> 00:46:32,910
+aberration كتير بدون diffractionأو يعطيني
+
+572
+00:46:32,910 --> 00:46:36,330
+aberration و diffraction اكتر جدا، لأ بدي يكون هذا
+
+573
+00:46:36,330 --> 00:46:40,510
+قليل و هذا قليل و متناسبين مع بعضهم البعض وهك احنا
+
+574
+00:46:40,510 --> 00:46:45,570
+بنكون .. يعني حددنا ال image equality طبعا بالنسبة
+
+575
+00:46:45,570 --> 00:46:48,730
+لأهم نقطتين بتحكمه في ال point spread function
+
+576
+00:46:48,730 --> 00:46:53,190
+اللي هم ال aberration و ال diffraction و يعطيكم
+
+577
+00:46:53,190 --> 00:46:56,410
+العافية والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/djia_eiaGes_raw.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/djia_eiaGes_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a356b2a8dca242a8b563b8b9faec26c910d1ba24
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/djia_eiaGes_raw.srt
@@ -0,0 +1,1924 @@
+1
+00:00:01,690 --> 00:00:06,450
+بسم الله الرحمن الرحيم بنواصل محاضرات ال physical
+
+2
+00:00:06,450 --> 00:00:10,750
+optics واتوقفنا عند refractive index and
+
+3
+00:00:10,750 --> 00:00:17,490
+dispersion اللي هو معامل الانكسار و التشتت طبعا
+
+4
+00:00:17,490 --> 00:00:21,990
+مقصود فيه ال dispersion للأطوار الموجية المختلفة
+
+5
+00:00:22,610 --> 00:00:26,170
+Electromagnetic waves travel fastest in a vacuum
+
+6
+00:00:26,170 --> 00:00:31,010
+and slower in any transparent material اللي
+
+7
+00:00:31,010 --> 00:00:34,870
+بنسميها medium يعني كل أنواع الطي في الكهر
+
+8
+00:00:34,870 --> 00:00:39,250
+والمغناطيسي من ال gamma rays لل X-rays لل
+
+9
+00:00:39,250 --> 00:00:44,380
+ultraviolet لل visible light لل infraredلل
+
+10
+00:00:44,380 --> 00:00:47,980
+microwave لل radio waves كل أنواع ال
+
+11
+00:00:47,980 --> 00:00:53,420
+electromagnetic waves سرعتها واحدة في الفراق في ال
+
+12
+00:00:53,420 --> 00:00:57,520
+vacuum ليه تقريبا تلتميت ألف كيلومتر في الثانية
+
+13
+00:00:57,520 --> 00:01:03,320
+ولمّا بتدخل هذه الموجات بما فيها الضوء المرئي أي
+
+14
+00:01:03,320 --> 00:01:08,700
+medium آخر بتختلف سرعتها حسب طولها الموجكل ما كان
+
+15
+00:01:08,700 --> 00:01:13,700
+طولها الموجي أطول كل ما كانت أسرع وكل ما كان طولها
+
+16
+00:01:13,700 --> 00:01:17,360
+الموجي أقصر كل ما كانت أبطأ في أي material تدخل
+
+17
+00:01:17,360 --> 00:01:22,420
+يعني اذا فرضنا جدلا ان عندي موجات من ال gamma rays
+
+18
+00:01:22,420 --> 00:01:26,860
+وموجات من ال ultraviolet تسير في الفراغ ال
+
+19
+00:01:26,860 --> 00:01:31,200
+ultraviolet و ال gamma rays طبعا في الفراغ اللي هم
+
+20
+00:01:31,200 --> 00:01:35,800
+نفس السرعة لو هذه الموجات دخلت مفرض مادة الزجاج
+
+21
+00:01:36,440 --> 00:01:40,500
+هنلاقي ان ال ultraviolet أسرع من الجامعات ليش لأنه
+
+22
+00:01:40,500 --> 00:01:45,020
+أطول موجة أطول موجة All electromagnetic
+
+23
+00:01:45,020 --> 00:01:49,180
+frequencies travel at the same speed in vacuum but
+
+24
+00:01:49,180 --> 00:01:52,820
+in any transparent medium each frequency travels
+
+25
+00:01:52,820 --> 00:01:57,630
+at different speedطيب اختلاف الصراعات لما بندخل اي
+
+26
+00:01:57,630 --> 00:02:01,530
+مادة اخرى غير الفراغ اختلاف صراعات الموجات
+
+27
+00:02:01,530 --> 00:02:07,030
+الكهرومغناطسية هذه الظاهرة بيسموها dispersion this
+
+28
+00:02:07,030 --> 00:02:10,910
+phenomenon called dispersion بمعنى اخر لو حبينا
+
+29
+00:02:10,910 --> 00:02:15,430
+نعطي مثال من الحياة العامة بنقول الناس اتفقواإنه
+
+30
+00:02:15,430 --> 00:02:21,130
+يخرجوا في نزهة أو رحلة يعني عشر مثلا تلمير ولكن
+
+31
+00:02:21,130 --> 00:02:25,950
+ماشوا مع بعضهم بسرعات مختلفة بعد فترة من الزمن
+
+32
+00:02:25,950 --> 00:02:30,630
+هنقول عنهم تشتتوا، بطلت هذه الرحلة أصبح كل إنسان
+
+33
+00:02:30,630 --> 00:02:34,850
+يسير أو كل تلمير يسير لوحده بعد فترة من الزمن، إيش
+
+34
+00:02:34,850 --> 00:02:38,980
+السبب؟ إن سرعاتهم مختلفةوهنا نفس القضية لما
+
+35
+00:02:38,980 --> 00:02:43,000
+الأطوال الموجية المختلفة سواء في الضوء المرئي أو
+
+36
+00:02:43,000 --> 00:02:46,760
+في باقي الطيف الكهرومغناطيسي أو الموجات
+
+37
+00:02:46,760 --> 00:02:51,440
+الكهرومغناطيسية لما سرعتها في المواد بتختلف معناته
+
+38
+00:02:51,440 --> 00:02:55,840
+بيصير إليها تشتت وهذا ما يسمى بال dispersion طيب
+
+39
+00:02:55,840 --> 00:02:59,760
+الآن ال refractive index معامل الانكسار واللي مر
+
+40
+00:02:59,760 --> 00:03:03,800
+علينا في مادة ال geometric optics واللي بنرمزله
+
+41
+00:03:03,800 --> 00:03:08,330
+بالرمز Mis the ratio of speed of light in vacuum
+
+42
+00:03:08,330 --> 00:03:13,190
+divided by its speed in a given material يعني لو
+
+43
+00:03:13,190 --> 00:03:16,530
+بدأ أحسب ال refractive index لمaterial معينة لم
+
+44
+00:03:16,530 --> 00:03:22,090
+medium المادسين بقول سرعة الضوء في الفراغعلى سرعة
+
+45
+00:03:22,090 --> 00:03:26,750
+الضوء في المادة C بيطلع هذا ال .. ال .. الكمية أو
+
+46
+00:03:26,750 --> 00:03:31,730
+هذا الكاسر بيطلع هو اللي هو ال refractive index
+
+47
+00:03:31,730 --> 00:03:36,370
+للضوء في المادة C، في المادة C، إذا بقسم سرعة
+
+48
+00:03:36,370 --> 00:03:40,010
+الضوء في الفراغ على سرعة الضوء في المادة اللي بدي
+
+49
+00:03:40,010 --> 00:03:43,010
+أحسبي لها ال refractive index بتطلع نتيجة
+
+50
+00:03:43,010 --> 00:03:47,110
+refractive index لهذه المادة، لهذه المادة
+
+51
+00:03:50,110 --> 00:03:56,550
+الآن ال dispersion بيقاس .. بيقاس بواسطة معادلة
+
+52
+00:03:56,550 --> 00:04:00,950
+هذه المعادلة بيسموها ال ab number أو ال V number
+
+53
+00:04:00,950 --> 00:04:06,130
+ab number أو ال V number البعض بيلفظها ab number
+
+54
+00:04:06,130 --> 00:04:11,110
+مش .. مش هي القضية يعني المركزية في هذا الموضوع
+
+55
+00:04:11,110 --> 00:04:16,470
+وإنما التشتت أو ال dispersion بيقاس بواسطة ال ab
+
+56
+00:04:16,470 --> 00:04:21,090
+number أو ال V number إذا ال dispersionis measured
+
+57
+00:04:21,090 --> 00:04:25,190
+using refractive index at three different
+
+58
+00:04:25,190 --> 00:04:29,890
+wavelengths يعني لو قلنا عندي مادة و هذه المادة
+
+59
+00:04:29,890 --> 00:04:34,170
+مثلا زجاج و بدى أجيس كده هذا النوع من الزجاج،
+
+60
+00:04:34,170 --> 00:04:39,950
+الزجاج أنواع كتيرة لو اخترت نوع معين من الزجاج و
+
+61
+00:04:39,950 --> 00:04:44,190
+حبيت أجيس كده هذا النوع اللي انا اخترته كده بيعمل
+
+62
+00:04:44,190 --> 00:04:46,210
+تشتت للأطوال الموجية
+
+63
+00:04:48,780 --> 00:04:52,500
+بحسب ال refractive index لهذا النوع اللي انا
+
+64
+00:04:52,500 --> 00:04:56,920
+اختارته عند تلت أطوال موجية مختلفة الطول الموجي D
+
+65
+00:04:56,920 --> 00:05:02,900
+و الطول الموجي F و الطول الموجي C بحسب ال N يعني
+
+66
+00:05:02,900 --> 00:05:07,100
+ال refractive index عند الطول الموجي D و بحسب ال N
+
+67
+00:05:07,100 --> 00:05:09,560
+عند الطول الموجي F اللي هو ال refractive index
+
+68
+00:05:09,560 --> 00:05:13,120
+أيضا لنفس المادة احنا قلنا طالما السرعات بتختلف
+
+69
+00:05:13,120 --> 00:05:18,440
+طالما سرعة الضوء طالما سرعة الضوءفي هذه المادة
+
+70
+00:05:18,440 --> 00:05:22,700
+بتختلف باختلاف الطول الموجي للضوء اذا عندي كذا
+
+71
+00:05:22,700 --> 00:05:25,300
+refractive index ممكن الانسان يقول كيف .. كيف هذه
+
+72
+00:05:25,300 --> 00:05:28,800
+القضية؟ بنقوله تعالي نشوف هذه القضية بشكل عملي ..
+
+73
+00:05:28,800 --> 00:05:34,300
+بشكل عملي هاي انا عندي .. الضوء يسري في مادة زي
+
+74
+00:05:34,300 --> 00:05:41,040
+الماء .. يسري في مادة زي الماء جديش ال refractive
+
+75
+00:05:41,040 --> 00:05:47,840
+index للميه .. لل waterعند الطول الموجي البنفسجي
+
+76
+00:05:47,840 --> 00:05:51,600
+اللي هو أقصر الأطوار الموجية تلاتمية و تمانين نانو
+
+77
+00:05:51,600 --> 00:05:55,320
+متر تلاتمية و تمانين نانو متر أقصر طول موجي مرئي
+
+78
+00:05:55,320 --> 00:05:58,460
+اللي هو الطول البنفسجي high refractive index لل
+
+79
+00:05:58,460 --> 00:06:01,800
+water الضوء بيسري في ال water اللي هو الجزء الأعلى
+
+80
+00:06:01,800 --> 00:06:10,040
+من الصورة الجزء
+
+81
+00:06:10,040 --> 00:06:14,020
+الأعلى من الصورة هي واحد point تلاتة أربعة خمسكل
+
+82
+00:06:14,020 --> 00:06:20,120
+ما زاد الطول الموجي بيقسر
+
+83
+00:06:20,120 --> 00:06:22,000
+او بيقل ال refractive index
+
+84
+00:06:31,530 --> 00:06:35,310
+لو طلعنا على ال refractive index للمي هي نفس المي
+
+85
+00:06:35,310 --> 00:06:40,030
+ما تغيرت المي ولكن كل ما زاد طول الموجي بيقل ال
+
+86
+00:06:40,030 --> 00:06:45,910
+refractive index طيب كل ما قصرت طول الموجي بيزيد
+
+87
+00:06:45,910 --> 00:06:49,350
+ال refractive index بيزيد ال refractive index ممكن
+
+88
+00:06:49,350 --> 00:06:52,330
+إنسان يقول طب هذا بالنسبة للمي وهذا بالنسبة لأي
+
+89
+00:06:52,330 --> 00:06:57,270
+مادة أخرى يعني مثلا لجلاس لجلاس هي أقصر طول الموجي
+
+90
+00:06:58,700 --> 00:07:03,980
+الـ refractive index 1.518 لأن لما بدنا نزود هلاجي
+
+91
+00:07:03,980 --> 00:07:07,620
+انه بيجي الجاعة ال refractive index اذا كل ما
+
+92
+00:07:07,620 --> 00:07:12,680
+ازدادت الطول الموجي كل ما اقل ال refractive index
+
+93
+00:07:12,680 --> 00:07:19,900
+كل ما اقل ال refractive index فبالتالي هذا
+
+94
+00:07:19,900 --> 00:07:23,980
+بيقدي إلى انه العلاقة بين الطول الموجي و
+
+95
+00:07:23,980 --> 00:07:29,310
+refractive index علاقة عكسية علاقة عكسيةوعشان احنا
+
+96
+00:07:29,310 --> 00:07:37,390
+يعني ناخد ال .. الكلام بشكل يعني ملخص و .. واضح
+
+97
+00:07:37,390 --> 00:07:47,850
+جدا، هنكتبها باللغة العربية كل ما .. كل ما ازداد
+
+98
+00:07:47,850 --> 00:07:52,110
+الطول
+
+99
+00:07:52,110 --> 00:07:52,770
+الموجة
+
+100
+00:07:57,190 --> 00:08:03,310
+هذا يساوي معامل
+
+101
+00:08:03,310 --> 00:08:09,970
+انكسار أقل
+
+102
+00:08:09,970 --> 00:08:13,610
+ويساوي
+
+103
+00:08:13,610 --> 00:08:29,100
+سرعة في المادة أعلى طيب العكسكل ما قصرة الطول
+
+104
+00:08:29,100 --> 00:08:35,000
+الموجي، يعني روحنا باتجاه اللون الأزرق والبنفسجي،
+
+105
+00:08:35,000 --> 00:08:45,860
+هذا إيش يساوي؟ معامل انكسار أعلى،
+
+106
+00:08:45,860 --> 00:08:52,740
+سرعة في المادة أقل
+
+107
+00:08:56,720 --> 00:09:00,780
+وهذا يعني الكلام اللي بيلخص ليه إيش علاقة الطول
+
+108
+00:09:00,780 --> 00:09:04,720
+الموجي بمعامل الإنكسار بسرعة هذا الطول الموجي في
+
+109
+00:09:04,720 --> 00:09:09,480
+المادة طول الموجي الأطول سرعته أعلى معامل إنكساره
+
+110
+00:09:09,480 --> 00:09:15,220
+أقل الطول الموجي الأقصر سرعته أقل ومعامل إنكساره
+
+111
+00:09:15,220 --> 00:09:16,220
+أعلى
+
+112
+00:09:19,470 --> 00:09:24,410
+بنقول عشان نجيس التشتت اللي بتعمل إياه أي مادة
+
+113
+00:09:24,410 --> 00:09:28,990
+نفرض مادة أو نوع معين من الزجاج التشتت اللي بتعمله
+
+114
+00:09:28,990 --> 00:09:35,510
+اللضوء هل تشتت كتير ولا قليل بيقاس بواسطة ال up
+
+115
+00:09:35,510 --> 00:09:40,250
+number او اختصارا بيقولو ال V number كيف يحسب ال V
+
+116
+00:09:40,250 --> 00:09:43,750
+number او ال up number بنحسب ال refractive index
+
+117
+00:09:43,750 --> 00:09:47,860
+للمادة اللي اخترناهاعند تلت أطوال موجية مختلفة
+
+118
+00:09:47,860 --> 00:09:51,600
+هنلاقي بيختلف ال refractive index عند طول الموج D
+
+119
+00:09:51,600 --> 00:09:57,320
+منه عند طول الموج F منه عند طول الموج C وبالتالي
+
+120
+00:09:57,320 --> 00:10:01,240
+بدخل بس أحسب ال refractive index بدخله في المعادلة
+
+121
+00:10:01,240 --> 00:10:05,220
+وبحسبه بطلع عندي رقم معين هذا الرقم بيدلني على
+
+122
+00:10:05,220 --> 00:10:08,840
+مقدار التشتت وهنشاهد بعد قليل ان شاء الله تعالى
+
+123
+00:10:08,840 --> 00:10:16,010
+فيديو بيحكي باختصار عن هذه القضية طيبWhere N D و N
+
+124
+00:10:16,010 --> 00:10:22,310
+F و N C represents wavelength in a material of
+
+125
+00:10:22,310 --> 00:10:27,970
+طبعاً F F خمسمية و سبعة و تمانين و ستة من عشرة
+
+126
+00:10:27,970 --> 00:10:33,710
+نانومتر C أربعمية و ستة و تمانين و واحد من عشرة
+
+127
+00:10:33,710 --> 00:10:42,520
+نانومتر و Dاللي هي 656.3 نانو متر بمعنى ان انا
+
+128
+00:10:42,520 --> 00:10:46,380
+بحسب ال refractive index M عند هذه الأطوار الموجية
+
+129
+00:10:46,380 --> 00:10:50,100
+التلاتة و بدخلها كل واحد في مكانه في المعادلة
+
+130
+00:10:50,100 --> 00:10:56,840
+وبحسب ال V number طيب خلاصة القول إذا طلع عندي ال
+
+131
+00:10:56,840 --> 00:11:00,840
+V number أو ال up number عالي معناته المادة جيدة
+
+132
+00:11:00,840 --> 00:11:05,980
+أو بتشتت أقلبينما لو عندى ال V number قليل معناته
+
+133
+00:11:05,980 --> 00:11:11,460
+المادة سيئة و بتعمل تشتت كتير طبعا يفضل عند صناعة
+
+134
+00:11:11,460 --> 00:11:15,000
+او اختيار مادة زجاجية معينة او اي مادة اخرى
+
+135
+00:11:15,000 --> 00:11:18,660
+transparent عشان نصنع منها العدسات او العدسات
+
+136
+00:11:18,660 --> 00:11:21,980
+اللاصقة او ال intraocular lens اللى بتزرع بعد
+
+137
+00:11:21,980 --> 00:11:25,820
+عملية ال cataractيفضل إنه نختار مادة ال app number
+
+138
+00:11:25,820 --> 00:11:29,420
+ده هعالي شوية عشان ما تعمليش تشتيت وتعملي
+
+139
+00:11:29,420 --> 00:11:32,880
+chromatic aberration أو يعني زيغ لوني زي ما هنشوف
+
+140
+00:11:32,880 --> 00:11:36,640
+بعد شوية في الفيديو زي ما هنشوف بعد شوية في
+
+141
+00:11:36,640 --> 00:11:44,160
+الفيديو ننتقل لفيديو اللي بدنا نحضره هنحضره أول
+
+142
+00:11:44,160 --> 00:11:49,580
+مرة و بعدين هعلق عليه بالتدريج Appie value refers
+
+143
+00:11:49,580 --> 00:11:51,760
+to the clarity of transparent materials
+
+144
+00:11:54,060 --> 00:11:57,260
+Theoretically perfect transparency is 100 on the
+
+145
+00:11:57,260 --> 00:11:59,680
+abbey scale. But because light travels through
+
+146
+00:11:59,680 --> 00:12:02,420
+both the cornea and the crystalline lens, the
+
+147
+00:12:02,420 --> 00:12:07,160
+abbey value of the eye is between 45 and 50. In an
+
+148
+00:12:07,160 --> 00:12:09,900
+ideal world, the abbey value of a lens should not
+
+149
+00:12:09,900 --> 00:12:14,200
+be lower than that of the eye. In practice, only
+
+150
+00:12:14,200 --> 00:12:17,080
+three lens materials have abbey values close to
+
+151
+00:12:17,080 --> 00:12:21,320
+that of the eye. All remaining lens materials have
+
+152
+00:12:21,320 --> 00:12:22,360
+lower abbey values.
+
+153
+00:12:26,580 --> 00:12:28,920
+أقل قيمة heavy يمكن أن يتسبب في اتسابقات كرماتية
+
+154
+00:12:28,920 --> 00:12:34,300
+عندما تزداد التسابقات.بعض الناس أكثر مستطابة
+
+155
+00:12:34,300 --> 00:12:38,660
+لتسابقات كرماتية من البقية.لتحرك هذا، يجب أن تجرب
+
+156
+00:12:38,660 --> 00:12:42,340
+مواد مع قيمة heavy عالية.إذا كانت مصورتك كثيرة،
+
+157
+00:12:42,340 --> 00:12:45,460
+يمكنك أن تجرب صورة أكتر التي ستقوم بتقلي كمية
+
+158
+00:12:45,460 --> 00:12:49,230
+مصورتك.An additional solution is to order fully
+
+159
+00:12:49,230 --> 00:12:51,990
+personalized lenses which have optimal viewing in
+
+160
+00:12:51,990 --> 00:12:54,930
+all directions. If chromatic aberration is not an
+
+161
+00:12:54,930 --> 00:12:57,550
+issue, you will be well served by any of our lens
+
+162
+00:12:57,550 --> 00:13:06,950
+materials.طبعا
+
+163
+00:13:06,950 --> 00:13:13,520
+ال ABI valueبيرجع ل clarity of transparent
+
+164
+00:13:13,520 --> 00:13:16,900
+material يعني جداش هي شفافة و جداش هي نقية هذه ال
+
+165
+00:13:16,900 --> 00:13:20,720
+material اللي انا اخترتها عشان اصنع منها العدسات
+
+166
+00:13:20,720 --> 00:13:26,640
+طبعا
+
+167
+00:13:26,640 --> 00:13:32,170
+لما بدنا نيجي نحكي بنقول احنا ال ..الـ Perfect
+
+168
+00:13:32,170 --> 00:13:35,950
+Transparency أو الشفافية الكاملة هي المفروض تاخد
+
+169
+00:13:35,950 --> 00:13:40,510
+درجة مائة بالمائة على الـ Abbey Scale أو على مقياس
+
+170
+00:13:40,510 --> 00:13:46,070
+الـ Abbey ولكن العين لأن فيها optical system اللي
+
+171
+00:13:46,070 --> 00:13:49,130
+هو عبارة عن القرانية و عن ال crystalline lens لما
+
+172
+00:13:49,130 --> 00:13:53,770
+جاسوا لعين الإنسان ال Abbey number أو ال V number
+
+173
+00:13:53,770 --> 00:13:57,930
+وجدوها تتراوح بين خمسة و أربعين لخمسين على هذا
+
+174
+00:13:57,930 --> 00:13:59,530
+المقياس وأيضا
+
+175
+00:14:01,840 --> 00:14:05,840
+العدسات اللي احنا بنصنع منها النضارات او ما شابه
+
+176
+00:14:05,840 --> 00:14:12,080
+لازم تكون ايضا زي العين لا تقل عن 45 ل50 اللي هو
+
+177
+00:14:12,080 --> 00:14:16,720
+ال V number بتاعها او ال A number بتاعها حقيقة
+
+178
+00:14:16,720 --> 00:14:22,160
+الأمر ان فيها فقط 3 أنواع من ال material بتوفر
+
+179
+00:14:22,160 --> 00:14:26,660
+لهذا الشرطيعني عندي ال standard index glass اللي
+
+180
+00:14:26,660 --> 00:14:29,520
+هو ال refractive index بتاع واحد و نص ال ab value
+
+181
+00:14:29,520 --> 00:14:32,760
+بتاعه تسعة و خمسين اذا حتى اكتر من ال ab number او
+
+182
+00:14:32,760 --> 00:14:36,100
+ال V number بتاع العين يعني كمية التشتيت اللي
+
+183
+00:14:36,100 --> 00:14:42,380
+بتعمليها لضوء قليلة جدا و تعتبر material ممتازة في
+
+184
+00:14:42,380 --> 00:14:46,160
+مادة اخر يعني نوع اخر من ال material اللي بيسموه
+
+185
+00:14:46,160 --> 00:14:49,960
+trivex و ال refractive index بتاعه واحد و تلاتة و
+
+186
+00:14:49,960 --> 00:14:54,190
+خمسين من ميةالـ Abby number بتاعه 45 يعني زي العين
+
+187
+00:14:54,190 --> 00:14:57,830
+زي العين أو مشابه للعين في مادة تالتة أو نوع تالت
+
+188
+00:14:57,830 --> 00:15:02,430
+من ال material اللي هو Xeram ال refractive index
+
+189
+00:15:02,430 --> 00:15:08,790
+بتاعه 51.58% وال Abby value تقريبا 44 ملاحظين أن
+
+190
+00:15:08,790 --> 00:15:11,530
+ال Abby number أو ال V number لهده ال three
+
+191
+00:15:11,530 --> 00:15:15,910
+material يشابه أو يفوق ال Abby number بتاع العين
+
+192
+00:15:15,910 --> 00:15:20,970
+إذا هده التلت أنواع من ال materialحقيقة ال quality
+
+193
+00:15:20,970 --> 00:15:25,870
+بتاعتهم ممتازة وكمية التشتيت بتاعهم قليلة كمية
+
+194
+00:15:25,870 --> 00:15:35,410
+التشتيت بتاعهم قليلة نشوف باقية المواد زي
+
+195
+00:15:35,410 --> 00:15:40,050
+ال mid index ال mid index material نوع من الجزاز
+
+196
+00:15:40,050 --> 00:15:43,870
+او نوع من ال material ال refractive index بتاعه زي
+
+197
+00:15:43,870 --> 00:15:47,870
+ما احنا شايفين 157 بس المهماللي هو ال ABI value
+
+198
+00:15:47,870 --> 00:15:51,810
+بتاعه أقل من اربعين سبعة و تلاتين وبالتالي يعني
+
+199
+00:15:51,810 --> 00:15:55,750
+بيعطيني نوع من التشتيت ال polycarbonateأيضًا
+
+200
+00:15:55,750 --> 00:15:59,330
+Material تاني شفاف ال ABI number بتاعه أسوأ يعني
+
+201
+00:15:59,330 --> 00:16:02,210
+تلاتين يا كل ما قلل ال ABI number معناته التشتيت
+
+202
+00:16:02,210 --> 00:16:07,290
+عندي هيزيد ال high index يعني high index من اسمها
+
+203
+00:16:07,290 --> 00:16:11,290
+يعني نوع من ال materials أو الجزاز ال refractive
+
+204
+00:16:11,290 --> 00:16:15,550
+index بتاعه عالي واحد و .. واحد وستين من المية و
+
+205
+00:16:15,550 --> 00:16:18,610
+ال ABI number بتاعه واحد واربين طبعًا يعتبر شوية
+
+206
+00:16:18,610 --> 00:16:25,100
+low ال extra high indexالـ Extra High Index ليه
+
+207
+00:16:25,100 --> 00:16:29,060
+وحد و سبعة و ستين ال refractive index بينما ال ABI
+
+208
+00:16:29,060 --> 00:16:33,360
+value سيء كتير اتنين و تلاتين على مقياس اللي هو
+
+209
+00:16:33,360 --> 00:16:38,100
+على ال ABI scale يعني هيعمل ليه تشتيت عالي طبعا ال
+
+210
+00:16:38,100 --> 00:16:42,920
+premium high index واحد و اربعة و سبعين يعني عالي
+
+211
+00:16:42,920 --> 00:16:46,270
+جدا ال refractive index بتاعهو ال ABI value عنده
+
+212
+00:16:46,270 --> 00:16:50,430
+36 طبعا تحت الأربعين يعتبر يعني ال quality أقل و
+
+213
+00:16:50,430 --> 00:16:54,230
+كل ما قل ال ABI number كانت تشتيت أكتر ممكن إنسان
+
+214
+00:16:54,230 --> 00:16:57,190
+يسأل نفسه طب احنا ليش بنلجأ لهذه المواد طالما ال
+
+215
+00:16:57,190 --> 00:17:01,870
+ABI number تعها عالي و .. او عفوا منخفض و بتعملي
+
+216
+00:17:01,870 --> 00:17:05,250
+تشتيت عالي أو تشتيت كتيربنقول لما ال refractive
+
+217
+00:17:05,250 --> 00:17:09,590
+index بيكون أعلى، بيكون سمك العدسة أقل، سمك العدسة
+
+218
+00:17:09,590 --> 00:17:15,230
+أقل، يعني احنا .. يعني بين .. يعني حدي .. حدي
+
+219
+00:17:15,230 --> 00:17:19,570
+النصل أو بين شيئين
+
+220
+00:17:19,570 --> 00:17:24,610
+أو بين مرين أو بين شيئين أحلى هما مروا، انه إذا
+
+221
+00:17:24,610 --> 00:17:29,030
+أنا بدأ أختار material، ال refractive index بتاعه
+
+222
+00:17:29,390 --> 00:17:32,710
+refractive index بتاعه القليل هيكون سميك العدسة
+
+223
+00:17:32,710 --> 00:17:37,770
+هتكون سميكة والتشتت قليل لأن ال a number غالبا
+
+224
+00:17:37,770 --> 00:17:42,010
+بيكون أكتر من أربعين وإذا بدي أختار العكس يعني
+
+225
+00:17:42,010 --> 00:17:45,830
+هيعطيني عدسة رفيعة لأن ال index of refraction عالي
+
+226
+00:17:45,830 --> 00:17:49,590
+زي ما أنا بقشر هنا بينما ال a ال a number جليل
+
+227
+00:17:49,590 --> 00:17:53,730
+فممكن .. ممكن في هذه الحالة نلاقي الحل اللي هنعرضه
+
+228
+00:17:53,730 --> 00:17:55,310
+بعض شوية في نفس هذا الفيديو
+
+229
+00:18:01,100 --> 00:18:05,240
+طبعا لما بيكون عندي هنا مقارنة بين اني اطلع من
+
+230
+00:18:05,240 --> 00:18:09,280
+خلال عدسة ال a b number بتاعها high يعني التشتيت
+
+231
+00:18:09,280 --> 00:18:14,560
+قليل نركز على الأحرف اللي داخل الدائرة البيضاوية
+
+232
+00:18:14,560 --> 00:18:18,780
+او الجسم البيضاوي او الشكل البيضاوي هنلاقيها واضحة
+
+233
+00:18:18,780 --> 00:18:23,560
+بينما لما بستخدم عدسة أخرى low a b value الانسان
+
+234
+00:18:23,560 --> 00:18:26,790
+اللي بتطلع من خلالها هيشوف الأحرفهيشوف الهالات
+
+235
+00:18:26,790 --> 00:18:31,130
+اللونية اللى حوالها زى ما هو واضح عندى بشكل يعني
+
+236
+00:18:31,130 --> 00:18:47,490
+واضح ان شاء الله انكمل طيب
+
+237
+00:18:47,490 --> 00:18:51,710
+مالحل مالحل اذا انا عندى refractive error عالى
+
+238
+00:18:51,710 --> 00:18:57,940
+كتير وبدى عدسة اخميلة تمامفبدى انا اختار high
+
+239
+00:18:57,940 --> 00:19:03,300
+refractive index medium عساس انه العدسة ما تكونش
+
+240
+00:19:03,300 --> 00:19:08,460
+سميكة على الآخر احد الحلول اني اصفر الإطار .. اصفر
+
+241
+00:19:08,460 --> 00:19:12,960
+الإطار لانه بتضل ال central lens طبعا بالذات في ال
+
+242
+00:19:12,960 --> 00:19:16,920
+myopia بتضل ال central lens يعني رقيقة نوعا ما
+
+243
+00:19:16,920 --> 00:19:20,560
+تسخير إطار النضارة يعتبر احد الحلول
+
+244
+00:19:26,210 --> 00:19:33,070
+أو اختار عدسة مفصلة تفصيل خاص بحيث انها تقللي اللي
+
+245
+00:19:33,070 --> 00:19:39,530
+هو التشتت بتاع الضوء .. التشتت بتاع الضوء هنا
+
+246
+00:19:39,530 --> 00:19:44,330
+أنواع مختلفة من ال material طبعا كل مكان .. كل
+
+247
+00:19:44,330 --> 00:19:48,330
+مكان ال ab number أعلى و كل مكان أفضل و كل مكان ال
+
+248
+00:19:48,330 --> 00:19:53,050
+ab number أقل يعني السطر الأعلى هنا ال material
+
+249
+00:19:53,050 --> 00:19:57,000
+ممتازة و بتعملش تشتيتالسطر التاني والتالت ال
+
+250
+00:19:57,000 --> 00:20:00,880
+materials أقل جودة يعني بتعمل تشتيت أعلى .. بتعمل
+
+251
+00:20:00,880 --> 00:20:08,140
+تشتيت أعلى وهنا
+
+252
+00:20:08,140 --> 00:20:14,660
+بنتوقف عن الفيديو عساس أنه
+
+253
+00:20:14,660 --> 00:20:22,560
+.. بنرجع للاستكمال .. إذا whereNB, NF and NC
+
+254
+00:20:22,560 --> 00:20:27,000
+represent wavelengths in a material طبعا وقلنا
+
+255
+00:20:27,000 --> 00:20:30,500
+لخلاصة انه larger up numbers indicate the lower
+
+256
+00:20:30,500 --> 00:20:37,180
+dispersion هي عند ال up number اللي هو ال optical
+
+257
+00:20:37,180 --> 00:20:41,710
+dispersionبحسب ال refractive index عند طول الموجي
+
+258
+00:20:41,710 --> 00:20:44,810
+D اللي هو طول الموجي خمسمية وتسعة وتمانين point
+
+259
+00:20:44,810 --> 00:20:48,330
+اتنين من عشرة nanometer وبحسب الطول الموجي عند
+
+260
+00:20:48,330 --> 00:20:51,890
+الطول او بحسب ال refractive index عند طول الموجي F
+
+261
+00:20:51,890 --> 00:20:55,750
+اللي هو اربعمية وستة و تمانين واحد من عشرة وبحسب
+
+262
+00:20:55,750 --> 00:21:02,830
+ال refractive index عند طول الموجي C اللي هو الطول
+
+263
+00:21:02,830 --> 00:21:05,550
+الموجي C اللي هو ستمية و ستة و خمسين point تلاتة
+
+264
+00:21:05,550 --> 00:21:11,020
+من عشرة nanometerفي شغلة تانية حاببين ان اريدها
+
+265
+00:21:11,020 --> 00:21:17,440
+يعني عن طريق الحساب بتاع الطول الموجي طبعا اول شئ
+
+266
+00:21:17,440 --> 00:21:21,700
+في هذه الرسمة البيانية بدي ان الاحظ انه هاي عندي
+
+267
+00:21:21,700 --> 00:21:27,460
+انا تلت انواع من المواد fused quartz وعندي ال BK
+
+268
+00:21:27,460 --> 00:21:32,920
+اللي هو borosilicate crown glass BK7 borosilicate
+
+269
+00:21:32,920 --> 00:21:38,080
+crown glass مادة تانيةوعندي le flint glass لو أسقى
+
+270
+00:21:38,080 --> 00:21:42,340
+في حداشر le flint glass هاي الرسمة بتاعته طبعا لو
+
+271
+00:21:42,340 --> 00:21:46,020
+يعني سألنا أنفسنا السؤال عند مرور الضوء في ال
+
+272
+00:21:46,020 --> 00:21:50,300
+fused quartz لبرزم المصنوع من ال fused quartz أو
+
+273
+00:21:50,300 --> 00:21:54,020
+في البرزم المصنوع من ال borosilicate crown glass
+
+274
+00:21:54,020 --> 00:21:58,460
+أو من ال .. ال .. ال .. البرزم المصنوع من le flint
+
+275
+00:21:58,460 --> 00:22:03,360
+glass أيهما يعطي أكتر تشتت حسب الصورة أنه عندي أنا
+
+276
+00:22:03,360 --> 00:22:08,850
+تشتت هنا أكترهنا أقل للضوء هنا أقل و أقل ال
+
+277
+00:22:08,850 --> 00:22:13,590
+dispersion أقل ال dispersion أقل طبعا طريقة حساب
+
+278
+00:22:13,590 --> 00:22:18,470
+ال refractive أو طريقة حساب ال V number ال V
+
+279
+00:22:18,470 --> 00:22:21,870
+number يعني هنا عند حاسبين ال V number أو ال up
+
+280
+00:22:21,870 --> 00:22:26,860
+number للمادة دي و ال up number للمادة E طبعابحسب
+
+281
+00:22:26,860 --> 00:22:30,420
+ال refractive index عن تلت أطوار موجية و بدخلهم في
+
+282
+00:22:30,420 --> 00:22:35,280
+المعادلة و بطلع عندي يعني ال up number و بطلع عندي
+
+283
+00:22:35,280 --> 00:22:38,820
+ال up number لو احنا حابينه نقارن بين المادة D و
+
+284
+00:22:38,820 --> 00:22:44,080
+المادة A ال up number بتاع المادة D أعلى بشوية من
+
+285
+00:22:44,080 --> 00:22:48,580
+ال up number بتاع المادة A إذا المادة D أقل كشتيتا
+
+286
+00:22:48,580 --> 00:22:53,260
+أقل كشتيتا للضوء من المادة D من المادة A طبعا هنا
+
+287
+00:22:53,260 --> 00:22:57,530
+ال refractive index Mوهنا الطول الموجي واضح انه كل
+
+288
+00:22:57,530 --> 00:23:01,010
+ما بيزيد الطول الموجي كل ما بنروح باتجاه زيادة
+
+289
+00:23:01,010 --> 00:23:04,510
+الطول الموجي كل ما بيقل عندي انا ال refractive
+
+290
+00:23:04,510 --> 00:23:07,410
+index كل ما بيهبط عندي ال refractive index
+
+291
+00:23:07,410 --> 00:23:11,710
+فبالتالي هذه القضية بده تكون ايش واضحة ان شاء الله
+
+292
+00:23:11,710 --> 00:23:20,930
+تعالى تكون واضحة ان شاء الله تعالى نيجي لموضوع ال
+
+293
+00:23:20,930 --> 00:23:25,300
+reflection و لتransmissionوالabsorption ال
+
+294
+00:23:25,300 --> 00:23:29,540
+reflection والtransmission والabsorption بنقول
+
+295
+00:23:29,540 --> 00:23:33,280
+consider light striking the interface between two
+
+296
+00:23:33,280 --> 00:23:38,820
+materials such as air and glass some light is
+
+297
+00:23:38,820 --> 00:23:42,960
+reflected according to the law of reflection and
+
+298
+00:23:42,960 --> 00:23:47,000
+some transmitted refracted according to Snell's
+
+299
+00:23:47,000 --> 00:23:50,180
+law of refraction
+
+300
+00:23:50,590 --> 00:23:54,730
+the question is how much light is reflected and
+
+301
+00:23:54,730 --> 00:24:00,930
+how much is transmitted بنأكد أنه لما الضوء بينتقل
+
+302
+00:24:00,930 --> 00:24:08,170
+من مادة لمادة يصير معاه تلت أشياء هاي الضوء عندي
+
+303
+00:24:08,170 --> 00:24:17,170
+تم إيقافه، الضوء بده ينتقل من مثلا الهواء
+
+304
+00:24:21,140 --> 00:24:24,800
+بنتقل من الهواء اللي هو باللون الأبيض واضح عندنا
+
+305
+00:24:24,800 --> 00:24:28,600
+للماء اللي هو باللون الأزرق واضح عندنا هاي الضوء
+
+306
+00:24:28,600 --> 00:24:34,520
+بدنتقل بيحدث معاه تلت أشياء عند استضامه بالسطح
+
+307
+00:24:34,520 --> 00:24:39,740
+الفاصل بين المادتين بين الهواء والماء جزء بينعكس
+
+308
+00:24:39,740 --> 00:24:45,580
+حسب قانون الانعكاس وجزء بينكسر حسب قانون الانكسار
+
+309
+00:24:45,580 --> 00:24:49,700
+اللي هو Snell's Lawوالجزء التالد .. والجزء التالد
+
+310
+00:24:49,700 --> 00:24:55,380
+بيمطص بواسطة السطح الفاصل بتحول لحرارة احنا طبعا
+
+311
+00:24:55,380 --> 00:24:59,440
+الجزء اللي بيمطص يعتبر ضئيل جدا مقارنة مع الجزء
+
+312
+00:24:59,440 --> 00:25:03,900
+اللي بينعكس والجزء اللي بيمره الآن العلماء في سؤال
+
+313
+00:25:03,900 --> 00:25:10,720
+كبير مطروح أمامهم يا ترى الضوء سقط جديش انعكس منه
+
+314
+00:25:10,720 --> 00:25:15,320
+وجديش مر منه يعني لو فرضنا ان حزمة ضوئية من مائة
+
+315
+00:25:15,320 --> 00:25:20,470
+ألف شعاعقداش من المائة ألف شعاع انعكس وقداش من
+
+316
+00:25:20,470 --> 00:25:24,570
+المائة ألف شعاع مر يعني هل مثلا انعكس ألف شعاع
+
+317
+00:25:24,570 --> 00:25:28,830
+وضال تسعة وتسعين ألف شعاع مر و لا المادة التانية و
+
+318
+00:25:28,830 --> 00:25:33,930
+لا إيش اللي .. اللي حدث و ما الذي يتحكم .. ما الذي
+
+319
+00:25:33,930 --> 00:25:38,810
+يتحكم في هذه القضية ما الذي يتحكم في هذه القضية
+
+320
+00:25:38,810 --> 00:25:44,450
+فبنقول كالقاتي how
+
+321
+00:25:44,450 --> 00:25:48,460
+much light is reflectedand how much transmitted
+
+322
+00:25:48,460 --> 00:25:53,500
+and how much transmitted applying electromagnetic
+
+323
+00:25:53,500 --> 00:25:58,660
+wave theory فرينيل هذا عالم طبعا ال S silent في
+
+324
+00:25:58,660 --> 00:26:02,900
+اسمه فرينيل demonstrated that the greater the
+
+325
+00:26:02,900 --> 00:26:06,420
+difference in refractive indices or the greater
+
+326
+00:26:06,420 --> 00:26:10,120
+the angle of incidence the greater the degree of
+
+327
+00:26:10,120 --> 00:26:12,880
+reflection and consequently the less light
+
+328
+00:26:12,880 --> 00:26:21,030
+transmitted هذه العبارةلنتائج تجارب العالم Fresnel
+
+329
+00:26:21,030 --> 00:26:27,610
+مقصومة لجزئين Fresnel بيحكي بيقول كل ما كان الفرج
+
+330
+00:26:27,610 --> 00:26:33,810
+في معامل الانكسار بين المادتين أكتر يعني لو ثبتنا
+
+331
+00:26:33,810 --> 00:26:38,490
+زاوية السقوط نفرض زاوية السقوط نفرض عشرين degree
+
+332
+00:26:38,490 --> 00:26:45,630
+وخلينها ثابتةبس معامل الانكسار غيرناه صار الفرق
+
+333
+00:26:45,630 --> 00:26:49,590
+مرة أقل و مرة أكتر كل ما زاد الفرق في معامل
+
+334
+00:26:49,590 --> 00:26:54,910
+الانكسار بين المادتين كل ما كان كمية المنعكس أكتر
+
+335
+00:26:54,910 --> 00:27:00,670
+وبالتالي كمية اللي بمر أقل الجملة التانية كل ما
+
+336
+00:27:00,670 --> 00:27:06,690
+كانت زاوية السقوط أكبر كل ما كان كمية المنعكس أكتر
+
+337
+00:27:06,690 --> 00:27:11,030
+وبالتالي كمية اللي بمر أقلهذه القضية بدنا احنا
+
+338
+00:27:11,030 --> 00:27:15,350
+نعملها بال simulation هنقسم
+
+339
+00:27:15,350 --> 00:27:20,090
+العبارة لجزئين ونقول كل ما اول حاجة كل ما the
+
+340
+00:27:20,090 --> 00:27:24,350
+greater the greater the difference in refractive
+
+341
+00:27:24,350 --> 00:27:29,150
+indices between طبعا the two materials بيكون كمية
+
+342
+00:27:29,150 --> 00:27:32,790
+الاش اللي بنعكس اكتر هنشوف بال simulation هذا كيف
+
+343
+00:27:32,790 --> 00:27:36,650
+هيحصل معناه هنجيب ال angle حدد ال angle زاوية
+
+344
+00:27:36,650 --> 00:27:42,680
+السقوط هنثبتها مثلانحكي عند على سبيل المثال تلاتين
+
+345
+00:27:42,680 --> 00:27:48,620
+هاي
+
+346
+00:27:48,620 --> 00:27:53,460
+تلاتين degree تلاتين degree وبنقول الضوء يسقط
+
+347
+00:27:53,460 --> 00:27:59,670
+بزاوية سقوط تلاتين degreeبين الهوى وبين المي الفرج
+
+348
+00:27:59,670 --> 00:28:03,730
+في ال refractive index بينهم point تلاتة تلاتة
+
+349
+00:28:03,730 --> 00:28:07,470
+تلاتة كيف الفرج عرفته واحد و تلاتة و تلاتين من مية
+
+350
+00:28:07,470 --> 00:28:11,070
+ناقص واحد بيبقى لعندي تلاتة و تلاتين من مية او
+
+351
+00:28:11,070 --> 00:28:14,670
+تلاتة تلاتة تلاتة من الف تمام تلاتة مية و تلاتة و
+
+352
+00:28:14,670 --> 00:28:19,010
+تلاتين من الف اذا بدنا نشوف جداش في هذه الحالة لما
+
+353
+00:28:19,010 --> 00:28:22,050
+الفرج يكون في refractive index بين المي و الهوى
+
+354
+00:28:22,050 --> 00:28:27,600
+تلتجدّاش انا بيكون عندي كمية الانعكس و كمية المر
+
+355
+00:28:27,600 --> 00:28:36,480
+خلّينا نشوف الانعكس
+
+356
+00:28:36,480 --> 00:28:39,880
+تلاتة و سبعة من مية في المية تقريبا تلاتة في المية
+
+357
+00:28:39,880 --> 00:28:45,020
+انعكس و جدّاش اللي مر تقريبا سبعة و تسعين في المية
+
+358
+00:28:45,020 --> 00:28:49,580
+اذا تلاتة في المية انعكس و سبعة و تسعين في المية
+
+359
+00:28:49,580 --> 00:28:57,270
+مر طيب انا بدي اغير ال waterخلّي glass أصبح
+
+360
+00:28:57,270 --> 00:29:05,490
+اللي مر 94% والانعكس جديش تقريبا 6% تقريبا 6% إلا
+
+361
+00:29:05,490 --> 00:29:09,950
+ربع نرجع بنقول لما زاد الفرج في معامل الانكسار بين
+
+362
+00:29:09,950 --> 00:29:15,470
+المادتين الفرج هنا تقريبا نص الفرج نص لما زاد
+
+363
+00:29:15,470 --> 00:29:20,390
+الفرج في معامل الانكسار بين المادتين زاد كمية
+
+364
+00:29:20,390 --> 00:29:25,050
+المنعكسزاد كمية الضوء المنعكس .. هنا الضوء المنعكس
+
+365
+00:29:25,050 --> 00:29:31,670
+تقريبا ستة إلى ربع في المية و طبعا اللي مر أقل
+
+366
+00:29:31,670 --> 00:29:35,070
+اربعة وتسعين و ربع في المية مجموعهم مية في المية
+
+367
+00:29:35,070 --> 00:29:40,310
+.. لو احنا خففنا الفرق يعني استعملنا مادة تانية ..
+
+368
+00:29:40,310 --> 00:29:41,310
+هنلاقي انه
+
+369
+00:29:44,870 --> 00:29:48,590
+هنا تلاتة في المياه انعكس بدل ستة في المياه و هنا
+
+370
+00:29:48,590 --> 00:29:52,450
+ال limar ستة وتسعين في المياه اذا كل ما بيجل الفرق
+
+371
+00:29:52,450 --> 00:29:56,770
+بين المادتين في ال refractive index كمية المنعكس
+
+372
+00:29:56,770 --> 00:30:00,690
+اذا بيجل الفرق كمية المنعكس اقل فبالتالي كمية
+
+373
+00:30:00,690 --> 00:30:04,690
+المرور اكتر بدنا نثبت هذه كمان بطريقة اكتر نقول
+
+374
+00:30:04,690 --> 00:30:08,150
+بدنا نخلي الدوء يمر من الهواء الى الهواء
+
+375
+00:30:10,790 --> 00:30:16,290
+طبعا فيش ساطح فاصل لإنه هذا هو كمية اللي بمره جديش
+
+376
+00:30:16,290 --> 00:30:20,330
+مية في المية طيب كمية المنعكس هتصيح صفر في المية
+
+377
+00:30:20,330 --> 00:30:26,570
+مافيش حاجة بتنعكس طيب ال .. ال .. ال water كمية
+
+378
+00:30:26,570 --> 00:30:32,030
+المنعكس تلاتة في المية ال glass كمية المنعكس
+
+379
+00:30:32,030 --> 00:30:36,740
+تقريبا ستة في المية يعني ليش لما ..حولنا المادة
+
+380
+00:30:36,740 --> 00:30:40,640
+التانية من water ل glass زاد كمية اللي بالعكس لأنه
+
+381
+00:30:40,640 --> 00:30:44,680
+زاد الفرق في ال refractive index إذا نرجع للجملة
+
+382
+00:30:44,680 --> 00:30:47,860
+the greater the difference in refractive index,
+
+383
+00:30:50,040 --> 00:30:56,080
+the greater the degree of reflectionطبعا .. كل ما
+
+384
+00:30:56,080 --> 00:30:58,820
+زاد كمية المنعكس .. معناته كمية اللي مر .. انا
+
+385
+00:30:58,820 --> 00:31:02,640
+عندي حصة ثابتة .. انعكس جزء اكبر منها .. معناته مر
+
+386
+00:31:02,640 --> 00:31:06,680
+جزء اقل منها .. جاء مر جزء اقل منها .. الان الجملة
+
+387
+00:31:06,680 --> 00:31:09,960
+التانية .. the greater the angle of incidence ..
+
+388
+00:31:09,960 --> 00:31:14,920
+كل ما كان زاوية السقوط اكبر .. هيكون كمية المنعكس
+
+389
+00:31:14,920 --> 00:31:19,180
+اكتر .. وبالتالي كمية اللي بمر اقل .. احنا هنا ..
+
+390
+00:31:20,030 --> 00:31:24,950
+سنبقى على الهواء لجلاس هاي زاوية السقوط جديش انعكس
+
+391
+00:31:24,950 --> 00:31:28,810
+في حالة زاوية السقوط تلاتين degree تقريبا ستة إلا
+
+392
+00:31:28,810 --> 00:31:32,150
+ربع في المية طب بدأ ازود زاوية السقوط ونشوف جديش
+
+393
+00:31:32,150 --> 00:31:36,350
+كمية المنعكس بتزيد كل ما زودنا زاوية السقوط
+
+394
+00:31:42,220 --> 00:31:46,120
+هذه زودنا زاوية السقوط كمية المنعكس صارت أكتر
+
+395
+00:31:46,120 --> 00:31:50,600
+وبالتالي كمية اللي بمر صارت أقل .. كل ما .. يعني
+
+396
+00:31:50,600 --> 00:31:55,720
+كمية اللي بمر أقل .. إذا في حاشتينفي حاجتين
+
+397
+00:31:55,720 --> 00:32:00,740
+بيزودولي كمية الضوء المنعكس الضوء جزء منه هينعكس
+
+398
+00:32:00,740 --> 00:32:05,440
+وجزء منه هينكسر وجزء منه هيمطص اللي هيمطص كمية
+
+399
+00:32:05,440 --> 00:32:09,600
+قليلة جدا لدرجة يمكن اهمالها او عدم اعتبارها بيضال
+
+400
+00:32:09,600 --> 00:32:13,360
+عندي اكبر جزءين الحزمة اللي انعكست والحزمة اللي
+
+401
+00:32:13,360 --> 00:32:19,090
+مرت من الضوء الكل اللي سقطعشان أعرف جديش اللي
+
+402
+00:32:19,090 --> 00:32:22,710
+انعكس وبالتالي أعرف جديش اللي مر، في حاجتين
+
+403
+00:32:22,710 --> 00:32:28,990
+أساسيات بتحكمه في هذه .. في هذا الموضوع، كل ما
+
+404
+00:32:28,990 --> 00:32:32,670
+زادت زاوية السقوط بتزيد كمية المنعكس، هاي الدليل
+
+405
+00:32:32,670 --> 00:32:36,400
+عندي واضحأنا المادتين هخليهم نفس المادتين يعني
+
+406
+00:32:36,400 --> 00:32:39,960
+الفرق في ال refractive index تابع بس هغير زاوية
+
+407
+00:32:39,960 --> 00:32:44,620
+السقوط وبالتالي نشوف جداش كمية المنعكس في حالة
+
+408
+00:32:44,620 --> 00:32:50,880
+زاوية سقوط 42.9 تقريبا 8.5 نعكس يعني جداش 8.5 يعني
+
+409
+00:32:50,880 --> 00:32:58,220
+91.5 مرة 91.5 مرة فبالتالي انا بدي لأ انا بهمن
+
+410
+00:32:58,220 --> 00:33:04,460
+المنعكس الآنهيف عند زاوية السقوط 42.9 تقريبا 8.5%
+
+411
+00:33:04,460 --> 00:33:10,700
+انعكس لان بده اجلل زاوية السقوط بتجل زاوية السقوط
+
+412
+00:33:10,700 --> 00:33:15,180
+بلاحظ انه
+
+413
+00:33:15,180 --> 00:33:19,160
+كل
+
+414
+00:33:19,160 --> 00:33:23,100
+ما جلت زاوية السقوط بتجل جاعدة كمية المنعكس
+
+415
+00:33:23,300 --> 00:33:26,440
+وبالتالي هتزيد كمية اللي مار الضوء مش هيروح مكان
+
+416
+00:33:26,440 --> 00:33:29,900
+تاني يا هينعكس يعني هنا عند زاوية السقوط تسعة
+
+417
+00:33:29,900 --> 00:33:33,400
+وعشرين وسبعة من عشرة تقريبا خمسة وسبعة من عشرة في
+
+418
+00:33:33,400 --> 00:33:39,320
+المية انعكس وبالتالي اللي مار اربعة وتسعين وتلاتة
+
+419
+00:33:39,320 --> 00:33:44,720
+من عشرة في المية كلما ازدادت زاوية السقوط كلما
+
+420
+00:33:44,720 --> 00:33:49,160
+ازدادت زاوية السقوط بتزيد نسبة الضوء اللي انعكس
+
+421
+00:33:54,210 --> 00:33:57,430
+وبالتالي بتجيل نسبة الضوء اللي مارك، واحد هياخد
+
+422
+00:33:57,430 --> 00:34:04,850
+على حساب التاني كل ما زودنا زاوية السقوط، هاي احنا
+
+423
+00:34:04,850 --> 00:34:08,610
+قاعدين بنزود في زاوية السقوط، هاي زاوية السقوط كل
+
+424
+00:34:08,610 --> 00:34:10,850
+ما زودناها بيزيد كمية المنعكس
+
+425
+00:34:14,720 --> 00:34:19,680
+يعني عند زاوية سقوط 60 درجة تقريبا 17% بنعكس
+
+426
+00:34:19,680 --> 00:34:24,920
+والباقي بيمر اللي هو 83 تقريبا او 82 وكسر في المية
+
+427
+00:34:24,920 --> 00:34:33,580
+لما بنجلل زاوية السقوط لما بنجلل زاوية السقوط قاعد
+
+428
+00:34:33,580 --> 00:34:37,360
+بيقل كمية المنعكس فبتزيد كمية
+
+429
+00:34:43,130 --> 00:34:47,250
+وبالتالي عندى هنا بتزيد كمية اللى بيمر هنا الانعكس
+
+430
+00:34:47,250 --> 00:34:55,290
+تقريبا 6 من 10 .. 6% و اللى مر تقريبا 94% .. 94%
+
+431
+00:34:55,290 --> 00:35:00,030
+إذا هذا الفرق الأول طب لو أنا قررت أنه بدي أثبت ..
+
+432
+00:35:00,030 --> 00:35:09,520
+أثبت زاوية السقوط خليها عند 32.4% كمية الانعكس6.11
+
+433
+00:35:09,520 --> 00:35:14,880
+% بدي اخلي اغير او اجلل الفرق في ال refractive
+
+434
+00:35:14,880 --> 00:35:18,920
+index لما جللت الفرق في ال refractive index بين
+
+435
+00:35:18,920 --> 00:35:25,800
+الماديتين قل كمية المنعكس لما بزود الفرق افضل لما
+
+436
+00:35:25,800 --> 00:35:32,480
+بزود الفرق بيزيد كمية المنعكس اذا الضوء المنعكس
+
+437
+00:35:32,480 --> 00:35:37,320
+تلخيصا لكل الكلام السابق الضوء المنعكس حصته تزيد
+
+438
+00:35:37,320 --> 00:35:43,880
+بحاجتينبحاجتين حصة الضوء المنعكس تزداد بحاجتين اما
+
+439
+00:35:43,880 --> 00:35:48,000
+بزيادة الفرق بين ال refractive index بتاع المادتين
+
+440
+00:35:48,000 --> 00:35:53,480
+او بزيادة زاوية السقوط او بزيادة زاوية السقوط عند
+
+441
+00:35:53,480 --> 00:35:59,060
+هذه النقطة ان شاء الله يتعالى هنتوقف و جابل ما
+
+442
+00:35:59,060 --> 00:36:03,800
+نتوقف خلينا احنا نقول كالقاتي نقول for an air
+
+443
+00:36:03,800 --> 00:36:09,110
+glass interfaceTypically about 4% of light is
+
+444
+00:36:09,110 --> 00:36:13,550
+reflected at low angles of incidence Tears have a
+
+445
+00:36:13,550 --> 00:36:17,290
+lower refractive index than glass, so an air tear
+
+446
+00:36:17,290 --> 00:36:21,450
+film interface reflects even less light يعني about
+
+447
+00:36:21,450 --> 00:36:28,120
+2% لو عندنا الضوء بيسقط بزاود سقوط صغيرةمن الهوى
+
+448
+00:36:28,120 --> 00:36:34,480
+للجزاز 4% منه بنعكس و 96% بيمر بينما لو سقط على
+
+449
+00:36:34,480 --> 00:36:37,840
+الدمع الدمع اللي هو بيغطي سطح العين ايضا هيسقط من
+
+450
+00:36:37,840 --> 00:36:41,720
+الهوى باتجاه الدمع وبعدين يدخل القرانية بس الحد
+
+451
+00:36:41,720 --> 00:36:48,200
+الفاصل بين سطح الدمع .. بين سطح الدمع الحد الفاصل
+
+452
+00:36:48,200 --> 00:36:51,540
+بين سطح الدمع هاي الدمع اللي هو ال lipid layer و
+
+453
+00:36:51,540 --> 00:36:55,300
+ال aqueous layer و ال myosin layer اللي اتضوق
+
+454
+00:36:55,300 --> 00:36:59,130
+لغاية ما يصل هنافي عندي حصات حفاصة بين الدمع اللي
+
+455
+00:36:59,130 --> 00:37:05,510
+هو ميه water وبين الهوى بنعكس جزء منه تقريبا 2%
+
+456
+00:37:05,510 --> 00:37:09,290
+إذا سقط بزاوية سقوط بسيطة إذا سقط بزاوية سقوط
+
+457
+00:37:09,290 --> 00:37:15,330
+بسيطة بنانعمل simulation لهذا الموضوع ونشوف جداش
+
+458
+00:37:15,330 --> 00:37:19,410
+عندي أنا بزاوية سقوط بسيطة
+
+459
+00:37:59,760 --> 00:38:03,480
+بزاوية سقوط أربعة degree هي زاوية السقوط اللي هي
+
+460
+00:38:03,480 --> 00:38:07,420
+منحصرة بين ال service normal والشعاع الساقط لما
+
+461
+00:38:07,420 --> 00:38:11,200
+يكون ساقط من الهواء للجزاز تقريبا أربعة في المية
+
+462
+00:38:11,200 --> 00:38:16,440
+بينعكس يعني ستة وتسعين في المية بينهم طيب ايش اللي
+
+463
+00:38:16,440 --> 00:38:21,340
+هنعمله احنا؟ احنا هنغير ال glass بالمي طب ايش معنى
+
+464
+00:38:21,340 --> 00:38:24,740
+اخترنا المي؟ المي هي الدمع الدمع طبعا
+
+465
+00:38:27,220 --> 00:38:32,140
+تقريبا 2% انعكس .. اذا لما جال الفارق .. لما جال
+
+466
+00:38:32,140 --> 00:38:36,560
+الفارق جال كمية المنعكس و بدالي كمية اللي مار أكتر
+
+467
+00:38:36,560 --> 00:38:38,920
+.. كمية اللي مار أكتر .. ممكن الإنسان يقول طب هذه
+
+468
+00:38:38,920 --> 00:38:42,640
+إيش الفايدة؟ طبعا العين عشان تتلقى الضوء من ال
+
+469
+00:38:42,640 --> 00:38:46,660
+object الأفضل أنه المعظم يدخل مش ينعكس يعني لو أنا
+
+470
+00:38:46,660 --> 00:38:52,600
+باطلع على object و بده ينعكس 40% او 30% من الضوء
+
+471
+00:38:52,600 --> 00:38:57,180
+الصادر منهيعني ماوصلنيش إلا 60% أو 70% طبعا هذا
+
+472
+00:38:57,180 --> 00:39:01,500
+أقل جودة من .. مما لو يصلني كمية أعلى منها يعني
+
+473
+00:39:01,500 --> 00:39:05,260
+لما تكون كمية المنعكس أقل بيكون أفضل .. كمية
+
+474
+00:39:05,260 --> 00:39:09,140
+المنعكس أقل بيكون أفضل ممكن إنسان يقول .. طب ليش
+
+475
+00:39:09,140 --> 00:39:12,140
+زاوية سقوط صغيرة؟ لأن الإنسان لما بتطلع .. بتطلع
+
+476
+00:39:12,140 --> 00:39:15,300
+دغري باتجاه الأشياء فبتالي زاوية سقوطها على العين
+
+477
+00:39:15,300 --> 00:39:19,820
+عادة بتكون صغيرة مش كبيرة يعني بتطلعش الإنسان على
+
+478
+00:39:19,820 --> 00:39:25,810
+شيء بشكل جانبي .. بشكل ..جانبي .. نتوقف عند هذه
+
+479
+00:39:25,810 --> 00:39:30,530
+النقطة و المرة القادمة ان شاء الله بنستكمل هذا
+
+480
+00:39:30,530 --> 00:39:34,750
+الموضوع و يعطيكم العافية و السلام عليكم و رحمة
+
+481
+00:39:34,750 --> 00:39:35,790
+الله و بركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ducsEpvuitg.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ducsEpvuitg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3ed220137453992e9f8fd24c1c837d2992cb0beb
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ducsEpvuitg.srt
@@ -0,0 +1,999 @@
+1
+00:00:01,430 --> 00:00:05,930
+بسم الله الرحمن الرحيم  الـ physical optics هو علم 
+
+2
+00:00:05,930 --> 00:00:12,330
+بَعني بدراسة أو بيعني بدراسة الخصائص الفيزيائية
+
+3
+00:00:12,330 --> 00:00:19,740
+للضوء وبعض الظواهر الفيزيائية المرتبطة بالضوء
+
+4
+00:00:19,740 --> 00:00:25,820
+وأيضا أثر الضوء على بعض الأنسجة الحيوية زي العين 
+
+5
+00:00:25,820 --> 00:00:31,380
+مثال يعني ما أثر ضوء الليزر على شبكة العين وما إلى
+
+6
+00:00:31,380 --> 00:00:38,630
+ذلك طبعا هنبدأ بِنتعرف على مصدر نشوء الضوء يعني طبعا
+
+7
+00:00:38,630 --> 00:00:42,090
+في مصادر كثيرة لنشوء الضوء ولكن احنا بدنا المصدر
+
+8
+00:00:42,090 --> 00:00:47,110
+الرئيسي في حياتنا واللي هو الشمس is an origin of 
+
+9
+00:00:47,110 --> 00:00:52,150
+visible light مصدر الضوء source المصدر in general
+
+10
+00:00:52,150 --> 00:00:55,630
+clinical optics concerns the focusing or 
+
+11
+00:00:55,630 --> 00:01:00,230
+processing of visible light البصريات الطبية حقيقة
+
+12
+00:01:00,230 --> 00:01:04,190
+بتعنى بدراسة يعني تركيز الضوء أن ينعّمه focus و أن
+
+13
+00:01:04,190 --> 00:01:06,990
+ييجي هذا الـ focus مثلا على الشبكية و تكون الصورة
+
+14
+00:01:06,990 --> 00:01:11,150
+واضحة وما إلى ذلك بينما الـ physical optics مجال
+
+15
+00:01:11,150 --> 00:01:15,050
+دراسته هو مختلف عن ذلك of course visible light
+
+16
+00:01:15,050 --> 00:01:19,770
+comes primarily from the sun بشكل رئيسي من الشمس 
+
+17
+00:01:19,770 --> 00:01:24,610
+أو الشموس أو النجوم children are taught يعني بيتم
+
+18
+00:01:24,610 --> 00:01:28,810
+تعليم الأطفال في مرحلة الطفولة أن الـ visible light
+
+19
+00:01:28,810 --> 00:01:32,590
+الضوء المرئي اللي جاي من الشمس also generates the 
+
+20
+00:01:32,590 --> 00:01:37,230
+energy necessary for life بيمدنا بالطاقة ..
+
+21
+00:01:37,230 --> 00:01:42,150
+بالطاقة اللازمة للحياة الـ visible light بيتراوح
+
+22
+00:01:42,150 --> 00:01:47,790
+طوله الموجي بين 400 nanometer لـ 700 nanometer طبعا
+
+23
+00:01:47,790 --> 00:01:53,270
+هذا الـ visible light يعتبر جزء بسيط من diffraction
+
+24
+00:01:53,270 --> 00:01:58,110
+من الـ electromagnetic spectrum طبعا في الحياة في 
+
+25
+00:01:58,110 --> 00:02:02,300
+شيء اسمه موجود الطيف الكهرومغناطيسي الطيف
+
+26
+00:02:02,300 --> 00:02:08,960
+الكهرومغناطيسي واسع جدا والضوء بشكل نوع من أنواع
+
+27
+00:02:08,960 --> 00:02:14,120
+الموجات الكهرومغناطيسية بشكل واحد في المية فقط من
+
+28
+00:02:14,120 --> 00:02:17,340
+كل الطيف الكهرومغناطيسي يعني احنا الطيف 
+
+29
+00:02:17,340 --> 00:02:20,240
+الكهرومغناطيسي اللي الضوء المرئي اللي بنشوفه 
+
+30
+00:02:20,240 --> 00:02:25,620
+بعيننا بشكل منه واحد في المية يعني الـ 99% من الطيف
+
+31
+00:02:25,620 --> 00:02:30,720
+الكهرومغناطيسي مش مرئي إلينا .. مش مرئي إلينا طبعا
+
+32
+00:02:30,720 --> 00:02:35,480
+الطيف الكهرومغناطيسي بيمتد من أقصر أطوال موجية
+
+33
+00:02:35,480 --> 00:02:40,560
+اللي هي أطوال موجات الـ ionizing radiation الشعة
+
+34
+00:02:40,560 --> 00:02:46,840
+المؤينة اللي هي طولها الموجي 1 في 10 أس سالب 7 من
+
+35
+00:02:46,840 --> 00:02:50,020
+الـ nanometer اللي هي الموجات الأقصر اللي هي
+
+36
+00:02:50,020 --> 00:02:55,020
+بيسموها موجات الجامّا أو أشعة جامّا أو أشعة جامّا
+
+37
+00:02:55,020 --> 00:02:59,160
+طبعا عشان نتخيل الـ nanometer الـ nanometer أصغر
+
+38
+00:02:59,160 --> 00:03:02,720
+بكثير من الـ micrometer و الـ micrometer أصغر بكثير
+
+39
+00:03:02,720 --> 00:03:07,340
+من الـ millimeter طبعا الـ micrometer جزء من ألف جزء
+
+40
+00:03:07,340 --> 00:03:10,400
+من الميلي و الـ millimeter لو شفناها على المسطرة
+
+41
+00:03:10,400 --> 00:03:16,600
+شيء بسيط جدا لا يكاد يذكر طبعا الموجات الجمّى اللي
+
+42
+00:03:16,600 --> 00:03:19,740
+هي تعتبر من ضمن الـ ionizing radiation الأشعة
+
+43
+00:03:19,740 --> 00:03:24,640
+المؤينة تعتبر واحد على عشر مليون .. واحد على عشر
+
+44
+00:03:24,640 --> 00:03:29,320
+مليون من الـ nanometer .. من الـ nanometer فذلك يعني
+
+45
+00:03:29,670 --> 00:03:36,850
+يعني متناهية جدا جدا جدا في الصغر طبعا هنا بداية
+
+46
+00:03:36,850 --> 00:03:40,190
+الطيف الكهرومغناطيسي اللي هو من الموجات الأقصر
+
+47
+00:03:40,190 --> 00:03:47,450
+وامتدادا للموجات الأطول اللي هي طبعا موجات الـ radio
+
+48
+00:03:47,450 --> 00:03:50,790
+الـ longest radio waves اللي بتكون طولها الموجي
+
+49
+00:03:50,790 --> 00:03:55,290
+تقريبا 1 في 10 أس 15 من الـ nanometer يعني الموجة
+
+50
+00:03:55,290 --> 00:03:58,770
+الواحدة ممكن يكون طولها kilometer كامل kilometer
+
+51
+00:03:58,770 --> 00:04:05,130
+كامل طبعا ممكن إنسان يقول كيف ينشأ الضوء من الشمس؟
+
+52
+00:04:05,530 --> 00:04:09,630
+أو إيش الشيء أو التفاعلات اللي بتأدي لنشوء الضوء
+
+53
+00:04:09,630 --> 00:04:17,130
+من الشمس طبعا العملية بتبدأ في باطن الشمس أو في 
+
+54
+00:04:17,130 --> 00:04:22,310
+قلب الشمس في بؤرة الشمس وطبعا هذه عملية شيقة جدا
+
+55
+00:04:22,310 --> 00:04:26,390
+ليش؟ لأن الـ visible light does not start out as
+
+56
+00:04:26,390 --> 00:04:30,450
+such in the core of the sun لا يبدأ بدوق مرئي .. لا
+
+57
+00:04:30,450 --> 00:04:36,030
+يبدأ بدوق مرئي وإنما يبدأ بموجات طاقتها عالية جدا
+
+58
+00:04:36,030 --> 00:04:42,050
+تعتبر موجات قصيرة اللي هي موجات الجمّى وبتتحول
+
+59
+00:04:42,050 --> 00:04:49,290
+لضوء في القصة اللي هنحكيها بعد قليل عشان قبل ما
+
+60
+00:04:49,290 --> 00:04:53,270
+نحكي قصة نشوء الضوء .. قبل ما نحكي قصة نشوء الضوء
+
+61
+00:04:53,270 --> 00:04:58,300
+حب العلماء إنهم يقارنوا بين أحجام الموجات الأطوال
+
+62
+00:04:58,300 --> 00:05:02,520
+الموجية المختلفة لكل الطيف الكهرومغناطيسي الطيف
+
+63
+00:05:02,520 --> 00:05:07,360
+الكهرومغناطيسي ببدأ من أقصر موجات كهرومغناطيسية
+
+64
+00:05:07,360 --> 00:05:10,860
+اللي هي موجات الـ gamma rays الـ gamma rays لو طلعنا
+
+65
+00:05:10,860 --> 00:05:17,520
+للعرض بيكون أفضل الـ gamma rays امتدادا لأطول موجات
+
+66
+00:05:17,520 --> 00:05:21,460
+اللي هي موجات الـ radio waves الـ radio waves طبعا
+
+67
+00:05:21,460 --> 00:05:28,290
+الـ gamma rays الأطول منها موجات الـ X-ray الأطول من
+
+68
+00:05:28,290 --> 00:05:31,770
+الـ X-ray اللي هي الـ ultraviolet الـ ultraviolet
+
+69
+00:05:31,770 --> 00:05:35,370
+اللي هي الأشعة فوق البنفسجية الأطول من الـ
+
+70
+00:05:35,370 --> 00:05:38,630
+ultraviolet هو الـ visible light اللي هو بشكل هذه
+
+71
+00:05:38,630 --> 00:05:43,150
+الخانة يعني بيمتد من أربعمائة نانو متر لسبعمية نانو
+
+72
+00:05:43,150 --> 00:05:47,390
+متر يعني هذا بشكل تقريبا واحد في المية يعني من كل
+
+73
+00:05:47,390 --> 00:05:50,350
+الطيف الكهرومغناطيسي يعني هذه الموجات في عند
+
+74
+00:05:50,350 --> 00:05:55,010
+الأطوال الموجية في الخانة هاي في الخانة هاي في هذه
+
+75
+00:05:55,010 --> 00:06:01,070
+الجزء ع جبال هذه المستطيل عيننا حساسة إليها ما هو
+
+76
+00:06:01,070 --> 00:06:05,690
+أقصر منها وما هو أطول منها عيننا غير حساسة لها
+
+77
+00:06:05,690 --> 00:06:10,010
+إطلاقا إذا الـ visible light بشكل 1% طبعا الأطول من
+
+78
+00:06:10,010 --> 00:06:13,050
+الـ visible light موجات الـ infrared الأشعة تحت
+
+79
+00:06:13,050 --> 00:06:17,650
+الحمراء أطول من موجات الأشعة تحت الحمراء بس مش
+
+80
+00:06:17,650 --> 00:06:21,770
+مذكورة هنا اللي موجات الـ microwave ثم موجات الـ
+
+81
+00:06:21,770 --> 00:06:25,810
+radio wave إذا لو حبينا طبعا العلماء حابوا يقارنوا
+
+82
+00:06:25,810 --> 00:06:31,720
+لو قارنت موجة واحدة من الـ gamma rays مع موجة واحدة
+
+83
+00:06:31,720 --> 00:06:35,360
+من الـ radio waves في طول .. في طول الموجة ساعتها
+
+84
+00:06:35,360 --> 00:06:40,120
+هذا بيشبه كإني بقارن .. كإني بقارن نواة ذرة ..
+
+85
+00:06:40,120 --> 00:06:46,320
+نواة ذرة مش ذرة .. نواة ذرة مع جبل طيب لو حبيت
+
+86
+00:06:46,320 --> 00:06:51,620
+أقارن .. أقارن موجة من موجات الضوء الموجي .. الضوء
+
+87
+00:06:51,620 --> 00:06:56,240
+المرئي عفوا موجة واحدة أقارن طولها بطول موجة الـ
+
+88
+00:06:56,240 --> 00:07:00,500
+radio wave هذا بيشبه كإني بقارن بكتيريا .. خلية
+
+89
+00:07:00,500 --> 00:07:07,600
+بكتيريا واحدة مع جبل طيب لو حبيت أقارن مثلا أشعة
+
+90
+00:07:07,600 --> 00:07:11,120
+الـ infrared .. أشعة الـ infrared اللي هي الأشعة تحت
+
+91
+00:07:11,120 --> 00:07:18,110
+الحمراء .. تحت الحمراء مع .. موجات الـ radio wave
+
+92
+00:07:18,110 --> 00:07:24,750
+كإني أنا بقارن سن قلم رصاص مع جبل فبالتالي هذه
+
+93
+00:07:24,750 --> 00:07:28,510
+المقارنات بس لتوضيح جديش أنه في فرق في الأطوال
+
+94
+00:07:28,510 --> 00:07:34,070
+الموجية بين الأقصر لأطول منه للأطول منه وصولا
+
+95
+00:07:34,070 --> 00:07:37,430
+للأطول اللي هي موجات الـ radio .. اللي هي موجات
+
+96
+00:07:38,240 --> 00:07:42,980
+الراديو، الآن نيجي لقصة نشوء الضوء .. نشوء الضوء،
+
+97
+00:07:42,980 --> 00:07:47,620
+طبعا نشوء الضوء ينشأ الضوء في باطن الشمس، في قلب
+
+98
+00:07:47,620 --> 00:07:53,300
+الشمس وينشأ الضوء بشكل غير مرئي بالأساس، بشكل
+
+99
+00:07:53,300 --> 00:07:59,330
+موجات كهرومغناطيسية كهرومغناطيسية طاقتها هائلة جدا
+
+100
+00:07:59,330 --> 00:08:06,390
+جدا جدا بشكل أشعة جامّا ثم يخترق .. تخترق أشعة
+
+101
+00:08:06,390 --> 00:08:11,830
+جامّا باتجاه سطح الشمس أثناء اختراقها بتفقد جزء
+
+102
+00:08:11,830 --> 00:08:15,890
+كبير من طاقتها ومعروف في قاعدة فيزيائية عند
+
+103
+00:08:15,890 --> 00:08:24,560
+العلماء الموجات الكهرومغناطيسية كلما فقدت جزء من
+
+104
+00:08:24,560 --> 00:08:30,120
+طاقتها بيبدأ الطول الموجي بتاعها يطول وبتبدأ تظهر
+
+105
+00:08:30,120 --> 00:08:34,940
+اللي هو الموجات الأطول يعني الـ gamma ray بتبدأ
+
+106
+00:08:34,940 --> 00:08:38,670
+تطول تتحول للـ X-ray بتطول أكثر، بتتحول للـ
+
+107
+00:08:38,670 --> 00:08:41,770
+ultraviolet، بتطول أكثر، بيبدأ يظهر الـ visible
+
+108
+00:08:41,770 --> 00:08:46,830
+light، الـ .. الـ infrared، الـ microwave و الـ radio
+
+109
+00:08:46,830 --> 00:08:51,490
+waves، إذا وصولا لسطح الشمس، انطلاقا من قلب الشمس
+
+110
+00:08:51,490 --> 00:08:55,670
+و وصولا لسطح الشمس، لغاية ما نصل لسطح الشمس، بنبدأ
+
+111
+00:08:55,670 --> 00:09:00,920
+احنا يظهر عندي الضوء المرئي الآن في إنسان ممكن يعني
+
+112
+00:09:00,920 --> 00:09:04,680
+يطلع على هذه الصورة ويختخيل أنه باطن الشمس مضيق
+
+113
+00:09:04,680 --> 00:09:10,200
+كما تبين الصورة باطن الشمس معتم للغاية .. معتم
+
+114
+00:09:10,200 --> 00:09:15,140
+للغاية وهنذكر ليش معتم للغاية بعد قليل طيب إيش
+
+115
+00:09:15,140 --> 00:09:22,430
+السبب في انطلاق طاقة هائلة جدا من .. من باطن الشمس
+
+116
+00:09:22,430 --> 00:09:30,290
+أو من قلب الشمس القصة بتبدأ بحقيقة أنه الشمس كانجم
+
+117
+00:09:30,290 --> 00:09:35,390
+تعتبر ضخمة جدا جدا بالنسبة لحجم الأرض تقريبا الشمس
+
+118
+00:09:35,390 --> 00:09:39,850
+حجمها مليون مرة جد حجم الأرض هذه المادة الكثيفة
+
+119
+00:09:39,850 --> 00:09:45,690
+للشمس .. لطبقات الشمس بتضغط على قلب الشمس بفعل
+
+120
+00:09:45,690 --> 00:09:51,230
+الوزن فبتتولد حرارة هائلة جدا إذا الضغط الكثيف
+
+121
+00:09:51,230 --> 00:09:55,550
+لمادة الشمس و لطبقات الشمس على قلب الشمس بيولد
+
+122
+00:09:55,550 --> 00:10:00,430
+حرارة هائلة جدا تصل هذه الحرارة .. تصل هذه الحرارة
+
+123
+00:10:00,430 --> 00:10:05,530
+إلى 16 مليون Kelvin ممكن إنسان يسأل إيش الـ Kelvin
+
+124
+00:10:05,530 --> 00:10:09,550
+هذا؟ الـ Kelvin هذا .. وحدة لقياس درجة الحرارة بس
+
+125
+00:10:09,550 --> 00:10:15,030
+بنبدأ فيها مش من الصفر بنبدأ من minus 273 يعني الـ
+
+126
+00:10:15,030 --> 00:10:19,610
+16 مليون Kelvin لما بدنا نحولهم لدرجة مئوية بس
+
+127
+00:10:19,610 --> 00:10:24,610
+بدنا نخص منهم 273 درجة مئوية يعني و كإني بقول
+
+128
+00:10:24,610 --> 00:10:31,470
+حرارة باطن الشمس تساوي 16 مليون درجة مئوية إلا 273
+
+129
+00:10:31,470 --> 00:10:37,120
+و هذه حرارة هائلة جدا جدا جدا الدرجة انه يمكن اعتبار
+
+130
+00:10:37,120 --> 00:10:41,320
+باطن الشمس أو قلب الشمس the core of the sun ممكن
+
+131
+00:10:41,320 --> 00:10:48,620
+اعتباره فرن ذري، فرن للتفاعلات الذرية والاندماج
+
+132
+00:10:48,620 --> 00:10:53,700
+النووي طبعا تحت تأثير هذه الحرارة الهائلة تحت
+
+133
+00:10:53,700 --> 00:11:00,600
+تأثير هذه الحرارة الهائلة بيتندمج بروتونات
+
+134
+00:11:00,600 --> 00:11:04,520
+الهيدروجين اللي هي أنوية الهيدروجين كل نواتين
+
+135
+00:11:04,520 --> 00:11:09,440
+بيندمجوا مع بعضهم البعض وبالتالي بيكونوا نوات
+
+136
+00:11:09,440 --> 00:11:13,520
+الهيليوم هذا التفاعل الاندماجي هذا التفاعل
+
+137
+00:11:13,520 --> 00:11:19,080
+الاندماجي بتنطلق منه طاقة هائلة جدا بشكل موجات
+
+138
+00:11:19,080 --> 00:11:24,360
+كهرومغناطيسية قصيرة للغاية هي موجات الجامّا ريز طب
+
+139
+00:11:24,360 --> 00:11:30,530
+ممكن إنسان يسأل في الثانية الواحدة جديش جديش بيفقد
+
+140
+00:11:30,530 --> 00:11:35,470
+من كتلة الشمس بشكل طاقة أو بشكل موجات كهرومغناطيسية
+
+141
+00:11:35,470 --> 00:11:40,950
+اللي هي الجمر كل ثانية بتفقد الشمس من كتلتها ما
+
+142
+00:11:40,950 --> 00:11:46,170
+مقداره أربعة مليون طن يعني لما بنقول واحد و بنسكت
+
+143
+00:11:46,170 --> 00:11:50,830
+في هذه .. في لحظة ما لفظنا كلمة واحد الشمس فقدت من
+
+144
+00:11:50,830 --> 00:11:55,010
+كتلتها أربعة مليون طن وين راحوا هدولة الأربعة
+
+145
+00:11:55,010 --> 00:11:58,770
+مليون طن من كتلة الشمس هدولة اتحولوا لطاقة عالية
+
+146
+00:11:58,770 --> 00:12:03,860
+جدا جدا بشكل موجات كهرومغناطيسية هي الـ gamma rays هي الـ
+
+147
+00:12:03,860 --> 00:12:08,100
+gamma rays الآن السؤال هل الـ gamma rays بيراه
+
+148
+00:12:08,100 --> 00:12:13,380
+الإنسان الجواب ببساطة شديدة لا لأنها لا تعتبر
+
+149
+00:12:13,380 --> 00:12:16,860
+visible light ليست ضمن نطاق الـ visible light وإنما
+
+150
+00:12:16,860 --> 00:12:21,470
+هي أقصر في طولها الموجي بكثير من الـ visible light لو
+
+151
+00:12:21,470 --> 00:12:26,870
+اتخيلنا جدلا أن إنسان لبسنا بدلة معينة واقع تحميه من
+
+152
+00:12:26,870 --> 00:12:31,770
+حرارة 16 مليون درجة وهذه طبعا مستحيل ولكن بنفرض
+
+153
+00:12:31,770 --> 00:12:36,410
+جدلا هذه القضية ووضعناه أنزلناه في داخل الشمس في 
+
+154
+00:12:36,410 --> 00:12:42,510
+قلب الشمس ماذا سيرى؟ سيرى عتمة كاملة وظلام دامس،
+
+155
+00:12:42,510 --> 00:12:47,470
+ليش؟ لأن عينه غير حساسة للجامّا ريز اللي بتنطلق من
+
+156
+00:12:47,470 --> 00:12:51,110
+قلب الشمس، عينه لا ترى الـ .. الـ .. الـ .. هذه
+
+157
+00:12:51,110 --> 00:12:55,450
+الموجات وبالتالي الإنسان يعتبر الإنسان يعتبر أعمى
+
+158
+00:12:55,450 --> 00:12:59,890
+للموجات الكهرومغناطيسية اللي عينه بتقدرش تشوفها،
+
+159
+00:12:59,890 --> 00:13:04,310
+يعني هيعتبر نفسه أو هو مش هيشوف ولا حاجة، بتاعة و
+
+160
+00:13:04,310 --> 00:13:09,930
+كأنه في ظلام دامس تماما، في ظلام دامس تماما، الآن
+
+161
+00:13:09,930 --> 00:13:16,310
+في نقطة بنوصل لها، إن طالما الشمس كل ثانية بتفقد
+
+162
+00:13:16,310 --> 00:13:22,550
+أربعة مليون طن من المادة أو من كتلتها بشكل طاقة،
+
+163
+00:13:22,550 --> 00:13:26,670
+إذا كل ثانية بنفقد أربع مليون، هيأتي يوم من الأيام
+
+164
+00:13:26,670 --> 00:13:32,690
+أو هيأتي وقت من الأوقات أن الشمس يعني تنتهي كنجم
+
+165
+00:13:32,690 --> 00:13:36,770
+.. تنتهي كنجم وهذا مصداق لقول الله سبحانه وتعالى
+
+166
+00:13:36,770 --> 00:13:42,960
+والشمس تجري لمستقر لها ذلك تقدير العزيز العليم طيب
+
+167
+00:13:42,960 --> 00:13:47,880
+الآن هذه الجامّات تصعد وتختارق مادة الشمس الكثيفة
+
+168
+00:13:47,880 --> 00:13:52,560
+طبعا في جميع الاتجاهات باتجاه سطح الشمس هذه الطاقة
+
+169
+00:13:52,560 --> 00:13:56,570
+لما تختارق مادة الشمس الكثيفة هذه الـ gamma rays
+
+170
+00:13:56,570 --> 00:14:01,150
+لما بدها تترحل يترجى أديش المسافة من قلب الشمس إلى
+
+171
+00:14:01,150 --> 00:14:06,850
+سطح الشمس من قلب الشمس إلى سطح الشمس في تقريبا 800
+
+172
+00:14:06,850 --> 00:14:11,570
+ألف كيلومتر يعني نص
+
+201
+00:16:17,520 --> 00:16:23,300
+infraredفبالتالي هذه القصة وصولا من قلب الشمس لسطح
+
+202
+00:16:23,300 --> 00:16:28,220
+الشمس، وصولا من قلب الشمس لسطح الشمس، إذا the
+
+203
+00:16:28,220 --> 00:16:31,820
+sun's core قلب الشمس may be considered يمكن 
+
+204
+00:16:31,820 --> 00:16:37,220
+اعتباره a furnace، فرن in which thermonuclear
+
+205
+00:16:37,220 --> 00:16:41,380
+fusion takes place، يعني في .. في هذا الفرن، الفرن 
+
+206
+00:16:41,380 --> 00:16:47,880
+الذري بتم اندماج أنوية هذا الاندماج أنوية تحت تأثير
+
+207
+00:16:47,880 --> 00:16:52,180
+الحرارة اندماج أنوية حراري أنويات مين؟ أنويات
+
+208
+00:16:52,180 --> 00:16:56,360
+الهيدروجين .. أنويات الهيدروجين here في قلب الشمس
+
+209
+00:16:56,360 --> 00:17:00,280
+طبعا هنا because of the crush of gravity تحت تأثير
+
+210
+00:17:00,280 --> 00:17:05,000
+الوزن الهائل لطبقات الشمس temperatures بتصير درجات
+
+211
+00:17:05,000 --> 00:17:09,080
+الحرارة close to 16 في 10 أس 6 Kelvin يعني 16
+
+212
+00:17:09,080 --> 00:17:13,320
+مليون Kelvinبتنتج هذه الحرارة الهائلة
+
+213
+00:17:40,690 --> 00:17:47,370
+طبعا و أيضا بتنطلق من هذا التفاعل عفوا طاقة بشكل
+
+214
+00:17:47,370 --> 00:17:51,950
+ال gamma rays طبعا the sun converts أربعة في عشرة
+
+215
+00:17:51,950 --> 00:17:55,590
+أس ستة طون يعني أربعة مليون طون الشمس بتتحول من
+
+216
+00:17:55,590 --> 00:18:00,570
+كتلتها of matter into energy every second كل ثانية
+
+217
+00:18:00,570 --> 00:18:05,790
+بتتحول أربعة مليون طون من كتلة الشمس لطاقة بشكل
+
+218
+00:18:05,790 --> 00:18:16,890
+أشعة gammaهذه الطاقة العالية
+
+219
+00:18:16,890 --> 00:18:20,330
+اللي طولها الموجي قصير اللي هي مقصود فيها الجامعة
+
+220
+00:18:20,330 --> 00:18:25,390
+ريز بتعدى أو بتمر عبر نص مليون ميل من قلب الشمس
+
+221
+00:18:25,390 --> 00:18:29,590
+لسطح الشمس طبعا ال نص مليون ميل هو عبارة عن تمنميت
+
+222
+00:18:29,590 --> 00:18:34,670
+الف كيلومتر of dense solar matter بتخترق مادة
+
+223
+00:18:34,670 --> 00:18:39,350
+الشمس الكثيفة before reaching the sun's surfaceقبل
+
+224
+00:18:39,350 --> 00:18:44,370
+ما تصل لسطح الشمس طبعا حرارة سطح الشمس 6000 Kelvin
+
+225
+00:18:44,370 --> 00:18:49,210
+يعني بالدرجات المئوية 6000 بدنا نخصم منها 273 درجة
+
+226
+00:18:49,210 --> 00:18:53,990
+بيعطيني بالدرجة المئوية طبعا حرارة سطح الشمس حامية
+
+227
+00:18:53,990 --> 00:18:58,950
+جدا جدا ولكن مقارنة معقلب الشمس تعتبر لا شيء يعني
+
+228
+00:18:58,950 --> 00:19:03,030
+لما بنقارن سطح الشمس حرارته 6000 Kelvin و قلب
+
+229
+00:19:03,030 --> 00:19:07,370
+الشمس 16 مليون Kelvin يعتبر سطح الشمس بارد جدا
+
+230
+00:19:07,370 --> 00:19:13,850
+مقارنة مع يعني باطن أو قلب الشمس .. مع قلب الشمس
+
+231
+00:19:16,730 --> 00:19:20,470
+during this long and slow journey هذه الرحلة اللي
+
+232
+00:19:20,470 --> 00:19:24,130
+بترحلها ال gamma rays من قلب الشمس لسطح الشمس هي
+
+233
+00:19:24,130 --> 00:19:28,270
+رحلة طويلة تمنميت الف كيلومتر و رحلة بطيئة ليش
+
+234
+00:19:28,270 --> 00:19:31,610
+بطيئة لإنه ال gamma rays لهذه الموجات
+
+235
+00:19:31,610 --> 00:19:35,430
+الكهرومغناطيسية اللي بنسميها أشعة gamma بدا تخترق
+
+236
+00:19:35,430 --> 00:19:39,310
+مادة الشمس الكثيفة فبتخترقها ببطء ده photons
+
+237
+00:19:39,310 --> 00:19:43,090
+فوتونات ال gamma ray فوتونات ال gamma ray lose
+
+238
+00:19:43,090 --> 00:19:47,720
+energy بتفقد الطاقة and hence وبذلكincrease in
+
+239
+00:19:47,720 --> 00:19:51,440
+wavelength بتبدأ تطول موجيا وهذه قاعدة بيرفوها
+
+240
+00:19:51,440 --> 00:19:56,280
+علماء الفيزيا طيب وصلنا لسطح الشمس مين اللي بيصل؟
+
+241
+00:19:56,280 --> 00:19:59,840
+بتبدأ تطول موجيا يعني معناته بيبدأ تتحول من ال
+
+242
+00:19:59,840 --> 00:20:04,220
+gamma rays لأنواع أخرى من الموجات الكهرومغناطيسية
+
+243
+00:20:04,220 --> 00:20:10,160
+الاشعة
+
+244
+00:20:10,160 --> 00:20:14,260
+اللي بتغادر سطح الشمس اللي بتغادر سطح الشمس بصورة
+
+245
+00:20:14,260 --> 00:20:17,860
+رئيسية بتكون عبارة عن طيف بيتراوح بين ال
+
+246
+00:20:17,860 --> 00:20:21,760
+ultraviolet و ال infrared طبعا و ما بينهما اللي في
+
+247
+00:20:21,760 --> 00:20:24,120
+النص اللي هو ال visible light اللي احنا بين ال
+
+248
+00:20:24,120 --> 00:20:29,340
+ultraviolet و ال infrared و اللي بيكون بينهم له
+
+249
+00:20:29,340 --> 00:20:32,750
+هذه الموجات في هذا النطاقUltraviolet, visible
+
+250
+00:20:32,750 --> 00:20:37,390
+light, infrared هذا بشكل رئيسي .. بشكل رئيسي اللي
+
+251
+00:20:37,390 --> 00:20:42,040
+بغادرسطح الشمس بشكل رئيسي اللي بيغادر سطح الشمس مع
+
+252
+00:20:42,040 --> 00:20:46,220
+كمية قليلة with a small fraction of ionizing
+
+253
+00:20:46,220 --> 00:20:49,760
+radiation ال ionizing radiation اللي هي ال x-ray
+
+254
+00:20:49,760 --> 00:20:54,220
+الأشعة المؤينة المؤينة اللي بتعمل تأيين في الأوساط
+
+255
+00:20:54,220 --> 00:20:58,060
+اللي بتدخل فيها اللي هي عبارة عن ال gamma rays و
+
+256
+00:20:58,060 --> 00:21:01,860
+ال x-ray هدولة هما بيسموهم ionizing radiation و
+
+257
+00:21:01,860 --> 00:21:05,660
+هدولة ال ionizing radiation ضارة جدا و بالذات لجسم
+
+258
+00:21:05,660 --> 00:21:11,750
+الإنسانولا باقي الكائنات with a small fraction of
+
+259
+00:21:11,750 --> 00:21:16,770
+ionizing radiation in the forms of x-ray طبعا ال
+
+260
+00:21:16,770 --> 00:21:19,470
+wavelength بتاع ال x-ray عشر أقص ناقص عشرة من
+
+261
+00:21:19,470 --> 00:21:23,230
+المتر وال gamma rays ال wavelength بتاعتها عشر أقص
+
+262
+00:21:23,230 --> 00:21:28,280
+ناقص أربعتاش من المترطبعا بشكل رئيسي سطح الشمس
+
+263
+00:21:28,280 --> 00:21:32,380
+بيصدر منه .. بيصدر منه ال ultraviolet و ال visible
+
+264
+00:21:32,380 --> 00:21:36,200
+light و ال infrared مع كمية قليلة من ال ionizing
+
+265
+00:21:36,200 --> 00:21:40,160
+radiation اللي هي ال X-ray و الجامعة ريه ال X-ray
+
+266
+00:21:40,160 --> 00:21:46,490
+و الجامعة ريه this ionizing radiationاللي هي تعتبر
+
+267
+00:21:46,490 --> 00:21:50,810
+جزء من ال cosmic radiation أو الأشعة الفضائية
+
+268
+00:21:50,810 --> 00:21:54,150
+لأنها بتنتشر في الفضاء ال ionizing radiation اللي
+
+269
+00:21:54,150 --> 00:21:58,270
+هي الجمرة وال X-ray اللي صدرت من سطح الشمس و اللي
+
+270
+00:21:58,270 --> 00:22:01,370
+تعتبر part of the entire cosmic radiation اللي
+
+271
+00:22:01,370 --> 00:22:05,530
+تعتبر جزء من الأشعة الكونية can destroy life
+
+272
+00:22:05,530 --> 00:22:09,630
+however يعني هذه الكميات القليلة جدا من الجمرة وال
+
+273
+00:22:09,630 --> 00:22:14,230
+X-ray ممكن تنهي الحياة بشكل كامل على سطح الأرض
+
+274
+00:22:14,540 --> 00:22:19,140
+طبعاً هناك وسائل للحماية .. وسائل الحماية رب
+
+275
+00:22:19,140 --> 00:22:22,940
+العالمين خلقها إلنا عشان يحمينا من هذه ال ionizing
+
+276
+00:22:22,940 --> 00:22:26,500
+radiation وهذه وسائل الحماية ان شاء الله تعالى ..
+
+277
+00:22:26,500 --> 00:22:31,400
+يعني نشرحها في المحاضرة الجاية و جزاكم الله خيرا و
+
+278
+00:22:31,400 --> 00:22:32,720
+يعطيكم العافية 
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ducsEpvuitg_raw.json b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ducsEpvuitg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..49cceba3918d3475a58f94ff711c2d84d734b22f
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ducsEpvuitg_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 1343, "start": 1.43, "end": 13.43, "text": "بسم الله الرحمن الرحيم ال physical optics هو علم بعني بدراسة أو بيعنى بدراسة الخصائص الفيزيائية للضوء", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 2423, 4001, 42599, 31439, 11203, 2304, 45030, 22653, 47525, 23557, 3794, 3660, 34051, 4724, 40228, 1863, 7578, 47525, 23557, 3794, 3660, 33962, 9381, 16373, 9381, 27188, 1829, 11622, 1829, 16373, 10632, 24976, 11242, 2407, 38207], "avg_logprob": -0.09149305754237705, "compression_ratio": 1.3543307086614174, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1.43, "end": 1.75, "word": "بسم", "probability": 0.886474609375}, {"start": 1.75, "end": 1.91, "word": " الله", "probability": 0.9736328125}, {"start": 1.91, "end": 2.25, "word": " الرحمن", "probability": 0.9537760416666666}, {"start": 2.25, "end": 2.83, "word": " الرحيم", "probability": 0.994140625}, {"start": 2.83, "end": 4.23, "word": " ال", "probability": 0.91845703125}, 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diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/icx5CDGEGns_raw.json b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/icx5CDGEGns_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7e01e47a9a125a57869d07e31dfb7f19d9c89b6b
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@@ -0,0 +1 @@
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66.27, "word": " يعني", "probability": 0.897705078125}, {"start": 66.27, "end": 66.49, "word": " مش", "probability": 0.982421875}, {"start": 66.49, "end": 66.89, "word": " نافذ", "probability": 0.87841796875}, {"start": 66.89, "end": 67.35, "word": " بنسبة", "probability": 0.91455078125}, {"start": 67.35, "end": 67.59, "word": " مائة", "probability": 0.7605794270833334}, {"start": 67.59, "end": 67.99, "word": " بالمائة", "probability": 0.93212890625}, {"start": 67.99, "end": 68.17, "word": " يعني", "probability": 0.9150390625}, {"start": 68.17, "end": 68.45, "word": " صحيح", "probability": 0.96875}, {"start": 68.45, "end": 68.57, "word": " في", "probability": 0.81689453125}, {"start": 68.57, "end": 68.85, "word": " جريح", "probability": 0.94580078125}, {"start": 68.85, "end": 68.99, "word": " في", "probability": 0.87353515625}, {"start": 68.99, "end": 69.51, "word": " القرانية", "probability": 0.899658203125}, {"start": 69.51, "end": 69.87, "word": " بس", "probability": 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"temperature": 1.0}, {"id": 5, "seek": 11851, "start": 99.65, "end": 118.51, "text": "هنا متهتكة بس ال seed of the test هيأكيد لإنه في في الوقت الحالي سيولة أو السائل الأكواسيهيومر بيطلع برات وياضح جدا هذه القضية seed of the test positive .. seed of the test positive ويعطيكم العافية والسلام عليكم ورحمة الله وبركاته", "tokens": [3224, 8315, 44650, 3224, 2655, 4117, 3660, 4724, 3794, 2423, 8871, 295, 264, 1500, 39896, 10721, 4117, 25708, 5296, 28814, 1863, 3224, 8978, 8978, 2423, 30543, 2655, 21542, 6027, 1829, 8608, 1829, 12610, 3660, 34051, 21136, 16373, 1211, 16247, 4117, 2407, 32277, 1829, 3224, 1829, 20498, 2288, 4724, 1829, 9566, 1211, 3615, 4724, 2288, 9307, 4032, 1829, 46958, 5016, 10874, 28259, 29538, 25062, 11242, 10632, 8871, 295, 264, 1500, 3353, 4386, 8871, 295, 264, 1500, 3353, 4032, 40228, 9566, 1829, 24793, 18863, 31845, 10632, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.20531249597668647, 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0.332763671875}, {"start": 111.31, "end": 111.75, "word": " القضية", "probability": 0.9866536458333334}, {"start": 111.75, "end": 112.03, "word": " seed", "probability": 0.87939453125}, {"start": 112.03, "end": 112.17, "word": " of", "probability": 0.9853515625}, {"start": 112.17, "end": 112.25, "word": " the", "probability": 0.880859375}, {"start": 112.25, "end": 112.55, "word": " test", "probability": 0.88623046875}, {"start": 112.55, "end": 113.27, "word": " positive", "probability": 0.93359375}, {"start": 113.27, "end": 113.35, "word": " ..", "probability": 0.426513671875}, {"start": 113.35, "end": 113.55, "word": " seed", "probability": 0.69873046875}, {"start": 113.55, "end": 113.67, "word": " of", "probability": 0.98876953125}, {"start": 113.67, "end": 113.75, "word": " the", "probability": 0.931640625}, {"start": 113.75, "end": 113.91, "word": " test", "probability": 0.90185546875}, {"start": 113.91, "end": 114.47, "word": " positive", "probability": 0.94873046875}, {"start": 114.47, "end": 115.39, "word": " ويعطيكم", "probability": 0.8263671875}, {"start": 115.39, "end": 115.83, "word": " العافية", "probability": 0.9684244791666666}, {"start": 115.83, "end": 116.23, "word": " والسلام", "probability": 0.8753255208333334}, {"start": 116.23, "end": 116.67, "word": " عليكم", "probability": 0.95947265625}, {"start": 116.67, "end": 117.07, "word": " ورحمة", "probability": 0.990966796875}, {"start": 117.07, "end": 117.39, "word": " الله", "probability": 0.97607421875}, {"start": 117.39, "end": 118.51, "word": " وبركاته", "probability": 0.98603515625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 120.859875, "duration_after_vad": 107.06187499999999}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/jBEZ9eqMtl4_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/jBEZ9eqMtl4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..77a5b4d696e75f6a9fe88e9d709fa60065b48898
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/jBEZ9eqMtl4_postprocess.srt
@@ -0,0 +1,1640 @@
+1
+00:00:02,720 --> 00:00:07,360
+بسم الله الرحمن الرحيم بنستكمل مع محاضرات ال
+
+2
+00:00:07,360 --> 00:00:14,260
+physical optics ووصلنا لتجربة العالم Thomas Young
+
+3
+00:00:14,260 --> 00:00:21,610
+قبل ما نشرح هذه التجربة بدنا نذكر ببعض الأشياءأول
+
+4
+00:00:21,610 --> 00:00:24,370
+شيء بدأ نذكر فيه أن الـ diffraction .. الـ
+
+5
+00:00:24,370 --> 00:00:27,830
+diffraction يعني ممكن توضح الصورة هاي أنه لما
+
+6
+00:00:27,830 --> 00:00:30,790
+الضوء بدخل من جدار بينتشر و بيصير له divergence
+
+7
+00:00:30,790 --> 00:00:37,130
+بيبقى يعني ساير في خطوط مستقيمة بيحيد عن طريقة هذه
+
+8
+00:00:37,130 --> 00:00:39,970
+الظاهرة مهمة جدا في التجربة، ظاهرة الـ diffraction
+
+9
+00:00:39,970 --> 00:00:44,350
+تاني ظاهرة بتساعدنا في فهم التجربة هي قضية ال
+
+10
+00:00:44,350 --> 00:00:48,070
+superposition of wavesال waves لما بتكون of
+
+11
+00:00:48,070 --> 00:00:51,850
+identical frequency يعني تردد high أو طولها الموجي
+
+12
+00:00:51,850 --> 00:00:55,690
+هو نفس تردد high فإذا التقوا قمة مع قمة بيصير
+
+13
+00:00:55,690 --> 00:00:59,090
+constructive interference يعني تداخل بنائي و بتصير
+
+14
+00:00:59,090 --> 00:01:03,530
+الموجة الناتجة ارتفاعها ضعف ارتفاع أي من الموجتين
+
+15
+00:01:03,530 --> 00:01:08,150
+المتداخلتين أيضا لما يكون لهم نفس ال frequency نفس
+
+16
+00:01:08,150 --> 00:01:13,150
+الطول الموجي بس عكس بعضهم يعني قمة مع قاع و قاع مع
+
+17
+00:01:13,150 --> 00:01:19,260
+قمةساعتها بيصير destructive interference وبيلغوا
+
+18
+00:01:19,260 --> 00:01:23,320
+بعضهم البعض لما بيتداخلوا الموجتين من نفس الطول
+
+19
+00:01:23,320 --> 00:01:28,480
+الموجي بس مش تماما out of phase ولا تماما أو
+
+20
+00:01:28,480 --> 00:01:31,640
+totally in phase ولا out of phase يعني بين البينين
+
+21
+00:01:31,640 --> 00:01:35,020
+يعني بين الخيار الأول والتاني يعني هنا القمة مثلا
+
+22
+00:01:35,020 --> 00:01:39,900
+جاية مقابل مقطع من الموجة لا هو قاع ولا هوقمة
+
+23
+00:01:39,900 --> 00:01:43,980
+ساعتها بيكون الموجة الناتجة بين صفر وبين اتنين بين
+
+24
+00:01:43,980 --> 00:01:50,300
+صفر وبين اتنين ارتفاع اما لو تداخلت موجات of
+
+25
+00:01:50,300 --> 00:01:53,700
+differing frequency بيعطيني changing interference
+
+26
+00:01:53,700 --> 00:01:57,860
+pattern مرة بيقوى مرة بيضعف مرة كذا فبالتالي هذا
+
+27
+00:01:57,860 --> 00:02:02,340
+سريع التغير جدا لدرجة انه انا مابقدرش الاحظه
+
+28
+00:02:02,340 --> 00:02:07,140
+بالعين المجردة هاي مثلا مسافة زمانية من هنالهنا
+
+29
+00:02:07,140 --> 00:02:12,780
+تقدر بإنها واحد في عشر أقص ناقص أربعتاش من الثانية
+
+30
+00:02:12,780 --> 00:02:17,040
+.. واحد في عشر أقص ناقص أربعتاش من الثانية يعني
+
+31
+00:02:17,040 --> 00:02:21,640
+جزء من ميت ألف مليار جزء من الثانية يعني شيء لا ..
+
+32
+00:02:21,640 --> 00:02:26,440
+لا يكاد يصدق يعني كمية ضئيلة للغاية من الزمنفي هذه
+
+33
+00:02:26,440 --> 00:02:30,820
+الكمية الضوء كان وسط صار أجواء صار أجواء صار أجواء
+
+34
+00:02:30,820 --> 00:02:35,680
+جدا بدأ يضعف يضعف بدأ يضعف على الآخر هذه التغيرات
+
+35
+00:02:35,680 --> 00:02:39,240
+الخمسة أو الستة صارت في هذه الجزء من الزمن وهذا
+
+36
+00:02:39,240 --> 00:02:43,900
+طبعا عين الإنسان وإحساس الإنسان لا يستطيع أنه
+
+37
+00:02:43,900 --> 00:02:49,400
+يستطيع يعني يدركه لسبب تداخل موجاتبسبب طبعا سرعته
+
+38
+00:02:49,400 --> 00:02:55,460
+الشهقة وهذا طبعا نتج من تداخل موجات ضوئية مش نفس
+
+39
+00:02:55,460 --> 00:02:58,380
+ال frequency او مش نفس الطول الموجي مش نفس الطول
+
+40
+00:02:58,380 --> 00:03:03,080
+الموجي اذا ظاهرة ال superposition وظاهرة ال
+
+41
+00:03:03,080 --> 00:03:07,880
+diffraction هدولة الظاهرتين هنستخدمهم في فهم ايش
+
+42
+00:03:07,880 --> 00:03:15,080
+اللي هيحصل معنا في تجربة Thomas Young في تجربة
+
+43
+00:03:15,080 --> 00:03:20,850
+Thomas Youngفي تجربة Thomas Young اللي هنبدأ نشرح
+
+44
+00:03:20,850 --> 00:03:27,090
+فيها الآن بنقول consider single section of wave
+
+45
+00:03:27,090 --> 00:03:32,030
+train from a broad point source illuminating two
+
+46
+00:03:32,030 --> 00:03:36,530
+small closely spaced pinholes in an otherwise
+
+47
+00:03:36,530 --> 00:03:41,350
+opaque screen بدنا نشرح هذه القضية بنقول كالعادي
+
+48
+00:03:41,350 --> 00:03:43,930
+بدنا احنا نجيب opaque screen
+
+49
+00:03:47,440 --> 00:03:53,300
+يعني حاجز معتم وبدنا نعمل فيه two pinhole أو ممكن
+
+50
+00:03:53,300 --> 00:04:00,090
+نعمل فيه two slitstwo slits يعني فتحتين بشكل شق و
+
+51
+00:04:00,090 --> 00:04:03,430
+شق بس هما يكونوا closely spaced طبعا الرسم هنا
+
+52
+00:04:03,430 --> 00:04:06,590
+موضح انهم بعاد عن بعض كتير لأ هم هما يكونوا
+
+53
+00:04:06,590 --> 00:04:11,310
+closely spaced يعني قريبين جدا من بعضهم البعض حتى
+
+54
+00:04:11,310 --> 00:04:15,830
+تتم ظاهرة التداخل بعد ما تتم ظاهرة ال diffraction
+
+55
+00:04:15,830 --> 00:04:19,750
+ظاهرة ال diffraction انه لما قطار من الموجات
+
+56
+00:04:19,750 --> 00:04:23,500
+الضوئية يدخل في هذا ال slitوقطار من .. من نفس
+
+57
+00:04:23,500 --> 00:04:26,340
+الموجات الضوئية لأنهم صادرين من نفس المصدر يعني
+
+58
+00:04:26,340 --> 00:04:30,020
+ضفقة من الضوء تدخل من هذا ال slid جزء منها و هذا
+
+59
+00:04:30,020 --> 00:04:33,480
+ال slid جزء منها هنا هيصير diffraction وهنا هيصير
+
+60
+00:04:33,480 --> 00:04:37,540
+diffraction فبالتالي لما يكونوا جراب من بعض بعد ال
+
+61
+00:04:37,540 --> 00:04:40,960
+diffraction طبعا هنا مبينين إن هم بعاد عن بعض كتير
+
+62
+00:04:41,950 --> 00:04:45,930
+و هنا مبينين انه بعاد عن بعض اكتر طبعا هم جراب جدا
+
+63
+00:04:45,930 --> 00:04:51,610
+من بعض هتدخل حزمة ضوئية هنا و حزمة ضوئية هنا اللي
+
+64
+00:04:51,610 --> 00:04:55,170
+هم نفس الطول الموجي اللي هم نفس الطول الموجي لأن
+
+65
+00:04:55,170 --> 00:04:59,590
+هذا قطار انطلق اول دفقة منه لها طول معين الدفقة
+
+66
+00:04:59,590 --> 00:05:04,110
+التانية لها طول موجي اخر و هكذا طبعا لما بيدخلوا
+
+67
+00:05:04,110 --> 00:05:10,100
+الموجات الضوئية او ال pencils of lightمن فتحات في
+
+68
+00:05:10,100 --> 00:05:13,200
+جدار أول ظاهرة هتصير ظاهرة ال diffraction يعني
+
+69
+00:05:13,200 --> 00:05:15,680
+الضوء هينتشر و يصير له divergence في جميع
+
+70
+00:05:15,680 --> 00:05:20,340
+الاتجاهات بعد الجدار يعني هيحيد عن طريقه و هنا نفس
+
+71
+00:05:20,340 --> 00:05:24,360
+الاشي طيب احنا بدنا ناخد من .. من هذا الضوء اللي
+
+72
+00:05:24,360 --> 00:05:27,840
+صار له diffraction الجزء اللي اتجه للأسفل حسب
+
+73
+00:05:27,840 --> 00:05:33,260
+الرسمةوحناخد من هذه الموجات الضوئية اللي دخلت من
+
+74
+00:05:33,260 --> 00:05:38,140
+الفتحة السفلة الجزء من الموجات اللي صار لها
+
+75
+00:05:38,140 --> 00:05:42,960
+diffraction باتجاه الأعلى حسب الرسمة ليش أخدنا هنا
+
+76
+00:05:42,960 --> 00:05:46,640
+اللي باتجاه الأسفل وليش أخدنا هنا باتجاه الأعلى
+
+77
+00:05:46,640 --> 00:05:51,620
+عشان هيصير لهم تداخل هيلتقيوا مع بعضهم البعض ويصير
+
+78
+00:05:51,620 --> 00:05:54,820
+لهم تداخل يا ترى إيش اللي هيحصل قبل ما نقول إيش
+
+79
+00:05:54,820 --> 00:06:00,880
+اللي هيحصل بدنا نشوف الرسمةالتوضيحية بنقول ضوء ضوء
+
+80
+00:06:00,880 --> 00:06:05,260
+لمبة عادي طبعا عشان يعطيني broadband يعني sections
+
+81
+00:06:05,260 --> 00:06:09,160
+كتيرة sections كتيرة بنذكر بال broadband بنقول ال
+
+82
+00:06:09,160 --> 00:06:13,540
+broadband هو اللي بيعطيني مقاطع كتيرة أو قطار من
+
+83
+00:06:13,540 --> 00:06:16,840
+الموجات الضوئية كل section فيه بيختلف عن يعني
+
+84
+00:06:16,840 --> 00:06:21,000
+عروضه كثيرة يعني أنواع موجاته كثيرة موجات طويلة
+
+85
+00:06:21,000 --> 00:06:25,440
+موجات وسط موجات قصيرة يعني في بعض المصادر الضوئية
+
+86
+00:06:25,440 --> 00:06:28,780
+بتعطي عشرات الأنواعمن الأطوار الموجية بيسموها
+
+87
+00:06:28,780 --> 00:06:32,900
+broadband واسعة الموجة أو واسعة أنواع الموجة وفي
+
+88
+00:06:32,900 --> 00:06:35,960
+narrow band يعني بيعطي موجة أو موجتين ومابيعطيش
+
+89
+00:06:35,960 --> 00:06:38,900
+غيرهم يعني عنده العروض قليلة احنا هنستخدم
+
+90
+00:06:38,900 --> 00:06:44,370
+broadband broadband light sourceA broadband light
+
+91
+00:06:44,370 --> 00:06:48,790
+source زي اللي هو ال sun light مثلا ممكن تجري على
+
+92
+00:06:48,790 --> 00:06:53,770
+ال sun light تمام و بدنا نمرر هذا الضوء عبر two
+
+93
+00:06:53,770 --> 00:06:58,110
+slits slit الأول و ال slit التاني ملاحظين بعد ..
+
+94
+00:06:58,110 --> 00:07:00,850
+خليني أطلع على العرض المكبر يكون أوضح ان شاء الله
+
+95
+00:07:00,850 --> 00:07:06,010
+بعد ما مر الضوء بعد ما مر الضوء في ال two slits
+
+96
+00:07:06,010 --> 00:07:10,630
+أول ظاهرة صارتله ال diffractionيعني من .. من ال
+
+97
+00:07:10,630 --> 00:07:14,830
+slit رقم واحد انتشر صارله divergence تشتت عن بعض
+
+98
+00:07:14,830 --> 00:07:18,890
+البعض ومن الدوق رقم اتنين او من ال slit رقم اتنين
+
+99
+00:07:18,890 --> 00:07:21,450
+الدوق اللي دخل فيه برضه صارله diffraction يعني اذا
+
+100
+00:07:21,450 --> 00:07:25,950
+اول ظاهرة بتصير ظاهرة ال diffraction طيب لأن ال
+
+101
+00:07:25,950 --> 00:07:29,450
+two slits جراب من بعض لأن ال two slits طبعا في
+
+102
+00:07:29,450 --> 00:07:34,410
+الرسمة هنا يعني للاضاح فقط يعني مرسومين بعاد عن
+
+103
+00:07:34,410 --> 00:07:41,010
+بعض لأنه جراب من بعض هذا ..الـ diffracted waves و
+
+104
+00:07:41,010 --> 00:07:44,950
+هنا الـ diffracted waves بيتداخلوا مع بعضهم البعض
+
+105
+00:07:44,950 --> 00:07:50,610
+و أنا بتلقهم بعد ما يتداخلوا بتلقهم على حاجز أو
+
+106
+00:07:50,610 --> 00:07:55,130
+لوح التلقي أو غرفة أو ما شابه والله هيعطوني المنظر
+
+107
+00:07:55,130 --> 00:08:01,250
+هذا بقع مضيئة أو مناطق مضيئة و بينها مناطق معتمة
+
+108
+00:08:01,250 --> 00:08:05,500
+يا ترا إيش اللي حصل عندى؟ نتيجة التداخلإذا كان
+
+109
+00:08:05,500 --> 00:08:09,400
+التداخل قمة لقمة .. طبعا هدول الموجات و هدول
+
+110
+00:08:09,400 --> 00:08:12,800
+الموجات .. هدول الموجات و هدول الموجات .. اللهم
+
+111
+00:08:12,800 --> 00:08:16,080
+نفس الطول الموجي لأن عندي هي القطار الأول من
+
+112
+00:08:16,080 --> 00:08:21,040
+الموجات .. هي القطار التاني مرسوم عنه بطريقة تانية
+
+113
+00:08:21,040 --> 00:08:24,740
+أو بلون تاني .. هي القطار التالت من الموجات وقتله
+
+114
+00:08:24,740 --> 00:08:28,760
+الرابع والخامس والسادس والعشر تلاف إلى آخرينإحنا
+
+115
+00:08:28,760 --> 00:08:31,780
+ليش سمينا هذه عربة في القطار أو أنواع من الموجات
+
+116
+00:08:31,780 --> 00:08:35,280
+لأنه لها نفس الطول الموجي فهي هيكون نصيبها أول إشي
+
+117
+00:08:35,280 --> 00:08:39,520
+تدخل في ال slit الأول عشان ينقيها يعني يثبت يعني
+
+118
+00:08:39,520 --> 00:08:43,660
+يضمن إنها نفس الموجات الضوئية تمام طيب الآن
+
+119
+00:08:43,660 --> 00:08:44,260
+كالقاتل
+
+120
+00:08:46,940 --> 00:08:52,080
+احنا قلنا انه اي مصدر ضوء بيصدر الموجات بشكل قطار
+
+121
+00:08:52,080 --> 00:08:55,580
+او اذا صح التعبير قطار من الموجات الضوئية ايش يعني
+
+122
+00:08:55,580 --> 00:08:58,720
+قطار؟ احنا معروف ان القطار في حياتنا العادية
+
+123
+00:08:58,720 --> 00:09:03,400
+المتعرف عليه مكون من عشرات العربات لو تصورنا ان كل
+
+124
+00:09:03,400 --> 00:09:07,760
+عربة فيها يعني نوع من المسافرين طلاب في العربة
+
+125
+00:09:07,760 --> 00:09:13,060
+الأولى، حجاج ومعتمرين في العربة التانيةفي العربة
+
+126
+00:09:13,060 --> 00:09:15,740
+التالتة مرضى رايحين للعلاج بالخارج، في العربة
+
+127
+00:09:15,740 --> 00:09:20,660
+الخامسة مثلا رجال أعمال إلى آخرى وسألنا سؤال يا
+
+128
+00:09:20,660 --> 00:09:26,080
+ترى إيش اللي بيربطركاب كل عربة من عربات القطار مع
+
+129
+00:09:26,080 --> 00:09:30,100
+بعضهم البعض بنقول الجواب وحدة الهدف هنا نفس
+
+130
+00:09:30,100 --> 00:09:33,900
+الاشيان دي قطار من الموجة الضوئية صدر من نقطة ما
+
+131
+00:09:33,900 --> 00:09:38,860
+من المصدر من المصدر لو سألنا كل section أو كل عربة
+
+132
+00:09:38,860 --> 00:09:43,600
+أو كل مقطع من هذا القطار بتاع الموجات كل مقطع إيش
+
+133
+00:09:43,600 --> 00:09:46,960
+بربط موجاتهم مع بعض بنقول الجواب ببساطة إلها نفس
+
+134
+00:09:46,960 --> 00:09:50,340
+الطول الموجي بنرجع لتجربة young two slit
+
+135
+00:09:50,340 --> 00:09:54,830
+experimentوبنقول مثلا عندي مصدر broadband ال
+
+136
+00:09:54,830 --> 00:09:58,170
+sunlight ضوء الشمس broadband ليش؟ لأنه بيعطيني
+
+137
+00:09:58,170 --> 00:10:03,030
+أنواع عديدة جدا لحصر الله من الموجات بتمتد طول
+
+138
+00:10:03,030 --> 00:10:07,590
+هالموج من 400 نانومتر تجاوزا او جدلا إلى 700
+
+139
+00:10:07,590 --> 00:10:12,590
+نانومتر يعني ممكن يعطيني موجات 400, 401, 402, 403,
+
+140
+00:10:12,810 --> 00:10:18,120
+450, 451وهكذا يعني في أنواع كثيرة من الموجات
+
+141
+00:10:18,120 --> 00:10:26,700
+الضوئية المختلفة في الطول الموج الان احنا كل مقطع
+
+142
+00:10:26,700 --> 00:10:32,620
+هذا عربة في غطارهتدخل أول إشي من ال slit رقم zero
+
+143
+00:10:32,620 --> 00:10:36,380
+تمام؟ طبعا هذا ممكن ما أستخدمهش ال slit رقم zero و
+
+144
+00:10:36,380 --> 00:10:41,140
+ممكن أني أستخدمه القصد أنه لو ما استخدمتوش .. لو
+
+145
+00:10:41,140 --> 00:10:44,500
+ما استخدمتوش المقطع الأول و اللي له نفس الطول
+
+146
+00:10:44,500 --> 00:10:50,100
+الموجي هيصل لل two slits مع بعض .. مع بعض ليش؟
+
+147
+00:10:50,100 --> 00:10:55,930
+هنحكي ليش .. بنقول كالقادةاحنا بدنا التجربة ان
+
+148
+00:10:55,930 --> 00:11:01,950
+استخدمنا مصدر ضوئي broadband يعني بصدر اول section
+
+149
+00:11:01,950 --> 00:11:04,410
+هو مرسوم ياندي اول section ال section التاني مش
+
+150
+00:11:04,410 --> 00:11:08,090
+مرسوم بختلف عنه في الطول الموجي ال section التالت
+
+151
+00:11:08,090 --> 00:11:11,110
+برضه بختلف عنهم في الطول الموجي و هكذا احنا رسمنا
+
+152
+00:11:11,110 --> 00:11:15,560
+بس ال section الاول فقطيعني أول section إذا قلنا
+
+153
+00:11:15,560 --> 00:11:19,420
+هذا المصدر الضوء يبعده عن ال slit الأول أو ال pin
+
+154
+00:11:19,420 --> 00:11:23,660
+hole الأول يساوي بعده عن ال slit التاني لو جايب
+
+155
+00:11:23,660 --> 00:11:28,760
+النص بينهم .. جايب النص بينهم بيكون تلقائيا مفهوم
+
+156
+00:11:28,760 --> 00:11:35,530
+.. تلقائيا مفهوم أنه ..الموجات هاي و الموجات هاي
+
+157
+00:11:35,530 --> 00:11:40,010
+هيصلوا لسلت الأول و لسلت التاني في نفس اللحظة ايش
+
+158
+00:11:40,010 --> 00:11:44,150
+معنى في نفس اللحظة؟ لأنه هيقطع نفس المسافة من
+
+159
+00:11:44,150 --> 00:11:49,630
+المصدر المسافة من المصدر لسلت الأول و المسافة من
+
+160
+00:11:49,630 --> 00:11:52,950
+المصدر لسلت التاني متساوية، هاي رقم واحد، رقم
+
+161
+00:11:52,950 --> 00:11:57,550
+اتنين، الطول الموجي، نفس الطول الموجي، رقم تلاتة
+
+162
+00:11:57,710 --> 00:12:00,830
+الضوء هنا حيسر في الفراغ و هنا حيسر .. او في
+
+163
+00:12:00,830 --> 00:12:04,150
+الهواء خلّينا نقول و هنا حيسر في الهواء الظروف
+
+164
+00:12:04,150 --> 00:12:10,110
+موحجة و الطول الموجي موحد حيصلوا لل slit الأول و
+
+165
+00:12:10,110 --> 00:12:14,820
+لل slit التاني موجات متساوية في الطولويلها نفس
+
+166
+00:12:14,820 --> 00:12:18,520
+السرعة و قطعت نفس المسافة .. إذا في اللحظة اللي
+
+167
+00:12:18,520 --> 00:12:24,020
+المقطع الأول بيصل هنا .. المقطع الأول هو نفسه من
+
+168
+00:12:24,020 --> 00:12:28,780
+القطار تمام .. هيصل أيضا لل slid اللي جاوز .. اللي
+
+169
+00:12:28,780 --> 00:12:32,760
+هو الأول طيب وصل و إيش معناة الكلام هذا .. أيضا
+
+170
+00:12:32,760 --> 00:12:39,000
+النقطة Oالنقطة O اللي هي في لوحة التلقي بتبعد عن
+
+171
+00:12:39,000 --> 00:12:43,700
+لسلطة الأول وبتبعد عن لسلطة التاني نفس المسافة اذا
+
+172
+00:12:43,700 --> 00:12:49,560
+هيصلوا ايضا للنقطة O للنقطة O بنفس التوقيت تماما
+
+173
+00:12:49,560 --> 00:12:54,340
+ليش؟ لأن المسافة high تساوي high وhigh تساوي high
+
+174
+00:12:54,340 --> 00:13:00,040
+معناته المقطع الأول من قطار الموجات قطع مسافة هنا
+
+175
+00:13:00,690 --> 00:13:04,830
+تساوي المسافة اللي قطعها هنا فهيصلوا الموجات مع
+
+176
+00:13:04,830 --> 00:13:08,930
+بعض هيتداخلوا بشكل constructive interference يعني
+
+177
+00:13:08,930 --> 00:13:12,090
+هتيجي القاع على القاع و القمة على القمة و القاع
+
+178
+00:13:12,090 --> 00:13:15,430
+على القاع و القمة على القمة فهتكون النقطة ا مضيئة
+
+179
+00:13:15,430 --> 00:13:19,390
+بشكل واضح هاي مقابل هاي ها ده مقطع من الجدار
+
+180
+00:13:19,390 --> 00:13:24,110
+المقابل له أو هي نفس ا بس موجهة ناحيتنا مش رسم
+
+181
+00:13:24,110 --> 00:13:31,000
+تمثيل موجهة ناحيتنا فهيكون إيش؟الإضاءة عالية بسبب
+
+182
+00:13:31,000 --> 00:13:35,040
+تداخل الموجات بشكل بنائي .. بشكل بنائي هذه النقطة
+
+183
+00:13:35,040 --> 00:13:39,480
+O واضح إن إضاءتها كويسة جدا طب إيش اللي هيحصل
+
+184
+00:13:39,480 --> 00:13:46,540
+حوالين O عند النقطة Q عند النقطة .. عفوا هنا P عند
+
+185
+00:13:46,540 --> 00:13:51,200
+النقطة P النقطة P أعلى من النقطة O احنا النقطة O
+
+186
+00:13:51,900 --> 00:13:56,900
+فسرنا كيف صار عندها إضاءة عالية بسبب تداخل الموجات
+
+187
+00:13:56,900 --> 00:14:00,220
+القادمة من السلطة الأول والسلطة التانية أو ال
+
+188
+00:14:00,220 --> 00:14:03,760
+pinhole الأول والسلطة التانية بشكل constructive
+
+189
+00:14:03,760 --> 00:14:07,640
+interference إيش معنى؟ السبب إليهم نفس الطول
+
+190
+00:14:07,640 --> 00:14:10,520
+الموجي .. نفس الطول الموجي يعني نفس ال frequency
+
+191
+00:14:11,100 --> 00:14:14,780
+وقطعوا نفس المسافة ماحدش فيهم هيتأخر عن التاني
+
+192
+00:14:14,780 --> 00:14:19,540
+هيصلوا قمة مع قمة و قاع مع قاع و كل المقطع الأول
+
+193
+00:14:19,540 --> 00:14:23,740
+هيتداخل مع كل المقطع الأول اللي دخل في ال pinhole
+
+194
+00:14:23,740 --> 00:14:28,800
+التاني طيب عند النقطة P اللي هي أعلى شوية صغيرة من
+
+195
+00:14:28,800 --> 00:14:34,660
+النقطة O في الجدار أو في ورقة التلقي النقطة P أقرب
+
+196
+00:14:34,660 --> 00:14:38,320
+لل pinhole الأول منها لل pinhole التاني يعني
+
+197
+00:14:38,320 --> 00:14:43,330
+المسافة highاللي أنا بأشر عليها أقصر من المسافة
+
+198
+00:14:43,330 --> 00:14:48,260
+هذهطيب احنا عندنا two sections من .. من الموجات
+
+199
+00:14:48,260 --> 00:14:51,700
+اللي هم نفس ال frequency و هيسروا في الفرار اللي
+
+200
+00:14:51,700 --> 00:14:54,920
+هم .. او في الهواء اللي هم نفس السرعة و اللي هم
+
+201
+00:14:54,920 --> 00:14:58,580
+نفس الطول الموجي .. نفس ال frequency بس الموجات
+
+202
+00:14:58,580 --> 00:15:00,900
+هاي اللي اغدخلت في ال .. في ال pin hole الأعلى
+
+203
+00:15:00,900 --> 00:15:06,860
+هتقطع مسافة أقصر فهتصل قبل فهي هتتأخر عنها بمقدار
+
+204
+00:15:06,860 --> 00:15:12,080
+نص موجة فقط التأخر البسيط نتيجة الطول البسيط جدا
+
+205
+00:15:12,550 --> 00:15:16,870
+يعني هذا الطريق أطول شوية جدا من الطريق الفجاني
+
+206
+00:15:16,870 --> 00:15:21,050
+فبالتالي هتتأخر بمقدار نص موجة تأخرها بمقدار نص
+
+207
+00:15:21,050 --> 00:15:27,550
+موجة خلّى أنه التداخل يتم بشكل قمة مع قاع و قاع مع
+
+208
+00:15:27,550 --> 00:15:32,730
+قمة و قمة مع قاع و قاع مع قمة .. إذا التداخل
+
+209
+00:15:32,730 --> 00:15:36,810
+destructive ألغوا بعضهم البعض عشان هيك عند النقطة
+
+210
+00:15:36,810 --> 00:15:41,380
+B شايفين عتمةعتمة فبالتالي مافيش إضاءة لإن
+
+211
+00:15:41,380 --> 00:15:46,380
+الموجتين قلقوا بعضهم البعض بسبب الفرج البسيط في
+
+212
+00:15:46,380 --> 00:15:51,400
+المسافة نص طول موجي يعني إيش نص طول موجي؟ يعني لو
+
+213
+00:15:51,400 --> 00:15:55,640
+تخيلنا إن هدولة الموجتين كل واحدة منها طولها
+
+214
+00:15:55,640 --> 00:15:59,910
+خمسمية نانومترضمن الضوء المرئي طبعا لأن لو مش ضمن
+
+215
+00:15:59,910 --> 00:16:02,970
+الضوء المرئي مش هنشوف التجربة كلها الضوء المرئي
+
+216
+00:16:02,970 --> 00:16:07,690
+بيمتد من 400 نانومتر طول الموجة ل 700 لو تخيلنا
+
+217
+00:16:07,690 --> 00:16:11,710
+أنه الضوء ال .. ال .. ال .. ال sections هدولة طول
+
+218
+00:16:11,710 --> 00:16:16,090
+كل واحد منهم 500 نانومتر بتكون ال .. ال .. ال ..
+
+219
+00:16:16,090 --> 00:16:21,510
+الطريق السفلى هاي تأخرت .. تأخرت بمقدار 250
+
+220
+00:16:21,510 --> 00:16:27,780
+نانومتر250 نانومتر يعني .. يعني ربع مايكرون عن
+
+221
+00:16:27,780 --> 00:16:31,820
+الطريق الفجاني الربع مايكرون يعني .. يعني واحد على
+
+222
+00:16:31,820 --> 00:16:35,860
+أربع تلاف من الملي يعني شوف قديش المسافة بسيطة جدا
+
+223
+00:16:35,860 --> 00:16:39,640
+في التأخر وبالتالي صار destructive interference
+
+224
+00:16:39,640 --> 00:16:45,720
+عندي طيب بنرجع تاني بنقول عند
+
+225
+00:16:45,720 --> 00:16:51,330
+النقطة Qاللي هي أعلى من النقطة P هي النقطة O هي
+
+226
+00:16:51,330 --> 00:16:57,050
+النقطة P عجبالها إعتام تماما عند النقطة Q اللي هي
+
+227
+00:16:57,050 --> 00:17:03,030
+أبعد و أبعد هتكون أقرب أكتر لل pin hole الأعلى و
+
+228
+00:17:03,030 --> 00:17:07,690
+أبعد أكتر عن ال pin hole الأسفل بنقول هيتم التأخر
+
+229
+00:17:07,690 --> 00:17:12,620
+بزيادةطيب تم التأخر بزيادة للموجات القادمة من ال
+
+230
+00:17:12,620 --> 00:17:17,340
+pin hole الأسفل فهتتأخر بمقدار موجة كاملة .. موجة
+
+231
+00:17:17,340 --> 00:17:22,820
+كاملة فحيصير عندي يرجع قمة مع قمة و قاع مع قاع و
+
+232
+00:17:22,820 --> 00:17:27,100
+قمة مع قمة و قاع مع قاع فهيتم التداخل بشكل
+
+233
+00:17:27,100 --> 00:17:31,140
+constructive interference عشان هيكهتلاقيه ان
+
+234
+00:17:31,140 --> 00:17:36,920
+المنطقة high يعني مضيقة بينما اللي عاجباه ال P ..
+
+235
+00:17:36,920 --> 00:17:40,860
+اللي عاجباه ال P معتمد بينما Q أصبح .. طبعا احنا
+
+236
+00:17:40,860 --> 00:17:44,620
+.. احنا هذه الأرقام O و P و Q يعني أحرف بس عشان
+
+237
+00:17:44,620 --> 00:17:48,620
+نرمز للمناطق يعني عشان نميزها عن بعض البعض فهنلاقي
+
+238
+00:17:48,620 --> 00:17:52,760
+ان هذه المنطقة مضيقة .. مضيقة ممكن إنسان يسأل سؤال
+
+239
+00:17:52,760 --> 00:17:59,680
+منطقي جدا بنقول كالاتييعني أول شيء بدنا نعرف هنا
+
+240
+00:17:59,680 --> 00:18:03,900
+مضيق هنا معتم هنا مضيق بس لو قارننا المضيق هنا مع
+
+241
+00:18:03,900 --> 00:18:07,960
+المضيق هنا هنلاقي هنا أوضح .. هنا أوضح .. اه بنرجع
+
+242
+00:18:07,960 --> 00:18:13,870
+بنقارن الرسم رقم C مع الرسم رقم Aالتداخل هنا بين
+
+243
+00:18:13,870 --> 00:18:17,550
+كل المقطع مع كل المقطع يعني لو تصورنا أن هذا
+
+244
+00:18:17,550 --> 00:18:21,730
+المقطع مكوّن من تلت أربع موجات وهذا المقطع اللي له
+
+245
+00:18:21,730 --> 00:18:25,250
+نفس الطول الموجي مكوّن من تلت أربع موجات كل التلت
+
+246
+00:18:25,250 --> 00:18:31,790
+أو الأربع موجات تداخل هنا بسبب تأخر القطار الأسفل
+
+247
+00:18:31,790 --> 00:18:35,170
+هذه الموجات اللي أنا قاعد أشير عليها أصبحت خارج
+
+248
+00:18:35,170 --> 00:18:39,840
+الطبط يعني ما تداخلتش معموجات من هذا المقطع لأنها
+
+249
+00:18:39,840 --> 00:18:46,360
+متأخرة عنه وهذه الموجة الأول موجة في الخط الأعلى
+
+250
+00:18:46,360 --> 00:18:50,430
+أو في القطار الأعلىأيضًا سبّجات ما تداخلتش وكانوا
+
+251
+00:18:50,430 --> 00:18:54,290
+هدولة خرجوا من اللعبة التداخل تم بين هذه الموجات
+
+252
+00:18:54,290 --> 00:18:58,770
+اللي هو اللي ضلت اللي هي رقم اتنين ورقم تلاتة تمام
+
+253
+00:18:58,770 --> 00:19:02,710
+و هنا رقم واحد و رقم اتنين هم اللي تداخلوا مع
+
+254
+00:19:02,710 --> 00:19:06,450
+بعضهم الموجة الأخيرة هنا في القطار المتأخر والموجة
+
+255
+00:19:06,450 --> 00:19:11,090
+الأولى في القطار الموجي المسبج ما تم تداخلهم
+
+256
+00:19:11,090 --> 00:19:16,050
+وبالتالي هذا هيكون هذا و التداخل على النقطة اللي
+
+257
+00:19:16,050 --> 00:19:21,720
+بعد Qهيقل .. هيقل .. هيقل لغاية ما قطار .. هنصل
+
+258
+00:19:21,720 --> 00:19:28,320
+للوضع دي عند النقطة R قطار الموجات العليا سبق كل
+
+259
+00:19:28,320 --> 00:19:31,740
+ال section هذا سبق ال section أخوه اللي جاي من
+
+260
+00:19:31,740 --> 00:19:36,820
+أسفل بسبب طول المسافة سبقه بمقدار section كامل طيب
+
+261
+00:19:36,820 --> 00:19:40,760
+إيش اللي هيحصل ساعتها؟ ساعتها هيكون هذا مقابله
+
+262
+00:19:41,110 --> 00:19:46,410
+موجات من طول موجي آخر وهذا مقابله موجات من طول
+
+263
+00:19:46,410 --> 00:19:50,550
+موجي آخر فبالتالي هيصير عندي changing interference
+
+264
+00:19:50,550 --> 00:19:54,850
+pattern مش stable interference pattern وقلنا عن ال
+
+265
+00:19:54,850 --> 00:19:59,310
+changing interference pattern is too fast to be
+
+266
+00:19:59,310 --> 00:20:04,870
+observable يعني مابقدرش من سرعته ان ايش الاحظه
+
+267
+00:20:04,870 --> 00:20:09,780
+لأنه بتغيربشكل هائل السرعة زي ما اقول لما بنوصل
+
+268
+00:20:09,780 --> 00:20:15,360
+لوضع انه نوع من الموجات يتداخل مع نوع اخر من
+
+269
+00:20:15,360 --> 00:20:18,880
+الموجات يعني لها طول موج اخر ساعات هتعطيني
+
+270
+00:20:18,880 --> 00:20:22,180
+changing interference pattern فهبطل الاحظ هذا
+
+271
+00:20:22,180 --> 00:20:25,680
+النظام من الإضاءة والاعتامة اللي انا جاعد ايش
+
+272
+00:20:25,680 --> 00:20:30,110
+باحكي اللي انا جاعد باحكي ان في المنطقة هايفي
+
+273
+00:20:30,110 --> 00:20:34,830
+المنطقة هذه بلاحظ قطع مضيئة، قطع معتمة، قطع مضيئة،
+
+274
+00:20:34,830 --> 00:20:39,330
+قطع معتمة والإضاءة بتجلكل ما ذهبنا لأطراف هذا بسبب
+
+275
+00:20:39,330 --> 00:20:43,390
+أول حاجة صار diffraction وبعد ال diffraction
+
+276
+00:20:43,390 --> 00:20:48,070
+تداخلوا قطارين الموجات طالما التداخل بين موجات
+
+277
+00:20:48,070 --> 00:20:52,250
+موحدة الطول فبنشوف إذا كان التداخل constructive
+
+278
+00:20:52,250 --> 00:20:55,330
+ولا destructive طب إيش اللي هيخليه constructive؟
+
+279
+00:20:55,330 --> 00:20:59,840
+إنه تيجي قمة على قمة وقاع على قاعإيش اللي هيخليه
+
+280
+00:20:59,840 --> 00:21:04,080
+destructive؟ إنه يتيجي عندي قاع على قمة و قمة على
+
+281
+00:21:04,080 --> 00:21:07,380
+قاع يعني عكس بعضهم فبيلغوا بعضهم بيعطوا اعتام و
+
+282
+00:21:07,380 --> 00:21:12,160
+تفسير ليش أنا المنطقة المركزية في التجربة ففي لوحة
+
+283
+00:21:12,160 --> 00:21:17,380
+التلقي أكثر إضاءة و بعدين اقل إضاءة أقل .. كل ما
+
+284
+00:21:17,380 --> 00:21:21,080
+نتجه للأطراف بتقل الإضاءة بنقول بسبب أن عدد
+
+285
+00:21:21,080 --> 00:21:26,080
+الموجات الموحدة الطول المتداخلة بجل كل ما يعني
+
+286
+00:21:26,080 --> 00:21:30,660
+ابعدنا عن نقطة المركزكانت في الأول كل القطار مع كل
+
+287
+00:21:30,660 --> 00:21:34,560
+القطار أو خليني أقول كل ال section مع كل ال
+
+288
+00:21:34,560 --> 00:21:39,220
+section متداخل بشكل كامل بدأت عندي يعني في المناطق
+
+289
+00:21:39,220 --> 00:21:43,600
+المضيئة الأخرى يعني موجات تخرج خارج موضوع التداخل
+
+290
+00:21:43,600 --> 00:21:47,120
+يعني صارت تتداخل مع موجات مختلفة .. هذه حتى
+
+291
+00:21:47,120 --> 00:21:50,200
+التداخل مع ال section اللي بعده وهذه حتى التداخل
+
+292
+00:21:50,200 --> 00:21:54,490
+مع ال sectionاللي قبله و هيك أثبتت تجربة Thomas
+
+293
+00:21:54,490 --> 00:21:58,710
+Young قضية أنه الضوء بيصيرله diffraction رقم واحد
+
+294
+00:21:58,710 --> 00:22:07,550
+و تاني إشي بيصيرله يعني تداخلوهذا التداخل بينتج
+
+295
+00:22:07,550 --> 00:22:11,050
+عنه superposition للموجات اما destructive
+
+296
+00:22:11,050 --> 00:22:15,750
+interference او constructive interference وبنصل
+
+297
+00:22:15,750 --> 00:22:20,070
+لنقطة بعد هيك لما بتداخل او بنصل لنقطة بعيدة بيصير
+
+298
+00:22:20,070 --> 00:22:24,590
+انا عندي قطار او section في القطار مسبج ال section
+
+299
+00:22:24,590 --> 00:22:27,830
+النظير بتاعه او المثيل بتاعه اللي له نفس الطول
+
+300
+00:22:27,830 --> 00:22:32,190
+الموج مسبجه بطول section كاملفبصير عندى تداخل
+
+301
+00:22:32,190 --> 00:22:35,530
+section مع section أخر مختلف عنه في الطول الموجي
+
+302
+00:22:35,530 --> 00:22:40,090
+يمكن هذا أوضح تداخل section مع section أخر مختلف
+
+303
+00:22:40,090 --> 00:22:43,590
+عنه في الطول الموجي وهذا ال section أيضا هيتداخل
+
+304
+00:22:43,590 --> 00:22:48,210
+مع section أخر من القطار الأول أيضا مختلف عنه في
+
+305
+00:22:48,210 --> 00:22:53,150
+الطول الموجي و بقدرش ألاحظ بعد هذا لبرا منه لهين
+
+306
+00:22:53,150 --> 00:22:57,900
+أو لهين بقدرش ألاحظتغيروا في الإضاءة، بالعكس بيكون
+
+307
+00:22:57,900 --> 00:23:03,240
+هنا حدود التجربة أو حدود الملاحظة توقفت بسبب ال
+
+308
+00:23:03,240 --> 00:23:08,100
+changing interference pattern على العموم انا يعني
+
+309
+00:23:08,100 --> 00:23:13,660
+نزل او هنزل فيديو ان شاء الله تعالى للتجربة بشكل
+
+310
+00:23:13,660 --> 00:23:19,650
+معملي واضح طبعا ومشروح ان شاء الله تعالىوهذه
+
+311
+00:23:19,650 --> 00:23:23,610
+القضية أثبتت الطبيعة الموجية للضوء وهي حقيقة من
+
+312
+00:23:23,610 --> 00:23:27,630
+التجارب المهمة جدا والمركزية في علم الفيزيا والضوء
+
+313
+00:23:27,630 --> 00:23:34,550
+ونقرأ بس الكلام اللي بنقول
+
+314
+00:23:34,550 --> 00:23:40,210
+كالقاتي consider single section of wave train from
+
+315
+00:23:40,210 --> 00:23:44,190
+broad band point source illuminating two small
+
+316
+00:23:44,190 --> 00:23:48,130
+closely spaced pinholes in an otherwise opaque
+
+317
+00:23:48,130 --> 00:23:53,130
+screenيعني هذه شروط التجربة بنجيب broadband ..
+
+318
+00:23:53,130 --> 00:23:56,210
+broadband point source point source ضروري تكون
+
+319
+00:23:56,210 --> 00:24:02,110
+point source و بنضويها او بنصلضوها على two small
+
+320
+00:24:02,110 --> 00:24:07,430
+closely spaced pinholes في جدار معتم each section
+
+321
+00:24:07,430 --> 00:24:13,860
+arrives at both pinholesimultaneously كل مقطع بيصل
+
+322
+00:24:13,860 --> 00:24:17,820
+ل ال pinhole الخاص فيه في نفس اللحظة لأنهم لهم نفس
+
+323
+00:24:17,820 --> 00:24:21,460
+السرعة و نفس الطول الموجي and is diffracted أول
+
+324
+00:24:21,460 --> 00:24:24,720
+ظاهرة بيصير ال diffraction حيود الموجات بعد دخولها
+
+325
+00:24:24,720 --> 00:24:28,180
+ال two pinholes by the pinholes the distance from
+
+326
+00:24:28,180 --> 00:24:32,860
+each pinhole to the point O is identical so both
+
+327
+00:24:32,860 --> 00:24:37,150
+sections produce bright spotby constructive low
+
+328
+00:24:37,150 --> 00:24:42,090
+additive interference لأن مسافتهم للنقطة O للنقطة
+
+329
+00:24:42,090 --> 00:24:50,010
+O النقطة O هنا هي النقطة O يمكن الرسم اللي كنا
+
+330
+00:24:50,010 --> 00:24:55,190
+نشرح عليها أوضح مسافة ال two pin holes من النقطة O
+
+331
+00:24:55,190 --> 00:24:58,770
+هي نفس المسافة إذا ال two sections هيصلوا في نفس
+
+332
+00:24:58,770 --> 00:24:59,670
+اللحظة
+
+333
+00:25:04,320 --> 00:25:10,840
+في نقطة P، واحدة من المقاطع تسير بطولة أكتر من
+
+334
+00:25:10,840 --> 00:25:15,120
+الأخرى، فالمقاطعين تغلقوا، ويصيبوا مكان مظلم
+
+335
+00:25:15,120 --> 00:25:21,840
+بإدخال أو إدخاليعني نرجع للنقطة P بنقول واحد من ال
+
+336
+00:25:21,840 --> 00:25:24,860
+two sections بتأخر اللي هو ال .. ال .. ال section
+
+337
+00:25:24,860 --> 00:25:28,380
+الأسفل بتأخر لأنه مسافته أطول بتأخر في الوصول
+
+338
+00:25:28,380 --> 00:25:32,140
+بمقدار نص موجة بيصير عندي destructive interference
+
+339
+00:25:32,140 --> 00:25:36,300
+السبب ليش بتأخر لأن النقطة P أقرب للبنهول الأعلى
+
+340
+00:25:36,300 --> 00:25:41,020
+منها للبنهول الأسفل بمقدار نص موجة .. بمقدار نص
+
+341
+00:25:41,020 --> 00:25:41,680
+موجة
+
+342
+00:25:49,440 --> 00:25:53,800
+At point Q لأبعد من P, the sections differ by a
+
+343
+00:25:53,800 --> 00:25:57,260
+full wavelength and again produce a bright spot by
+
+344
+00:25:57,260 --> 00:26:01,920
+constructive interference نرجع للنقطة Q، بنقول
+
+345
+00:26:01,920 --> 00:26:06,360
+النقطة Q أبعد وأبعد، بس ساعتها الآن هتفرج عندي،
+
+346
+00:26:06,360 --> 00:26:10,440
+هتفرج عندي موجة كاملة، فبرجع بيصير عندي صحيح
+
+347
+00:26:10,440 --> 00:26:14,380
+متأخر، الغطار الأسفل متأخر بمقدار موجة كاملة، بس
+
+348
+00:26:14,380 --> 00:26:18,360
+برجع عندي ال interference التداخل قمة مع قمة وقاع
+
+349
+00:26:18,360 --> 00:26:22,690
+مع قاعوقمة مع قمة فبيصير عندي تداخل بنائي أو
+
+350
+00:26:22,690 --> 00:26:25,750
+constructive interference وبالتالي بيعطيني bright
+
+351
+00:26:25,750 --> 00:26:31,050
+spot طبعا ال bright spot عند Q أقل منها عند O ليش؟
+
+352
+00:26:31,050 --> 00:26:34,830
+لأن فقدنا هنا موجة وفقدنا هنا موجة ما تداخلوش مع
+
+353
+00:26:34,830 --> 00:26:40,370
+بعضهم البعض بسبب التأخر فبالتالي أصبح كمية الموجات
+
+354
+00:26:40,370 --> 00:26:45,670
+المتداخلة بنائيا أقل فبالتالي ال bright spot هتكون
+
+355
+00:26:45,670 --> 00:26:51,550
+عند النقطة Qأقل معانا .. أقل كمية إضاءة منها عند O
+
+356
+00:26:51,550 --> 00:26:52,730
+منها عند O
+
+357
+00:26:57,870 --> 00:27:01,130
+However, as the distance from point O increases,
+
+358
+00:27:01,330 --> 00:27:06,190
+the wave transitions overlap less and less تداخل
+
+359
+00:27:06,190 --> 00:27:10,710
+قطارين الموجات من ال pinhole الأعلى و من ال
+
+360
+00:27:10,710 --> 00:27:14,310
+pinhole الأسفل كل ما بعدت المسافة عن واحد من ال
+
+361
+00:27:14,310 --> 00:27:18,010
+pinhole بيصير ال two sections تداخلهم أقل وأقل
+
+362
+00:27:18,010 --> 00:27:22,030
+وهذا بيعمل decreasing the degree of fringe
+
+363
+00:27:22,030 --> 00:27:25,630
+contrast ال fringe contrast اللي هذي بيسموها
+
+364
+00:27:25,630 --> 00:27:30,650
+fringesالأصابع هذه واحدة مضيئة واحدة معتمرة واحدة
+
+365
+00:27:30,650 --> 00:27:33,750
+.. واحدة مضيئة واحدة معتمرة بيسموها fringes تمام
+
+366
+00:27:33,750 --> 00:27:38,290
+هنا هتكون في الوسط أكثر لمعانا أقل أقل أقل بسبب
+
+367
+00:27:38,290 --> 00:27:44,350
+قلة التداخل من موجات القطارين قلة التداخل من موجات
+
+368
+00:27:44,350 --> 00:27:52,570
+القطارين طيب إذا
+
+369
+00:27:52,570 --> 00:27:56,390
+زي ما حكينا ده point EQAt the point Q, the
+
+370
+00:27:56,390 --> 00:27:59,270
+sections differed by a full wavelength and again
+
+371
+00:27:59,270 --> 00:28:01,650
+produced a bright spot by constructive
+
+372
+00:28:01,650 --> 00:28:04,910
+interference. Alternating intervals of
+
+373
+00:28:04,910 --> 00:28:08,270
+constructive and destructive interference produced
+
+374
+00:28:08,270 --> 00:28:09,810
+a fringe pattern
+
+375
+00:28:15,990 --> 00:28:19,530
+بالتالي، فإن المسافة من نقطة O تزداد، فإن المسافة
+
+376
+00:28:19,530 --> 00:28:24,050
+بين القطعين تتعامل أكتر و أكتر، فإن المسافة بينها
+
+377
+00:28:24,050 --> 00:28:24,570
+تتعامل أكتر و أكتر، فإن المسافة بينها تتعامل أكتر
+
+378
+00:28:24,570 --> 00:28:25,750
+و أكتر، فإن المسافة بينها تتعامل أكتر و أكتر، فإن
+
+379
+00:28:25,750 --> 00:28:27,190
+المسافة بينها تتعامل أكتر و أكتر، فإن المسافة
+
+380
+00:28:27,190 --> 00:28:31,790
+بينها تتعامل أكتر و أكتر، فإن المسافة بينها تتعامل
+
+381
+00:28:31,790 --> 00:28:38,050
+أكتر و أكتر، فإن المسافة بينها تتعامل أكتر و أكتر،
+
+382
+00:28:38,050 --> 00:28:43,160
+فإن المسافbecause the superposition of non
+
+383
+00:28:43,160 --> 00:28:46,000
+-identical sections does not produce stable
+
+384
+00:28:46,000 --> 00:28:49,400
+interference، the fringes are no longer visible
+
+385
+00:28:53,940 --> 00:28:57,800
+الاضاءة والاعتام والاضاءة والاعتام لغاية حد معين
+
+386
+00:28:57,800 --> 00:29:01,880
+بعدها بنبطل نشوفها وكان انه خلاص خرجنا خارج نطاق
+
+387
+00:29:01,880 --> 00:29:06,460
+التجربة بسبب انه عند نقطة معينة بعيدة هنا ونقطة
+
+388
+00:29:06,460 --> 00:29:10,740
+معينة بعيدة هنا التداخل بيتم بين مقاطع من الموجات
+
+389
+00:29:10,740 --> 00:29:14,400
+ليست متساوية في طول الموج يعني هذا ال section و
+
+390
+00:29:14,400 --> 00:29:17,300
+هذا ال section متساوين في الطول الموجي بس هذا ال
+
+391
+00:29:17,300 --> 00:29:21,590
+section التحتانيتأخر بمقدار طول .. طول section
+
+392
+00:29:21,590 --> 00:29:24,990
+كامل فبالتالي هذا ال section أصبح يتداخل مع
+
+393
+00:29:24,990 --> 00:29:28,890
+section آخر من القطار الأعلى وهذا ال section أصبح
+
+394
+00:29:28,890 --> 00:29:32,030
+يتداخل مع section آخر من القطار الأسفل .. إيش يعني
+
+395
+00:29:32,030 --> 00:29:35,790
+section آخر؟ يعني بيختلف عنه في الطول الموجي طب ما
+
+396
+00:29:35,790 --> 00:29:38,390
+يختلف عنه في الطول الموجي .. وإيش المشكلة؟ أه
+
+397
+00:29:38,390 --> 00:29:42,110
+المشكلة أنه لما بتداخل two sections ما اللي همش
+
+398
+00:29:42,110 --> 00:29:45,770
+نفس الطول الموجيساعتها حيصير عندى changing
+
+399
+00:29:45,770 --> 00:29:49,730
+interference pattern وهذا لا يلاحظ بالعين وكأنه
+
+400
+00:29:49,730 --> 00:29:55,510
+حلاحظ بس انه هذه الفرنجز الفرنجز بلاحظها لعند حد
+
+401
+00:29:55,510 --> 00:29:58,970
+معين و بعدين ببطل ألاحظها المناطق اللي بلاحظاش
+
+402
+00:29:58,970 --> 00:30:04,250
+فيها لازم أكون على يقين ان هذه بسبب تداخل sections
+
+403
+00:30:04,250 --> 00:30:08,050
+من الضوء من ال two slits أو من ال tubing holes ليس
+
+404
+00:30:08,050 --> 00:30:11,590
+لها نفس الطول الموجي هتعطيني changing interference
+
+405
+00:30:12,090 --> 00:30:17,910
+button changing interference button فبالتالي ضروري
+
+406
+00:30:17,910 --> 00:30:23,590
+نفهم هذه النقطة .. ضروري نفهم هذه النقطة فساعتها
+
+407
+00:30:23,590 --> 00:30:30,450
+ال fringes are no longer visible هنتوقف
+
+408
+00:30:30,450 --> 00:30:32,970
+عند هذه النقطة و هنكمل ان شاء الله في المحاضرة
+
+409
+00:30:32,970 --> 00:30:36,190
+الجاية ان شاء الله تعالى و يعطيكم العافية والسلام
+
+410
+00:30:36,190 --> 00:30:38,510
+عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/jBEZ9eqMtl4_raw.json b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/jBEZ9eqMtl4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..02a18ff671e07367cf65cab3736df435adf0082a
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/jBEZ9eqMtl4_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 2062, "start": 2.72, "end": 20.62, "text": "بسم الله الرحمن الرحيم بنستكمل مع محاضرات ال physical optics ووصلنا لتجربة العالم Thomas Young قبل ما نشرح هذه التجربة بدنا نذكر ببعض الأشياء", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 44945, 14851, 24793, 1211, 20449, 3714, 5016, 46958, 2288, 9307, 2423, 4001, 42599, 4032, 2407, 36520, 8315, 5296, 2655, 7435, 25513, 3660, 18863, 45340, 8500, 8160, 12174, 36150, 19446, 8717, 46309, 5016, 29538, 16712, 7435, 25513, 3660, 47525, 8315, 8717, 8848, 37983, 4724, 3555, 3615, 11242, 16247, 8592, 1829, 16606], "avg_logprob": -0.07350260491172472, "compression_ratio": 1.401197604790419, "no_speech_prob": 5.543231964111328e-06, "words": [{"start": 2.72, "end": 2.92, "word": "بسم", "probability": 0.906982421875}, {"start": 2.92, "end": 3.1, "word": " الله", "probability": 0.9755859375}, {"start": 3.1, "end": 3.38, "word": " الرحمن", "probability": 0.95166015625}, {"start": 3.38, "end": 3.92, 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destructive interference وبيلغوا بعضهم البعض لما بيتداخلوا الموجتين من نفس الطول الموجي بس مش تماما out of phase ولا تماما أو totally in phase ولا out of phase يعني بين البينين يعني بين الخيار الأول والتاني يعني هنا القمة مثلا جاية مقابل مقطع من الموجة لا هو قاع ولا هو", "tokens": [3794, 995, 34268, 11296, 4724, 1829, 9381, 13546, 26960, 24497, 4032, 21292, 1211, 17082, 14407, 45030, 11242, 16095, 29739, 3615, 11242, 5296, 15042, 4724, 36081, 3215, 47283, 1211, 14407, 9673, 29245, 2655, 9957, 9154, 8717, 36178, 41950, 12610, 9673, 29245, 1829, 4724, 3794, 37893, 46811, 10943, 995, 484, 295, 5574, 49429, 46811, 10943, 995, 34051, 3879, 294, 5574, 49429, 484, 295, 5574, 37495, 22653, 49374, 29739, 9957, 9957, 37495, 22653, 49374, 33962, 1829, 9640, 16247, 12610, 16070, 2655, 7649, 1829, 37495, 22653, 34105, 25062, 46007, 50113, 15040, 10874, 995, 10632, 3714, 4587, 16758, 1211, 3714, 47432, 3615, 9154, 9673, 29245, 3660, 20193, 31439, 12174, 45761, 49429, 31439], "avg_logprob": 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"text": "يعني حاجز معتم وبدنا نعمل فيه two pinhole أو ممكن نعمل فيه two slits", "tokens": [40228, 22653, 11331, 26108, 11622, 20449, 39237, 4032, 44510, 8315, 8717, 25957, 1211, 8978, 3224, 732, 5447, 14094, 34051, 3714, 43020, 8717, 25957, 1211, 8978, 3224, 732, 1061, 1208], "avg_logprob": -0.14322916517655054, "compression_ratio": 1.1797752808988764, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 227.44, "end": 227.82, "word": "يعني", "probability": 0.7890625}, {"start": 227.82, "end": 228.38, "word": " حاجز", "probability": 0.9921875}, {"start": 228.38, "end": 228.9, "word": " معتم", "probability": 0.799560546875}, {"start": 228.9, "end": 230.62, "word": " وبدنا", "probability": 0.69189453125}, {"start": 230.62, "end": 230.94, "word": " نعمل", "probability": 0.9915364583333334}, {"start": 230.94, "end": 231.24, "word": " فيه", "probability": 0.977783203125}, {"start": 231.24, "end": 231.46, "word": " two", "probability": 0.884765625}, {"start": 231.46, "end": 232.04, 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بعد هيك لما بتداخل او بنصل لنقطة بعيدة بيصير انا عندي قطار او section في القطار مسبج ال section النظير بتاعه او المثيل بتاعه اللي له نفس الطول الموج مسبجه بطول section كامل", "tokens": [2407, 3224, 15730, 16712, 28259, 9778, 1211, 4724, 9957, 2655, 7435, 18871, 3224, 1687, 38078, 5296, 19528, 29245, 9307, 1975, 15042, 26960, 24497, 1975, 2407, 30223, 24497, 4032, 3555, 1863, 36520, 5296, 1863, 47432, 3660, 39182, 39896, 4117, 5296, 15042, 39894, 3215, 47283, 1211, 1975, 2407, 44945, 36520, 5296, 1863, 47432, 3660, 45030, 25708, 3660, 4724, 1829, 9381, 13546, 1975, 8315, 18871, 16254, 12174, 9566, 9640, 1975, 2407, 3541, 8978, 25062, 9566, 9640, 47524, 3555, 7435, 2423, 3541, 28239, 19913, 13546, 39894, 45761, 3224, 1975, 2407, 9673, 12984, 26895, 39894, 45761, 3224, 13672, 1829, 46740, 8717, 36178, 41950, 12610, 9673, 29245, 47524, 3555, 7435, 3224, 4724, 9566, 12610, 3541, 9122, 10943, 1211], "avg_logprob": -0.16205752423379274, "compression_ratio": 1.8860759493670887, 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broad", "probability": 0.8017578125}, {"start": 1420.77, "end": 1421.13, "word": " band", "probability": 0.32275390625}, {"start": 1421.13, "end": 1421.49, "word": " point", "probability": 0.935546875}, {"start": 1421.49, "end": 1422.03, "word": " source", "probability": 0.849609375}, {"start": 1422.03, "end": 1423.31, "word": " illuminating", "probability": 0.9189453125}, {"start": 1423.31, "end": 1423.61, "word": " two", "probability": 0.9287109375}, {"start": 1423.61, "end": 1424.19, "word": " small", "probability": 0.93798828125}, {"start": 1424.19, "end": 1424.81, "word": " closely", "probability": 0.8076171875}, {"start": 1424.81, "end": 1425.35, "word": " spaced", "probability": 0.92041015625}, {"start": 1425.35, "end": 1425.97, "word": " pinholes", "probability": 0.71630859375}, {"start": 1425.97, "end": 1426.69, "word": " in", "probability": 0.96533203125}, {"start": 1426.69, "end": 1427.01, "word": " an", "probability": 0.88818359375}, {"start": 1427.01, "end": 1427.73, "word": " otherwise", "probability": 0.8701171875}, {"start": 1427.73, "end": 1428.13, "word": " opaque", "probability": 0.85205078125}, {"start": 1428.13, "end": 1428.59, "word": " screen", "probability": 0.87841796875}], "temperature": 1.0}, {"id": 63, "seek": 144925, "start": 1429.11, "end": 1449.25, "text": "يعني هذه شروط التجربة بنجيب broadband .. broadband point source point source ضروري تكون point source و بنضويها او بنصلضوها على two small closely spaced pinholes في جدار معتم each section arrives at both pinhole", "tokens": [40228, 22653, 29538, 13412, 32887, 9566, 16712, 7435, 25513, 3660, 44945, 7435, 1829, 3555, 37718, 4386, 37718, 935, 4009, 935, 4009, 48812, 2288, 13063, 1829, 6055, 30544, 935, 4009, 4032, 44945, 11242, 45865, 11296, 1975, 2407, 44945, 36520, 11242, 2407, 11296, 15844, 732, 1359, 8185, 43766, 5447, 37894, 8978, 10874, 3215, 9640, 20449, 39237, 1184, 3541, 20116, 412, 1293, 5447, 14094], "avg_logprob": -0.1907762058319584, "compression_ratio": 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{"start": 1435.17, "end": 1435.61, "word": " source", "probability": 0.921875}, {"start": 1435.61, "end": 1436.01, "word": " ضروري", "probability": 0.937255859375}, {"start": 1436.01, "end": 1436.21, "word": " تكون", "probability": 0.989501953125}, {"start": 1436.21, "end": 1436.53, "word": " point", "probability": 0.9912109375}, {"start": 1436.53, "end": 1436.97, "word": " source", "probability": 0.8896484375}, {"start": 1436.97, "end": 1437.83, "word": " و", "probability": 0.72705078125}, {"start": 1437.83, "end": 1438.97, "word": " بنضويها", "probability": 0.787841796875}, {"start": 1438.97, "end": 1439.15, "word": " او", "probability": 0.736083984375}, {"start": 1439.15, "end": 1440.03, "word": " بنصلضوها", "probability": 0.739208984375}, {"start": 1440.03, "end": 1440.39, "word": " على", "probability": 0.85400390625}, {"start": 1440.39, "end": 1441.61, "word": " two", "probability": 0.9501953125}, {"start": 1441.61, "end": 1442.11, "word": " small", "probability": 0.94580078125}, {"start": 1442.11, "end": 1442.57, "word": " closely", "probability": 0.791015625}, {"start": 1442.57, "end": 1443.09, "word": " spaced", "probability": 0.9296875}, {"start": 1443.09, "end": 1443.71, "word": " pinholes", "probability": 0.6806640625}, {"start": 1443.71, "end": 1445.13, "word": " في", "probability": 0.94384765625}, {"start": 1445.13, "end": 1445.65, "word": " جدار", "probability": 0.96875}, {"start": 1445.65, "end": 1446.11, "word": " معتم", "probability": 0.909423828125}, {"start": 1446.11, "end": 1446.85, "word": " each", "probability": 0.4375}, {"start": 1446.85, "end": 1447.43, "word": " section", "probability": 0.91552734375}, {"start": 1447.43, "end": 1448.09, "word": " arrives", "probability": 0.87353515625}, {"start": 1448.09, "end": 1448.39, "word": " at", "probability": 0.97216796875}, {"start": 1448.39, "end": 1448.65, "word": " both", "probability": 0.86767578125}, {"start": 1448.65, "end": 1449.25, "word": " pinhole", "probability": 0.727294921875}], "temperature": 1.0}, {"id": 64, "seek": 147500, "start": 1451.24, "end": 1475.0, "text": "simultaneously كل مقطع بيصل ل ال pinhole الخاص فيه في نفس اللحظة لأنهم لهم نفس السرعة و نفس الطول الموجي and is diffracted أول ظاهرة بيصير ال diffraction حيود الموجات بعد دخولها ال two pinholes by the pinholes the distance from each pinhole to the point O is identical so both sections produce bright spot", "tokens": [30937, 723, 13131, 28242, 3714, 47432, 3615, 4724, 1829, 36520, 5296, 2423, 5447, 14094, 33962, 33546, 8978, 3224, 8978, 8717, 36178, 13672, 5016, 19913, 3660, 5296, 33456, 16095, 5296, 16095, 8717, 36178, 21136, 2288, 27884, 4032, 8717, 36178, 41950, 12610, 9673, 29245, 1829, 293, 307, 7593, 1897, 292, 5551, 12610, 1357, 116, 40294, 25720, 4724, 1829, 9381, 13546, 2423, 7593, 26766, 11331, 1829, 23328, 9673, 29245, 9307, 39182, 11778, 9778, 12610, 11296, 2423, 732, 5447, 37894, 538, 264, 5447, 37894, 264, 4560, 490, 1184, 5447, 14094, 281, 264, 935, 422, 307, 14800, 370, 1293, 10863, 5258, 4730, 4008], "avg_logprob": -0.1788194513682163, "compression_ratio": 1.592156862745098, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 1451.2400000000002, "end": 1452.0800000000002, "word": "simultaneously", "probability": 0.7721354166666666}, {"start": 1452.0800000000002, "end": 1452.92, "word": " كل", "probability": 0.55126953125}, {"start": 1452.92, "end": 1453.38, "word": " مقطع", "probability": 0.9925130208333334}, {"start": 1453.38, "end": 1453.86, "word": " بيصل", "probability": 0.9410807291666666}, {"start": 1453.86, "end": 1454.26, "word": " ل", "probability": 0.66845703125}, {"start": 1454.26, "end": 1454.42, "word": " ال", "probability": 0.1527099609375}, {"start": 1454.42, "end": 1454.84, "word": " pinhole", "probability": 0.526611328125}, {"start": 1454.84, "end": 1455.4, "word": " الخاص", "probability": 0.953125}, {"start": 1455.4, "end": 1455.78, "word": " فيه", "probability": 0.918212890625}, {"start": 1455.78, "end": 1456.12, "word": " في", 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two", "probability": 0.83203125}, {"start": 1465.0, "end": 1465.52, "word": " pinholes", "probability": 0.858154296875}, {"start": 1465.52, "end": 1466.22, "word": " by", "probability": 0.78662109375}, {"start": 1466.22, "end": 1466.42, "word": " the", "probability": 0.82373046875}, {"start": 1466.42, "end": 1466.84, "word": " pinholes", "probability": 0.896484375}, {"start": 1466.84, "end": 1467.4, "word": " the", "probability": 0.59375}, {"start": 1467.4, "end": 1467.88, "word": " distance", "probability": 0.95166015625}, {"start": 1467.88, "end": 1468.18, "word": " from", "probability": 0.93115234375}, {"start": 1468.18, "end": 1468.5, "word": " each", "probability": 0.95849609375}, {"start": 1468.5, "end": 1469.02, "word": " pinhole", "probability": 0.908203125}, {"start": 1469.02, "end": 1469.2, "word": " to", "probability": 0.970703125}, {"start": 1469.2, "end": 1469.38, "word": " the", "probability": 0.83984375}, {"start": 1469.38, "end": 1469.74, "word": " point", "probability": 0.97607421875}, {"start": 1469.74, "end": 1470.08, "word": " O", "probability": 0.51416015625}, {"start": 1470.08, "end": 1470.74, "word": " is", "probability": 0.9482421875}, {"start": 1470.74, "end": 1471.5, "word": " identical", "probability": 0.9248046875}, {"start": 1471.5, "end": 1472.34, "word": " so", "probability": 0.72119140625}, {"start": 1472.34, "end": 1472.86, "word": " both", "probability": 0.91162109375}, {"start": 1472.86, "end": 1473.4, "word": " sections", "probability": 0.8681640625}, {"start": 1473.4, "end": 1473.98, "word": " produce", "probability": 0.89404296875}, {"start": 1473.98, "end": 1474.5, "word": " bright", "probability": 0.8916015625}, {"start": 1474.5, "end": 1475.0, "word": " spot", "probability": 0.7119140625}], "temperature": 1.0}, {"id": 65, "seek": 149967, "start": 1475.35, "end": 1499.67, "text": "by constructive low additive interference لأن مسافتهم للنقطة O للنقطة O النقطة O هنا هي النقطة O يمكن الرسم اللي كنا نشرح عليها أوضح مسافة ال two pin holes من النقطة O هي نفس المسافة إذا ال two sections هيصلوا في نفس اللحظة", "tokens": [2322, 30223, 2295, 45558, 24497, 5296, 33456, 47524, 31845, 2655, 16095, 24976, 1863, 47432, 3660, 422, 24976, 1863, 47432, 3660, 422, 28239, 47432, 3660, 422, 34105, 39896, 28239, 47432, 3660, 422, 7251, 43020, 34892, 38251, 13672, 1829, 9122, 8315, 8717, 46309, 5016, 25894, 11296, 34051, 11242, 5016, 47524, 31845, 3660, 2423, 732, 5447, 8118, 9154, 28239, 47432, 3660, 422, 39896, 8717, 36178, 9673, 3794, 31845, 3660, 11933, 15730, 2423, 732, 10863, 39896, 36520, 14407, 8978, 8717, 36178, 13672, 5016, 19913, 3660], "avg_logprob": -0.15844131497348227, "compression_ratio": 1.7258883248730965, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1475.35, "end": 1475.67, "word": "by", "probability": 0.474853515625}, {"start": 1475.67, "end": 1476.51, "word": " constructive", "probability": 0.8486328125}, {"start": 1476.51, "end": 1477.15, "word": " low", "probability": 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1800.89, "end": 1801.21, "word": " هذه", "probability": 0.5322265625}, {"start": 1801.21, "end": 1802.11, "word": " بسبب", "probability": 0.9195963541666666}, {"start": 1802.11, "end": 1802.87, "word": " تداخل", "probability": 0.8662109375}, {"start": 1802.87, "end": 1804.25, "word": " sections", "probability": 0.7744140625}, {"start": 1804.25, "end": 1804.51, "word": " من", "probability": 0.99267578125}, {"start": 1804.51, "end": 1804.93, "word": " الضوء", "probability": 0.79351806640625}, {"start": 1804.93, "end": 1805.17, "word": " من", "probability": 0.9541015625}, {"start": 1805.17, "end": 1805.51, "word": " ال", "probability": 0.98291015625}, {"start": 1805.51, "end": 1805.77, "word": " two", "probability": 0.57373046875}, {"start": 1805.77, "end": 1806.17, "word": " slits", "probability": 0.835205078125}, {"start": 1806.17, "end": 1806.39, "word": " أو", "probability": 0.529296875}, {"start": 1806.39, "end": 1806.51, "word": " من", "probability": 0.9189453125}, {"start": 1806.51, "end": 1806.65, "word": " ال", "probability": 0.92578125}, {"start": 1806.65, "end": 1806.89, "word": " tubing", "probability": 0.53466796875}, {"start": 1806.89, "end": 1807.29, "word": " holes", "probability": 0.83544921875}, {"start": 1807.29, "end": 1808.05, "word": " ليس", "probability": 0.9375}, {"start": 1808.05, "end": 1808.33, "word": " لها", "probability": 0.987060546875}, {"start": 1808.33, "end": 1808.91, "word": " نفس", "probability": 0.953125}, {"start": 1808.91, "end": 1809.23, "word": " الطول", "probability": 0.9384765625}, {"start": 1809.23, "end": 1809.75, "word": " الموجي", "probability": 0.9130859375}, {"start": 1809.75, "end": 1810.37, "word": " هتعطيني", "probability": 0.8428548177083334}, {"start": 1810.37, "end": 1810.83, "word": " changing", "probability": 0.9326171875}, {"start": 1810.83, "end": 1811.59, "word": " interference", "probability": 0.93798828125}], "temperature": 1.0}, {"id": 79, "seek": 183851, "start": 1812.09, "end": 1838.51, "text": "button changing interference button فبالتالي ضروري نفهم هذه النقطة .. ضروري نفهم هذه النقطة فساعتها ال fringes are no longer visible هنتوقف عند هذه النقطة و هنكمل ان شاء الله في المحاضرة الجاية ان شاء الله تعالى و يعطيكم العافية والسلام عليكم ورحمة الله وبركاته", "tokens": [5955, 1756, 4473, 24497, 2960, 6156, 3555, 6027, 2655, 6027, 1829, 48812, 2288, 13063, 1829, 8717, 5172, 16095, 29538, 28239, 47432, 3660, 4386, 48812, 2288, 13063, 1829, 8717, 5172, 16095, 29538, 28239, 47432, 3660, 6156, 3794, 995, 34268, 11296, 2423, 431, 278, 279, 366, 572, 2854, 8974, 8032, 29399, 30543, 5172, 43242, 29538, 28239, 47432, 3660, 4032, 8032, 1863, 24793, 1211, 16472, 13412, 16606, 21984, 8978, 9673, 5016, 46958, 25720, 25724, 995, 10632, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 4032, 37495, 9566, 1829, 24793, 18863, 31845, 10632, 16070, 3794, 37440, 25894, 24793, 4032, 2288, 35571, 3660, 21984, 4032, 26890, 4117, 9307, 3224], "avg_logprob": -0.09247295486812408, "compression_ratio": 1.8060344827586208, "no_speech_prob": 6.496906280517578e-06, "words": [{"start": 1812.09, "end": 1812.77, "word": "button", "probability": 0.6978759765625}, {"start": 1812.77, "end": 1813.25, "word": " changing", "probability": 0.5283203125}, {"start": 1813.25, "end": 1813.93, "word": " interference", "probability": 0.921875}, {"start": 1813.93, "end": 1814.69, "word": " button", "probability": 0.91357421875}, {"start": 1814.69, "end": 1816.95, "word": " فبالتالي", "probability": 0.9772135416666666}, {"start": 1816.95, "end": 1817.91, "word": " ضروري", "probability": 0.940673828125}, {"start": 1817.91, "end": 1818.25, "word": " نفهم", "probability": 0.98291015625}, {"start": 1818.25, "end": 1818.63, "word": " هذه", "probability": 0.82470703125}, {"start": 1818.63, "end": 1819.85, "word": " النقطة", "probability": 0.978515625}, {"start": 1819.85, "end": 1819.91, "word": " ..", "probability": 0.461181640625}, {"start": 1819.91, "end": 1820.09, "word": " ضروري", "probability": 0.9554443359375}, {"start": 1820.09, "end": 1820.41, "word": " نفهم", "probability": 0.9943033854166666}, {"start": 1820.41, "end": 1820.81, "word": " هذه", "probability": 0.9677734375}, {"start": 1820.81, "end": 1822.27, "word": " النقطة", "probability": 0.98193359375}, {"start": 1822.27, "end": 1823.59, "word": " فساعتها", "probability": 0.94931640625}, {"start": 1823.59, "end": 1823.91, "word": " ال", "probability": 0.89501953125}, {"start": 1823.91, "end": 1824.51, "word": " fringes", "probability": 0.8343098958333334}, {"start": 1824.51, "end": 1824.75, "word": " are", "probability": 0.95361328125}, {"start": 1824.75, "end": 1825.01, "word": " no", "probability": 0.884765625}, {"start": 1825.01, "end": 1825.47, "word": " longer", "probability": 0.96142578125}, {"start": 1825.47, "end": 1826.05, "word": " visible", "probability": 0.9365234375}, {"start": 1826.05, "end": 1830.45, "word": " هنتوقف", "probability": 0.863037109375}, {"start": 1830.45, "end": 1830.67, "word": " عند", "probability": 0.99267578125}, {"start": 1830.67, "end": 1830.89, "word": " هذه", "probability": 0.95703125}, {"start": 1830.89, "end": 1831.37, "word": " النقطة", "probability": 0.98388671875}, {"start": 1831.37, "end": 1831.51, "word": " و", "probability": 0.97412109375}, {"start": 1831.51, "end": 1831.91, "word": " هنكمل", "probability": 0.918701171875}, {"start": 1831.91, "end": 1832.07, "word": " ان", "probability": 0.76904296875}, {"start": 1832.07, "end": 1832.21, "word": " شاء", "probability": 0.97607421875}, {"start": 1832.21, "end": 1832.29, "word": " الله", "probability": 0.9580078125}, {"start": 1832.29, "end": 1832.43, "word": " في", "probability": 0.939453125}, {"start": 1832.43, "end": 1832.97, "word": " المحاضرة", "probability": 0.98974609375}, {"start": 1832.97, "end": 1834.13, "word": " الجاية", "probability": 0.7805989583333334}, {"start": 1834.13, "end": 1834.29, "word": " ان", "probability": 0.791015625}, {"start": 1834.29, "end": 1834.41, "word": " شاء", "probability": 0.991943359375}, {"start": 1834.41, "end": 1834.51, "word": " الله", "probability": 0.9462890625}, {"start": 1834.51, "end": 1834.81, "word": " تعالى", "probability": 0.9803059895833334}, {"start": 1834.81, "end": 1834.91, "word": " و", "probability": 0.94580078125}, {"start": 1834.91, "end": 1835.29, "word": " يعطيكم", "probability": 0.9129638671875}, {"start": 1835.29, "end": 1835.75, "word": " العافية", "probability": 0.978515625}, {"start": 1835.75, "end": 1836.19, "word": " والسلام", "probability": 0.798095703125}, {"start": 1836.19, "end": 1836.75, "word": " عليكم", "probability": 0.925048828125}, {"start": 1836.75, "end": 1837.25, "word": " ورحمة", "probability": 0.9091796875}, {"start": 1837.25, "end": 1837.55, "word": " الله", "probability": 0.9736328125}, {"start": 1837.55, "end": 1838.51, "word": " وبركاته", "probability": 0.98466796875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1838.648875, "duration_after_vad": 1794.531249999996}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/oMo4psrRkQI_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/oMo4psrRkQI_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f06deadf6021b63a6ea60e9f9b5b46176799e964
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/oMo4psrRkQI_postprocess.srt
@@ -0,0 +1,212 @@
+1
+00:00:01,850 --> 00:00:05,590
+بسم الله الرحمن الرحيم، هنعرض تجربة عن ال optical
+
+2
+00:00:05,590 --> 00:00:12,570
+density و ال transmittance أول شي عندنا حوض زجاجي
+
+3
+00:00:12,570 --> 00:00:20,480
+فارغ، احنا بنطلع على الرسم أسفل الحوض الزجاجييعني
+
+4
+00:00:20,480 --> 00:00:24,400
+على ورقة تحت الحوض الزجاجي الضوء سقط على هذه
+
+5
+00:00:24,400 --> 00:00:29,220
+الورقة و الآن بنعكس باتجاه أعيننا .. باتجاه عينينا
+
+6
+00:00:29,220 --> 00:00:33,340
+يعني الضوء الصادر من الرسم هاي المنعكس من الرسم
+
+7
+00:00:33,340 --> 00:00:38,720
+هاي بده يخترق الزجاج ثم الهواء .. الزجاج طبعا قاع
+
+8
+00:00:38,720 --> 00:00:44,840
+الحوض ثم الهواء ثم يصل إلى أعيننا الآن الزجاج له
+
+9
+00:00:44,840 --> 00:00:52,790
+شفافية معينة و الهواءاللي له شفافية معينة ثم تصل
+
+10
+00:00:52,790 --> 00:00:57,910
+الرسمة إلى .. إلى أعيننا، الآن لما بدنا نضيف نضيف
+
+11
+00:00:57,910 --> 00:01:07,330
+مادة عبارة عن كورات زجاجية أو مطاطية شفافة عشان
+
+12
+00:01:07,330 --> 00:01:11,030
+نزيدالكثافة البصرية للوسط عشان نزيد الكثافة
+
+13
+00:01:11,030 --> 00:01:17,070
+البصرية للوسط ونشوف كيف الرسمة هتروح من تحت او من
+
+14
+00:01:17,070 --> 00:01:21,050
+امامنا لأن ال transmittance هيجل هتزيد الكثافة ال
+
+15
+00:01:21,050 --> 00:01:25,350
+optical density هتزيد فال transmittance هيجل فال
+
+16
+00:01:25,350 --> 00:01:33,730
+transmittance هيجل نشغل الفيديو هاي
+
+17
+00:01:33,730 --> 00:01:44,460
+الآن احنا بنزيد في الكثافةالان بدت تقريبا اشي قليل
+
+18
+00:01:44,460 --> 00:01:48,960
+اللى بينفذ قلنا اشي
+
+19
+00:01:48,960 --> 00:01:54,080
+اقل اللى بينفذ قلنا طبعا
+
+20
+00:01:54,080 --> 00:02:03,500
+لما بتزيد الكثافة للوسط تقريبا لا شيءبيظهر إلنا،
+
+21
+00:02:03,500 --> 00:02:07,360
+الآن هيرفع الرسمة و هيخلي في رسمة تانية مش ظاهرة
+
+22
+00:02:07,360 --> 00:02:11,840
+بالمرة، في رسمة تانية مش ظاهرة بالمرة، الآن بدنا
+
+23
+00:02:11,840 --> 00:02:18,140
+نخفف .. بدنا نخفف كثافة الوسط بإضافة الماءبإضافة
+
+24
+00:02:18,140 --> 00:02:21,340
+الماء بتصير الكثافة البصرية أو ال optical density
+
+25
+00:02:21,340 --> 00:02:26,420
+أقل فحنشوف إيش هيحصل معنا وكيف الرسمة التالية هو
+
+26
+00:02:26,420 --> 00:02:28,680
+شال الرسمة الأولى اللي كان رسمها و اللي كنا
+
+27
+00:02:28,680 --> 00:02:33,380
+شايفينها و هيخفف الكثافة البصرية ال optical
+
+28
+00:02:33,380 --> 00:02:37,640
+density و نشوف كيف ال transmittance هيزيد فبالتالي
+
+29
+00:02:37,640 --> 00:02:41,320
+هنشوف ال .. ال .. الاشي المكتوب بعد الرسمة فليه
+
+30
+00:02:41,320 --> 00:02:47,870
+نشاهد مع بعض الآن المياهلما تتخلل أو تيجي بين كرات
+
+31
+00:02:47,870 --> 00:02:55,950
+الشفافة هاي اللي إلها كثافة معينة بدأت الكثافة تخف
+
+32
+00:02:55,950 --> 00:03:00,430
+فظهر اسم الموقع طبعا اللي ناشر الفيديو
+
+33
+00:03:05,660 --> 00:03:10,520
+لأن صارت الكثافة البصرية قليلة لأنه يشفط الميه
+
+34
+00:03:10,520 --> 00:03:15,160
+تاني عشان يزيد الكثافة ال optical density ونشوف
+
+35
+00:03:15,160 --> 00:03:19,140
+كيف الاسم قاعد بيختفي لأن الضوء اللي وصلنا منه ل
+
+36
+00:03:19,140 --> 00:03:23,580
+transmittance بيجل كل ما لما بيجل وهذه شغلة واضحة
+
+37
+00:03:23,580 --> 00:03:28,800
+جدا انه قاعدين احنا يعني بيختفي من أمامنا الاسم
+
+38
+00:03:29,770 --> 00:03:33,790
+بالشكل اللي احنا شايفينه زيادة ال optical density
+
+39
+00:03:33,790 --> 00:03:41,590
+قل لل transmitted الان مرة تانية لما بيسحب الماء
+
+40
+00:03:41,590 --> 00:03:45,470
+لما
+
+41
+00:03:45,470 --> 00:03:46,370
+بيسحب الماء
+
+42
+00:03:49,290 --> 00:03:53,770
+بيتزيد الكثافة لأن الوسط أصبح مكون فقط من الكرار
+
+43
+00:03:53,770 --> 00:03:58,890
+وبالتالي يعني مافي transmittance أو قليل جدا لدرجة
+
+44
+00:03:58,890 --> 00:04:03,510
+أن احنا مش قادرين نميز الجسم أو الضوء اللي يشتغل
+
+45
+00:04:03,510 --> 00:04:08,520
+أكتر من الجسم اللي تحت الحوتقليل جدا اللى بيوصلنا
+
+46
+00:04:08,520 --> 00:04:12,740
+ل transmitted light وبالتالي ماقدرناش نشوفه لان
+
+47
+00:04:12,740 --> 00:04:17,500
+بخفف الكثافة مرة تانية عدة مرات بيجري هذه التجربة
+
+48
+00:04:17,500 --> 00:04:22,080
+وهذه بتدل ان العلاقة بين ال optical density للوسط
+
+49
+00:04:22,080 --> 00:04:26,240
+البصري وبين ال transmittance علاقة عكسية كل ما
+
+50
+00:04:26,240 --> 00:04:33,380
+زادت كثافة الوسط كل ماكل ما أقل ال transmittance
+
+51
+00:04:33,380 --> 00:04:37,840
+كل ما خفت كثافة الوسط كل ما زاد ال transmittance
+
+52
+00:04:37,840 --> 00:04:41,340
+كل ما زاد ال transmittance و عند هذا بنتوقف و
+
+53
+00:04:41,340 --> 00:04:45,600
+يعطيكم العافية والسلام عليكم ورحمة الله وبركة
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/pyp5znL34Y8.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/pyp5znL34Y8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..11aad086745790db1b8f7a7fe1dd623f7fa7181f
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/pyp5znL34Y8.srt
@@ -0,0 +1,1601 @@
+1
+00:00:01,530 --> 00:00:04,710
+بسم الله الرحمن الرحيم بنواصل محاضرات الـ physical
+
+2
+00:00:04,710 --> 00:00:10,070
+optics و توقفنا المرة الماضية عند موضوع الـ
+
+3
+00:00:10,070 --> 00:00:14,610
+Brewster angle و حكينا أنه الـ Brewster angle هي
+
+4
+00:00:14,610 --> 00:00:19,390
+عبارة عن زاوية سقوط بس زاوية سقوط خاصة، ايش يعني 
+
+5
+00:00:19,390 --> 00:00:24,010
+زاوية سقوط خاصة؟ أن الضوء لو سقط بهذه الزاوية
+
+6
+00:00:24,010 --> 00:00:30,520
+الجزء المنعكس منه كله عن بكرة أبي الجزء المنعكس الـ
+
+7
+00:00:30,520 --> 00:00:34,880
+reflected part بيكون كله polarized واتجاه الـ
+
+8
+00:00:34,880 --> 00:00:38,980
+polarization اتجاه الـ electric field parallel to
+
+9
+00:00:38,980 --> 00:00:43,820
+the optical interface أو to the surface اللي بتفصل
+
+10
+00:00:43,820 --> 00:00:47,340
+بين الـ two medium إذا فرنيل also showed that
+
+11
+00:00:47,340 --> 00:00:50,590
+reflected light reflected light tends to be
+
+12
+00:00:50,590 --> 00:00:53,990
+linearly polarized parallel to the interface هذا
+
+13
+00:00:53,990 --> 00:00:57,870
+إذا سقط بزاوية سقوط أي زاوية سقوط يعني بيكون
+
+14
+00:00:57,870 --> 00:01:02,830
+غالبيته polarized ممكن بعض يكون يعني مش polarized
+
+15
+00:01:02,830 --> 00:01:07,310
+reflected light is completely polarized completely
+
+16
+00:01:07,310 --> 00:01:09,910
+polarized يعني كل الـ reflected light بيكون
+
+17
+00:01:09,910 --> 00:01:14,360
+completely polarized if the angle of incidence
+
+18
+00:01:14,360 --> 00:01:19,280
+equals the Brewster angle ايش هي الـ Brewster angle؟
+
+19
+00:01:19,280 --> 00:01:25,780
+الـ Brewster angle معادلتها بسيطة تقول الـ Brewster
+
+20
+00:01:25,780 --> 00:01:32,640
+angle هي طبعا زاوية السقوط حسابها tan<sup>-1</sup> ناقص واحد
+
+21
+00:01:32,640 --> 00:01:39,100
+n<sub>T</sub> على n<sub>I</sub> tan<sup>-1</sup> ناقص واحد مقلوب ظل زاوية السقوط
+
+22
+00:01:39,100 --> 00:01:44,850
+تمام؟ أو مقلوب اللي هو الـ shift tan أو الـ arc tan
+
+23
+00:01:44,850 --> 00:01:48,210
+n<sub>T</sub> الـ refractive index بتاع المادة اللي رايح إلها
+
+24
+00:01:48,210 --> 00:01:53,530
+الضوء و n<sub>I</sub> الـ refractive index بتاع المادة اللي
+
+25
+00:01:53,530 --> 00:01:59,690
+سقط منها الضوء .. اللي سقط منها الضوء يعني الضوء
+
+26
+00:02:01,130 --> 00:02:04,890
+اللي هو unpolarized incident light ايش يعني
+
+27
+00:02:04,890 --> 00:02:08,270
+unpolarized يعني الـ electric field فيه بيكون
+
+28
+00:02:08,270 --> 00:02:11,470
+عشوائي الاتجاه مرة بيكون vertical مرة بيكون
+
+29
+00:02:11,470 --> 00:02:13,970
+oblique مرة بيكون horizontal اتجاه الـ electric
+
+30
+00:02:13,970 --> 00:02:21,270
+field بس بشكل غير منتظم لما بسقط الضوء بيصير عندي
+
+31
+00:02:21,270 --> 00:02:28,930
+جزء منه بيمر جزء منه بيمر وجزء منه بينعكس وجزء منه
+
+32
+00:02:28,930 --> 00:02:34,920
+بينعكس الآن إذا كان الضوء إذا كان الضوء سقط بزاوية
+
+33
+00:02:34,920 --> 00:02:39,760
+سقوط تساوي الـ Brewster angle هي رمزنالها بالرمز θ
+
+34
+00:02:39,760 --> 00:02:43,880
+P يعني θ بدل I حكينا θ<sub>P</sub> عشان كلمة
+
+35
+00:02:43,880 --> 00:02:49,660
+الـ Brewster طبعا هي انعكس جزء منه طبعا زاوية السقوط
+
+36
+00:02:49,660 --> 00:02:53,600
+تساوي زاوية الانعكاس قولا واحدا هذا قانون الانعكاس
+
+37
+00:02:53,600 --> 00:02:57,220
+بس الموضوع مش عن هيك بيحكي الموضوع إنه إذا الضوء
+
+38
+00:02:57,220 --> 00:03:03,060
+سقط بزاوية تساوي الـ Brewster angle طبعا الجزء المنعكس
+
+39
+00:03:03,060 --> 00:03:08,140
+كله بيكون completely polarized لو سقط عندي مائة
+
+40
+00:03:08,140 --> 00:03:12,980
+ألف شعاع وانعكسوا منهم ألف شعاع الألف شعاع كلهم
+
+41
+00:03:12,980 --> 00:03:16,640
+اللي انعكسوا بيكونوا completely polarized يعني في
+
+42
+00:03:16,640 --> 00:03:19,640
+اتجاه للـ polarization بتاعه وهذا الاتجاه بيكون
+
+43
+00:03:19,640 --> 00:03:23,420
+parallel to the surface زي ما احنا شايفين الخط هذا
+
+44
+00:03:23,420 --> 00:03:27,700
+اللي هو سطح الفاصل بين المادتين والخط هذا اللي هو
+
+45
+00:03:27,700 --> 00:03:30,960
+اتجاه الـ polarization تحت ضوء المنعكس، إذا الـ
+
+46
+00:03:30,960 --> 00:03:36,500
+electric field بيكون polarized ب .. باتجاه موازي
+
+47
+00:03:36,500 --> 00:03:41,560
+للـ surface اللي هي الـ service أو الـ optical interface
+
+48
+00:03:41,560 --> 00:03:46,200
+إذا ملاحظين حاجة ايضا اضافية بدنا نحكيها في حالة
+
+49
+00:03:46,200 --> 00:03:51,240
+سقوط الضوء بزاوية تساوي الـ Brewster angle بيكون الجزء
+
+50
+00:03:51,240 --> 00:03:55,540
+اللي انعكس والجزء اللي مر بينهم زاوية 90 درجة
+
+51
+00:03:55,540 --> 00:04:00,920
+بينهم زاوية 90 درجة بينتج من هذا إذا لاحظت في
+
+52
+00:04:00,920 --> 00:04:05,780
+تجربة ما إن الضوء المنعكس .. إن الضوء المنعكس .. و
+
+53
+00:04:05,780 --> 00:04:09,280
+الضوء اللي مار للمادة .. الزجاج أو الماء أو أي
+
+54
+00:04:09,280 --> 00:04:13,540
+مادة أخرى إذا الزاوية بين الـ reflected light و الـ
+
+55
+00:04:13,540 --> 00:04:17,880
+transmitted light تسعين درجة لازم أكون على يقين إن
+
+56
+00:04:17,880 --> 00:04:22,060
+الضوء اللي سقط .. سقط بزاوية تسمى أو تساوي الـ
+
+57
+00:04:22,060 --> 00:04:26,360
+Brewster angle في حالة سقوط الضوء بزاوية تساوي الـ
+
+58
+00:04:26,360 --> 00:04:30,900
+Brewster angle بيكون في عندي معلومتين أكيدتين لما
+
+59
+00:04:30,900 --> 00:04:34,580
+بسقط الضوء بزاوية تساوي الـ Brewster angle أول شي الـ
+
+60
+00:04:34,580 --> 00:04:38,380
+reflected light و الـ transmitted light بينهم زاوية
+
+61
+00:04:38,380 --> 00:04:42,240
+تسعين درجة تاني حاجة الـ reflected light كله
+
+62
+00:04:42,240 --> 00:04:47,200
+polarized واتجاه الـ polarization parallel to the
+
+63
+00:04:47,200 --> 00:04:51,580
+surface بنشوف شغل عملية بتوضع هذه القضية بنقول
+
+64
+00:04:51,580 --> 00:04:58,780
+كالآتي هي أنا عندي .. هي أنا عندي ضوء سقط من
+
+65
+00:04:58,780 --> 00:05:03,820
+الهواء إلى الزجاج سقط بزاوية سقوط 56.3 degree الجزء اللي انعكس منه هينعكس
+
+66
+00:05:03,820 --> 00:05:08,020
+بزاوية 56.3 degree ليش؟ لأن
+
+67
+00:05:08,020 --> 00:05:11,700
+زاوية السقوط تساوي زاوية الانعكاس حسب قانون
+
+68
+00:05:11,700 --> 00:05:15,580
+الانعكاس الآن θ<sub>T</sub> تساوي 33.7 حسب قانون الانكسار
+
+69
+00:05:23,340 --> 00:05:27,380
+حسب قانون الانكسار وقلنا لما الضوء بينتقل من وسط
+
+70
+00:05:27,380 --> 00:05:30,420
+أقل كثافة أو أقل في الـ refractive index لوسط
+
+71
+00:05:30,420 --> 00:05:33,900
+أعلى كثافة أو أعلى في الـ refractive index الشعاع
+
+72
+00:05:33,900 --> 00:05:37,680
+المنكسر أو المار بيقترب من الـ surface normal على
+
+73
+00:05:37,680 --> 00:05:43,060
+العموم احنا في عندنا الزاوية high والزاوية high لو
+
+74
+00:05:43,060 --> 00:05:47,580
+جمعناهم بيطلعوا 90 درجة بيطلعوا 90 درجة وهذا الكلام
+
+76
+00:05:48,530 --> 00:05:56,450
+بنقول 56.3 زائد 33.7 الناتج 90 طيب ليش احنا بدنا
+
+77
+00:05:56,450 --> 00:06:01,950
+نجمعهم؟ بدنا نجمعهم عشان في هدف آخر بدنا نصلهم إذا
+
+78
+00:06:01,950 --> 00:06:05,830
+كانوا هدول الزاويتين 90 درجة فالزاوية هاي
+
+79
+00:06:05,830 --> 00:06:12,510
+التالتة المتبقية بتكمل الـ 180 لأن هاي زاوية مستقيمة
+
+80
+00:06:12,510 --> 00:06:18,570
+180 درجة 180 درجة لما أطرح منها 90 بيظل عندي 90
+
+81
+00:06:18,570 --> 00:06:25,250
+180 لما أطرح منها 90 بيظل منها 90 خلينا احنا نشوف
+
+82
+00:06:25,250 --> 00:06:30,730
+هذه
+
+83
+00:06:30,730 --> 00:06:35,210
+الزاوية المستقيمة اللي بنقشرها بالجُس عبارة عن 180
+
+84
+00:06:35,210 --> 00:06:39,370
+درجة لو شيلنا منها 56.3 و 33.7 بيظل الزاوية
+
+85
+00:06:39,370 --> 00:06:42,570
+high الزاوية high عبارة عن 90 درجة طب برضه أنا
+
+86
+00:06:48,250 --> 00:06:53,570
+ليش بدي أصل لهذا الكلام بنقول كالآتي 180
+
+88
+00:06:53,570 --> 00:06:56,730
+ناقص
+
+89
+00:06:56,730 --> 00:07:05,170
+56.3 ناقص 33.7
+
+90
+00:07:05,170 --> 00:07:12,010
+point 7 من عشرة و يساوي 90 degree
+
+91
+00:07:14,380 --> 00:07:17,840
+اللي ضلت هي زاوية تساوي 90 degree ما معناه
+
+92
+00:07:17,840 --> 00:07:21,100
+الكلام هذا؟ معناه الكلام هذا إن هاي 90 degree
+
+93
+00:07:21,100 --> 00:07:25,720
+معناته الزاوية بين الشعاع المنعكس والشعاع المار
+
+94
+00:07:25,720 --> 00:07:29,640
+90 degree طب في هذه الحالة معناته الضوء قولا
+
+95
+00:07:29,640 --> 00:07:34,380
+واحدا سقط بزاوية سقوط تساوي الـ Brewster angle بزاوية
+
+96
+00:07:34,380 --> 00:07:38,100
+سقوط تساوي الـ Brewster angle ليش؟ لأنه كيف عرفنا أن
+
+97
+00:07:38,100 --> 00:07:43,050
+زاوية السقوط تساوي الـ Brewster angle؟ لأن الزاوية بين
+
+98
+00:07:43,050 --> 00:07:47,270
+الشعاع المنعكس والشعاع المار تساوي 90 degree
+
+99
+00:07:47,270 --> 00:07:53,750
+تساوي 90 degree زي ما احنا وضحنا قبل قليل لما
+
+100
+00:07:53,750 --> 00:07:57,770
+الزاوية بين الشعاع المنعكس والزاوية بين الشعاع
+
+101
+00:07:57,770 --> 00:08:01,470
+المنعكس والشعاع المار تساوي 90 degree بأعرف
+
+102
+00:08:01,470 --> 00:08:05,290
+فورا أنه زاوية السقوط تساوي الـ Brewster angle و
+
+103
+00:08:05,290 --> 00:08:08,930
+أيضا بأستنتج فورا أنه طالما سقط الضوء بـ Brewster
+
+104
+00:08:08,930 --> 00:08:13,870
+angle كل المنعكس بيكون polarized parallel to the
+
+105
+00:08:13,870 --> 00:08:18,520
+surface هذا الكلام احنا محتاجين نثبته ايضا
+
+106
+00:08:18,520 --> 00:08:22,080
+بالحسابات بنقول الـ refractive index بتاع الهواء
+
+107
+00:08:22,080 --> 00:08:26,280
+واحد والـ refractive index بتاع الـ glass 1.5
+
+108
+00:08:26,280 --> 00:08:32,880
+.. 1.5 فبالتالي أنا بدي احسب الـ Brewster angle
+
+109
+00:08:32,880 --> 00:08:39,020
+n<sub>I</sub> عندي واحد و n<sub>T</sub> 1.5 المعادلة بتقول
+
+110
+00:08:42,850 --> 00:08:47,870
+المعادلة بتقول لـ Brewster angle تساوي tan<sup>-1</sup> ناقص واحد
+
+111
+00:08:47,870 --> 00:08:52,790
+n<sub>T</sub> على n<sub>I</sub> بدنا نحسب ونشوف هل هذا بيطلع معنا 56.3 degree ولا ما بيطلعش معنا 56.3
+
+112
+00:08:52,790 --> 00:08:56,970
+degree بنقول احنا بنروح
+
+113
+00:08:56,970 --> 00:09:00,430
+على الدالة هنا tan<sup>-1</sup> n<sub>T</sub> اللي
+
+115
+00:09:07,810 --> 00:09:09,990
+هي 1.5
+
+116
+00:09:13,040 --> 00:09:21,300
+على n<sub>I</sub> واحد ده بيش طلع معانا الزاوية 56.3 degree 56.3
+
+117
+00:09:21,300 --> 00:09:24,900
+degree إذا فعلا هي الـ Brewster angle إذا فعلا هي الـ
+
+118
+00:09:24,900 --> 00:09:30,060
+Brewster angle اللي هي لما الضوء بيسقط بزاوية
+
+119
+00:09:30,060 --> 00:09:35,500
+الـ Brewster angle أول حاجة بتأكد إذا سقط بزاوية سقوط
+
+120
+00:09:35,500 --> 00:09:40,560
+تساوي الـ Brewster angle بتأكد أن الـ reflected light والـ
+
+121
+00:09:40,560 --> 00:09:44,700
+transmitted light بينهم زاوية 90 درجة تاني حاجة
+
+122
+00:09:48,380 --> 00:09:52,020
+بكون متأكد أن الـ reflected light كله polarized
+
+123
+00:09:44,700 --> 00:09:48,380
+بكون متأكد ان ال reflected light كله polarized 
+124
+00:09:52,020 --> 00:09:56,240
+parallel to the surface على فكرة أحد الوسائل
+
+125
+00:09:56,240 --> 00:09:59,820
+للحصول على polarized light linearly polarized
+
+126
+00:09:59,820 --> 00:10:04,180
+light linearly polarized light من unpolarized
+
+127
+00:10:04,180 --> 00:10:08,780
+light أنه بطريقة الانعكاس بطريقة الانعكاس بأسقط
+
+128
+00:10:08,780 --> 00:10:14,920
+ضوء مش polarized أو randomly polarized على سطح فاصل
+
+129
+00:10:14,920 --> 00:10:23,480
+بين مادتين ساعتها أنا هحصل على .. على طبعا .. على
+
+130
+00:10:23,480 --> 00:10:29,320
+.. يعني polarized light من randomly polarized
+
+131
+00:10:29,320 --> 00:10:33,300
+light طيب احنا الآن بدنا نشوف بين الهواء وبين
+
+132
+00:10:33,300 --> 00:10:36,500
+الماء جداش الـ Brewster angle .. جداش الـ Brewster angle
+
+133
+00:10:38,310 --> 00:10:43,270
+بين الهواء و بين الماء هاي أنا عندي الهواء الضوء
+
+134
+00:10:43,270 --> 00:10:47,110
+هيسقط من الهواء وهيروح على الماء قبل ما أخلي
+
+135
+00:10:47,110 --> 00:10:50,570
+الزاوية هاي تسعين بالتحريك .. بتحريك النموذج أنا
+
+136
+00:10:50,570 --> 00:10:55,890
+بدأ أحسبها وبعدين اجى أحرك النموذج على طريقة ايش
+
+137
+00:10:55,890 --> 00:11:03,030
+بتطلع معايا الزاوية بنقول tan<sup>-1</sup> ناقص واحد n<sub>T</sub> اللي
+
+138
+00:11:03,030 --> 00:11:07,670
+هو الماء 1.33 على n<sub>I</sub>
+
+139
+00:11:07,670 --> 00:11:12,870
+واحد فالمفروض ان انا تطلع عندي الـ Brewster angle 53.1 degree نرجع الآن
+
+140
+00:11:12,870 --> 00:11:16,630
+النموذج بنقول هي أنا عندي air هي عندي water ف أنا
+
+141
+00:11:21,470 --> 00:11:25,570
+بدي يكون عندي الـ Brewster angle زي ما طلعت اللي هي
+
+142
+00:11:16,630 --> 00:11:21,470
+النموذج بنقول هي أنا عندي air هي عندي water ف أنا 
+143
+00:11:25,570 --> 00:11:31,260
+زاوية سقوط 53.1 خلينا نشوف هي
+
+144
+00:11:31,260 --> 00:11:48,700
+53.1 
+
+145
+00:11:48,700 --> 00:11:52,860
+من 10 طبعا هذه الـ Brewster angle كيف عرفت أنها
+
+146
+00:11:52,860 --> 00:11:57,640
+الـ Brewster angle طبعا هذه الزاوية تساوي 53.1
+
+147
+00:11:57,640 --> 00:12:02,660
+أيضا لأنها هي زاوية الانعكاس وزاوية الانكسار تساوي
+
+148
+00:12:02,660 --> 00:12:06,240
+36.9 لو جمعنا 53.1 مع 36.9 نجمع
+
+149
+00:12:06,240 --> 00:12:10,780
+53.1 مع
+
+150
+00:12:10,780 --> 00:12:18,860
+53.1 
+
+151
+00:12:18,860 --> 00:12:25,300
+زائد 36.9 بيكون
+
+152
+00:12:25,300 --> 00:12:29,840
+الناتج 90 إذا المتبقي من الزاوية المستقيمة اللي
+
+153
+00:12:29,840 --> 00:12:34,800
+هو هذا المتبقي من الزاوية الكلية يساوي 90 طبعا
+
+154
+00:12:34,800 --> 00:12:39,320
+طالما يساوي 90 معناته الزاوية بين الشعاع الـ
+
+155
+00:12:39,320 --> 00:12:42,080
+reflected والشعاع اللي transmitted 90 معناته
+
+156
+00:12:42,080 --> 00:12:46,320
+هذه زاوية السقوط فعلا هي الـ Brewster angle وهذا
+
+157
+00:12:46,320 --> 00:12:49,840
+ينطبق على الحسابات اللي احنا قبل شوية اجرناها ان
+
+158
+00:12:49,840 --> 00:12:53,440
+زاوية السقوط أو زاوية الـ Brewster angle بين الهواء
+
+159
+00:12:53,440 --> 00:12:58,230
+والماء 53.1 degree إذا
+
+160
+00:12:58,230 --> 00:13:06,190
+الـ Brewster angle تساوي tan<sup>-1</sup> ناقص واحد n<sub>T</sub> على n<sub>I</sub> طيب
+
+161
+00:13:06,190 --> 00:13:10,090
+ايش فايدة الـ Brewster angle فايدة الـ Brewster angle إذا
+
+162
+00:13:10,090 --> 00:13:14,510
+الضوء سقط بزاوية سقوط تساوي الـ Brewster angle معناته
+
+163
+00:13:14,510 --> 00:13:19,850
+كل الضوء اللي انعكس بيكون linearly polarized
+
+164
+00:13:22,510 --> 00:13:32,050
+parallel to the surface كما توضح هذه الرسمة زي ما
+
+165
+00:13:32,050 --> 00:13:35,430
+احنا عارفين ان هاي الـ incident ray الشعاع الساقط
+
+166
+00:13:35,430 --> 00:13:38,970
+وهي الـ reflected ray هنا مش مرسوم الـ surface
+
+167
+00:13:38,970 --> 00:13:43,840
+normal ولا محددة زاوية السقوط ولا محددة زاوية
+
+168
+00:13:43,840 --> 00:13:47,760
+الانعكاس ولا حتى محددة زاوية المرور التي هي θ
+
+169
+00:13:47,760 --> 00:13:52,040
+T بس طالما الـ reflected ray و الـ transmitted ray
+
+170
+00:13:52,910 --> 00:13:57,410
+بينهم زاوية 90 degree معناته الـ incident ray أو
+
+171
+00:13:57,410 --> 00:14:02,290
+زاوية السقوط سقط بزاوية تساوي الـ Brewster angle
+
+172
+00:14:02,290 --> 00:14:05,110
+لأنني عرفت انه بين الـ reflected ray و الـ
+
+173
+00:14:05,110 --> 00:14:09,630
+transmitted ray في زاوية 90 درجة في زاوية 90
+
+174
+00:14:09,630 --> 00:14:15,690
+درجة الـ Brewster angle all the reflected light كل
+
+175
+00:14:15,690 --> 00:14:19,590
+الـ reflected light وهنا كلمة all مهمة جدا انه كل
+
+176
+00:14:19,590 --> 00:14:24,310
+اللي انعكس is linearly polarized but not all the
+
+177
+00:14:24,310 --> 00:14:28,470
+linearly polarized light is reflected يعني جزء من
+
+178
+00:14:28,470 --> 00:14:33,310
+الـ linearly polarized light الضوء سقط randomly
+
+179
+00:14:33,310 --> 00:14:38,830
+polarized ربما يكون الرسم
+
+201
+00:16:10,850 --> 00:16:16,450
+كله ينعكس أو جزء منه بيمر consequently وينتج من
+
+202
+00:16:16,450 --> 00:16:19,830
+هذا the transmitted light is a mixture of linearly 
+
+203
+00:16:19,830 --> 00:16:24,370
+and randomly polarized light وهذا الكلام واضح جدا
+
+204
+00:16:24,370 --> 00:16:27,470
+في هذه القضية، إيش يعني partially polarized؟ يعني
+
+205
+00:16:27,470 --> 00:16:30,870
+جزء منه polarized و جزء منه randomly أو .. أو
+
+206
+00:16:30,870 --> 00:16:33,670
+unpolarized أو خلّينا نقول randomly polarized
+
+207
+00:16:33,670 --> 00:16:37,650
+light جزء منه لمرة polarized، linearly polarized و
+
+208
+00:16:37,650 --> 00:16:42,330
+جزء منه يعني randomly أو unpolarized light بينما
+
+209
+00:16:42,330 --> 00:16:46,430
+اللي انعكس كله polarized طبعا احنا بنحكي كل هات
+
+210
+00:16:46,430 --> 00:16:50,310
+الكلام في حالة السقوط بزاوية سقوط تساوي الـ Brewster
+
+211
+00:16:50,310 --> 00:16:55,690
+angle و اللي حسابها بيتم بطريقة تان أس ناقص واحد
+
+212
+00:16:55,690 --> 00:17:02,910
+T على n I الآن نحكي عن زاوية سقوط أخرى، زاوية سقوط
+
+213
+00:17:02,910 --> 00:17:07,730
+أخرى اللي هي الـ critical angle، الـ critical angle
+
+214
+00:17:09,370 --> 00:17:13,610
+حكينا عنها في الـ Geometric Optics بس هنحكي عنها
+
+215
+00:17:13,610 --> 00:17:18,530
+أيضا في اللي هي الـ Physical Optics When light
+
+216
+00:17:18,530 --> 00:17:21,530
+moves from a higher to lower refractive index
+
+217
+00:17:21,530 --> 00:17:25,710
+medium, it will be completely reflected, total
+
+218
+00:17:25,710 --> 00:17:29,420
+internal reflection if the angle of incidence
+
+219
+00:17:29,420 --> 00:17:33,260
+exceeds the critical angle طبعاً لما الضوء بينتقل
+
+220
+00:17:33,260 --> 00:17:36,460
+من وسط أعلى في الـ refractive index يعني أعلى في
+
+221
+00:17:36,460 --> 00:17:39,960
+الكثافة لوسط أقل في الـ refractive index يعني أقل
+
+222
+00:17:39,960 --> 00:17:46,580
+في الكثافة إذا فاقت .. إذا فاقت زاوية السقوط
+
+223
+00:17:46,580 --> 00:17:50,620
+الزاوية الحرجة الـ critical angle سوف ينعكس كل
+
+224
+00:17:50,620 --> 00:17:57,480
+الضوء بالتالي في داخل المادة التي أتى منها الضوء
+
+225
+00:17:57,480 --> 00:18:02,920
+هينتقل من وسط أعلى في الكثافة اللي هو الزجاج ال
+
+226
+00:18:02,920 --> 00:18:07,840
+glass لوسط أقل في الكثافة طبعا لما الضوء بيسقط
+
+227
+00:18:07,840 --> 00:18:13,930
+بزاوية سقوط بسيطة، هنا زاوية السقوط 25 و 2 من 10 جزء
+
+228
+00:18:13,930 --> 00:18:20,830
+منه بيمر، طيب لو زودنا زاوية السقوط لسه فيه جزء
+
+229
+00:18:20,830 --> 00:18:24,950
+بيمر، لو زودنا .. هاي .. هاي الجزء اللي مر للهواء
+
+230
+00:18:24,950 --> 00:18:31,190
+انتقالا من الزجاج، كل ما زودنا زاوية السقوط بتزيد
+
+231
+00:18:31,190 --> 00:18:35,030
+زاوية الانكسار أو الـ angle of transmission theta T
+
+232
+00:18:35,030 --> 00:18:39,750
+بتزيد theta T لغاية ما نصل لـ critical angle
+
+233
+00:18:42,930 --> 00:18:47,190
+الآن كل ما زاد عن الـ critical angle انعكاس كامل
+
+234
+00:18:47,190 --> 00:18:54,210
+داخل الزجاج، يعني بمعنى لا يوجد .. لا يوجد أي يعني
+
+235
+00:18:54,210 --> 00:19:01,230
+مجال للضوء أنه يخترق، أنه يخترق، إذا عند سقوط الضوء
+
+236
+00:19:01,230 --> 00:19:04,570
+من الوسط الأعلى في الكثافة لوسط أقل في الكثافة
+
+237
+00:19:04,570 --> 00:19:09,790
+ساعتها إذا سقط بزاوية سقوط أكبر من الـ critical
+
+238
+00:19:09,790 --> 00:19:13,910
+angle اللي هي theta C ساعتها الضوء كله هينعكس
+
+239
+00:19:13,910 --> 00:19:18,330
+هيصير له total internal reflection مثال آخر بنشوف
+
+240
+00:19:18,330 --> 00:19:20,470
+الـ glass مع الـ water
+
+241
+00:19:24,340 --> 00:19:27,080
+الـ glass و الـ water الفرق في الـ refractive index
+
+242
+00:19:27,080 --> 00:19:31,320
+بتاعهم بسيط، بس الـ glass أعلى من الـ water في ال
+
+243
+00:19:31,320 --> 00:19:34,420
+refractive index إذا أن الضوء هينتقل من أعلى لأقل
+
+244
+00:19:34,420 --> 00:19:42,180
+إذا زادت زاوية السقوط عن الـ critical angle ساعتها
+
+245
+00:19:42,180 --> 00:19:49,620
+كل الضوء هينعكس داخل المادة اللي جاء منها، هيك الآن
+
+246
+00:19:49,620 --> 00:19:52,760
+احنا عدينا لـ critical angle فكل الضوء اللي سقط
+
+247
+00:19:52,760 --> 00:19:57,460
+بينعكس داخل الزجاج وبنتقلش للماء، إذا لـ critical
+
+248
+00:19:57,460 --> 00:20:02,040
+angle، لـ critical angle ونشوف كيف بنحسبها when
+
+249
+00:20:02,040 --> 00:20:06,190
+light moves from a higher to lower refractive index
+
+250
+00:20:06,190 --> 00:20:10,590
+medium it will be completely reflected وهذا يسمى
+
+251
+00:20:10,590 --> 00:20:14,450
+total internal reflection if the angle of
+
+252
+00:20:14,450 --> 00:20:18,770
+incidence exceeds the critical angle كيف تحسب ال
+
+253
+00:20:18,770 --> 00:20:23,660
+critical angle؟ احنا الـ Brewster angle حسبناها ten
+
+254
+00:20:23,660 --> 00:20:30,720
+أس ناقص واحد و T على و I الـ critical angle تحسب
+
+255
+00:20:30,720 --> 00:20:38,800
+sin أس ناقص واحد و T على و I طيب، بنقول
+
+256
+00:20:38,800 --> 00:20:42,620
+كالاتي، نيجي نحسب الـ critical angle بين مثلا
+
+257
+00:20:42,620 --> 00:20:51,540
+الزجاج والماء فبنقول nt اللي هي تاعة الماء، ضوء
+
+258
+00:20:51,540 --> 00:20:55,140
+رايح للماء و ni اللي هو سقط من الزجاج، بنقول
+
+259
+00:20:55,140 --> 00:21:08,220
+كالتالي sin أس ناقص واحد نت الماء على ni الزجاج،
+
+260
+00:21:08,220 --> 00:21:13,600
+إذا تطلع عندي الزاوية تقريبا 62.7 من 10، نرجع،
+
+261
+00:21:13,600 --> 00:21:18,970
+بنقول هنا احنا فاقنا الـ 62 و 7 من 10 لو جلّنا عن ال
+
+262
+00:21:18,970 --> 00:21:22,990
+62 و 7 من 10 إذا الضوء مر ليش؟ لأن الـ critical
+
+263
+00:21:22,990 --> 00:21:27,850
+angle زاوية سقوط لازم بين الميه و الزجاج أو بين
+
+264
+00:21:27,850 --> 00:21:31,190
+الزجاج و الميه تكون 62 و 7 من 10 زي ما ال
+
+265
+00:21:31,190 --> 00:21:34,510
+calculator أعطانيها، الـ critical angle بين الميه
+
+266
+00:21:34,510 --> 00:21:37,170
+اللي هي higher refractive index بتاعها اللي هي nt
+
+267
+00:21:37,170 --> 00:21:40,010
+المادة اللي راح إليها الضوء، و الزجاج المادة اللي
+
+268
+00:21:40,010 --> 00:21:43,010
+انطلق منها الضوء وصار منه الـ incidence صار السقوط
+
+269
+00:21:43,010 --> 00:21:48,710
+منه، المفروض الزاوية تساوي 62.7 أي شعاع بيسقط
+
+270
+00:21:48,710 --> 00:21:54,250
+بزاوية سقوط أكثر من 62.7 بينعكس كليا، الدليل هي
+
+271
+00:21:54,250 --> 00:22:03,090
+زاوية سقوط أكثر من 62.7، 62.9 كله انعكس، طيب لو أقل
+
+272
+00:22:03,090 --> 00:22:04,050
+بيقول 62
+
+273
+00:22:13,410 --> 00:22:19,090
+هي 62 و 5 من 10 اللي هي 62 و 5 من 10 أقل من 62 و 7
+
+274
+00:22:19,090 --> 00:22:23,730
+من 10، إذا جزء من الشعاع مر، جزء من الشعاع مر، طب لو
+
+275
+00:22:23,730 --> 00:22:29,490
+جلّنا عن 62 برضه الجزء بيمر، أكثر من 62 و 7 من 10
+
+276
+00:22:29,490 --> 00:22:35,030
+هنلاقي كل الشعاع .. كل الشعاع يصير 63 و 1 من 10
+
+277
+00:22:35,030 --> 00:22:38,650
+أكثر منه، طيب نحسب مرة ثانية بس لمواد ثانية، بنقول
+
+278
+00:22:38,650 --> 00:22:46,080
+احنا الآن بين الزجاج .. بين الزجاج و الهواء نحسب ال
+
+279
+00:22:46,080 --> 00:22:50,300
+critical angle الزجاج هو مادة السقوط و الهواء رايح
+
+280
+00:22:50,300 --> 00:22:55,480
+إليه، إذا هو مادة المرور فبنقول sin أس ناقص واحد
+
+281
+00:22:55,480 --> 00:23:01,100
+nt للهواء اللي هي واحد على 1.5 الزجاج اللي
+
+282
+00:23:01,100 --> 00:23:07,250
+هي ni، المفروض بين الزجاج .. بين الزجاج و الهواء ل
+
+283
+00:23:07,250 --> 00:23:11,030
+critical angle 41.8 من عشرة، نشوف
+
+284
+00:23:11,030 --> 00:23:16,430
+.. هاي عندي الـ glass و هاي عندي الهواء، إذا أي شعاع
+
+285
+00:23:16,430 --> 00:23:19,970
+بيسقط بزاوية سقوط أقل من 41.8 من
+
+286
+00:23:19,970 --> 00:23:22,750
+عشرة هيسقط بزاوية انكسار 37 اللي هي أقل
+
+287
+00:23:22,750 --> 00:23:26,690
+من 41 بيمر جزء منه، لما بنصل للـ 41 و
+
+288
+00:23:26,690 --> 00:23:28,510
+8 من عشرة
+
+289
+00:23:31,440 --> 00:23:34,080
+مافيش، هنا وصلنا احنا .. هاي الـ critical angle
+
+290
+00:23:34,080 --> 00:23:38,220
+الشعاع بيجري على السطح، إذا حد يعني أو إذا كان
+
+291
+00:23:38,220 --> 00:23:42,000
+واضح الأمور الشعاع بيجري على السطح، على .. زودنا عن
+
+292
+00:23:42,000 --> 00:23:44,940
+الـ critical angle هين، كجلّنا .. هي ك .. هي ك ..
+
+293
+00:23:44,940 --> 00:23:49,000
+احنا بنزود، أصبحنا أكثر من 41 و 8
+
+294
+00:23:49,000 --> 00:23:52,860
+من عشرة أصبح انعكاس كامل .. إذا total internal
+
+295
+00:23:52,860 --> 00:23:57,000
+reflection .. إذا total internal reflection فهذه
+
+296
+00:23:57,000 --> 00:24:05,070
+أمثلة .. طيب احنا بنقول بين الماء والهواء، بين الماء
+
+297
+00:24:05,070 --> 00:24:10,250
+والهواء، نحسب الـ critical angle نحسب
+
+298
+00:24:10,250 --> 00:24:13,430
+الـ critical angle هذه الأمثلة بتساعد الـ critical
+
+299
+00:24:13,430 --> 00:24:20,710
+angle الضوء رايح للهواء إذا 1 على 
+
+300
+00:24:20,710 --> 00:24:25,670
+1.333 إذا بيعطيني critical angle 48.6 من عشرة، 48.6 من عشرة
+
+301
+00:24:25,670 --> 00:24:32,650
+نشوف الآن عندي هي من الماء باتجاه الهواء، 48.6 من
+
+302
+00:24:32,650 --> 00:24:37,810
+عشرة إذا عدينا 48.6 من عشرة ربما يكون عندي هنا
+
+303
+00:24:37,810 --> 00:24:43,430
+أكثر من 48.6 من عشرة، واحد على تمام، okay خليني نشوف
+
+304
+00:24:48,350 --> 00:24:56,640
+ربما يكون في احنا بدنا نزيد عن 48 49.1% Total
+
+305
+00:24:56,640 --> 00:25:04,820
+Internal Reflection 48
+
+306
+00:25:04,820 --> 00:25:14,080
+.7% 48.6% Total Internal Reflection
+
+307
+00:25:16,300 --> 00:25:21,260
+على السريع مرور الضوء، على السريع مرور الضوء هي مثلا 6
+
+308
+00:25:21,260 --> 00:25:23,700
+و 40 مش 8 و 40 لسه في عندي مرور
+
+309
+00:25:26,800 --> 00:25:30,580
+هيعطيني 48.5 من عشرة أقل بـ 1 من 
+
+310
+00:25:30,580 --> 00:25:34,480
+عشرة degree من الـ critical angle أيضا مرضوء لأنه
+
+311
+00:25:34,480 --> 00:25:38,420
+بيسقط بزاوية سقوط أقل من الـ critical angle، أكثر من
+
+312
+00:25:38,420 --> 00:25:41,660
+الـ critical angle هيصير عندي total internal
+
+313
+00:25:41,660 --> 00:25:46,940
+reflection الآن في شيء يعني interesting اكتشفوه
+
+314
+00:25:46,940 --> 00:25:51,620
+العلماء فوجدوا أنه لو أنا عندي مادتين ثابتتين
+
+315
+00:25:52,080 --> 00:25:56,660
+مادتين ثابتتين هنا مثلا قولنا الـ water و الهواء و
+
+316
+00:25:56,660 --> 00:26:01,120
+طبعا الضوء بتحرك من مادة أعلى لمادة أقل لو حسبت ال
+
+317
+00:26:01,120 --> 00:26:04,620
+critical angle و حسبت الـ Brewster angle طبعا ال
+
+318
+00:26:04,620 --> 00:26:07,780
+Brewster angle لموضوع ثاني و الـ critical angle
+
+319
+00:26:07,780 --> 00:26:10,280
+لموضوع ثاني، الـ Brewster angle لموضوع ال
+
+320
+00:26:10,280 --> 00:26:13,280
+polarization أنه بنعكس كله polarized parallel to
+
+321
+00:26:13,280 --> 00:26:16,660
+the surface و الـ critical angle عشان ظاهرة ال
+
+322
+00:26:16,660 --> 00:26:20,280
+total internal reflection، لاقوا العلماء دائما و
+
+323
+00:26:20,280 --> 00:26:26,120
+أبدا الـ critical angle أكبر حجما من الـ Brewster angle
+
+324
+00:26:26,120 --> 00:26:30,080
+أكبر حجما من الـ Brewster angle نفبط هذا بالحسابات
+
+325
+00:26:30,080 --> 00:26:34,690
+بنقول كالاتي، عندي high water وعندي air هخليهم
+
+326
+00:26:34,690 --> 00:26:37,970
+مادتين ثابتتين مرة بدأ أحسب اللي طبعا الضوء بتتحرك
+
+327
+00:26:37,970 --> 00:26:44,630
+من الـ water ل الـ air للهواء، بدأ أحسب مرة ل
+
+328
+00:26:44,630 --> 00:26:48,510
+critical angle و مرة بدأ أحسب لـ Brewster angle
+
+329
+00:26:48,510 --> 00:26:52,720
+خلينا نحسبهم بالـ calculator بنقول الـ Critical
+
+330
+00:26:52,720 --> 00:26:56,600
+Angle حسبناها قبل شوية بين الهواء والماء بين
+
+331
+00:26:56,600 --> 00:27:00,580
+الهواء والماء، sin أو ناقص واحد 1 على 1 و
+
+332
+00:27:00,580 --> 00:27:03,900
+33 اذا تطلع 48 degree طيب 48 و
+
+333
+00:27:03,900 --> 00:27:06,420
+6 من عشرة degree هذه الـ Critical Angle
+
+334
+00:27:06,420 --> 00:27:11,080
+أنا بدأ احسب الـ Brewster Angle تان أو ناقص واحد 1
+
+335
+00:27:11,080 --> 00:27:16,720
+على 1.333 إذا هاي الـ critical
+
+336
+00:27:16,720 --> 00:27:21,020
+angle وهي الـ Brewster angle لنفس الظروف، دائما ال
+
+337
+00:27:21,020 --> 00:27:25,120
+critical angle أعلى من الـ Brewster angle، ممكن ثاني
+
+338
+00:27:25,120 --> 00:27:28,000
+يقول يمكن هذه صدفة، لأ خليني احنا ناخد مثال آخر
+
+339
+00:27:28,000 --> 00:27:33,540
+بنقول احنا عندنا هاي الزجاج و الهوى، الزجاج و الهوى
+
+340
+00:27:33,540 --> 00:27:37,560
+نحسب لهم الـ Brewster angle و الـ critical angle ال
+
+341
+00:27:37,560 --> 00:27:41,620
+critical angle sin أس ناقص واحد anti اللي هو
+
+342
+00:27:41,620 --> 00:27:45,340
+الهوى 1 على 1.5
+
+344
+00:27:48,530 --> 00:27:51,530
+تطلع 41.8 من عشرة بينما ال
+
+345
+00:27:51,530 --> 00:27:56,790
+critical angle كان sin أس ناقص واحد 1 على 1.5
+
+346
+00:27:56,790 --> 00:28:02,810
+إذا الـ critical angle 41.8 من
+
+347
+00:28:02,810 --> 00:28:06,290
+عشرة و تحت نفس الظروف و نفس المواد الـ Brewster
+
+348
+00:28:06,290 --> 00:28:09,850
+angle 33.6 من عشرة، إذا الـ critical
+
+349
+00:28:09,850 --> 00:28:15,210
+angle أكبر من الـ Brewster angle دائما، مثال ثالث ال
+
+350
+00:28:15,210 --> 00:28:16,050
+glass و الماء
+
+351
+00:28:18,960 --> 00:28:21,920
+الزجاج والماء، بدنا نحسب الـ critical angle و
+
+352
+00:28:21,920 --> 00:28:25,340
+الـ Brewster angle، الـ critical angle بنقول sin أقصى
+
+353
+00:28:25,340 --> 00:28:31,240
+ناقص واحد 1.333 على 1.5
+
+354
+00:28:31,240 --> 00:28:35,700
+بيطلع عندي 62.7 degree هذه الـ critical
+
+355
+00:28:35,700 --> 00:28:40,680
+angle بينما الـ Brewster angle تان أقصى ناقص واحد 1
+
+356
+00:28:40,680 --> 00:28:47,700
+.333 على 1.5، إيش بيطلع 41
+
+357
+00:28:47,700 --> 00:28:51,080
+.4، إذا دائما الـ critical angle تفوق ال
+
+358
+00:28:51,080 --> 00:28:54,360
+Brewster angle، تفوق الـ Brewster angle تحت نفس
+
+359
+00:28:54,360 --> 00:28:58,480
+الظروف Note that the critical angle always exceeds
+
+360
+00:28:58,480 --> 00:29:02,900
+the Brewster angle، Total Internal Reflection is
+
+361
+00:29:02,900 --> 00:29:05,780
+what prevents visualization of the anterior
+
+362
+00:29:05,780 --> 00:29:10,320
+chamber angle during slit lamp examination يعني
+
+363
+00:29:10,320 --> 00:29:14,420
+لما بيسقط الضوء على الـ anterior chamber angle و
+
+364
+00:29:14,420 --> 00:29:17,500
+بينعكس من الـ anterior chamber angle و بيجي يخرج من
+
+365
+00:29:17,500 --> 00:29:20,900
+القرنية تحدث له ظاهرة الـ Total Internal
+
+366
+00:29:20,900 --> 00:29:24,720
+Reflection لأنه بيسقط على سطح القرنية الأمامي و
+
+367
+00:29:24,720 --> 00:29:28,400
+بده يحاول يخترق للهواء يعني لمادة أقل كثافة بس
+
+368
+00:29:28,400 --> 00:29:32,100
+للأسف زاوية سقوطه على سطح القرنية الأمامي و
+
+369
+00:29:32,100 --> 00:29:36,680
+محاولة اختراقه من القرنية باتجاه الهواء هو جاي من
+
+370
+00:29:36,680 --> 00:29:39,880
+الـ anterior chamber angle بعد ما ضوناها بعد ما
+
+371
+00:29:39,880 --> 00:29:43,640
+ضوناها و انعكس الضوء منها مر من السطح الخلفي
+
+372
+00:29:43,640 --> 00:29:48,620
+للقرنية ثم ييجي يطلع من السطح الأمامي وسقط بزاوية
+
+373
+00:29:48,620 --> 00:29:52,200
+سقوط أكبر من الـ critical angle فصار له total
+
+374
+00:29:52,200 --> 00:29:57,700
+internal reflection in rare cases the cornea might
+
+375
+00:29:57,700 --> 00:30:01,380
+be distorted that the angle is visible without
+
+376
+00:30:01,380 --> 00:30:04,660
+gonioscopy إلا في حالات قليلة جدا أو حالات
+
+377
+00:30:04,660 --> 00:30:09,760
+استثنائية، أحيانا القرنية بتكون فيها
+
+401
+00:32:14,940 --> 00:32:19,390
+total internal reflection هنا زاوية ثانية يعني ممكن
+
+402
+00:32:19,390 --> 00:32:22,970
+حتى أشوف الـ peripheral written بالطريقة هاي هنا الـ
+
+403
+00:32:22,970 --> 00:32:27,770
+anterior chamber angle بقدر أشوفها بواسطة إضافة
+
+404
+00:32:27,770 --> 00:32:30,930
+مادة لزجة هذه العدسة الـ three mirror أو الـ two
+
+405
+00:32:30,930 --> 00:32:36,130
+mirror الـ three mirror وبالتالي بقدر بواسطة المادة
+
+406
+00:32:36,130 --> 00:32:38,950
+اللزجة اللي قريبة في الـ refractive index من
+
+407
+00:32:38,950 --> 00:32:43,730
+القرنية إني أكبر الـ critical angle أكبر الـ
+
+408
+00:32:43,730 --> 00:32:47,370
+critical angle  لإذ ملاحظين الـ critical angle
+
+409
+00:32:47,370 --> 00:32:50,330
+خلينا نقول احنا بين الـ glass و الهواء
+
+410
+00:32:53,770 --> 00:33:00,510
+تقريبا 41.8 تقريبا 41.8 critical angle كله بينعكس
+
+411
+00:33:00,510 --> 00:33:04,350
+طيب لو أنا خليت الهواء ماء يعني جربت الفرق في الـ
+
+412
+00:33:04,350 --> 00:33:07,710
+refractive index لأن الفرق بين الـ glass و الهواء
+
+413
+00:33:07,710 --> 00:33:11,450
+واحد و نص بينما بين الـ glass و الـ water أقل من هيك
+
+414
+00:33:11,450 --> 00:33:16,490
+فبالتالي الـ critical angle بتصير أكبر عشان أصل الـ
+
+415
+00:33:16,490 --> 00:33:19,790
+critical angle و كل الضوء ينعكس بدا يكون أنا وصلت
+
+416
+00:33:19,790 --> 00:33:25,960
+لـ 62 و أكثر فبالتالي .. بالتالي .. كل ما زاد الفرق
+
+417
+00:33:25,960 --> 00:33:29,140
+بين الـ two media في الـ refractive index كل ما زاد
+
+418
+00:33:29,140 --> 00:33:33,080
+الفرق بتكبر الـ critical angle وبالتالي بيصير صعب
+
+419
+00:33:33,080 --> 00:33:36,760
+نوصل لها يعني في كتير أشعة هتسقط بزاوية سقوط أقل
+
+420
+00:33:36,760 --> 00:33:42,060
+من الـ critical angle في هذه الحالة و ساعتها هيكون
+
+421
+00:33:42,060 --> 00:33:46,120
+بعض الأشعة تنفذ و توصل لعين الفاحص .. لعين الفاحص
+
+422
+00:33:46,120 --> 00:33:52,110
+وهذا هو الفكرة من قضية أن أحط مادة لزجة مادة لزجة
+
+423
+00:33:52,110 --> 00:33:56,830
+زي مادة الهيلون أو ما شابه عشان بدل ما يكون الفرق
+
+424
+00:33:56,830 --> 00:34:00,130
+في الـ refractive index بين القرنية والهواء بيكون
+
+425
+00:34:00,130 --> 00:34:02,770
+بين القرنية والمادة اللزجة أقل فبالتالي الـ
+
+426
+00:34:02,770 --> 00:34:06,610
+critical angle بتصير كبيرة وكتير من الأشعة هتسقط
+
+427
+00:34:06,610 --> 00:34:10,390
+بزاوية سقوط أقل من الـ critical angle وهتنفذ للـ
+
+428
+00:34:10,390 --> 00:34:13,990
+three mirror يعني هنا هتصطدم بالـ mirror هاي صورة
+
+429
+00:34:13,990 --> 00:34:19,290
+الـ mirror هنا هذا المنظر هيشوف الفحص مقابل له يعني
+
+430
+00:34:19,290 --> 00:34:22,950
+عين الفحص هتكون بهذا الاتجاه وهذا المنظر هيبينله
+
+431
+00:34:22,950 --> 00:34:26,630
+ثلاث مرايا وهذه العدسة المركزية هذه العدسة
+
+432
+00:34:26,630 --> 00:34:32,650
+المركزية وهيستطيع أنه يشوف اللي هو الـ anterior
+
+433
+00:34:32,650 --> 00:34:36,690
+chamber angle بدون ما يكون فيه عنده total internal
+
+434
+00:34:36,690 --> 00:34:40,290
+reflection هذه العدسة بيسموها عدسة الـ three mirror
+
+435
+00:34:40,290 --> 00:34:44,590
+lens الـ three mirror lens هي فيه عدسة مركزية هذه
+
+436
+00:34:44,590 --> 00:34:48,770
+هي حط تحتها .. هيحط تحتها من الناحية التانية مادة
+
+437
+00:34:48,770 --> 00:34:52,190
+لزجة و ألسقها بالعين و الأشعة اللي طالعة إذا بدي
+
+438
+00:34:52,190 --> 00:34:55,410
+أشوف الـ retina هتستخدم المرايتين هدولة اللي أنا
+
+439
+00:34:55,410 --> 00:34:58,750
+بأشر عليهم كل واحدة إلى أنحنها عشان تجيب جزء من
+
+440
+00:34:58,750 --> 00:35:01,890
+أطراف الشبكية بينما إذا بدأت أشوف الـ anterior
+
+441
+00:35:01,890 --> 00:35:07,030
+chamber angle بدي أنا أستخدم هذه المراية اللي هي
+
+442
+00:35:07,030 --> 00:35:12,220
+بشكل قبة هيك عاملة بشكل قبة هذا الموضوع اللي هو الـ
+
+443
+00:35:12,220 --> 00:35:15,520
+total internal reflection كيف أنه ممكن يزعجني في
+
+444
+00:35:15,520 --> 00:35:18,760
+فحص هذا و كيف التغلب اللي هو الـ anterior chamber
+
+445
+00:35:18,760 --> 00:35:23,540
+angle و كيف أنا أستطيع أني أتغلب عليه هنتوقف عند
+
+446
+00:35:23,540 --> 00:35:26,860
+هذه النقطة و المرة القادمة إن شاء الله تعالى هنحكي
+
+447
+00:35:26,860 --> 00:35:30,520
+عن موضوع الـ absorption of light و الـ transmission
+
+448
+00:35:30,520 --> 00:35:33,360
+of light و يعطيكم العافية و السلام عليكم و رحمة 
+
+449
+00:35:33,360 --> 00:35:33,540
+الله
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/qJVW0BKN9jg.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/qJVW0BKN9jg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f2ceabfebdcea717deb1a3a50f21fed428ac522a
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/qJVW0BKN9jg.srt
@@ -0,0 +1,1428 @@
+1
+00:00:01,580 --> 00:00:05,420
+بسم الله الرحمن الرحيم بنواصل مع محاضرات ال
+
+2
+00:00:05,420 --> 00:00:09,940
+physical optics واتوقفنا عند الأثر الثالث من آثار
+
+3
+00:00:09,940 --> 00:00:13,850
+ال laser على العين وphoto disruption يعني التمزيق
+
+4
+00:00:13,850 --> 00:00:18,910
+باللازر وأكثر شيء نستعمل فيه ال photo disruption
+
+5
+00:00:18,910 --> 00:00:24,070
+هو ال posterior capsule بتاعة ال crystalline lens
+
+6
+00:00:24,070 --> 00:00:28,170
+ال posterior capsule is transparent to visible and
+
+7
+00:00:28,170 --> 00:00:33,730
+near infrared light including ال wavelength بتاع
+
+8
+00:00:33,730 --> 00:00:38,760
+اللازر ال Nd-Yag Laser أو ال nd:yag Laser له طول موجي
+
+9
+00:00:38,760 --> 00:00:44,420
+واحد وستة من مائة مايكرو متر يعني ألف وأربع وستين
+
+10
+00:00:44,420 --> 00:00:47,960
+نانو متر بالضبط ألف وأربع وستين نانو متر بالضبط
+
+11
+00:00:47,960 --> 00:00:50,560
+طبعًا هذا الطول الموجي بتاع اللازر جاي في ال
+
+12
+00:00:50,560 --> 00:00:55,460
+infrared region طبعًا ممكن الـ الـ ال infrared
+
+13
+00:00:55,460 --> 00:00:59,060
+laser اللي هو ال Nd:Yag laser يعني يسلط على ال
+
+14
+00:00:59,060 --> 00:01:02,820
+posterior capsule حتى يعمل تمزيق في ال posterior
+
+15
+00:01:02,820 --> 00:01:06,620
+capsule إيش الـ الـ السبب؟ ليش احنا بدنا نعمل
+
+16
+00:01:06,620 --> 00:01:11,860
+تمزيق في ال posterior capsule؟ this type of laser
+
+17
+00:01:11,860 --> 00:01:16,460
+is pulsed so that the energy it produces is
+
+18
+00:01:16,460 --> 00:01:20,220
+released in a very short time and produce a large
+
+19
+00:01:20,220 --> 00:01:24,860
+momentary power يعني ال Nd:Yag laser بيشتغل بطريقة
+
+20
+00:01:24,860 --> 00:01:28,960
+ال pulse laser مش ال continuous laser بنذكر في ال
+
+21
+00:01:28,960 --> 00:01:32,590
+pulse laser كان في رسم بياني بيوضح الفرق بين ال
+
+22
+00:01:32,590 --> 00:01:38,870
+continuous laser و ال pulse laser مر معنا في فترات
+
+23
+00:01:38,870 --> 00:01:43,910
+سابقة هي ال pulsed laser أنه في فترة قصيرة جدا من
+
+24
+00:01:43,910 --> 00:01:47,410
+الزمن بينعطى جرعة كبيرة من ال laser power عالية
+
+25
+00:01:47,410 --> 00:01:53,270
+جدا لأنه على يعني كمية قليلة جدا من الزمن بعكس ال
+
+26
+00:01:53,270 --> 00:01:57,410
+continuous laser اللي بيكون كميته ممتدة على طول
+
+27
+00:01:57,410 --> 00:02:01,850
+الزمن وإنما ال pulsed laser طبعًا لما حكينا عن ال
+
+28
+00:02:01,850 --> 00:02:04,870
+photo coagulation اللي هو أول أثر من آثار ال
+
+29
+00:02:04,870 --> 00:02:10,910
+laser اللي هو يستخدم في علاج الشبكية اللي عند مرضى
+
+30
+00:02:10,910 --> 00:02:16,110
+السكري هذا يعتبر نوع من أنواع ال continuous laser
+
+31
+00:02:16,110 --> 00:02:20,230
+بيسموه ال argon laser اسم المادة المستخدمة أو ال
+
+32
+00:02:20,230 --> 00:02:23,030
+active medium هي مادة اللي هو ال argon أو غاز ال
+
+33
+00:02:23,030 --> 00:02:26,760
+argon و ال Argon Laser إنما اليوم احنا بنستخدم
+
+34
+00:02:26,760 --> 00:02:33,320
+نوع ثاني من ال laser اللي هو ال Nd-Yag ال Nd-Yag
+
+35
+00:02:33,320 --> 00:02:37,300
+Laser اللي بنعطه بشكل pulses بنعطه بشكل pulses و
+
+36
+00:02:37,300 --> 00:02:41,080
+بينهم فترات فيش فيها laser طبعًا ليش بنعطه بشكل
+
+37
+00:02:41,080 --> 00:02:45,120
+pulses عشان ينعطه في short time و بالتالي قدرته ال
+
+38
+00:02:45,120 --> 00:02:49,730
+power بتاعته تكون عالية جدا جدا عالية جدا جدا إذا
+
+39
+00:02:49,730 --> 00:02:53,530
+ال Nd:Yag laser اللي هنستخدمه لل posterior capsule
+
+40
+00:02:53,530 --> 00:02:57,390
+عشان نعمل فيها disruption بنسميه photo disruption
+
+41
+00:02:57,390 --> 00:03:03,650
+طاقته عالية جدا أو ال power بتاعته عالية جدا عشان
+
+42
+00:03:03,650 --> 00:03:07,530
+يمزق هذه ال capsule و هنشوف كيف تتم هذه القضية
+
+43
+00:03:07,530 --> 00:03:15,490
+الآن الآن بدنا نسأل نفسنا سؤال لماذا نحتاج إلى
+
+44
+00:03:15,490 --> 00:03:20,250
+تمزيق ال posterior capsule القضية عشان نفهمها بنقول
+
+45
+00:03:20,250 --> 00:03:24,030
+الناس اللي بتصير عندها cataract عتمة في عدسة
+
+46
+00:03:24,030 --> 00:03:28,050
+العين وبتجري عملية جراحية الـ capsule ما
+
+47
+00:03:28,050 --> 00:03:31,130
+بتنشال في عملية ال cataract وإنما بتبقى عشان يتم
+
+48
+00:03:31,130 --> 00:03:34,910
+زراعة عدسة عليها نشوف الآن عملية cataract هاي
+
+49
+00:03:34,910 --> 00:03:38,290
+عندنا إنسان عنده ميه بيضه زي ما احنا شايفين و بدنا
+
+50
+00:03:38,290 --> 00:03:40,930
+احنا نشوف ..
+
+51
+00:03:47,510 --> 00:03:54,030
+هذه العملية بيسموها بيسموها
+
+52
+00:03:54,030 --> 00:03:59,030
+ال phaco emulsification هاي عامل incision هنا فتحة
+
+53
+00:03:59,030 --> 00:04:03,460
+صغيرة في القرنية هذه طبعًا بيسموها الفتحة الجانبية
+
+54
+00:04:03,460 --> 00:04:06,360
+الآن هيعمل ال main incision أو الفتحة الرئيسية هنا
+
+55
+00:04:06,360 --> 00:04:09,380
+من المكان اللي بقشر عليه في ال mouse بيحقق المادة
+
+56
+00:04:09,380 --> 00:04:13,460
+لزجة عشان ما تهبطش العين بمجرد ما عملنا فتحة فيها
+
+57
+00:04:13,460 --> 00:04:17,040
+عشان ما تهبط القرانية و تلتصق بالعدسة هذه بيسموها
+
+58
+00:04:17,040 --> 00:04:19,940
+viscoelastic substance اللي تم حقنها الآن ال main
+
+59
+00:04:19,940 --> 00:04:24,300
+incision الفتحة الرئيسية الآن بيعمل بواسطة هذه
+
+60
+00:04:24,300 --> 00:04:29,080
+الأداة بيعمل فتحة مستديرة في ال anterior capsule
+
+61
+00:04:29,080 --> 00:04:30,360
+في الغلاف الأمامي
+
+62
+00:04:36,940 --> 00:04:43,000
+بنشيل منها جزء بشكل دائري طبعًا
+
+63
+00:04:43,000 --> 00:04:45,980
+هاي الـ anterior capsule ضروري جدا أن يكون بشكل
+
+64
+00:04:45,980 --> 00:04:49,900
+دائري هاي
+
+65
+00:04:49,900 --> 00:04:53,040
+الميه البيضا مبينة في مناطق صافية من العدسة بس في
+
+66
+00:04:53,040 --> 00:04:56,780
+المنطقة المركزية منها كلها سموها nuclear cataract
+
+67
+00:04:57,890 --> 00:05:03,770
+الآن تم إزالة جزء من الـ الآن قبل ما نبدأ
+
+68
+00:05:03,770 --> 00:05:06,830
+بالخطوة الثانية حابب أنا أعلم في الميه البيضا احنا
+
+69
+00:05:06,830 --> 00:05:10,170
+بنشيل ال crystalline lens بنشيل ال nucleus و ال
+
+70
+00:05:10,170 --> 00:05:15,090
+cortex بتاعة ال lens بنخلي ال posterior capsule
+
+71
+00:05:15,090 --> 00:05:19,690
+كلها و جزء اللي هو المتصل فيها من ال anterior
+
+72
+00:05:19,690 --> 00:05:23,350
+capsule الجزء الطرفي أو ال peripheral part of the
+
+73
+00:05:23,350 --> 00:05:28,370
+anterior capsule الآن بده يقوم بحقن ماء ما بين ..
+
+74
+00:05:28,370 --> 00:05:32,090
+بين الـ الكابسول اللي شيلنا جزء منها الآن اللي
+
+75
+00:05:32,090 --> 00:05:35,730
+شيلنا ال central part منها الآن و بده يحقن بينها
+
+76
+00:05:35,730 --> 00:05:39,750
+.. بين حواف الكابسول و بين ال crystalline lens
+
+77
+00:05:39,750 --> 00:05:42,810
+solution
+
+78
+00:05:42,810 --> 00:05:47,570
+محلول على أساس أنه يفصل .. يفصل كل crystalline
+
+79
+00:05:47,570 --> 00:05:51,670
+lens عن الكابسول عن الكابسول نشوف كيف بنعمل هذه
+
+80
+00:05:51,670 --> 00:05:55,860
+القضية هو الآن جاع بيحقق و بيحرك في ال
+
+81
+00:05:55,860 --> 00:06:00,160
+crystalline lens عشان تتحرك عشان ما تضل ملتصقة
+
+82
+00:06:00,160 --> 00:06:04,480
+في الكابسول الغلاف بتاعها لأنه لازم الكابسول يضل و
+
+83
+00:06:04,480 --> 00:06:08,180
+ال crystalline lens نفسها اللي هي جوا الكابسول
+
+84
+00:06:08,180 --> 00:06:11,820
+لازم تنشال بواسطة عملية بيسموها ال phaco
+
+85
+00:06:11,820 --> 00:06:16,420
+emulsification أو عملية الشفط بتاعة ال crystalline
+
+86
+00:06:16,420 --> 00:06:19,920
+lens هاي الجهاز بتاع ال phaco emulsification الآن
+
+87
+00:06:19,920 --> 00:06:28,140
+هيبدأ بشفط العدسة بالتدريج لغاية
+
+88
+00:06:28,140 --> 00:06:33,280
+ما هيخلصها كلها الآن هيقوم بقسمها إلى قطعتين كبيرتين
+
+89
+00:06:33,280 --> 00:06:36,860
+الآن
+
+90
+00:06:36,860 --> 00:06:42,430
+زي ما بنلاحظ الآن هتقسم لقطعتين كبيرتين هيبدأ في شفط
+
+91
+00:06:42,430 --> 00:06:51,230
+كل نصف من العدسة لوحده لغاية ما ينهي هذه القضية
+
+92
+00:06:51,230 --> 00:06:54,730
+طبعًا
+
+93
+00:06:54,730 --> 00:06:59,910
+بستخدم ال ultrasound الموجات فوق الصوتية في تفتيت
+
+94
+00:06:59,910 --> 00:07:03,750
+العدسة وبعدين بيقوم بشفطها خلص النص الأول، الآن
+
+95
+00:07:03,750 --> 00:07:09,230
+النص الثاني هذه عملية الـ cataract بواسطة الـ phaco
+
+96
+00:07:09,230 --> 00:07:14,790
+emulsification يعني بواسطة الشفط طبعًا جرح صغير جدا
+
+97
+00:07:14,790 --> 00:07:21,150
+الآن بيبقى المنطقة اللي احنا شايفينها ما تبقى اللي
+
+98
+00:07:21,150 --> 00:07:25,610
+يسمونه ال cortex ال cortex القشرة بتاعة ال
+
+99
+00:07:25,610 --> 00:07:29,530
+crystalline lens اللي بده يبدأ يتخلص منها يشفطها
+
+100
+00:07:29,530 --> 00:07:35,630
+عشان تبقى عنده فقط الكابسول الخلفي المحفظة الخلفية
+
+101
+00:07:35,630 --> 00:07:40,230
+للعدسة اللي هي الغلاف الخلفي للعدسة والجزء الطرفي
+
+102
+00:07:40,230 --> 00:07:43,890
+من الغلاف الأمامي اللي متصل مع الجزء الخلفي إذا
+
+103
+00:07:43,890 --> 00:07:49,940
+ملاحظين هنا .. إذا ملاحظين هنا هاي حافة .. حافة الـ
+
+104
+00:07:49,940 --> 00:07:52,680
+anterior capsule الجزء اللي انشال وضايل الباقي
+
+105
+00:07:52,680 --> 00:07:56,480
+منها اللي هو أنا بعشر عليه بالماوس هذا الباقي متصل
+
+106
+00:07:56,480 --> 00:08:01,380
+مع الجزء الخلفي أو المحفظة الخلفية بتاعة العدسة
+
+107
+00:08:01,380 --> 00:08:07,300
+لأن لازم تخلص من كل ال cortex وبعدين بيجوا بزراعة
+
+108
+00:08:07,300 --> 00:08:11,720
+عدسة بقوة معينة يتم حسابها وفق معادلات معينة
+
+109
+00:08:18,220 --> 00:08:23,720
+أيو بتخلص جاع من ما تبقى من ال cortical matter
+
+110
+00:08:23,720 --> 00:08:30,860
+عملية
+
+111
+00:08:30,860 --> 00:08:38,320
+دقيقة و
+
+112
+00:08:38,320 --> 00:08:42,220
+طبعًا تتطلب خبرة عالية .. تتطلب خبرة عالية
+
+113
+00:08:52,020 --> 00:08:57,380
+أنا بيحقن مرة ثانية مادة لزجة عشان تمهيدا لزراعة
+
+114
+00:08:57,380 --> 00:09:02,700
+العدسة العدسة هنا هيحقنها .. هيحقنها دي بيسموها
+
+115
+00:09:02,700 --> 00:09:07,540
+foldable intraocular lens أو foldable IOL
+
+116
+00:09:07,540 --> 00:09:10,980
+intraocular lens من الجروح الصغير الجروح الصغير
+
+117
+00:09:10,980 --> 00:09:14,300
+عرضه تقريبا من اثنين واثنين من عشرة ملي لثلاثة
+
+118
+00:09:14,300 --> 00:09:19,900
+ملي حسب ال knife أو المشرط اللي استخدموه عبارة عن
+
+119
+00:09:19,900 --> 00:09:25,500
+مشرط مصنوع من الألماس نشوف كيف بده يحقن العدسة هذه
+
+120
+00:09:25,500 --> 00:09:30,900
+العدسة حقًا هذه foldable بتنفرد لحالها في داخل
+
+121
+00:09:30,900 --> 00:09:35,720
+الكابسول اللي احنا ما شيلناهاش يعني في المكان
+
+122
+00:09:35,720 --> 00:09:40,200
+الأصلي للعدسة في المكان الأصلي للعدسة طيب، الآن
+
+123
+00:09:40,200 --> 00:09:44,540
+فدي أنوه على شيء في هنا دعامات، دعامتين، هاي أنتم
+
+124
+00:09:44,540 --> 00:09:47,740
+شايفين طرف الدعامة العلوية وفي دعامة زيها في
+
+125
+00:09:47,740 --> 00:09:52,550
+الأسفل دولة بيسموهم ال haptics ال haptics الدعامات
+
+126
+00:09:52,550 --> 00:09:55,770
+وهذا الجزء الدائري من العدسة اللي زرعناها بيسموه
+
+127
+00:09:55,770 --> 00:09:59,630
+ال optic يعني هو نفسه العدسة الحقيقية اللي هتكون
+
+128
+00:09:59,630 --> 00:10:03,190
+مقام العدسة اللي شيلناها اللي كان فيها الميه
+
+129
+00:10:03,190 --> 00:10:04,530
+البيضاء نكمل
+
+130
+00:10:08,710 --> 00:10:12,010
+الآن بيزيل المادة اللي زي الجامد لازم تظل عشان
+
+131
+00:10:12,010 --> 00:10:17,150
+ما ترفعش ضغط العين هيك انتهت أو جربت تنتهي عملية
+
+132
+00:10:17,150 --> 00:10:21,010
+الميه البيضاء الآن هذه الشيء اللي بيعملوا و بيعملوا
+
+133
+00:10:21,010 --> 00:10:25,070
+بياض في الهدى هو بيحقن في .. في سمك القرنية بيحقن
+
+134
+00:10:25,070 --> 00:10:31,690
+محلول أو بيحقن saline محلول ملحي أو يعني محلول
+
+135
+00:10:31,690 --> 00:10:36,150
+ملحي متوازن عشان يعني تنتفخ ألياف الكولاجين و تصد
+
+136
+00:10:36,150 --> 00:10:41,270
+الجروح بدون حاجة للخياطة الآن الجرح زي شايفين لما
+
+137
+00:10:41,270 --> 00:10:46,190
+حقن صار في عندي whitening هنا عشان .. هنا الجرح
+
+138
+00:10:46,190 --> 00:10:51,590
+الجانبي اللي بدى فيه طبعًا بيحقن فيه سمكه مية بحيث
+
+139
+00:10:51,590 --> 00:10:56,630
+أنه يصير whitening الآن بتأكد أن هذه الجروح
+
+140
+00:10:56,630 --> 00:11:00,410
+مابتسيلش بيسموها self sealing بدون غرز الآن أصبحت
+
+141
+00:11:00,410 --> 00:11:05,830
+عندي العدسة مزروعة وصافية وخلصت عملية ال cataract
+
+142
+00:11:05,830 --> 00:11:11,110
+الآن مع علاقة هذا الأمر مع علاقة هذا الأمر في
+
+143
+00:11:11,110 --> 00:11:17,230
+موضوع ال photo disruption الآن عشان نعرف علاقة هذا
+
+144
+00:11:17,230 --> 00:11:22,690
+الأمر بدنا نيجي احنا نستعرض بعض الصورة بنقول هنا
+
+145
+00:11:22,690 --> 00:11:28,710
+cataract mature cataract هنا عندنا right cataract برضه
+
+146
+00:11:28,710 --> 00:11:32,030
+mature left eye normal هاي الشكل الطبيعي لل pupil
+
+147
+00:11:32,030 --> 00:11:37,450
+أنه بيبين أسود يعني مش زي ال pupil أو اللي خلفه
+
+148
+00:11:37,450 --> 00:11:40,550
+فيه ميه بيضاء في ال crystalline lens في ال
+
+149
+00:11:40,550 --> 00:11:43,890
+crystalline lens الآن هذه أنواع من العدسات اللي
+
+150
+00:11:43,890 --> 00:11:47,010
+تزرع هذا نوع وهذا نوع في أنواع كثيرة من العدسات
+
+151
+00:11:47,010 --> 00:11:49,490
+هاي احنا لو روحنا على العرض المكبر
+
+152
+00:11:51,940 --> 00:11:55,060
+هذه العدسة في مكانها وهذه ال posterior capsule
+
+153
+00:11:55,060 --> 00:12:00,260
+وهذه جزء من ال anterior capsule اللي الحافة مبينة
+
+154
+00:12:00,260 --> 00:12:05,020
+متعرجة بس الآن بيعتمدوا الحافة المستديرة تماما في
+
+155
+00:12:05,020 --> 00:12:08,040
+ال anterior capsule اللي من خلالها هيتم شفط الميه
+
+156
+00:12:08,040 --> 00:12:13,970
+البيضاء أطراف ال anterior capsule بتكمل من عند ال
+
+157
+00:12:13,970 --> 00:12:16,870
+equator بتاع ال lens وبتكمل ل ال posterior
+
+158
+00:12:16,870 --> 00:12:21,490
+capsule العدسة مفروض تزرع جوا ال capsule جوا محفظة
+
+159
+00:12:21,490 --> 00:12:24,730
+ل crystalline lens بعد ما نكون شيلنا ل crystalline
+
+160
+00:12:24,730 --> 00:12:29,300
+lens هذه نفس الشيء هذه نوع ثالث من العدسات لما
+
+161
+00:12:29,300 --> 00:12:33,520
+بنشوف الدوائر هاي هذه multifocal intraocular lens
+
+162
+00:12:33,520 --> 00:12:37,700
+طبعًا العدسات اللي احنا عرضناها monofocal يعني أما
+
+163
+00:12:37,700 --> 00:12:41,560
+بتصحح النظر للبعيد يكون النظر جيد للبعيد و بده
+
+164
+00:12:41,560 --> 00:12:44,360
+نضارات للقراءة يعني هذه العدسات ما بتعمل
+
+165
+00:12:44,360 --> 00:12:49,660
+accommodation فتم اختراع ال multifocal IOL اللي
+
+166
+00:12:49,660 --> 00:12:53,800
+شايفين شكل عبارة عن يعني مقاطع أو يعني عبارة عن
+
+167
+00:12:53,800 --> 00:12:59,700
+عدسة مصنوعة من مادة ال acrylic بس يعني مكونة من
+
+168
+00:12:59,700 --> 00:13:03,560
+يعني segments مكونة من segments و هنيجي لوظيفتها
+
+169
+00:13:03,560 --> 00:13:08,020
+يعني كيف .. كيف بتشتغل ك multifocal في حين إذا هذا
+
+170
+00:13:08,020 --> 00:13:11,280
+نوع آخر من العدسة هنا زي ما حكينا هي ال posterior
+
+171
+00:13:11,280 --> 00:13:15,100
+capsule من بينها هي العدسة داخل المحفظة و حواف ال
+
+172
+00:13:15,100 --> 00:13:18,580
+anterior capsule موجودة حواف ال anterior capsule
+
+173
+00:13:18,580 --> 00:13:22,020
+الآن نيجي للموضوع إيش علاقة ال cataract و علاقة ال
+
+174
+00:13:22,020 --> 00:13:26,820
+intraocular lens في ال photo disruption هذا الشخص
+
+175
+00:13:26,820 --> 00:13:31,320
+عمل عملية cataract بعد فترة من الزمن أشهر صار في
+
+176
+00:13:31,320 --> 00:13:34,880
+عندي تكاثر خلايا على ال posterior capsule وصار في
+
+177
+00:13:34,880 --> 00:13:40,820
+عتمة عتمة الآن احنا ال IOL أمام وهي خلفها .. هي حتى
+
+178
+00:13:40,820 --> 00:13:44,920
+الـ الحافة بتاعتها الـ Haptic بتاعها يعني مبين
+
+179
+00:13:44,920 --> 00:13:49,220
+طرفها مع التوسيع وهنا معتمة جدا .. معتمة جدا
+
+180
+00:13:49,220 --> 00:13:55,650
+فبالتالي لابد من إزالة جزء من ال Posterior Capsule
+
+181
+00:13:55,650 --> 00:13:59,990
+بس مش بعملية، الآن بدأ أستعمل الـ YAG Laser الـ
+
+182
+00:13
+
+201
+00:15:21,200 --> 00:15:26,000
+هنا منظر مكبر هذه بيسموهم ال-blood cells الخلايا
+
+202
+00:15:26,000 --> 00:15:30,860
+المنفوخة هاي هذه أيضا بتشوش على الرؤية كتير هذه
+
+203
+00:15:30,860 --> 00:15:34,920
+الخلايا تكاثرت وصارلها proliferation على ال
+
+204
+00:15:34,920 --> 00:15:37,840
+posterior على سطح ال-posterior capsule طبعا مكانها
+
+205
+00:15:37,840 --> 00:15:44,010
+خلف العدسة هنامنظر بيوضح before capsulotomy بعد ما
+
+206
+00:15:44,010 --> 00:15:48,850
+استعملنا الـYAG laser طبعا هي ال-IOL هي حفتها
+
+207
+00:15:48,850 --> 00:15:52,550
+طبعا هي تشغل كل المساحة هذه هذا المنظر المعتم اللي
+
+208
+00:15:52,550 --> 00:15:57,210
+شايفينه خلفها لأن بعد ما فتحنا فتحة في نسيج
+
+209
+00:15:57,210 --> 00:16:00,930
+البوستيريور الكابسول أصبح يورى السائل الزجاجي من ورا
+
+210
+00:16:00,930 --> 00:16:05,210
+وبالتالي المنظر صافي جدا بمعنى هذا الإنسان هيكون
+
+211
+00:16:05,210 --> 00:16:08,510
+يرى بشكل واضح جدا ممكن الإنسان يقول طب ليش ما
+
+212
+00:16:08,510 --> 00:16:11,590
+نزلناها كلها لأن هنا .. هنا العين أو البقبق اللي
+
+213
+00:16:11,590 --> 00:16:15,230
+بيبقى الموسع فبالتالي لما يرجع لحجمه الطبيعي هيكون
+
+214
+00:16:15,230 --> 00:16:19,870
+كل ال .. كل اللي ضايل يعني .. يعني هي .. هيغطي
+
+215
+00:16:19,870 --> 00:16:22,590
+المناطق هي .. هيغطي المناطق هي .. هتضل المناطق
+
+216
+00:16:22,590 --> 00:16:26,030
+الصافية هي اللي جاية central هي اللي جاية central
+
+217
+00:16:26,370 --> 00:16:32,210
+فبالتالي هنا أيضًا .. هنا واضح ال-optic وهذا ال-
+
+218
+00:16:32,210 --> 00:16:35,410
+haptic أحد الدعامات فيه دعامة تانية مش موجودة في
+
+219
+00:16:35,410 --> 00:16:39,610
+المنظر وواضح ال-PCO ال-posterior capsule opacity
+
+220
+00:16:39,610 --> 00:16:46,090
+وواضح بعد ما عملنا فتحة بالياج ليزر مزقنا ال-
+
+221
+00:16:46,090 --> 00:16:49,310
+posterior capsule كيف صار الأمر صافي جدا في
+
+222
+00:16:49,310 --> 00:16:53,190
+المنتصف طبعا هذه المناطق هيغطيها .. هتغطيها ال-
+
+223
+00:16:53,190 --> 00:16:57,270
+iris لما اتعاود لحجمها الطبيعي بعد ما يروح أثر ال-
+
+224
+00:16:57,270 --> 00:17:01,110
+dilatation بعد ما يروح أثر ال-dilatation اذا احنا
+
+225
+00:17:01,110 --> 00:17:06,610
+بنستخدم ال .. ال-yaag laser ال-yaag laser اللي
+
+226
+00:17:06,610 --> 00:17:09,190
+تمزيق ال-posterior capsule إذا the posterior
+
+227
+00:17:09,190 --> 00:17:12,270
+capsule is transparent بالأساس ال-posterior
+
+228
+00:17:12,270 --> 00:17:16,630
+capsule بتكون شفافة to visible and infrared light
+
+229
+00:17:16,630 --> 00:17:21,610
+including ..يعني بتمرج ال-visible light و بتمرج ال-
+
+230
+00:17:21,610 --> 00:17:25,450
+near infrared light بما في الطول الموجي بتاع ال-
+
+231
+00:17:25,450 --> 00:17:28,910
+Nd:YAG glazer بمعنى أثر المعلوم هذه بتقوللي أن ال-Nd:YAG
+
+232
+00:17:28,910 --> 00:17:34,060
+glazer بيستطيع أنه يصل لل-posterior capsule عشان
+
+233
+00:17:34,060 --> 00:17:38,120
+احنا مانضلش محتارين هدولة أربع عناصر نيوديميوم
+
+234
+00:17:38,120 --> 00:17:44,500
+نيوديميوم يتريوم ألمينيوم جارنيت الألمينيوم معروف
+
+235
+00:17:44,500 --> 00:17:49,520
+اليتريوم اليتريوم هو عنصر كيميائي والنيوديميوم
+
+236
+00:17:49,520 --> 00:17:52,500
+عنصر كيميائي واليتريوم عنصر كيميائي والألمينيوم
+
+237
+00:17:52,500 --> 00:17:56,320
+عنصر كيميائي الجارنيت اللي هو العقيق العقيق وكلنا
+
+238
+00:17:56,320 --> 00:17:59,120
+سمعناه في العقيق إذا ال-active medium في هذا ال-
+
+239
+00:17:59,120 --> 00:18:03,540
+laser هو عبارة عن خليط من هذه المواد الأربعة لما
+
+240
+00:18:03,540 --> 00:18:08,420
+بينتج منهم الليزر بيكون طول الموجي واحد صحيح و 600
+
+241
+00:18:08,420 --> 00:18:12,720
+ميكرو متر عشان نحوله لنانو متر بدنا نضرب في ألف
+
+242
+00:18:12,720 --> 00:18:16,760
+يعني ألف وستين نانو متر أو ألف واربعة وستين نانو
+
+243
+00:18:16,760 --> 00:18:22,390
+متر طيب بهذا الليزر بيستطيع أنه يصل للبوستيريور
+
+244
+00:18:22,390 --> 00:18:25,750
+كابسول نعم بيستطيع انه يصل للبوستيريور كابسول ممكن
+
+245
+00:18:25,750 --> 00:18:29,470
+انسان يسأل طب انا هذا ال-laser غير مرئي لأنه
+
+246
+00:18:29,470 --> 00:18:32,710
+infrared laser طوله الموجي بيقول انه infrared
+
+247
+00:18:32,710 --> 00:18:36,230
+معناته احنا مابنشوفوش كيف بدأ أسلطه على
+
+248
+00:18:36,230 --> 00:18:39,430
+البوستيريور كابسول وانا شخصيا مش شايفه بنقول سؤال
+
+249
+00:18:39,430 --> 00:18:44,220
+منطقي للغاية في حالات ما يكون ال-laser غير مرئي ..
+
+250
+00:18:44,220 --> 00:18:49,280
+غير مرئي بيتم مرافقته ب-laser آخر مرئي يعني بيكون
+
+251
+00:18:49,280 --> 00:18:53,300
+في عندي أنا بسلط ال-laser المرئي إذا أعملت
+
+252
+00:18:53,300 --> 00:18:57,080
+focusing على ال-posterior capsule لل-laser المرئي
+
+253
+00:18:57,080 --> 00:19:02,860
+معناته تلقائيا .. تلقائيا بيكون ال-laser الغير مرئي
+
+254
+00:19:02,860 --> 00:19:05,700
+اللي يقول يا laser بيكون أيضا focused على ال-
+
+255
+00:19:05,700 --> 00:19:08,660
+posterior capsule ال-laser الأول اللي أنا بستعين
+
+256
+00:19:08,660 --> 00:19:12,000
+فيه عشان يساعدني في ال-focusing بيسموه ال-aiming
+
+257
+00:19:12,000 --> 00:19:15,500
+laser ال-aiming laser اللي هو أيش بيساعدني في
+
+258
+00:19:15,500 --> 00:19:19,080
+الوصول للهدف أو انه اعمل focusing لل-non visible
+
+259
+00:19:19,080 --> 00:19:23,460
+laser اذا في laser اخر مرافق الهدف هو بس يساعدني
+
+260
+00:19:23,460 --> 00:19:26,820
+ان اقرا ان انا عملت focusing على ال-posterior
+
+261
+00:19:26,820 --> 00:19:31,250
+capsule طيب، الآن نحكي عن ال-laser، this type of
+
+262
+00:19:31,250 --> 00:19:35,810
+laser is pulsed laser لما بنقارنه بال-Argon Laser
+
+263
+00:19:35,810 --> 00:19:39,650
+اللي كنا نعمل فيه photo coagulation للشبكية هذا ك-
+
+264
+00:19:39,650 --> 00:19:44,070
+continuous laser بينما هذا pulsed laser يعني بنعطى
+
+265
+00:19:44,070 --> 00:19:48,810
+على جرعات في فترات زمانية قصيرة جدا ليش؟ so the
+
+266
+00:19:48,810 --> 00:19:52,270
+energy it produces is released in a very short
+
+267
+00:19:52,270 --> 00:19:56,370
+time ليش بديها في very short time producing large
+
+268
+00:19:56,370 --> 00:20:00,310
+momentary power لأنه بدي power أو قدرة عالية جدا
+
+269
+00:20:00,310 --> 00:20:05,030
+وقت عالي جدا Also, the laser beam is focused
+
+270
+00:20:05,030 --> 00:20:08,650
+concentrating the power into a very small area،
+
+271
+00:20:08,650 --> 00:20:13,550
+إذا أنا بعطيه بشكل pulsed على جرعات، في very short
+
+272
+00:20:13,550 --> 00:20:18,070
+time، في very small area، فبترتفع عندي القدرة بشكل
+
+273
+00:20:18,070 --> 00:20:22,810
+هائل جدا، فبتمزق النسيج، كيف بيحصل هذه القضية؟ In
+
+274
+00:20:22,810 --> 00:20:27,140
+the vicinity of the focus في المنطقة اللي انا ركزت
+
+275
+00:20:27,140 --> 00:20:30,960
+في المحيط اللي انا ركزت فيه ال-laser هذا ال-YAG
+
+276
+00:20:30,960 --> 00:20:34,740
+laser ال-electrons are stripped from their atoms
+
+277
+00:20:34,740 --> 00:20:38,800
+by ionization but they quickly recombine which
+
+278
+00:20:38,800 --> 00:20:42,240
+produces a spark and acoustic wave that
+
+279
+00:20:42,240 --> 00:20:45,440
+mechanically disrupts the posterior capsule نيجي
+
+280
+00:20:45,440 --> 00:20:49,100
+نفهم هذه القضية لما بيكون في عندي power عالية
+
+281
+00:20:49,100 --> 00:20:55,240
+power عالية الإلكترونات بتفلت من ذراتها وهذا بتسمى
+
+282
+00:20:55,240 --> 00:20:59,320
+plasma .. plasma إيش يعني plasma؟ يعني إحنا الذرّة
+
+283
+00:20:59,320 --> 00:21:02,700
+موجودة شكل الذرّة الطبيعي إنه في عندنا و فيها
+
+284
+00:21:02,700 --> 00:21:06,540
+بروتونات مشحونة موجبة حواليها إلكترونات مشحونة سالب
+
+285
+00:21:06,540 --> 00:21:09,900
+ب .. ب .. ب .. مجذوبة إليها و بتدور حواليها يعني
+
+286
+00:21:09,900 --> 00:21:12,660
+هدولة بتتحركوا مع بعض أو موجودين في ال .. في ال ..
+
+287
+00:21:12,660 --> 00:21:16,380
+في الفراق في مكان واحد لما بتيجي طاقة هائلة
+
+288
+00:21:16,380 --> 00:21:20,160
+بتفصلهم عن بعض بنقول في .. بتكوّر عندي خليط من
+
+289
+00:21:20,160 --> 00:21:25,070
+الإلكترونات و البروتونات وبالتالي هذا بسميهوش بقدرش
+
+290
+00:21:25,070 --> 00:21:27,750
+أسميه ذرّة لأن الذرّة إلها شكل معين لازم تكون
+
+291
+00:21:27,750 --> 00:21:30,970
+بروتونات في النواو وإلكترونات حواليها وأحيان
+
+292
+00:21:30,970 --> 00:21:34,850
+بيكون نيوترونات هذا مش شكل ذرّة هذا الإلكترونات
+
+293
+00:21:34,850 --> 00:21:41,310
+لحاله و البروتونات لحاله هي إلكترونات وهي بروتونات
+
+294
+00:21:41,940 --> 00:21:45,900
+سايبة في بعض يعني مش شكل منتظر فهذا بتسمى plasma
+
+295
+00:21:45,900 --> 00:21:50,540
+خليط plasma طيب الآن اللي بيحصل لما أنا بوجه طاقة
+
+296
+00:21:50,540 --> 00:21:53,440
+ال-laser طبعا هذا مثال على شيء آخر غير ال-laser بس
+
+297
+00:21:53,440 --> 00:21:58,480
+لتوضيح الفكرة بنقول لما بوجه طاقة ال-laser على ال-
+
+298
+00:21:58,480 --> 00:22:01,880
+posterior capsule في منطقة ال-posterior capsule ال-
+
+299
+00:22:01,880 --> 00:22:04,180
+posterior capsule محيط فيها سوائل اللي هو ال-
+
+300
+00:22:04,180 --> 00:22:09,760
+vitreous من ورا وال-aqueous من الأمامهذه الذرات
+
+301
+00:22:09,760 --> 00:22:13,620
+بإلكترونات تحت هذه السوائل في منطقة مسلط ال-YAG
+
+302
+00:22:13,620 --> 00:22:17,620
+Laser بيصير stripping أو انفصال للإلكترونات عن
+
+303
+00:22:17,620 --> 00:22:24,380
+اللي هي الأنوية بنفصل الإلكترون عن نواته طبعا في
+
+304
+00:22:24,380 --> 00:22:30,760
+العديد من الذرات ويرجع فورابينكمش تاني، بيرجع
+
+305
+00:22:30,760 --> 00:22:35,060
+للنواة، بيتمدد، بيهرب من النواة، وبعدين بيرجع
+
+306
+00:22:35,060 --> 00:22:39,240
+تاني للنواة، طب يترى إيش اللي بيحصل إذا انكمش
+
+307
+00:22:39,240 --> 00:22:43,960
+تاني، طيب، إذا in the vicinity، في محيط ال-focus
+
+308
+00:22:43,960 --> 00:22:48,340
+تاع ال-laser، electrons are stripped from their
+
+309
+00:22:48,340 --> 00:22:53,080
+atoms، بيتم نزع، نزع الإلكترونات من الذرات
+
+310
+00:22:53,080 --> 00:22:57,000
+بتاعتها، بواسطة عملية ال-ionization، نتيجة ال-
+
+311
+00:22:57,000 --> 00:23:01,140
+power العالية تاعة ال-laser طيب وقفة الأمور لعند
+
+312
+00:23:01,140 --> 00:23:05,180
+هنا لأ، but quickly الإلكترونات recombine، بيرجعوا
+
+313
+00:23:05,180 --> 00:23:10,760
+تاني لذراتهم، طيب رجوعهم، يعني تمددهم وهروبهم من
+
+314
+00:23:10,760 --> 00:23:17,940
+ذراتهم، و ثم رجوعهم الفوري إلها، بيحدث spark شرارة
+
+315
+00:23:17,940 --> 00:23:22,840
+and acoustic wave وموجة صوتية that mechanically
+
+316
+00:23:22,840 --> 00:23:26,520
+disrupts the posterior capsule الموجة الصوتية هاي
+
+317
+00:23:26,520 --> 00:23:32,200
+بتمزق بالصوت .. بالصوت بتمزق ال-posterior capsule
+
+318
+00:23:32,200 --> 00:23:36,280
+ال-spark الشرارة اللي بتحدث نتيجة تمدد الإلكترونات
+
+319
+00:23:36,280 --> 00:23:42,540
+ثم .. ثم انكماشها تاني ال-recombination هترجع
+
+320
+00:23:42,540 --> 00:23:49,800
+لذراتها تاني ال-spark هذا بيشبه ال-برق أو أو أو ال-
+
+321
+00:23:49,800 --> 00:23:55,060
+برق الضائل جدا كأنه صارت بالضبط مثل برق الشتاء مثل
+
+322
+00:23:55,060 --> 00:23:57,960
+البرق الضوء اللي احنا بنشوفه في الشتاء إذا the
+
+323
+00:23:57,960 --> 00:24:01,740
+spark is essentially a miniature lightning bolt
+
+324
+00:24:01,740 --> 00:24:06,080
+يعني كأنها شرارة برق شتاء بس miniature يعني صغيرة
+
+325
+00:24:06,080 --> 00:24:10,480
+جدا and the acoustic wave is analogous to thunder
+
+326
+00:24:10,480 --> 00:24:15,480
+والموجة الصوتية المرافقة لهذه العملية تشبه الرعد
+
+327
+00:24:15,480 --> 00:24:20,900
+تشبه الرعد إذا لما ال-laser بينعطى ال-laser وظيفته
+
+328
+00:24:20,900 --> 00:24:25,720
+فقط إنه قدرته عالية الوقت بتاعه عالية بينزع
+
+329
+00:24:25,720 --> 00:24:28,600
+الإلكترونات في المنطقة اللي صلت عليها بنزع
+
+330
+00:24:28,600 --> 00:24:32,580
+الإلكترونات من ذراتها ولكن هذه الإلكترونات فورا
+
+331
+00:24:32,580 --> 00:24:36,700
+بتروح بترجع لذراتها تمدد الإلكترونات بنزعها من
+
+332
+00:24:36,700 --> 00:24:40,800
+ذراتها من مداراتها ثم انكمشة تاني وعودتها لذراتها
+
+333
+00:24:40,800 --> 00:24:45,660
+بيحدث لي spark بيحدث لي شرارة وبيحدث لي في نفس الوقت
+
+334
+00:24:45,660 --> 00:24:51,600
+acoustic wave الشرارة بتشبه البرق وال-acoustic wave
+
+335
+00:24:51,600 --> 00:24:55,660
+بتشبه الرعد ال-acoustic wave هي اللي بتمزق ال-
+
+336
+00:24:55,660 --> 00:24:58,380
+posterior capsule هي اللي بتمزق ال-posterior
+
+337
+00:24:58,380 --> 00:25:02,600
+capsule during a photodisruption procedure it is
+
+338
+00:25:02,600 --> 00:25:06,200
+the mechanical اللي هي ال-acoustic wave and not
+
+339
+00:25:06,200 --> 00:25:09,380
+the laser light itself that breaks the capsule
+
+340
+00:25:09,380 --> 00:25:14,230
+ضروري ننتبه أن الموجة الصوتية الصادرة هي اللي
+
+341
+00:25:14,230 --> 00:25:17,890
+بتمزق ال-posterior capsule وليس ال-laser بنفسه، طب
+
+342
+00:25:17,890 --> 00:25:23,010
+ال-laser إيش وظيفته؟ إنه يعملي الخطوة الأولى، إنه
+
+343
+00:25:23,010 --> 00:25:26,990
+يعني ينزع الإلكترونات من ذراتها في المنطقة اللي هم
+
+344
+00:25:26,990 --> 00:25:31,130
+صلط عليها، ثم تعود الإلكترونات تنكمش لأن الأنوية
+
+345
+00:25:31,130 --> 00:25:36,650
+هتجذبها بسرعة هائلة وبالتالي هذا التمدد والانكماش
+
+346
+00:25:36,650 --> 00:25:40,990
+اللي .. اللي حدث في .. في .. في جزء بسيط للغاية من
+
+347
+00:25:40,990 --> 00:25:47,170
+الزمن هذا كأنه صار عندي شرارة وكأنه صار عندي موجة
+
+348
+00:25:47,170 --> 00:25:51,130
+صوتية تشبه الرعد وهذه الموجة الصوتية هي اللي بتمزق
+
+349
+00:25:51,130 --> 00:25:52,710
+ال-posterior capsule
+
+350
+00:25:56,990 --> 00:26:02,570
+نجي الآن نشوف على حقيقة الأمر فيديو بيوضح اللي هو
+
+351
+00:26:02,570 --> 00:26:06,290
+موضوع
+
+352
+00:26:06,290 --> 00:26:12,330
+الآن
+
+353
+00:26:12,330 --> 00:26:17,240
+ب .. ب simulation إن كيف بتتم زراعة عدسة الآن
+
+354
+00:26:17,240 --> 00:26:21,640
+العدسة مزروعة صار opacification صار صار عتامة تامة
+
+355
+00:26:21,640 --> 00:26:25,540
+فيها نتيجة تكاثر خلايا الآن بيجي ال-YAG laser بيعمل
+
+356
+00:26:25,540 --> 00:26:28,400
+فتحة فيها الآن هنشوفها على حقيقة الأمر بس هذا
+
+357
+00:26:28,400 --> 00:26:33,580
+simulation هذا simulation الآن هنحاول نشوف إيش
+
+358
+00:26:33,580 --> 00:26:40,120
+هيعمل ك ..
+
+359
+00:26:40,120 --> 00:26:43,600
+هاي ال-posterior capsule على فكرة هاي multifocal
+
+360
+00:26:43,600 --> 00:26:51,410
+IOL نشوف الصوت بارك يكون إنه turned cloudy هاي
+
+361
+00:26:51,410 --> 00:26:57,730
+العتامة خلف العدسة الآن بدأ يعمل laser هذا ال-
+
+362
+00:26:57,730 --> 00:27:03,710
+aiming laser ال-YAG laser بدأت تفتح فقط خلال الفتحة
+
+363
+00:27:03,710 --> 00:27:09,230
+الفتحة الصغيرة بدأت تفتح فقط خلال الفتحة الفتحة
+
+364
+00:27:09,230 --> 00:27:09,770
+الصغيرة بدأت تفتح فقط خلال الفتحة الفتحة الصغيرة
+
+365
+00:27:09,770 --> 00:27:10,730
+بدأت تفتح فقط خلال الفتحة الفتحة الصغيرة بدأت تفتح
+
+366
+00:27:10,730 --> 00:27:12,550
+فقط خلال الفتحة الفتحة الصغيرة بدأت تفتح فقط خلال
+
+367
+00:27:12,550 --> 00:27:14,010
+الفتحة الفتحة الصغيرة بدأت تفتح فقط خلال الفتحة
+
+368
+00:27:14,010 --> 00:27:18,070
+الفتحة الصغيرة بدأت تفتح فقط خلال الفتحة الفتحة
+
+369
+00:27:18,070 --> 00:27:24,230
+الصغيرة بدأت تفتح فقط خلال الفتحة الفتحة الصغيرة
+
+370
+00:27:24,230 --> 00:27:28,000
+بدأت تفتح فقط خلال ال-posterior capsule طبعا هذا
+
+371
+00:27:28,000 --> 00:27:30,180
+ما بيأثر على العدسة زي ما أنا شايف دي عدسة
+
+372
+00:27:30,180 --> 00:27:31,700
+multifocal اهو أقل
+
+373
+00:27:40,990 --> 00:27:44,230
+وهيك احنا بنكون يعني عرفنا كيف بيتم .. طبعا هذه
+
+374
+00:27:44,230 --> 00:27:47,550
+الفتات بتاع ال-posterior capsule بيتأثر في ال-
+
+375
+00:27:47,550 --> 00:27:52,410
+vitreous و بيتم ذوبانه و امتصاصه بعد ذلك يعني ما
+
+376
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uHrQ0Hu7IPc.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uHrQ0Hu7IPc.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2923c9a20fabc095e15270da57a5ec3fc6684b64
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uHrQ0Hu7IPc.srt
@@ -0,0 +1,119 @@
+1
+00:01:05,410 --> 00:01:13,210
+دهر مغناطيسية تتجلى عن اتحاد مجالين متعامدين وعامدين
+
+2
+00:01:13,210 --> 00:01:20,950
+على خط انتشارهما ويتذبذب في جميع المستويات وهذا ما
+
+3
+00:01:20,950 --> 00:01:28,970
+يسمى بالضوء غير المستقطب ولكن بطريقة ما نستطيع
+
+4
+00:01:28,970 --> 00:01:35,190
+تحويل الضوء غير المستقطب إلى ضوء مستقطب يتذبذب
+
+5
+00:01:35,190 --> 00:01:43,210
+مجاله الكهربائي في مستوى واحد وهل هذا ممكن؟ نعم
+
+6
+00:01:43,210 --> 00:01:50,140
+بطريقتين: إما استقطاب بالترشيح أو استقطاب بالانعكاس
+
+7
+00:01:50,140 --> 00:01:56,920
+فأما بالنسبة للاستقطاب بالترشيح فهو ينتج عن أن
+
+8
+00:01:56,920 --> 00:02:03,080
+جزيئات بعض المواد تترتب على شكل سلاسل طويلة تسمح 
+
+9
+00:02:03,080 --> 00:02:08,580
+بمرور الموجات الضوئية التي يكون مجالها الكهربائي
+
+10
+00:02:08,580 --> 00:02:16,210
+عامودي على هذه السلاسل وموازيا لمحور نفاذها ولكن
+
+11
+00:02:16,210 --> 00:02:25,450
+ماذا نقصد بمحور النفاذ؟ هو محور يسمح بمرور الموجات
+
+12
+00:02:25,450 --> 00:02:31,010
+الضوئية التي يكون اهتزاز مجالها الكهربائي موازيا 
+
+13
+00:02:31,010 --> 00:02:38,550
+له ويحجب البقية وأما بالنسبة للاستقطاب بالانعكاس
+
+14
+00:02:38,550 --> 00:02:42,850
+فإما أن يكون جزئيا أو كليا
+
+15
+00:02:46,440 --> 00:02:52,160
+إذا انتقل شعاع ضوئي بين وسطين بزاوية بين صفر
+
+16
+00:02:52,160 --> 00:03:00,320
+و90 فعندها يستقطب الشعاع المنعكس جزئيا وإذا
+
+17
+00:03:00,320 --> 00:03:05,000
+كانت الزاوية بين الشعاع المنعكس والمنكسر 90
+
+18
+00:03:05,000 --> 00:03:10,620
+درجة أي عندما يتعامد الشعاعين المنعكس والمنكسر
+
+19
+00:03:10,620 --> 00:03:15,780
+عندها يستقطب الشعاع المنعكس كليا
+
+20
+00:03:19,310 --> 00:03:24,230
+ويعتبر استخدام النظارات الشمسية لتقليل التوهج
+
+21
+00:03:24,230 --> 00:03:28,990
+باستقطاب الضوء المنعكس عن الطرق مثالا واضحا
+
+22
+00:03:28,990 --> 00:03:35,030
+للاستقطاب بالانعكاس وكذلك مرشحات الاستقطاب التي
+
+23
+00:03:35,030 --> 00:03:41,310
+يستخدمها المصورون في عدسات الكاميرات والسؤال هنا
+
+24
+00:03:42,190 --> 00:03:47,570
+كيف يمكننا معرفة مدى انخفاض شدة الضوء عند عبوره
+
+25
+00:03:47,570 --> 00:03:54,490
+خلال مرشح استقطاب؟ هنا يأتي دور العالم Malus الذي 
+
+26
+00:03:54,490 --> 00:04:00,150
+توصل إلى العلاقة التالية عند
+
+27
+00:04:00,150 --> 00:04:05,510
+وضع مرشحي استقطاب بحيث يكون محورا استقطابهما
+
+28
+00:04:05,510 --> 00:04:15,180
+متوازين تنفذ خلالهما أكبر كمية من الضوء، أما إذا كان
+
+29
+00:04:15,180 --> 00:04:27,780
+محور الاستقطاب متعامدين فلن ينفذ أي ضوء. شكرا 
+
+30
+00:04:27,780 --> 00:04:28,640
+معلمتي
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uHrQ0Hu7IPc_raw.json b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uHrQ0Hu7IPc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f454df5442217c26ad8af846fa53fea1963bed24
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uHrQ0Hu7IPc_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 8439, "start": 65.41, "end": 84.39, "text": "دهر مغناطيسية تتج عن اتحاد مجالين متعامدين وعامدين على خط انتشارهما ويتذبذب في جميع المستويات وهذا ما يسمى بالضوء الغير مستقطع", "tokens": [3215, 3224, 2288, 3714, 17082, 1863, 41193, 1829, 3794, 10632, 6055, 2655, 7435, 18871, 1975, 2655, 5016, 18513, 3714, 7435, 6027, 9957, 44650, 3615, 10943, 3215, 9957, 4032, 3615, 10943, 3215, 9957, 15844, 16490, 9566, 16472, 2655, 8592, 9640, 3224, 15042, 4032, 36081, 8848, 3555, 8848, 3555, 8978, 10874, 2304, 40228, 9673, 14851, 45865, 9307, 37037, 15730, 19446, 7251, 38251, 7578, 20666, 11242, 2407, 38207, 6024, 118, 13546, 3714, 14851, 47432, 3615], "avg_logprob": -0.10584331865180029, "compression_ratio": 1.5890410958904109, "no_speech_prob": 0.0017614364624023438, "words": [{"start": 65.41, "end": 65.81, "word": "دهر", "probability": 0.6595458984375}, {"start": 65.81, "end": 67.17, "word": " مغناطيسية", "probability": 0.95361328125}, {"start": 67.17, "end": 68.31, 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"end": 172.86, "word": " وتسعين", "probability": 0.8687744140625}, {"start": 172.86, "end": 174.26, "word": " فعندها", "probability": 0.91650390625}, {"start": 174.26, "end": 175.72, "word": " يستقطب", "probability": 0.9205322265625}, {"start": 175.72, "end": 176.44, "word": " الشعاع", "probability": 0.9876302083333334}, {"start": 176.44, "end": 177.3, "word": " المنعكس", "probability": 0.962109375}, {"start": 177.3, "end": 178.22, "word": " جزئيا", "probability": 0.849609375}, {"start": 178.22, "end": 180.32, "word": " وإذا", "probability": 0.8977864583333334}, {"start": 180.32, "end": 180.96, "word": " كانت", "probability": 0.9951171875}, {"start": 180.96, "end": 181.58, "word": " الزاوية", "probability": 0.98583984375}, {"start": 181.58, "end": 181.88, "word": " بين", "probability": 0.99169921875}, {"start": 181.88, "end": 182.48, "word": " الشعاع", "probability": 0.97216796875}, {"start": 182.48, "end": 183.26, "word": " المنعكس", "probability": 0.98955078125}, {"start": 183.26, "end": 184.16, "word": " والمنكسر", "probability": 0.88466796875}, {"start": 184.16, "end": 185.0, "word": " تسعين", "probability": 0.95703125}, {"start": 185.0, "end": 185.96, "word": " درجة", "probability": 0.9949544270833334}, {"start": 185.96, "end": 186.38, "word": " أي", "probability": 0.79296875}, {"start": 186.38, "end": 187.3, "word": " عندما", "probability": 0.940673828125}, {"start": 187.3, "end": 188.06, "word": " يتعامد", "probability": 0.97255859375}, {"start": 188.06, "end": 188.84, "word": " الشعاعين", "probability": 0.975830078125}, {"start": 188.84, "end": 189.7, "word": " المنعكس", "probability": 0.9892578125}, {"start": 189.7, "end": 190.62, "word": " والمنكسر", "probability": 0.91572265625}, {"start": 190.62, "end": 191.84, "word": " عندها", "probability": 0.9912109375}, {"start": 191.84, "end": 193.22, "word": " يستقطب", "probability": 0.98681640625}, {"start": 193.22, "end": 193.9, "word": " الشعاع", "probability": 0.9884440104166666}, {"start": 193.9, "end": 194.78, "word": " المنعكس", "probability": 0.9962890625}, {"start": 194.78, "end": 195.78, "word": " كليا", "probability": 0.80126953125}], "temperature": 1.0}, {"id": 6, "seek": 22131, "start": 199.31, "end": 221.31, "text": "ويعتبر استخدام النظارات الشمسية لتقليل التوهج باستقطاب الضوء المنعكس عن الطرق مثالا واضحا للاستقطاب بالانعكاس وكذلك مرشحات الاستقطاب التي يستخدمها المصورون في عدسات الكاميرات والسؤال هنا", "tokens": [45865, 34268, 26890, 44713, 9778, 3215, 10943, 28239, 19913, 9640, 9307, 25124, 2304, 3794, 10632, 5296, 2655, 4587, 20292, 1211, 16712, 2407, 3224, 7435, 4724, 995, 14851, 47432, 16758, 6024, 114, 2407, 38207, 9673, 1863, 3615, 4117, 3794, 18871, 41950, 2288, 4587, 50113, 6027, 995, 4032, 46958, 5016, 995, 24976, 995, 14851, 47432, 16758, 20666, 7649, 3615, 4117, 32277, 4032, 4117, 8848, 23275, 3714, 2288, 8592, 5016, 9307, 42963, 14851, 47432, 16758, 38392, 7251, 14851, 9778, 40448, 11296, 9673, 9381, 13063, 11536, 8978, 6225, 3215, 3794, 9307, 33251, 10943, 13546, 9307, 16070, 3794, 33604, 6027, 34105], "avg_logprob": -0.04389497545576587, "compression_ratio": 1.8457446808510638, "no_speech_prob": 0.0001690387725830078, "words": [{"start": 199.31, "end": 200.23, "word": "ويعتبر", "probability": 0.8504231770833334}, {"start": 200.23, "end": 201.01, "word": " استخدام", "probability": 0.9708251953125}, {"start": 201.01, "end": 201.83, "word": " النظارات", "probability": 0.9586181640625}, {"start": 201.83, "end": 202.55, "word": " الشمسية", "probability": 0.994384765625}, {"start": 202.55, "end": 203.47, "word": " لتقليل", "probability": 0.9837890625}, {"start": 203.47, "end": 204.23, "word": " التوهج", "probability": 0.9840087890625}, {"start": 204.23, "end": 205.23, "word": " باستقطاب", "probability": 0.9603515625}, {"start": 205.23, "end": 205.75, "word": " الضوء", "probability": 0.984130859375}, {"start": 205.75, "end": 206.39, "word": " المنعكس", "probability": 0.96103515625}, {"start": 206.39, "end": 206.57, "word": " عن", "probability": 0.9404296875}, {"start": 206.57, "end": 207.07, "word": " الطرق", "probability": 0.9788411458333334}, {"start": 207.07, "end": 208.31, "word": " مثالا", "probability": 0.8797200520833334}, {"start": 208.31, "end": 208.99, "word": " واضحا", "probability": 0.9344482421875}, {"start": 208.99, "end": 210.09, "word": " للاستقطاب", "probability": 0.93134765625}, {"start": 210.09, "end": 211.05, "word": " بالانعكاس", "probability": 0.9880859375}, {"start": 211.05, "end": 212.49, "word": " وكذلك", "probability": 0.9483642578125}, {"start": 212.49, "end": 213.53, "word": " مرشحات", "probability": 0.9783203125}, {"start": 213.53, "end": 214.43, "word": " الاستقطاب", "probability": 0.9754638671875}, {"start": 214.43, "end": 215.03, "word": " التي", "probability": 0.779296875}, {"start": 215.03, "end": 216.05, "word": " يستخدمها", "probability": 0.99111328125}, {"start": 216.05, "end": 216.99, "word": " المصورون", "probability": 0.981689453125}, {"start": 216.99, "end": 217.59, "word": " في", "probability": 0.96630859375}, {"start": 217.59, "end": 218.37, "word": " عدسات", "probability": 0.9852294921875}, {"start": 218.37, "end": 219.81, "word": " الكاميرات", "probability": 0.96337890625}, {"start": 219.81, "end": 220.93, "word": " والسؤال", "probability": 0.914306640625}, {"start": 220.93, "end": 221.31, "word": " هنا", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 7, "seek": 25151, "start": 222.19, "end": 251.51, "text": "كيف يمكننا معرفة مدى انخفاض شدة الضوء عند عبوره خلال مرشح استقطاب هنا يأتي دور العالم Malus الذي توصل إلى العلاقة التالية عند وضع مرشحي استقطاب بحيث يكون محورا استقطابهما متوازين تنفذ خلالهما أكبر كمية من الضوء", "tokens": [4117, 33911, 7251, 43020, 8315, 20449, 28480, 3660, 3714, 3215, 7578, 16472, 9778, 5172, 46958, 13412, 41891, 6024, 114, 2407, 38207, 43242, 6225, 3555, 13063, 3224, 16490, 1211, 6027, 3714, 2288, 8592, 5016, 44713, 47432, 16758, 34105, 7251, 10721, 31371, 11778, 13063, 18863, 45340, 5746, 301, 43527, 33427, 36520, 30731, 18863, 15040, 28671, 16712, 6027, 10632, 43242, 4032, 11242, 3615, 3714, 2288, 8592, 5016, 1829, 44713, 47432, 16758, 4724, 5016, 1829, 12984, 7251, 30544, 3714, 5016, 13063, 995, 44713, 47432, 16758, 3224, 15042, 44650, 2407, 31377, 9957, 6055, 1863, 5172, 8848, 16490, 1211, 6027, 3224, 15042, 5551, 4117, 26890, 9122, 2304, 10632, 9154, 6024, 114, 2407, 38207], "avg_logprob": -0.06311487047760575, "compression_ratio": 1.8047619047619048, "no_speech_prob": 1.0848045349121094e-05, "words": [{"start": 222.19, "end": 222.63, "word": "كيف", "probability": 0.9765625}, {"start": 222.63, "end": 223.45, "word": " يمكننا", "probability": 0.9934895833333334}, {"start": 223.45, "end": 224.07, "word": " معرفة", "probability": 0.9874674479166666}, {"start": 224.07, "end": 224.55, "word": " مدى", "probability": 0.9925130208333334}, {"start": 224.55, "end": 225.35, "word": " انخفاض", "probability": 0.975341796875}, {"start": 225.35, "end": 225.75, "word": " شدة", "probability": 0.9462890625}, {"start": 225.75, "end": 226.29, "word": " الضوء", "probability": 0.98193359375}, {"start": 226.29, "end": 226.91, "word": " عند", "probability": 0.97509765625}, {"start": 226.91, "end": 227.57, "word": " عبوره", "probability": 0.9859619140625}, {"start": 227.57, "end": 228.05, "word": " خلال", "probability": 0.9930013020833334}, {"start": 228.05, "end": 228.53, "word": " مرشح", "probability": 0.99169921875}, {"start": 228.53, "end": 229.21, "word": " استقطاب", "probability": 0.935546875}, {"start": 229.21, "end": 230.63, "word": " هنا", "probability": 0.591796875}, {"start": 230.63, "end": 231.81, "word": " يأتي", "probability": 0.9495442708333334}, {"start": 231.81, "end": 232.37, "word": " دور", "probability": 0.996337890625}, {"start": 232.37, "end": 233.07, "word": " العالم", "probability": 0.97900390625}, {"start": 233.07, "end": 233.71, "word": " Malus", "probability": 0.5882568359375}, {"start": 233.71, "end": 234.49, "word": " الذي", "probability": 0.66796875}, {"start": 234.49, "end": 235.17, "word": " توصل", "probability": 0.951904296875}, {"start": 235.17, "end": 235.47, "word": " إلى", "probability": 0.85546875}, {"start": 235.47, "end": 236.23, "word": " العلاقة", "probability": 0.9814453125}, {"start": 236.23, "end": 236.95, "word": " التالية", "probability": 0.9864908854166666}, {"start": 236.95, "end": 240.15, "word": " عند", "probability": 0.96044921875}, {"start": 240.15, "end": 240.71, "word": " وضع", "probability": 0.9969075520833334}, {"start": 240.71, "end": 241.53, "word": " مرشحي", "probability": 0.9923828125}, {"start": 241.53, "end": 242.29, "word": " استقطاب", "probability": 0.9791666666666666}, {"start": 242.29, "end": 243.15, "word": " بحيث", "probability": 0.9921875}, {"start": 243.15, "end": 243.73, "word": " يكون", "probability": 0.992919921875}, {"start": 243.73, "end": 244.37, "word": " محورا", "probability": 0.83233642578125}, {"start": 244.37, "end": 245.51, "word": " استقطابهما", "probability": 0.8443359375}, {"start": 245.51, "end": 246.73, "word": " متوازين", "probability": 0.912109375}, {"start": 246.73, "end": 248.05, "word": " تنفذ", "probability": 0.9586181640625}, {"start": 248.05, "end": 248.99, "word": " خلالهما", "probability": 0.9431640625}, {"start": 248.99, "end": 249.69, "word": " أكبر", "probability": 0.9287109375}, {"start": 249.69, "end": 250.47, "word": " كمية", "probability": 0.994140625}, {"start": 250.47, "end": 251.01, "word": " من", "probability": 0.994140625}, {"start": 251.01, "end": 251.51, "word": " الضوء", "probability": 0.9898681640625}], "temperature": 1.0}, {"id": 8, "seek": 26864, "start": 253.58, "end": 268.64, "text": "أما إذا كان محور الاستقطاب متعامدين فلن ينفذ أي ظلم شكرا معلمتي", "tokens": [10721, 15042, 11933, 15730, 25961, 3714, 5016, 13063, 42963, 14851, 47432, 16758, 44650, 3615, 10943, 3215, 9957, 6156, 1211, 1863, 7251, 1863, 5172, 8848, 36632, 1357, 116, 19528, 13412, 4117, 23557, 20449, 19528, 31371], "avg_logprob": -0.10970981929983412, "compression_ratio": 1.2365591397849462, "no_speech_prob": 0.00445556640625, "words": [{"start": 253.58, "end": 254.16, "word": "أما", "probability": 0.981201171875}, {"start": 254.16, "end": 254.64, "word": " إذا", "probability": 0.956298828125}, {"start": 254.64, "end": 255.18, "word": " كان", "probability": 0.99658203125}, {"start": 255.18, "end": 255.74, "word": " محور", "probability": 0.9845377604166666}, {"start": 255.74, "end": 256.78, "word": " الاستقطاب", "probability": 0.81280517578125}, {"start": 256.78, "end": 258.52, "word": " متعامدين", "probability": 0.98310546875}, {"start": 258.52, "end": 259.48, "word": " فلن", "probability": 0.9275716145833334}, {"start": 259.48, "end": 260.24, "word": " ينفذ", "probability": 0.990478515625}, {"start": 260.24, "end": 260.8, "word": " أي", "probability": 0.791015625}, {"start": 260.8, "end": 261.34, "word": " ظلم", "probability": 0.7534993489583334}, {"start": 261.34, "end": 267.78, "word": " شكرا", "probability": 0.89794921875}, {"start": 267.78, "end": 268.64, "word": " معلمتي", "probability": 0.8899739583333334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 334.1119375, "duration_after_vad": 208.25875}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80.srt
new file mode 100644
index 0000000000000000000000000000000000000000..13295856f6c719cf17cac4f8f245a46665bcda25
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80.srt
@@ -0,0 +1,1314 @@
+1
+00:00:02,580 --> 00:00:05,460
+بسم الله الرحمن الرحيم بنكمل مع محاضرات ال
+
+2
+00:00:05,460 --> 00:00:09,720
+physical optics ووصلنا لعنوان ال radiometry and 
+
+3
+00:00:09,720 --> 00:00:14,520
+photometry يعني القياس الإشعاعي و القياس الإضائي 
+
+4
+00:00:14,520 --> 00:00:18,120
+عشان نعرف إيش الفرق بين القياس الإشعاعي اللي هو ال
+
+5
+00:00:18,120 --> 00:00:22,840
+radiometry والقياس الإضائي اللي هو ال photometry
+
+6
+00:00:22,840 --> 00:00:27,880
+بدنا نعطي بعض المقدمات البسيطة بنقول it is 
+
+7
+00:00:27,880 --> 00:00:31,580
+necessary at times to measure the amount of light 
+
+8
+00:00:31,580 --> 00:00:36,320
+produced by a source or illuminating a surface
+
+9
+00:00:36,320 --> 00:00:40,120
+يعني في بعض الأحيان بنحتاج أن نعرف كمية الضوء 
+
+10
+00:00:40,120 --> 00:00:45,480
+الصادرة من مصدر ما أو كمية الضوء اللي أضاءت سطح
+
+11
+00:00:45,480 --> 00:00:50,450
+ما مثال على ذلك الرسم هاي بتوضحه عندي هاي مصدر
+
+12
+00:00:50,450 --> 00:00:54,970
+ضوء، هذا المصباح الكهربائي بيصدر ضوء أحيانا بنحتاج
+
+13
+00:00:54,970 --> 00:01:00,710
+نعرف قداش كمية الضوء اللي بيصدرها هذا المصدر الضوء
+
+14
+00:01:01,220 --> 00:01:04,680
+أيضا أحيانا بيكون احنا مش معنين بكمية الضوء
+
+15
+00:01:04,680 --> 00:01:09,240
+الصادرة من مصدر ما، ولكن كمية الضوء الساقطة على
+
+16
+00:01:09,240 --> 00:01:14,160
+سطح ما قداش مثلا للمتر المربع أو للسنتيمتر المربع
+
+17
+00:01:14,160 --> 00:01:18,620
+أو لوحدة المساحة قداش بيصلها إضاءة، إما الضوء
+
+18
+00:01:18,620 --> 00:01:22,420
+الصادر قداش كميته أو الضوء الساقط اللي هو 
+
+19
+00:01:22,420 --> 00:01:26,420
+illuminating a surface قداش كميته، إذا في بعض
+
+20
+00:01:26,420 --> 00:01:32,000
+الأحيان نحتاج لقياس أي واحد من الشيءين مثال على ذلك
+
+21
+00:01:32,000 --> 00:01:35,180
+يعني إيش الحاجة؟ يعني لماذا نحتاج أحياناً لقياس
+
+22
+00:01:35,180 --> 00:01:40,320
+الضوء الصادر من سطحنا أو الضوء الساقط على سطحنا؟
+
+23
+00:01:40,320 --> 00:01:40,420
+نقول 
+
+24
+00:02:01,410 --> 00:02:06,250
+جهاز ال perimeter هو جهاز فحص الساحة البصرية أو
+
+25
+00:02:06,250 --> 00:02:12,250
+الحقل البصري أو ال visual field هاي  أن أمثل هذا 
+
+26
+00:02:12,250 --> 00:02:17,730
+الجهاز .. هاي الجهاز عبارة عن بولحوب يعني جاي
+
+27
+00:02:17,730 --> 00:02:22,230
+بشكل عمودي هنا هذه القطعة بيسموها chin rest المريض
+
+28
+00:02:22,230 --> 00:02:28,130
+بيحط ذقنه عليها هذه بيسموها head rest بي .. بيحط ال
+
+29
+00:02:28,130 --> 00:02:31,470
+.. جبينه عليها، إذا الرأس المريض بتكون على ال head 
+
+30
+00:02:31,470 --> 00:02:34,290
+rest و ذقن المريض بتكون على ال chin rest و هو
+
+31
+00:02:34,290 --> 00:02:38,150
+بيكون مواجه .. وجهه مواجه لل bowel أو الحوض .. لل
+
+32
+00:02:38,150 --> 00:02:43,470
+bowel أو الحوض الآن بتم إغلاق عين واحدة أو عمل 
+
+33
+00:02:43,470 --> 00:02:47,430
+patching .. تسكير لعين واحدة عشان نفحص حقل الإبصار 
+
+34
+00:02:47,990 --> 00:02:52,250
+للعين الأخرى كيف يفحص حقل .. حقل الإبصار يفحص بإن 
+
+35
+00:02:52,250 --> 00:02:55,630
+المريض بيطلب منه أنه يركز على نقطة مركزية بيكون
+
+36
+00:02:55,630 --> 00:03:00,650
+لها إضاءة بلون معين و هذا الـ bowel فيه نقاط أخرى
+
+37
+00:03:00,650 --> 00:03:05,010
+بالضيق يعني بطريقة عشوائية مرة في المكان هذا مرة
+
+38
+00:03:05,010 --> 00:03:07,810
+في المكان هذا مرة في المكان هذا مرة في المكان هذا
+
+39
+00:03:07,810 --> 00:03:12,180
+مرة في المكان هذا الآن ضروري المريض يعني يركز بعينه
+
+40
+00:03:12,180 --> 00:03:15,660
+على ال central point اللي هو ال fixating point و ما
+
+41
+00:03:15,660 --> 00:03:21,340
+يحرك عينه بتاتا وإنما بيمسك في إيده يعني مكبس أو
+
+42
+00:03:21,340 --> 00:03:25,380
+.. أو زر و لمّا بي .. هو مركز في النقطة المركزية
+
+43
+00:03:25,380 --> 00:03:30,500
+إذا أيضه ظهر في الأطراف بيضغط يعني بمعنى انه شايف
+
+44
+00:03:30,500 --> 00:03:34,680
+هذا الضوء يعني هذا السهم الأصفر بيأشر لنقطة مضيئة
+
+45
+00:03:34,680 --> 00:03:37,660
+طبعا المريض ما بيتطلع على هذه النقطة وإنما هو
+
+46
+00:03:37,660 --> 00:03:41,840
+بيتطلع على النقطة المركزية إذا هذه النقطة سقطت على 
+
+47
+00:03:41,840 --> 00:03:44,840
+ال peripheral retina بتاعته و شافها معناته بيدغط 
+
+48
+00:03:44,840 --> 00:03:50,100
+وبالتالي الجهاز بيسجل ان المنطقة هذه ضمن حقل
+
+49
+00:03:50,100 --> 00:03:54,340
+الإبصار المرئي بالنسبة لهذه العين جهاز visual
+
+50
+00:03:54,340 --> 00:03:57,560
+field أحدث أيضا نفس القضية بس الأمر بيكون
+
+51
+00:03:57,560 --> 00:04:01,080
+computerized هذه ال .. ال .. ال .. ال .. ال ..
+
+52
+00:04:01,400 --> 00:04:05,960
+المقبس أو الزر اللي بيضغط عليه المريض لما يشوف 
+
+53
+00:04:05,960 --> 00:04:11,300
+النقطة اللي تم إضاءتها له في هذا الـ bowel القصد 
+
+54
+00:04:11,300 --> 00:04:15,420
+علاقة هذا الفحص عشان هذا الفحص يكون دقيق هذا الفحص 
+
+55
+00:04:15,420 --> 00:04:20,580
+فحص ال visual field أو الساحة البصرية بيفحص في 
+
+56
+00:04:20,580 --> 00:04:25,470
+العديد من الأمراض و لكن يعني من أكثر الأمراض اللي
+
+57
+00:04:25,470 --> 00:04:28,210
+بيفحص فيها ال visual field مرض الجلوكوما اللي هو
+
+58
+00:04:28,210 --> 00:04:32,990
+ارتفاع ضغط العين ارتفاع ضغط العين لأنه بيتلف العصب
+
+59
+00:04:32,990 --> 00:04:40,220
+البصري و بالتالي بيصير مناطق من ال retina يعني ما
+
+60
+00:04:40,220 --> 00:04:44,920
+بتشوف لأنه الألياف بتاعتها اللي بتشارك في تكوين
+
+61
+00:04:44,920 --> 00:04:48,680
+العصب البصري بتكون ماتت بسبب ال glucoma فبالتالي
+
+62
+00:04:48,680 --> 00:04:53,020
+بتصير هذه المناطق، مناطق يعني خارج ال visual field 
+
+63
+00:04:53,020 --> 00:04:55,960
+أو مناطق سوداء في ال visual field يعني مناطق
+
+64
+00:04:55,960 --> 00:04:57,960
+انعدام الرؤية
+
+65
+00:05:00,050 --> 00:05:04,790
+ضروري جدا عشان يكون الفحص دقيق لازم أعمل الفحص 
+
+66
+00:05:04,790 --> 00:05:09,570
+يعني في مرات عديدة، يعني ممكن أعمل الفحص للمريض 
+
+67
+00:05:09,570 --> 00:05:14,010
+اليوم، بعد ثلاثة شهور، بعد ستة شهور، بعد سنة، بعد
+
+68
+00:05:14,010 --> 00:05:16,810
+سنتين، إلى آخره، عشان أتابع هل الجلوكوما
+
+69
+00:05:16,810 --> 00:05:22,210
+progressive، يعني بتتطور للأسوأ، ولا stable، يعني
+
+70
+00:05:22,210 --> 00:05:28,160
+مستقرة و مستجيبة للعلاج اللي بتم إعطاؤه طيب عشان يكون
+
+71
+00:05:28,160 --> 00:05:31,160
+الفحص دقيق ضروري ال illumination ال background 
+
+72
+00:05:31,160 --> 00:05:35,240
+illumination الإضاءة الأساسية للجهاز مش إضاءة
+
+73
+00:05:35,240 --> 00:05:39,280
+النقطة هي هذا الجهاز فيه له إضاءة أساسية يعني زي
+
+74
+00:05:39,280 --> 00:05:43,460
+ما أنتم لاحظين إن بين مضيق بس النقطة حتكون إضاءتها
+
+75
+00:05:43,460 --> 00:05:46,920
+أعلى منها ولكن هو له إضاءة أساسية بسمها ال 
+
+76
+00:05:46,920 --> 00:05:50,500
+background illumination إذا أنا اجيت فحصت المريض
+
+77
+00:05:50,500 --> 00:05:56,510
+بسن ال background illumination اليوم يعني له مقدار 
+
+78
+00:05:56,510 --> 00:06:00,490
+معين إضاءة معينة ثم عند ال follow-up يعني في
+
+79
+00:06:00,490 --> 00:06:05,610
+المراجعة بعد ثلاثة شهور أو ستة شهور فحصته بإضاءة أقل
+
+80
+00:06:05,610 --> 00:06:09,590
+أو أكثر background illumination أكثر أو أقل بيكون
+
+81
+00:06:09,590 --> 00:06:12,650
+مفحص غير دقيق ضروري إن ال illumination بتاع الـ bowel
+
+82
+00:06:12,650 --> 00:06:16,790
+يكون ثابت عشان نقدر نعمل comparison عشان نقدر نعمل 
+
+83
+00:06:16,790 --> 00:06:21,500
+comparison إذا for example the power of a perimeter
+
+84
+00:06:21,500 --> 00:06:26,480
+حوض ال perimeter حوض جهاز فحص الساحة البصرية must
+
+85
+00:06:26,480 --> 00:06:30,920
+be accurately illuminated لابد من إضاءته بشكل دقيق
+
+86
+00:06:30,920 --> 00:06:36,020
+و ثابت in order عشان أقدر for any comparisons of 
+
+87
+00:06:36,020 --> 00:06:39,320
+visual field measurements performed on different 
+
+88
+00:06:39,320 --> 00:06:42,780
+instruments سواء المريض عمل عند الفحص أو عمل عند
+
+89
+00:06:42,780 --> 00:06:46,820
+أي من الزملاء الآخرين في أي من المراكز الطبية عشان
+
+90
+00:06:46,820 --> 00:06:50,220
+نقدر نقول أو نقدر نقارن بين الفحص الأول والثاني
+
+91
+00:06:50,220 --> 00:06:53,300
+والثالث والرابع ضروري ال background illumination 
+
+92
+00:06:53,300 --> 00:06:57,700
+بتاعة الـ bowel بتاعة الحوض بتاعة ال perimeter إنه
+
+93
+00:06:57,700 --> 00:07:02,620
+تكون ثابتة و مش متغيرة لأن هذا هيأثر على استجابة
+
+94
+00:07:02,620 --> 00:07:12,210
+المريض إذا هذا يعني لي إنه الضوء الصادر من الـ bowel
+
+95
+00:07:12,210 --> 00:07:16,950
+لازم يكون قياسه دقيق يعني كميته موحدة كميته موحدة 
+
+96
+00:07:16,950 --> 00:07:19,690
+احنا بنقول كالتالي عشان ال visual field 
+
+97
+00:07:19,690 --> 00:07:23,270
+measurements performed on different instruments أو
+
+98
+00:07:23,270 --> 00:07:26,170
+on the same instruments at different times to be
+
+99
+00:07:26,170 --> 00:07:30,070
+meaningful عشان أقدر أقارن بينهم بنشوف مثال بنقول 
+
+100
+00:07:30,070 --> 00:07:33,690
+هذا ال baseline visual field مريض اجى أنعمل له ال
+
+101
+00:07:33,690 --> 00:07:36,750
+visual field واضح المناطق السوداء هي إنه ما بيشوفش
+
+102
+00:07:36,750 --> 00:07:41,040
+فيها هذه ال visual field ككل المناطق هاي ما بيشوفش
+
+103
+00:07:41,040 --> 00:07:45,060
+فيها بعد سنة أنعمل الفحص بعد سنة أخرى أنعمل الفحص
+
+104
+00:07:45,060 --> 00:07:49,740
+واضح ان المناطق بتزداد بعد ثلاثة سنين من ال baseline 
+
+105
+00:07:49,740 --> 00:07:54,820
+test أنعمل الفحص و بعد أربع سنين عشان أقدر أقارن
+
+106
+00:07:54,820 --> 00:07:58,140
+أقول إن والله فيه progression يعني زي ما هذا الصوت 
+
+107
+00:07:58,140 --> 00:08:02,380
+ضروري ال illumination بتاع ال .. بتاع ال .. ال
+
+108
+00:08:02,380 --> 00:08:05,920
+bowel بتاع ال perimeter إنه يكون ثابت و مش مرة أحط
+
+109
+00:08:05,920 --> 00:08:11,470
+مثلا كم معين و مرة ثانية كم آخر و مرة ثالثة كم ثالث 
+
+110
+00:08:11,470 --> 00:08:15,370
+.. ساعتها مش أقدر أعمل المقارنات طبعا هذه ممكن
+
+111
+00:08:15,370 --> 00:08:19,050
+تكون للعين اليمنى و هذه للعين اليسرى أيضا بعد سنة
+
+112
+00:08:19,050 --> 00:08:22,050
+.. بعد سنتين .. بعد ثلاثة .. بعد أربع .. لو اجينا
+
+113
+00:08:22,050 --> 00:08:25,870
+نقول بعد أربع سنوات شايفين المناطق .. مناطق
+
+114
+00:08:25,870 --> 00:08:28,650
+بيسموها scotoma يعني منطقة انعدام الرؤية اللي 
+
+115
+00:08:28,650 --> 00:08:33,010
+باللون الأسود و هنا ال scotoma طبعا واضح من الصور 
+
+116
+00:08:33,010 --> 00:08:37,870
+إنه في progression يعني المرض بيزداد سوءًا طب لو
+
+117
+00:08:37,870 --> 00:08:43,210
+احنا أخذنا معلومة إنه ال background illumination
+
+118
+00:08:43,210 --> 00:08:46,690
+ما كانش موحد إذا كل المقارنة هذه لا فائدة منها لابد
+
+119
+00:08:46,690 --> 00:08:50,930
+للمريض منه نقوم بإعادة هذا ال test background 
+
+120
+00:08:50,930 --> 00:08:55,410
+illumination موحد background illumination موحد 
+
+121
+00:08:55,410 --> 00:08:59,370
+نيجي
+
+122
+00:08:59,370 --> 00:09:06,310
+نحكي عن القياس الإشعاعيالراديومتري القياس الإشعاعي
+
+123
+00:09:06,310 --> 00:09:17,750
+هو أن أنا 
+
+124
+00:09:17,750 --> 00:09:21,150
+أجيس الـ electromagnetic radiation بين هدول
+
+125
+00:09:21,150 --> 00:09:25,490
+الترددين نشوف مع بعض إيش هدول الترددين نطلع على
+
+126
+00:09:25,490 --> 00:09:31,420
+المنظر المكبر هي عندي 10 أس 11 و هي أنا عندي 10 أس 
+
+127
+00:09:31,420 --> 00:09:36,060
+16 يعني هنا بيشمل عندي ال .. شوية من ال microwave 
+
+128
+00:09:36,060 --> 00:09:40,100
+شوية من ال infrared و ال visible light و ال
+
+129
+00:09:40,100 --> 00:09:44,120
+ultraviolet و بداية ال إيش ال x-ray إذا هذا ال
+
+130
+00:09:44,120 --> 00:09:48,800
+range لما أجيسه لما أجيس الكمية ال electromagnetic
+
+131
+00:09:48,800 --> 00:09:53,540
+radiation كمية الإشعاع الصادرة من مصدرنا بيصدر لي 
+
+132
+00:09:53,540 --> 00:09:57,710
+هذه ال radiation بسميها أنا بكون عملت radiometry
+
+133
+00:09:57,710 --> 00:10:02,790
+radiometry يعني لو تصورنا أن في جهاز بيصدر إشعاعات 
+
+134
+00:10:02,790 --> 00:10:06,730
+بيصدر electromagnetic waves و هذه ال
+
+135
+00:10:06,730 --> 00:10:09,810
+electromagnetic waves اللي بيصدرها هذا الجهاز 
+
+136
+00:10:09,810 --> 00:10:15,210
+ترددها بتراوح بين عشرة أس ثلاثة في عشرة أس أحد عشر 
+
+137
+00:10:15,210 --> 00:10:20,410
+لتلاتة في عشرة أس ستة عشر هرتز ذبذبة معناته هو
+
+138
+00:10:20,410 --> 00:10:24,680
+هذا الجهاز بيصدر له microwaves بيصدر لي infrared 
+
+139
+00:10:24,680 --> 00:10:29,260
+بيصدر visible light و بيصدر ultraviolet و بيصدر قليل 
+
+140
+00:10:29,260 --> 00:10:33,900
+بيسموها ال soft x-ray بيسموها ال soft x-ray ليه 
+
+141
+00:10:33,900 --> 00:10:37,760
+ترددها قريب من تردد ال ultraviolet إذا هذا الجهاز
+
+142
+00:10:37,760 --> 00:10:41,980
+بيصدر كل هذه ال electromagnetic radiation لما أجيس
+
+143
+00:10:41,980 --> 00:10:45,900
+الإشعاع اللي صادر من هذا الجهاز هذه العملية تسمى 
+
+144
+00:10:45,900 --> 00:10:50,090
+radiometry إذا الـ Radiometry is the measurement هو
+
+145
+00:10:50,090 --> 00:10:56,130
+قياس الـ electromagnetic radiation إشعاع الموجات
+
+146
+00:10:56,130 --> 00:11:01,090
+الكهرومغناطيسية اللي ذبذبتها بتتراوح بين 3 في 10 
+
+147
+00:11:01,090 --> 00:11:07,830
+أس 11 هرتز ذبذبة ل 3 في 10 أس 16 هرتز هذا ال 
+
+148
+00:11:07,830 --> 00:11:11,990
+range corresponding to wavelengths من 10 نانومتر ل
+
+149
+00:11:11,990 --> 00:11:19,790
+1 مليمتر 10 nanometer أقل من 400 nanometer و أقل 
+
+150
+00:11:19,790 --> 00:11:23,750
+من 700 nanometer يعني من 400 ل 700 nanometer جاية 
+
+151
+00:11:23,750 --> 00:11:27,310
+بين العشرة للواحد مليمتر يعني ال visible light 
+
+152
+00:11:27,310 --> 00:11:30,970
+جاية ضمن هذا ال range و أيضا ال infrared جاية و ال
+
+153
+00:11:30,970 --> 00:11:36,500
+ultraviolet جاية و شوية microwave و شوية x-ray إذا 
+
+154
+00:11:36,500 --> 00:11:41,320
+therefore radiometry spans the microwave infrared 
+
+155
+00:11:41,320 --> 00:11:46,180
+visible light ultraviolet and soft x-ray regions
+
+156
+00:11:46,180 --> 00:11:50,740
+of the electromagnetic spectrum يعني أي مصدر أي
+
+157
+00:11:50,740 --> 00:11:56,260
+مصدر بيصدر لي هذه الذبذبات من هذا ال range لعند هذا
+
+158
+00:11:56,260 --> 00:12:01,890
+ال range هذا قياس ال .. الموجات الكهرومغناطيسية 
+
+159
+00:12:01,890 --> 00:12:05,990
+الصادرة من هذا المصدر يسمى عملية الـ Radiometry
+
+160
+00:12:05,990 --> 00:12:11,970
+القياس الإشعاعي غالبا احنا بنحتاجش .. بنحتاجش أن
+
+161
+00:12:11,970 --> 00:12:16,510
+نقيس كل هذا القياس يعني عندي مصدر صحيح بيصدر كل
+
+162
+00:12:16,510 --> 00:12:19,390
+هذه الأنواع من الموجات بيصدر لي microwave و 
+
+163
+00:12:19,390 --> 00:12:23,090
+infrared و visible و ultraviolet إلى آخره أحيانا 
+
+164
+00:12:23,090 --> 00:12:29,210
+بركز القياس على نوع معين فقط من كل هذه الموجات اللي
+
+165
+00:12:29,210 --> 00:12:34,330
+بيصدرها هذا المصدر إذا ركزت قياسي على نوع معين هذا
+
+166
+00:12:34,330 --> 00:12:39,090
+بتسمى Spectral Radiometry Spectral Radiometry
+
+167
+00:12:39,090 --> 00:12:44,170
+فبالتالي هذه القضية ضروري إحنا نفهمها often such 
+
+168
+00:12:44,170 --> 00:12:47,890
+broad measurements هذا يعتبر قياس عريض ليش؟ لأن 
+
+169
+00:12:47,890 --> 00:12:52,870
+أنا أخدت من عند ال microwave ووصلت لل soft x-ray 
+
+170
+00:12:52,870 --> 00:12:57,320
+يعني أخدت شملت حاجات كثيرة فهذا عادة القياس مش
+
+171
+00:12:57,320 --> 00:13:00,820
+ضروري، مش ضروري، إذا often such broad measurements
+
+172
+00:13:00,820 --> 00:13:06,100
+are not necessary، هذه القياسات اللي هي العريضة
+
+173
+00:13:06,100 --> 00:13:10,060
+اللي بتشمل موجات، أنواع موجات كثيرة، غالبا مش لازم
+
+174
+00:13:11,130 --> 00:13:14,990
+فبالتالي بدل ما نعمل Radiometry بنعمل Spectral 
+
+175
+00:13:14,990 --> 00:13:20,150
+Radiometry يعني الإشعاع الطيفي أو قياس الإشعاع 
+
+176
+00:13:20,150 --> 00:13:24,230
+الطيفي يعني بركز على طيف معين أو Spectrum معين إذا
+
+177
+00:13:24,230 --> 00:13:28,110
+Spectral Radiometry is used instead to measure a 
+
+178
+00:13:28,110 --> 00:13:32,740
+narrow portion of the electromagnetic spectrum هذا
+
+179
+00:13:32,740 --> 00:13:37,
+
+201
+00:15:10,970 --> 00:15:15,350
+أثر نفسي على العين أثر نفسي أو الـ psychology على
+
+202
+00:15:15,840 --> 00:15:18,820
+العين، يعني هو هيسقط على العين على مساحة من
+
+203
+00:15:18,820 --> 00:15:23,980
+الشبكية ثم ينقل عبر الـ visual system ويعطي شعور
+
+204
+00:15:23,980 --> 00:15:29,000
+معين عند الإنسان، شعور معين عند الإنسان فبالتالي
+
+205
+00:15:29,000 --> 00:15:36,000
+هذه لما بنجيس هذا الشعور أو بنجيس الأثر .. بنجيس الـ
+
+206
+00:15:36,000 --> 00:15:38,680
+.. الأثر النفسي الـ psychological أو الـ
+
+207
+00:15:38,680 --> 00:15:42,500
+psychophysical response توليد بنكون احنا بنعمل
+
+208
+00:15:42,500 --> 00:15:46,380
+عملية الـ photometry إذا basically photometry is a
+
+209
+00:15:46,380 --> 00:15:50,300
+type of radiometry هي نوع من أنواع الـ radiometry
+
+210
+00:15:50,300 --> 00:15:54,140
+بس إيش بتختلف عنها؟ that takes into account the
+
+211
+00:15:54,140 --> 00:15:57,360
+varying sensitivity of the eye to different
+
+212
+00:15:57,360 --> 00:16:01,080
+wavelengths اللي بتاخد الفوتومتري بتاخد في حسابها
+
+213
+00:16:01,080 --> 00:16:07,320
+أن العين البشرية حساسة بطريقة مختلفة حسب الـ
+
+214
+00:16:07,320 --> 00:16:11,940
+wavelength الساقطة عليها حساسة بطريقة مختلفة حسب
+
+215
+00:16:11,940 --> 00:16:14,480
+الـ wavelength الساقطة عليها
+
+216
+00:16:16,940 --> 00:16:21,320
+مثال على ذلك لما بسقط infrared wavelength مافيش ..
+
+217
+00:16:21,320 --> 00:16:26,500
+مافيش أي شعور عند الإنسان بيتولد لأنه غير مرئي لما
+
+218
+00:16:26,500 --> 00:16:32,060
+بسقط blue في شعور باللون الأزرق لما بسقط الـ green
+
+219
+00:16:32,060 --> 00:16:36,120
+في شعور باللون الأخضر و هكذا .. إذا في اختلاف في
+
+220
+00:16:36,120 --> 00:16:39,460
+الشعور .. في اختلاف في الشعور هذا الاختلاف في
+
+221
+00:16:39,460 --> 00:16:43,200
+الشعور ناجم عن اختلاف الطول الموجي الساقط على
+
+222
+00:16:43,200 --> 00:16:48,990
+مساحة ما من الشبكية هجوا العلماء قالوا الأمر هذا
+
+223
+00:16:48,990 --> 00:16:56,510
+بده يعني وضع ضمن قواعد، ليش بده وضع ضمن قواعد؟ الـ
+
+224
+00:16:56,510 --> 00:17:03,300
+photometry طبعا العالم لازال ينتج مصادر ضوئية بعدد
+
+225
+00:17:03,300 --> 00:17:08,520
+هائل قد يكون عدد لا يمكن الحصول عليه مصابيح كهربائية
+
+226
+00:17:08,520 --> 00:17:14,500
+أدوات إضاءة أدوات اللي هي الشاشات الذكية اللي
+
+227
+00:17:14,500 --> 00:17:19,400
+بتصدر إضاءات مختلفة وما إلى ذلك إذا في مصادر
+
+228
+00:17:19,400 --> 00:17:25,620
+إضائية تصنع مختلفة ومتنوعة وغالبيتها العظمى بيصدر
+
+229
+00:17:25,620 --> 00:17:30,600
+.. بيصدر electromagnetic waves في الـ range بتاع
+
+230
+00:17:30,600 --> 00:17:37,440
+الضوء المرئية فعشان ما نجيش احنا عند كل اختراع
+
+231
+00:17:37,440 --> 00:17:44,510
+أداة تصدر ضوء على سبيل المثال تم اختراع جوال ويله
+
+232
+00:17:44,510 --> 00:17:50,010
+شاشة معينة هاتف نقال ويله شاشة معينة بتصدر إضاءة
+
+233
+00:17:50,010 --> 00:17:56,130
+بطريقة معينة أو مكونة من أطياف معينة يعني نفرض 650
+
+234
+00:17:56,130 --> 00:18:01,470
+نانومتر 550 نانومتر 547 نانومتر يعني بتصدر خليط من
+
+235
+00:18:01,470 --> 00:18:05,630
+الأطوال الموجية المرئية بدل ما احنا نجري دراسات
+
+236
+00:18:05,630 --> 00:18:12,680
+على الناس كل ما بنصنع مصدر ضوئي كل ما بنصنع مصدر
+
+237
+00:18:12,680 --> 00:18:15,800
+ضوئي بدل ما نعمل دراسات على الناس اجوا عملوا
+
+238
+00:18:15,800 --> 00:18:21,780
+دراسات موسعة على البشر عشان يعرفوا .. عشان يعرفوا
+
+239
+00:18:21,780 --> 00:18:26,080
+أثر الأطوال الموجية المختلفة الأثر النفسي
+
+240
+00:18:26,080 --> 00:18:31,040
+والفيزيائي للأطوال الموجية المختلفة على عيون البشر
+
+241
+00:18:31,040 --> 00:18:35,850
+بمعنى based on data from measurements of numerous
+
+242
+00:18:35,850 --> 00:18:40,530
+people, weighting factors presented graphically as
+
+243
+00:18:40,530 --> 00:18:44,070
+luminous efficacy curves have been developed for
+
+244
+00:18:44,070 --> 00:18:47,450
+each wavelength across the visible spectrum نفهم
+
+245
+00:18:47,450 --> 00:18:52,890
+هذا الموضوع، هاي الـ visible spectrum بتكون من
+
+246
+00:18:52,890 --> 00:18:57,510
+الأحمر، البرتقالي، الأصفر، الأخضر، الأزرق، النيلي،
+
+247
+00:18:57,510 --> 00:19:02,440
+البنفسجي جابوا مجموعة هائلة من الناس وعرضوا أعينهم
+
+248
+00:19:02,440 --> 00:19:07,640
+لضوء أحمر بشدة إضاءة معينة، زودوا شدة الإضاءة،
+
+249
+00:19:07,640 --> 00:19:10,260
+زودوا شدة الإضاءة، وشافوا الـ response تعادلهم
+
+250
+00:19:10,260 --> 00:19:15,020
+للناس وعملوا curve لللون الأحمر، اسمه الـ luminous
+
+251
+00:19:15,020 --> 00:19:20,040
+efficacy curve كل ما زدنا شدة الـ luminosity تاعت
+
+252
+00:19:20,040 --> 00:19:23,560
+هذا المصدر اللي بيعطيني الضوء الأحمر كيف بيكون الـ
+
+253
+00:19:23,560 --> 00:19:26,660
+response تاع أعين الناس لكتير اللي أجرينا عليهم
+
+254
+00:19:26,660 --> 00:19:30,960
+التجربة و هذا الـ curve صار هو المعدل أو المتوسط أو
+
+255
+00:19:30,960 --> 00:19:34,900
+الـ standard بتاعنا الآن هذه التجربة أجريت لللون
+
+256
+00:19:34,900 --> 00:19:38,960
+الأحمر لللون البرتقالي و لللون الأصفر و كل واحد
+
+257
+00:19:38,960 --> 00:19:45,060
+أصبح له curve بيسموه luminous efficacy curve بمعنى
+
+258
+00:19:45,060 --> 00:19:51,900
+آخر لما بنصنع مصباح كهربائي أو أداة تصدر ضوء بنيجي
+
+259
+00:19:51,900 --> 00:19:57,500
+بنقول هذه الأداة أول حاجة إيش بدنا نقيمها وقداش
+
+260
+00:19:57,500 --> 00:20:02,360
+متوقع تأثرها على عين
+
+261
+00:20:02,360 --> 00:20:06,720
+الإنسان احنا أنتجنا أداة وبنعرف قداش بتأثر على عين
+
+262
+00:20:06,720 --> 00:20:11,460
+الإنسان أول حاجة أول خطوة في التصنيع spectral
+
+263
+00:20:11,460 --> 00:20:15,550
+characteristics of light source are determined يعني
+
+264
+00:20:15,550 --> 00:20:20,230
+بنقول هذا الـ light source scene صنعنا light source
+
+265
+00:20:20,230 --> 00:20:23,950
+مصدر ضوئي سميناه scene إيش الـ spectral
+
+266
+00:20:23,950 --> 00:20:27,010
+characteristics إله؟ إيش عن الـ spectral
+
+267
+00:20:27,010 --> 00:20:29,250
+characteristics يعني؟ إيش الأطوال الموجية اللي
+
+268
+00:20:29,250 --> 00:20:33,670
+بصدر؟ نفرض إنه بصدر طول الموج الأحمر والأخضر
+
+269
+00:20:33,670 --> 00:20:36,810
+والأصفر فقط، بصدرش الأزرق، طب ماشي إذا أنا عرفنا
+
+270
+00:20:36,810 --> 00:20:42,300
+بصدر الأحمر والأخضر والأصفر فقط بنجي بنقول الأحمر
+
+271
+00:20:42,300 --> 00:20:46,520
+بنضربه في الـ luminous efficacy curve بتاعه يعني في
+
+272
+00:20:46,520 --> 00:20:49,640
+شدة إضاءة معينة قداش بيأثر في شدة إضاءة معينة قداش
+
+273
+00:20:49,640 --> 00:20:53,600
+بيأثر الأخضر نفس الشيء والأصفر نفس الشيء ساعتها
+
+274
+00:20:54,570 --> 00:20:58,850
+الاستجابات المتوقعة كلها بتتجمع وبنقول هذا المصدر
+
+275
+00:20:58,850 --> 00:21:04,050
+الضوئي بيأثر على العين بالشكل التالي تمام فبالتالي
+
+276
+00:21:04,050 --> 00:21:08,650
+بنقدر نعرف أي مصدر ضوئي أثره الـ psycho physical
+
+277
+00:21:08,650 --> 00:21:12,810
+أثره النفسي الفيزيائي على الـ visual system بتاع
+
+278
+00:21:12,810 --> 00:21:17,010
+العين بدون ما نعيد إجراء التجربة لأن كل واحدة من
+
+279
+00:21:17,010 --> 00:21:21,680
+الأطوال الموجية المرئية لها luminous efficacy curve
+
+280
+00:21:21,680 --> 00:21:26,240
+بيقول لأن عند شدة إضاءة معينة من هذا اللون بيكون
+
+281
+00:21:26,240 --> 00:21:30,180
+أثره على العين كذا عند شدة إضاءة أخرى من نفس اللون
+
+282
+00:21:30,180 --> 00:21:34,220
+بيكون كذا طيب هذا الـ curve خاص بالأحمر وفيه curve
+
+283
+00:21:34,220 --> 00:21:37,080
+خاص بالأخضر وفيه curve خاص بالأزرق وفيه curve خاص
+
+284
+00:21:37,080 --> 00:21:43,410
+بالبنفسجي و هكذا طيب عندي مصدر بيصدر نوعين من الـ
+
+285
+00:21:43,410 --> 00:21:48,410
+.. الـ .. الـ electromagnetic waves مثلا البرتقالي و
+
+286
+00:21:48,410 --> 00:21:52,830
+الأزرق على سبيل المثال بنشوف قداش بيصدر شدة إضاءة
+
+287
+00:21:52,830 --> 00:21:56,690
+برتقالي و شدة إضاءة أزرق و بنضربهم في الـ luminous
+
+288
+00:21:56,690 --> 00:22:00,670
+efficacy curve بتطلع الـ response لكل واحد منهم
+
+289
+00:22:00,670 --> 00:22:03,770
+بنجمعهم بتطلع الـ response العام لهذا المصدر بنقول
+
+290
+00:22:03,770 --> 00:22:08,330
+هذا المصدر هيأثر كذا كذا كذا على هذا فبالتالي هذه
+
+291
+00:22:08,330 --> 00:22:13,780
+القضية اللي في الـ photometry احنا بنعملها طيب إذا
+
+292
+00:22:13,780 --> 00:22:18,540
+ما الذي نصنعه؟
+
+293
+00:22:18,540 --> 00:22:22,800
+different luminous efficacy curves are used to
+
+294
+00:22:22,800 --> 00:22:26,240
+assist vision under photopic and scoptopic
+
+295
+00:22:26,240 --> 00:22:29,580
+lighting conditions وهذه القضية اللي احنا عملناها
+
+296
+00:22:29,580 --> 00:22:33,480
+بنجريها يعني في .. في luminous efficacy curve
+
+297
+00:22:33,480 --> 00:22:40,410
+للطيف الأحمر والعين في النهار وفي نفس luminous
+
+298
+00:22:40,410 --> 00:22:44,890
+efficacy curve آخر للأحمر أيضا أثناء العين و هي في
+
+299
+00:22:44,890 --> 00:22:48,470
+الظلام فساعتها احنا بنقدر نقول قداش هذا المصدر
+
+300
+00:22:48,470 --> 00:22:54,090
+الضوء ايه بي .. بيأثر على العين .. بيأثر على العين
+
+301
+00:22:54,090 --> 00:23:00,950
+طيب بدنا نشوف example بسيط example بسيط أنه في
+
+302
+00:23:00,950 --> 00:23:05,650
+عندي light source مصدر ضوء بس بيصدر فقط
+
+303
+00:23:05,650 --> 00:23:10,740
+ultraviolet light هذا المصدر الضوء اللي بيصدر فقط
+
+304
+00:23:10,740 --> 00:23:15,360
+ultraviolet light has radiometric intensity، إله
+
+305
+00:23:15,360 --> 00:23:19,900
+شدة إشعاع، بس الـ luminous intensity عنده صفر، ليش؟
+
+306
+00:23:19,900 --> 00:23:23,980
+لأنه غير مرئي، مهما زادت الإشعاع بتاعه، لو
+
+307
+00:23:23,980 --> 00:23:28,120
+حطيناه على أقوى إشعاع من الـ ultraviolet ممكن،
+
+308
+00:23:28,120 --> 00:23:31,540
+وإنسان واقف أمامه، لن يحدث عنده أثر لا psychology
+
+309
+00:23:31,540 --> 00:23:35,960
+ولا فيزيائي psychophysiological response هيكون صفر
+
+310
+00:23:35,960 --> 00:23:41,660
+لأنه غير مرئي غير مرئي فبالتالي عشان نعرف أثر أي
+
+311
+00:23:41,660 --> 00:23:45,000
+مصدر لازم في الأول أحدد الأطياف الصادرة من هذا
+
+312
+00:23:45,000 --> 00:23:49,950
+المصدر أطوال الموجية الصادرة من هذا المصدر وكل طول
+
+313
+00:23:49,950 --> 00:23:53,070
+موجي each wavelength بنضربها في الـ luminous
+
+314
+00:23:53,070 --> 00:23:56,230
+efficacy curve بتاعها بعدين الـ responses
+
+315
+00:23:56,230 --> 00:24:00,850
+الاستجابات لكل طيف are summed يعني بيتم جمعها
+
+316
+00:24:00,850 --> 00:24:04,070
+across the visible spectrum to estimate the
+
+317
+00:24:04,070 --> 00:24:08,910
+response of the visual system عشان نقدر قداش الـ
+
+318
+00:24:08,910 --> 00:24:11,450
+visual system أو إيش طبيعة الاستجابة بتاعة الـ
+
+319
+00:24:11,450 --> 00:24:16,990
+visual system هاي عندنا مثلا الـ luminous efficacy
+
+320
+00:24:16,990 --> 00:24:21,030
+هذا المصباح اللي اخترعه اديسون في البداية اديسون
+
+321
+00:24:21,030 --> 00:24:25,770
+light bulb الـ luminous efficacy طبعا في الـ 1880
+
+322
+00:24:25,770 --> 00:24:29,350
+هذا مصباح من سنة الـ 1880 الـ luminous efficacy
+
+323
+00:24:29,350 --> 00:24:35,490
+بتاعته منخفضة جدا أعلى منه يعني بمجال كبير تمام
+
+324
+00:24:35,490 --> 00:24:38,950
+طبعا الـ luminous efficacy تقاس باللومن لكل وات
+
+325
+00:24:38,950 --> 00:24:42,870
+باللومن لكل وات هنا تقريبا اتنين لومن لكل وات هنا
+
+326
+00:24:43,680 --> 00:24:47,940
+عشر أضعافه اللي هي الـ incandescent lamp اللي هي
+
+327
+00:24:47,940 --> 00:24:53,080
+بنعرفها كلنا تقريبا عشرين أو ثمانية عشر لومن لكل
+
+328
+00:24:53,080 --> 00:24:57,670
+وات هنا الـ compact fluorescent lamp اللي المصابيح
+
+329
+00:24:57,670 --> 00:25:01,970
+المعتادة عندنا واللي هي تقدر تقريبا ما يقرب من
+
+330
+00:25:01,970 --> 00:25:07,670
+الستين ستين لومن لكل وات هنا الـ neon اللي هو light
+
+331
+00:25:07,670 --> 00:25:12,810
+linear fluorescent lamp تقريبا فوق السبعين آخر
+
+332
+00:25:12,810 --> 00:25:15,890
+حاجة الـ led اللي هي light emitting diode الـ
+
+333
+00:25:15,890 --> 00:25:19,490
+luminous efficacy بتاعته أعلى تقريبا تقترب من مئتين
+
+334
+00:25:19,490 --> 00:25:24,730
+لومن يعني مئة ضعف اللي هي مصباح اديسون فبالتالي
+
+335
+00:25:24,730 --> 00:25:31,550
+حسب الأطياف اللي صادرة من كل مصدر كام .. كام طياف
+
+336
+00:25:31,550 --> 00:25:39,190
+مرئي و هذه الأطياف كل واحد منها بده ينضرب في الـ
+
+337
+00:25:39,190 --> 00:25:43,530
+luminous efficacy curve بتاعه ونجمع أثرها كلها على
+
+338
+00:25:43,530 --> 00:25:47,610
+النظام البصري لعين الإنسان على النظام البصري لعين
+
+339
+00:25:47,610 --> 00:25:51,110
+الإنسان كثير من الناس اللي بيشتغلوا في المجال
+
+340
+00:25:51,110 --> 00:25:55,050
+الطبي بيتلخبطوا في قضية أنه يفرقوا بين الـ
+
+341
+00:25:55,050 --> 00:25:57,730
+radiometric و الـ photometric units طبعا الـ
+
+342
+00:25:57,730 --> 00:26:01,570
+photometric units بتقيس النشاط أو بتقيس الكمية
+
+343
+00:26:01,570 --> 00:26:08,520
+الإشعاعية اللي بتحدث أثر على أثر نفسي فيزيائي على
+
+344
+00:26:08,520 --> 00:26:11,820
+عين الإنسان أو على النظام البصري بتاع الإنسان أو
+
+345
+00:26:11,820 --> 00:26:16,040
+على الإنسان ككل يعني احنا بنحكي عن قياس في المجال
+
+346
+00:26:16,040 --> 00:26:20,820
+المرئي بينما الـ radiometric measurements اللي هي
+
+347
+00:26:20,820 --> 00:26:24,360
+القياس الإشعاعي في الـ range اللي حكيناه واللي
+
+348
+00:26:24,360 --> 00:26:28,300
+بتروح من الـ microwave لغاية الـ soft x-ray هيك
+
+349
+00:26:28,300 --> 00:26:32,100
+بتنتهي المحاضرة ويعطيكم العافية والسلام عليكم
+
+350
+00:26:32,100 --> 00:26:33,620
+ورحمة الله وبركاته
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6f385d622c6c0ec29af79136c9979af7c5728961
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80_postprocess.srt
@@ -0,0 +1,1400 @@
+1
+00:00:02,580 --> 00:00:05,460
+بسم الله الرحمن الرحيم بنكمل مع محاضرات ال
+
+2
+00:00:05,460 --> 00:00:09,720
+physical optics ووصلنا لعنوان ال radiometry and
+
+3
+00:00:09,720 --> 00:00:14,520
+photometry يعني القياس الإشعاعي و القياس الإضائي
+
+4
+00:00:14,520 --> 00:00:18,120
+عشان نعرف إيش الفرق بين القياس الإشعاعي اللي هو ال
+
+5
+00:00:18,120 --> 00:00:22,840
+radiometryوالقياس الإضاءي اللي هو ال photometry
+
+6
+00:00:22,840 --> 00:00:27,880
+بدنا نعطي بعض المقدمات البسيطة بنقول it is
+
+7
+00:00:27,880 --> 00:00:31,580
+necessary at times to measure the amount of light
+
+8
+00:00:31,580 --> 00:00:36,320
+produced by a source or illuminating a surface
+
+9
+00:00:36,320 --> 00:00:40,120
+يعني في بعض الأحيان بنحتاج أن نعرف كمية الضوء
+
+10
+00:00:40,120 --> 00:00:45,480
+الصادرة من مصدر ماء أو كمية الضوء اللي أضاءت سطح
+
+11
+00:00:45,480 --> 00:00:50,450
+ماء مثال على ذلك الرسم هاي بتوضحهعندي هاي مصدر
+
+12
+00:00:50,450 --> 00:00:54,970
+ضوء، هذا المصباح الكهربائي بيصدر ضوء أحيانا بنحتاج
+
+13
+00:00:54,970 --> 00:01:00,710
+نعرف قداش كمية الضوء اللي بيصدرها هذا المصدر الضوء
+
+14
+00:01:01,220 --> 00:01:04,680
+أيضا أحيانا بيكون احنا مش معنين بكمية الضوء
+
+15
+00:01:04,680 --> 00:01:09,240
+الصادرة من مصدر ما، ولكن كمية الضوء الصادقة على
+
+16
+00:01:09,240 --> 00:01:14,160
+سطح ما جداش مثلا للمتر المربع أو لصنتيمتر المربع
+
+17
+00:01:14,160 --> 00:01:18,620
+أو لوحدة المساحة جداش بيصلها إضاءة، إما الضوء
+
+18
+00:01:18,620 --> 00:01:22,420
+الصادر جداش كميته أو الضوء الصاقط اللي هو
+
+19
+00:01:22,420 --> 00:01:26,420
+illuminating a surface جداش كميته، إذا في بعض
+
+20
+00:01:26,420 --> 00:01:32,000
+الأحيان نحتاج لقياس أي واحد من الشيءينمثال على ذلك
+
+21
+00:01:32,000 --> 00:01:35,180
+يعني إيش الحاجة؟ يعني لماذا نحتاج أحياناً لقياس
+
+22
+00:01:35,180 --> 00:01:40,320
+الضوء الصادر من سطحنا أو الضوء الصاقط على سطحنا؟
+
+23
+00:01:40,320 --> 00:01:40,420
+نقول
+
+24
+00:02:01,410 --> 00:02:06,250
+جهاز ال perimeter هو جهاز فحص الساحة البصرية أو
+
+25
+00:02:06,250 --> 00:02:12,250
+الحقل البصري أو ال visual field هاي أن أمثل هذا
+
+26
+00:02:12,250 --> 00:02:17,730
+الجهاز .. هاي الجهاز عبارة عن بويلحوب يعني جاي
+
+27
+00:02:17,730 --> 00:02:22,230
+بشكل عمودي هنا هذه القطعة بيسموها chin rest المريض
+
+28
+00:02:22,230 --> 00:02:28,130
+بيحط ذقنه عليها هذه بيسموها head restبي .. بيحط ال
+
+29
+00:02:28,130 --> 00:02:31,470
+.. جبينه عليها، إذا الرأس المريض بتكون على ال head
+
+30
+00:02:31,470 --> 00:02:34,290
+rest و ذقن المريض بتكون على ال chin rest و هو
+
+31
+00:02:34,290 --> 00:02:38,150
+بيكون مواجه .. وجهه مواجه لل bowel أو الحوض .. لل
+
+32
+00:02:38,150 --> 00:02:43,470
+bowel أو الحوض الآن بتم إغلاق عين واحدة أو عمل
+
+33
+00:02:43,470 --> 00:02:47,430
+patching .. تسكير لعين واحدة عشان نفحص حق للإبصار
+
+34
+00:02:47,990 --> 00:02:52,250
+لأ العين الأخرى كيف يفحص حق .. حق للإبصار يفحص بإن
+
+35
+00:02:52,250 --> 00:02:55,630
+المريض بيطلب منه أنه يركز على نقطة مركزية بيكون
+
+36
+00:02:55,630 --> 00:03:00,650
+إلها إضاءة بلون معين و هذا البول في نقاط أخرى
+
+37
+00:03:00,650 --> 00:03:05,010
+بالضيق يعني بطريقة عشوائية مرة في المكان هذا مرة
+
+38
+00:03:05,010 --> 00:03:07,810
+في المكان هذا مرة في المكان هذا مرة في المكان هذا
+
+39
+00:03:07,810 --> 00:03:12,180
+مرة في المكان هذا الآن ضروري المريضيعني يركز بعينه
+
+40
+00:03:12,180 --> 00:03:15,660
+على ال central point اللي هو ال fixating point وما
+
+41
+00:03:15,660 --> 00:03:21,340
+يحرك عينه بتاتا وإنما بيمسك في إيده يعني مكبس أو
+
+42
+00:03:21,340 --> 00:03:25,380
+.. أو زر ولمّا بي .. هو مركز في النقطة المركزية
+
+43
+00:03:25,380 --> 00:03:30,500
+إذا أيضه ظهر في الأطرافبيضغط يعني بمعنى انه شايف
+
+44
+00:03:30,500 --> 00:03:34,680
+هذا الضوء يعني هذا السهم الأصفر بيأشر لنقطة مضيئة
+
+45
+00:03:34,680 --> 00:03:37,660
+طبعا المريض ما بيتطلع على هذه النقطة وانما هو
+
+46
+00:03:37,660 --> 00:03:41,840
+بيتطلع على النقطة المركزية اذا هذه النقطة سقطت على
+
+47
+00:03:41,840 --> 00:03:44,840
+ال peripheral retina بتاعته وشافها معناته بيدغط
+
+48
+00:03:44,840 --> 00:03:50,100
+وبالتالي الجهاز بيسجل ان المنطقة هذهضمن حقل
+
+49
+00:03:50,100 --> 00:03:54,340
+الإبصار المرئي بالنسبة لهذه العين جهاز visual
+
+50
+00:03:54,340 --> 00:03:57,560
+field أحدث أيضا نفس القضية بس الأمر بيكون
+
+51
+00:03:57,560 --> 00:04:01,080
+computerized هذه ال .. ال .. ال .. ال .. ال ..
+
+52
+00:04:01,400 --> 00:04:05,960
+المقبس أو الزر اللى بيضغط عليه المريض لما يشوف
+
+53
+00:04:05,960 --> 00:04:11,300
+النقطة اللى تم إضاءتها له في هذا الـ bowel القصد
+
+54
+00:04:11,300 --> 00:04:15,420
+علاقة هذا الفحص عشان هذا الفحص يكون دقيق هذا الفحص
+
+55
+00:04:15,420 --> 00:04:20,580
+فحص ال visual field أو الساحة البصرية بيفحص في
+
+56
+00:04:20,580 --> 00:04:25,470
+العديد من الأمراض ولكنيعني من أكتر الأمراض اللى
+
+57
+00:04:25,470 --> 00:04:28,210
+بيفحص فيها ال visual field مرض لجليكوما اللى هو
+
+58
+00:04:28,210 --> 00:04:32,990
+ارتفاع ضغط العين ارتفاع ضغط العين لأنه بيتلف العصب
+
+59
+00:04:32,990 --> 00:04:40,220
+البصري وبالتاليبيصير مناطق من ال retina يعني ما
+
+60
+00:04:40,220 --> 00:04:44,920
+بتشوف لأنه الألياف بتاعتها اللي بتشارك في تكوين
+
+61
+00:04:44,920 --> 00:04:48,680
+العصب البصري بتكون ماتت بسبب ال glucoma فبالتالي
+
+62
+00:04:48,680 --> 00:04:53,020
+بتصير هذه المناطق، مناطق يعني خارج ال visual field
+
+63
+00:04:53,020 --> 00:04:55,960
+أو مناطق سوداء في ال visual field يعني مناطق
+
+64
+00:04:55,960 --> 00:04:57,960
+انعدام الرؤية
+
+65
+00:05:00,050 --> 00:05:04,790
+ضروري جدا عشان يكون الفحص تقيق لازم أعمل الفحص
+
+66
+00:05:04,790 --> 00:05:09,570
+يعني في مرات عديدة، يعني ممكن أعمل الفحص للمريض
+
+67
+00:05:09,570 --> 00:05:14,010
+اليوم، بعد تلت شهور، بعد ست شهور، بعد سنة، بعد
+
+68
+00:05:14,010 --> 00:05:16,810
+سنتين، إلى آخر، عشان أتابع هل الجلوكومة
+
+69
+00:05:16,810 --> 00:05:22,210
+progressive، يعني بتتطور للأسوأ، ولا stable، يعني
+
+70
+00:05:22,210 --> 00:05:28,160
+مستقرة ومستجيبة للعلاج اللي بتم إعطاهطيب عشان يكون
+
+71
+00:05:28,160 --> 00:05:31,160
+الفحص دقيق ضروري ال illumination ال background
+
+72
+00:05:31,160 --> 00:05:35,240
+illumination الإضاءة الأساسية للجهاز مش إضاءة
+
+73
+00:05:35,240 --> 00:05:39,280
+النقطة هى هذا الجهاز فيه إله إضاءة أساسية يعني زي
+
+74
+00:05:39,280 --> 00:05:43,460
+ما أنتم لاحظين انبين مضيق بس النقطة هتكون إضاءتها
+
+75
+00:05:43,460 --> 00:05:46,920
+أعلى منه ولكن هو إله إضاءة أساسية بسمها ال
+
+76
+00:05:46,920 --> 00:05:50,500
+background illumination إذا أنا اجيت فحصت المريض
+
+77
+00:05:50,500 --> 00:05:56,510
+سين ال background illumination اليوميعني إله مقدار
+
+78
+00:05:56,510 --> 00:06:00,490
+معين إضاءة معينة ثم عند ال follow-up يعني في
+
+79
+00:06:00,490 --> 00:06:05,610
+المراجعة بعد تلت شهور أو ست شهور فحصته بإضاءة أقل
+
+80
+00:06:05,610 --> 00:06:09,590
+أو أكتر background illumination أكتر أو أقل بيكون
+
+81
+00:06:09,590 --> 00:06:12,650
+مفحص غير دقيق ضروري إن ال illumination بتاع البو
+
+82
+00:06:12,650 --> 00:06:16,790
+يكون ثابت عشان نقدر نعمل comparison عشان نقدر نعمل
+
+83
+00:06:16,790 --> 00:06:21,500
+comparison إذا for examplethe power of a perimeter
+
+84
+00:06:21,500 --> 00:06:26,480
+حوض ال perimeter حوض جهاز فحص الساحة البصرية must
+
+85
+00:06:26,480 --> 00:06:30,920
+be accurately illuminated لابد من إضاءته بشكل دقيق
+
+86
+00:06:30,920 --> 00:06:36,020
+و ثابت in order عشان أقدر for any comparisons of
+
+87
+00:06:36,020 --> 00:06:39,320
+visual field measurements performed on different
+
+88
+00:06:39,320 --> 00:06:42,780
+instruments سواء المريض عمل عند الفحص أو عمل عند
+
+89
+00:06:42,780 --> 00:06:46,820
+أي من الزملاء الآخرين في أي من المراكز الطبيةعشان
+
+90
+00:06:46,820 --> 00:06:50,220
+نقدر نقول أو نقدر نقارن بين الفحص الأول والتاني
+
+91
+00:06:50,220 --> 00:06:53,300
+والتالت والرابع ضروري ال background illumination
+
+92
+00:06:53,300 --> 00:06:57,700
+بتاعة ال bowel بتاعة الحوض بتاعة ال perimeter انه
+
+93
+00:06:57,700 --> 00:07:02,620
+تكون ثابتة ومش متغيرة لان هذا هيأثر على استجابة
+
+94
+00:07:02,620 --> 00:07:12,210
+المريض اذا هذا يعني لي انهالضوء الصادر من الباول
+
+95
+00:07:12,210 --> 00:07:16,950
+لازم يكون قياسه دقيقة يعني كميته موحدة كميته موحدة
+
+96
+00:07:16,950 --> 00:07:19,690
+احنا بنقول كالقاتي عشان ال visual field
+
+97
+00:07:19,690 --> 00:07:23,270
+measurements performed on different instruments او
+
+98
+00:07:23,270 --> 00:07:26,170
+on the same instruments at different times to be
+
+99
+00:07:26,170 --> 00:07:30,070
+meaningful عشان اقدر اقارن بينهم بنشوف مثال بنقول
+
+100
+00:07:30,070 --> 00:07:33,690
+هذا ال baseline visual field مريض اجا انعمله ال
+
+101
+00:07:33,690 --> 00:07:36,750
+visual field واضح المناطق السوداء هي انه مابيشوفش
+
+102
+00:07:36,750 --> 00:07:41,040
+فيهاهذه ال visual field ككل المناطق هاي ما بيشوفش
+
+103
+00:07:41,040 --> 00:07:45,060
+فيها بعد سنة انعمل الفحص بعد سنة أخرى انعمل الفحص
+
+104
+00:07:45,060 --> 00:07:49,740
+واضح ان المناطق بتزداد بعد تلت سنين من ال baseline
+
+105
+00:07:49,740 --> 00:07:54,820
+test انعمل الفحص و بعد أربع سنين عشان أقدر أقارن
+
+106
+00:07:54,820 --> 00:07:58,140
+أقول إن والله فيه progression يعني زي ما هذا الصوت
+
+107
+00:07:58,140 --> 00:08:02,380
+ضروري ال illumination بتاع ال .. بتاع ال .. ال
+
+108
+00:08:02,380 --> 00:08:05,920
+bowel بتاع ال perimeter أنه يكون ثابت ومش مرة أحط
+
+109
+00:08:05,920 --> 00:08:11,470
+مثلاكم معين و مرة تانية كم آخر و مرة تالتة كم تالت
+
+110
+00:08:11,470 --> 00:08:15,370
+.. ساعتها مش أقدر أعمل المقارنات طبعا هذه ممكن
+
+111
+00:08:15,370 --> 00:08:19,050
+تكون للعين اليمين و هذه للعين الشمال أيضا بعد سنة
+
+112
+00:08:19,050 --> 00:08:22,050
+.. بعد سنتين .. بعد تلاتة .. بعد أربع .. لو أجينا
+
+113
+00:08:22,050 --> 00:08:25,870
+نقول بعد أربع سنوات شايفين المناطق .. مناطق
+
+114
+00:08:25,870 --> 00:08:28,650
+بيسموها scotoma يعني منطقة انعدام الرؤية اللي
+
+115
+00:08:28,650 --> 00:08:33,010
+باللون الأسود و هنا ال scotoma طبعاواضح من الصور
+
+116
+00:08:33,010 --> 00:08:37,870
+انه في progression يعني المرض بيزداد سوءًا طب لو
+
+117
+00:08:37,870 --> 00:08:43,210
+احنا أخدنا معلومة انه ال background illumination
+
+118
+00:08:43,210 --> 00:08:46,690
+ماكانش موحد اذا كل المقارنة هذه لا فائدة منها لابد
+
+119
+00:08:46,690 --> 00:08:50,930
+للمريض منه نقم يعيد هذا ال test background
+
+120
+00:08:50,930 --> 00:08:55,410
+illumination موحد background illumination موحد
+
+121
+00:08:55,410 --> 00:08:59,370
+نيجي
+
+122
+00:08:59,370 --> 00:09:06,310
+نحكي عن القياس الإشعاعيالراديومتري القياس الإشعائي
+
+123
+00:09:06,310 --> 00:09:17,750
+هو ان انا
+
+124
+00:09:17,750 --> 00:09:21,150
+اجيس الـ electromagnetic radiation بين هدول
+
+125
+00:09:21,150 --> 00:09:25,490
+الترددين نشوف مع بعض ايش هدول الترددين نطلع على
+
+126
+00:09:25,490 --> 00:09:31,420
+المنظر المكبرهي عندي 10 اقص 11 وهي انا عندي 10 اقص
+
+127
+00:09:31,420 --> 00:09:36,060
+16 يعني هنا بيشمل عندي ال .. شوية من ال microwave
+
+128
+00:09:36,060 --> 00:09:40,100
+شوية من ال infrared و ال visible light و ال
+
+129
+00:09:40,100 --> 00:09:44,120
+ultraviolet و بداية ال إيش ال x-ray إذا هذا ال
+
+130
+00:09:44,120 --> 00:09:48,800
+range لما أجيسه لما أجيس الكمية ال electromagnetic
+
+131
+00:09:48,800 --> 00:09:53,540
+radiation كمية الإشعاع الصادرة من مصدرنا بصدرلي
+
+132
+00:09:53,540 --> 00:09:57,710
+هذه ال radiation بسميهاأنا بكون عملت radiometry
+
+133
+00:09:57,710 --> 00:10:02,790
+radiometry يعني لو تصورنا أن في جهاز بيصدر إشعاعات
+
+134
+00:10:02,790 --> 00:10:06,730
+بيصدر electromagnetic waves وهذه ال
+
+135
+00:10:06,730 --> 00:10:09,810
+electromagnetic waves اللي بيصدرها هذا الجهاز
+
+136
+00:10:09,810 --> 00:10:15,210
+ترددها بتراوح بين عشرة تلاتة في عشرة أُس إحداش
+
+137
+00:10:15,210 --> 00:10:20,410
+لتلاتة في عشرة أُس ستة عشر هيرتز ذبذبه معناته هو
+
+138
+00:10:20,410 --> 00:10:24,680
+هذا الجهاز بيصدر ليه microwavesبصدرلي infrared
+
+139
+00:10:24,680 --> 00:10:29,260
+بصدر visible light و بصدر ultraviolet و بصدر قليل
+
+140
+00:10:29,260 --> 00:10:33,900
+بيسموها ال soft x-ray بيسموها ال soft x-ray ليه
+
+141
+00:10:33,900 --> 00:10:37,760
+ترددها قريب من تردد ال ultraviolet إذا هذا الجهاز
+
+142
+00:10:37,760 --> 00:10:41,980
+بيصدر كل هذه ال electromagnetic radiation لما بجيس
+
+143
+00:10:41,980 --> 00:10:45,900
+الإشعاع اللي صادر من هذا الجهاز هذه العملية تسمى
+
+144
+00:10:45,900 --> 00:10:50,090
+radiometryإذا الـ Radiometry is the measurement هو
+
+145
+00:10:50,090 --> 00:10:56,130
+قياس الـ electromagnetic radiation إشعاع الموجات
+
+146
+00:10:56,130 --> 00:11:01,090
+الكهرومغناطسية اللي ذبذبتها بتتراوح بين 3 في 10
+
+147
+00:11:01,090 --> 00:11:07,830
+أقصى 11 هيرتز ذبذبة ل 3 في 10 أقصى 16 هيرتز هذا ال
+
+148
+00:11:07,830 --> 00:11:11,990
+range corresponding to wavelengths من 10 نانومتر ل
+
+149
+00:11:11,990 --> 00:11:19,790
+1 ملي متر10 nanometer أقل من 400 nanometer و أقل
+
+150
+00:11:19,790 --> 00:11:23,750
+من 700 nanometer يعني من 400 ل 700 nanometer جاية
+
+151
+00:11:23,750 --> 00:11:27,310
+بين العشرة للواحد ملي متر يعني ال visible light
+
+152
+00:11:27,310 --> 00:11:30,970
+جاية ضمن هذا ال range و ايضا ال infrared جاية و ال
+
+153
+00:11:30,970 --> 00:11:36,500
+ultraviolet جاية و شوية microwave و شويةx-ray إذا
+
+154
+00:11:36,500 --> 00:11:41,320
+therefore radiometry spans the microwave infrared
+
+155
+00:11:41,320 --> 00:11:46,180
+visible light ultraviolet and soft x-ray regions
+
+156
+00:11:46,180 --> 00:11:50,740
+of the electromagnetic spectrum يعني أي مصدر أي
+
+157
+00:11:50,740 --> 00:11:56,260
+مصدر بيصدرلي هذه الذبذبات من هذا ال range لعند هذا
+
+158
+00:11:56,260 --> 00:12:01,890
+ال range هذا قياس ال ..الموجات الكهرومغناطسية
+
+159
+00:12:01,890 --> 00:12:05,990
+الصادرة من هذا المصدر يسمى عملية الـ Radiometry
+
+160
+00:12:05,990 --> 00:12:11,970
+القياس الإشعاعي غالبا احنا بنحتاجش .. بنحتاجش ان
+
+161
+00:12:11,970 --> 00:12:16,510
+نقيس كل هذا القياس يعني عندي مصدر صحيح بيصدر كل
+
+162
+00:12:16,510 --> 00:12:19,390
+هذه الأنواع من الموجات بيصدرلي microwave و
+
+163
+00:12:19,390 --> 00:12:23,090
+infrared و visible و ultraviolet إلى آخرى أحيانا
+
+164
+00:12:23,090 --> 00:12:29,210
+بركز القياس على نوع معينفقط من كل هذه الموجات اللي
+
+165
+00:12:29,210 --> 00:12:34,330
+بصدرها هذا المصدر إذا ركزت قياسي على نوع معين هذا
+
+166
+00:12:34,330 --> 00:12:39,090
+بتسمى Spectral Radiometry Spectral Radiometry
+
+167
+00:12:39,090 --> 00:12:44,170
+فبالتالي هذه القضية ضرورية إحنا نفهمها often such
+
+168
+00:12:44,170 --> 00:12:47,890
+broad measurements هذا يعتبر قياس عريض ليش؟ لأن
+
+169
+00:12:47,890 --> 00:12:52,870
+أنا أخدت من عند ال microwave ووصلت لل soft x-ray
+
+170
+00:12:52,870 --> 00:12:57,320
+يعني أخدت شملت حاجات كتيرةفهذا عادة القياس مش
+
+171
+00:12:57,320 --> 00:13:00,820
+ضروري، مش ضروري، إذا often such broad measurements
+
+172
+00:13:00,820 --> 00:13:06,100
+are not necessary، هذه القياسات اللي هي العريضة
+
+173
+00:13:06,100 --> 00:13:10,060
+اللي بتشمل موجات، أنواع موجات كتيرة، غالبا مش لازم
+
+174
+00:13:11,130 --> 00:13:14,990
+فبالتالي بدل ما نعمل Radiometry بنعمل Spectral
+
+175
+00:13:14,990 --> 00:13:20,150
+Radiometry يعني الإشعاع الطيفي أو قياس الإشعاع
+
+176
+00:13:20,150 --> 00:13:24,230
+الطيفي يعني بركز على طيف معين أو Spectrum معين إذا
+
+177
+00:13:24,230 --> 00:13:28,110
+Spectral Radiometry is used instead to measure a
+
+178
+00:13:28,110 --> 00:13:32,740
+narrow portion of the electromagnetic spectrumهذا
+
+179
+00:13:32,740 --> 00:13:37,340
+بالنسبة لقياس الإشعاعي، الآن القياس الإضائي الـ
+
+180
+00:13:37,340 --> 00:13:41,780
+photometry هو نوع من أنواع القياس الإشعاعي، بس
+
+181
+00:13:41,780 --> 00:13:46,340
+طالما يقولنا photometry معناته إحنا بنقصد فيه قياس
+
+182
+00:13:46,340 --> 00:13:50,320
+الإشعاعات في مجال الضوء المرئي، إذا photometry
+
+183
+00:13:50,320 --> 00:13:54,420
+measures the human visual systems psychological
+
+184
+00:13:54,420 --> 00:14:00,220
+response to light، إذاالـ photometry بتجيثني
+
+185
+00:14:00,220 --> 00:14:05,280
+استجابة النظام البصري بتاع الإنسان الاستجابة
+
+186
+00:14:05,280 --> 00:14:10,500
+النفسية ال psychological response بتاع عين الإنسان
+
+187
+00:14:10,500 --> 00:14:13,560
+أو psychological response بتاع ال human visual
+
+188
+00:14:13,560 --> 00:14:16,740
+system لل light و لما بنقول لل light معناته احنا
+
+189
+00:14:16,740 --> 00:14:22,450
+بنقصد فقط الضوء المرئيBasically ال photometry is a
+
+190
+00:14:22,450 --> 00:14:26,730
+type of radiometry عشان نكون دقيقين ال photometry
+
+191
+00:14:26,730 --> 00:14:30,690
+نوع من أنواع ال radiometry لأنها بتجيس ليه بتجيس
+
+192
+00:14:30,690 --> 00:14:36,230
+ليه الموجات المرئية واللي هي تعتبر جزء من الطيف
+
+193
+00:14:36,230 --> 00:14:40,470
+الكهرومغناطيسيطيب إذا ال photometry is a type of
+
+194
+00:14:40,470 --> 00:14:43,850
+radiometry بس لو حد سؤالني .. سألني قاللي ال
+
+195
+00:14:43,850 --> 00:14:47,690
+radiometry تعتبر نوع من أنواع ال photometry؟
+
+196
+00:14:47,690 --> 00:14:52,990
+بنقوله لأ ال photometryالـ photometry is a type of
+
+197
+00:14:52,990 --> 00:14:56,630
+radiometry but radiometry is not a type of
+
+198
+00:14:56,630 --> 00:15:01,190
+photometry لأن ال radiometry عبارة عن قياس أوسع ال
+
+199
+00:15:01,190 --> 00:15:06,590
+radiometry من ال microwave لعين ال soft x-ray ال
+
+200
+00:15:06,590 --> 00:15:10,970
+photometry أثر هذا الجزء من الطيف الكهرومغناطيسي
+
+201
+00:15:10,970 --> 00:15:15,350
+أثر نفسي على العين أثر نفسي أو ال psychology على
+
+202
+00:15:15,840 --> 00:15:18,820
+العين، يعني هو هيسقط على العين على مساحة من
+
+203
+00:15:18,820 --> 00:15:23,980
+الشبكية ثم ينقل عبر ال visual system ويعطي شعور
+
+204
+00:15:23,980 --> 00:15:29,000
+معين عند الإنسان، شعور معين عند الإنسان فبالتالي
+
+205
+00:15:29,000 --> 00:15:36,000
+هذه لما بنجيس هذا الشعور أو بنجيسالأثر .. بنجيس ال
+
+206
+00:15:36,000 --> 00:15:38,680
+.. الأثر النفسي الـ psychological أو الـ
+
+207
+00:15:38,680 --> 00:15:42,500
+psychophysical response توليد بنكون احنا بنعمل
+
+208
+00:15:42,500 --> 00:15:46,380
+عملية ال photometry إذا basically photometry is a
+
+209
+00:15:46,380 --> 00:15:50,300
+type of radiometry هي نوع من أنواع ال radiometry
+
+210
+00:15:50,300 --> 00:15:54,140
+بس إيش بتختلف عنها؟that takes into account the
+
+211
+00:15:54,140 --> 00:15:57,360
+varying sensitivity of the eye to different
+
+212
+00:15:57,360 --> 00:16:01,080
+wavelengths اللي بتاخد الفوتومتري بتاخد في حسابها
+
+213
+00:16:01,080 --> 00:16:07,320
+ان العين البشرية حساسة بطريقة مختلفة حسب ال
+
+214
+00:16:07,320 --> 00:16:11,940
+wavelength الساقطة عليها حساسة بطريقة مختلفة حسب
+
+215
+00:16:11,940 --> 00:16:14,480
+ال wavelength الساقطة عليها
+
+216
+00:16:16,940 --> 00:16:21,320
+مثال على ذلك لما بسقط infrared wavelength مافيش ..
+
+217
+00:16:21,320 --> 00:16:26,500
+مافيش أي شعور عند الإنسان بيتولد لأنه غير مريض لما
+
+218
+00:16:26,500 --> 00:16:32,060
+بسقط blue في شعور باللون الأزرق لما بسقط ال green
+
+219
+00:16:32,060 --> 00:16:36,120
+في شعور باللون الأخضر و هكذا .. إذا في اختلاف في
+
+220
+00:16:36,120 --> 00:16:39,460
+الشعور .. في اختلاف في الشعور هذا الاختلاف في
+
+221
+00:16:39,460 --> 00:16:43,200
+الشعور نادج عن اختلاف الطول الموجي الصابط على
+
+222
+00:16:43,200 --> 00:16:48,990
+مساحة ما من الشبكيةهجوا العلماء قالوا الأمر هذا
+
+223
+00:16:48,990 --> 00:16:56,510
+بده يعني وضع ضمن قواعد، ليش بده وضع ضمن قواعد؟ ال
+
+224
+00:16:56,510 --> 00:17:03,300
+photometryطبعا العالم لازال ينتج مصادر ضوئية بعدد
+
+225
+00:17:03,300 --> 00:17:08,520
+هائل قد يكون عدد لا يمكن الحصول مصابيح كهربائية
+
+226
+00:17:08,520 --> 00:17:14,500
+أدوات إضاءة أدوات اللي هي الشاشات الذكية اللي
+
+227
+00:17:14,500 --> 00:17:19,400
+بتصدر إضاءات مختلفة وما إلى ذلك إذا في مصادر
+
+228
+00:17:19,400 --> 00:17:25,620
+إضائية تصنع مختلفة ومتنوعةوغالبيتها العظمة بيصدر
+
+229
+00:17:25,620 --> 00:17:30,600
+.. بيصدر electromagnetic waves في ال range بتاع
+
+230
+00:17:30,600 --> 00:17:37,440
+الضوء المرقية فعشان ما نجيش احنا عند كل اختراع
+
+231
+00:17:37,440 --> 00:17:44,510
+اداة تصدر ضوءعلى سبيل المثال تم اختراع جوال ويله
+
+232
+00:17:44,510 --> 00:17:50,010
+شاشة معينة هاتف نقال ويله شاشة معينة بتصدر إضاءة
+
+233
+00:17:50,010 --> 00:17:56,130
+بطريقة معينة أو مكونة من أطياف معينة يعني نفرض 650
+
+234
+00:17:56,130 --> 00:18:01,470
+نانومتر 550 نانومتر 547 نانومتر يعني بتصدر خليط من
+
+235
+00:18:01,470 --> 00:18:05,630
+الأطوال الموجية المرئية بدل ما احنا نجري دراسات
+
+236
+00:18:05,630 --> 00:18:12,680
+على الناس كل ما بنصنعمصدر طوئي كل ما بنصنع مصدر
+
+237
+00:18:12,680 --> 00:18:15,800
+طوئي بدل ما نعمل دراسات على الناس اجوا عملوا
+
+238
+00:18:15,800 --> 00:18:21,780
+دراسات موسعة على البشر عشان يعرفوا .. عشان يعرفوا
+
+239
+00:18:21,780 --> 00:18:26,080
+أثر الأطوال الموجية المختلفة الأثر النفسي
+
+240
+00:18:26,080 --> 00:18:31,040
+الفيزيائي للأطوال الموجية المختلفة على عيون البشر
+
+241
+00:18:31,040 --> 00:18:35,850
+بمعنى based on datafrom measurements of numerous
+
+242
+00:18:35,850 --> 00:18:40,530
+people, weighting factors presented graphically as
+
+243
+00:18:40,530 --> 00:18:44,070
+luminous efficacy curves have been developed for
+
+244
+00:18:44,070 --> 00:18:47,450
+each wavelength across the visible spectrum نفهم
+
+245
+00:18:47,450 --> 00:18:52,890
+هذا الموضوع، هاي ال visible spectrum بتكون من
+
+246
+00:18:52,890 --> 00:18:57,510
+الأحمر، البرتقالي، الأصفر، الأخضر، الأزرق، النيلي،
+
+247
+00:18:57,510 --> 00:19:02,440
+البنفسكيجابوا مجموعة هائلة من الناس وعرضوا أعينهم
+
+248
+00:19:02,440 --> 00:19:07,640
+لضوء أحمر بشدة إضاءة معينة، زودوا شدة الإضاءة،
+
+249
+00:19:07,640 --> 00:19:10,260
+زودوا شدة الإضاءة، وشافوا الـ response تعادوا
+
+250
+00:19:10,260 --> 00:19:15,020
+للناس وعملوا curve لللون الأحمر، اسمه الـ luminous
+
+251
+00:19:15,020 --> 00:19:20,040
+efficacy curveكل ما زدنا شدة ال luminosity تاعت
+
+252
+00:19:20,040 --> 00:19:23,560
+هذا المصدر اللي بيعطيني الضوء الأحمر كيف بيكون ال
+
+253
+00:19:23,560 --> 00:19:26,660
+response تاع أعين الناس لكتير اللي أجرينا عليهم
+
+254
+00:19:26,660 --> 00:19:30,960
+التجربة و هذا ال curve صار هو المعدل أو المتوسط أو
+
+255
+00:19:30,960 --> 00:19:34,900
+ال standard بتاعنا الآن هذه التجربة أجريت لللون
+
+256
+00:19:34,900 --> 00:19:38,960
+الأحمر لللون البرتقالي و لللون الأصفر و كل واحد
+
+257
+00:19:38,960 --> 00:19:45,060
+أصبح له curve بيسموه luminous efficacy curve بمعنى
+
+258
+00:19:45,060 --> 00:19:51,900
+آخرلما بنصنع مصباح كهربائي أو أداة تصدر ضوء بنيجي
+
+259
+00:19:51,900 --> 00:19:57,500
+بنقول هذه الأداة أول حاجة إيش بدنا نقيمها وقداش
+
+260
+00:19:57,500 --> 00:20:02,360
+متوقع تأثر على عين
+
+261
+00:20:02,360 --> 00:20:06,720
+الإنسان احنا أنتجنا أداة وبنعرف قداش بتأثر على عين
+
+262
+00:20:06,720 --> 00:20:11,460
+الإنسان أول حاجة أول خطوة في التصنيع spectral
+
+263
+00:20:11,460 --> 00:20:15,550
+characteristics of light source are determinedيعني
+
+264
+00:20:15,550 --> 00:20:20,230
+بنقول هذا ال light source scene صنعنا light source
+
+265
+00:20:20,230 --> 00:20:23,950
+مصدر ضوئي سميناه scene إيش ال spectral
+
+266
+00:20:23,950 --> 00:20:27,010
+characteristics إله؟ إيش عن ال spectral
+
+267
+00:20:27,010 --> 00:20:29,250
+characteristics يعني؟ إيش الأطوال الموجية اللي
+
+268
+00:20:29,250 --> 00:20:33,670
+بصدر؟ نفرض إنه بصدر طول الموج الأحمر والأخضر
+
+269
+00:20:33,670 --> 00:20:36,810
+والأصفر فقط، بصدرش الأزرق، طب ماشي إذا أنا عرفنا
+
+270
+00:20:36,810 --> 00:20:42,300
+بصدر الأحمر والأخضر والأصفر فقطبنجي بنقول الأحمر
+
+271
+00:20:42,300 --> 00:20:46,520
+بنضربه في ال luminous efficacy curve بتاعه يعني في
+
+272
+00:20:46,520 --> 00:20:49,640
+شدة إضاءة معينة جداش بيأثر في شدة إضاءة معينة جداش
+
+273
+00:20:49,640 --> 00:20:53,600
+بيأثر الأخضر نفس الاشي والأصفر نفس الاشي ساعتها
+
+274
+00:20:54,570 --> 00:20:58,850
+الاستجابات المتوقعة كلها تجمع وبنقول هذا المصدر
+
+275
+00:20:58,850 --> 00:21:04,050
+الضوءي بيأثر على العين بالشكل التالي تمام فبالتالي
+
+276
+00:21:04,050 --> 00:21:08,650
+بنقدر نعرف أي مصدر ضوءي أثره ال psycho physical
+
+277
+00:21:08,650 --> 00:21:12,810
+أثره النفسي الفيزيائي على ال visual system بتاع
+
+278
+00:21:12,810 --> 00:21:17,010
+العين بدون ما نعيد إجراء التجربة لأن كل واحدة من
+
+279
+00:21:17,010 --> 00:21:21,680
+الأطوال الموجية المرئيةلها luminous efficacy curve
+
+280
+00:21:21,680 --> 00:21:26,240
+بيقول لإنه عند شدة إضاءة معينة من هذا اللون بيكون
+
+281
+00:21:26,240 --> 00:21:30,180
+أثر على العين كذا عند شدة إضاءة أخرى من نفس اللون
+
+282
+00:21:30,180 --> 00:21:34,220
+بيكون كذا طيب هذا ال curve خاص بالأحمر وفيه curve
+
+283
+00:21:34,220 --> 00:21:37,080
+خاص بالأخضر وفيه curve خاص بالأزرق وفيه curve خاص
+
+284
+00:21:37,080 --> 00:21:43,410
+بالبنفس دي و هكذا طيب عندي مصدر بيصدر نوعين منال
+
+285
+00:21:43,410 --> 00:21:48,410
+.. ال .. ال electromagnetic waves مثلا البرتقالي و
+
+286
+00:21:48,410 --> 00:21:52,830
+الأزرق على سبيل المثال بنشوف قداش بيصدر شدة إضاءة
+
+287
+00:21:52,830 --> 00:21:56,690
+برتقالي و شدة إضاءة أزرق و بنضربهم في ال luminous
+
+288
+00:21:56,690 --> 00:22:00,670
+efficacy curve بتلع ال response لكل واحد منهم
+
+289
+00:22:00,670 --> 00:22:03,770
+بنجمعهم بتلع ال response العام لهذا المصدر بنقول
+
+290
+00:22:03,770 --> 00:22:08,330
+هذا المصدر هيأثر كذا كذا كذا على هذا فبالتالي هذه
+
+291
+00:22:08,330 --> 00:22:13,780
+القضية اللي في ال photometry احنا بنعملهاطيب إذا
+
+292
+00:22:13,780 --> 00:22:18,540
+ما الذي نصنعه؟
+
+293
+00:22:18,540 --> 00:22:22,800
+different luminous efficacy curves are used to
+
+294
+00:22:22,800 --> 00:22:26,240
+assist vision under photopic and scoptopic
+
+295
+00:22:26,240 --> 00:22:29,580
+lighting conditions وهذه القضية اللي احنا عملناها
+
+296
+00:22:29,580 --> 00:22:33,480
+بنجريها يعني في .. في luminous efficacy curve
+
+297
+00:22:33,480 --> 00:22:40,410
+للطيف الأحمر والعين في النهار وفي نفسLuminous
+
+298
+00:22:40,410 --> 00:22:44,890
+efficacy curve آخر للأحمر أيضا أثناء العين و هي في
+
+299
+00:22:44,890 --> 00:22:48,470
+الظلام فساعتها احنا بنقدر نقول جداش هذا المصدر
+
+300
+00:22:48,470 --> 00:22:54,090
+الضوء ايه بي .. بيأثر على العين .. بيأثر على العين
+
+301
+00:22:54,090 --> 00:23:00,950
+طيب بدنا نشوف example بسيط example بسيط انه في
+
+302
+00:23:00,950 --> 00:23:05,650
+عندي light source مصدر ضوء بس بيصدر فقط
+
+303
+00:23:05,650 --> 00:23:10,740
+ultraviolet lightهذا المصدر الضوء اللي بيصدر فقط
+
+304
+00:23:10,740 --> 00:23:15,360
+ultraviolet light has radiometric intensity، إله
+
+305
+00:23:15,360 --> 00:23:19,900
+شدة إشعاع، بس ال luminous intensity عنده صفر، ليش؟
+
+306
+00:23:19,900 --> 00:23:23,980
+لأنه غير مر إيه، مهما زادت الإشعاع بتاعه، لو
+
+307
+00:23:23,980 --> 00:23:28,120
+حطيناه على أقوى إشعاع من ال ultraviolet ممكن،
+
+308
+00:23:28,120 --> 00:23:31,540
+وإنسان واقف أمامه، لن يحدث عنده أثر لا psychology
+
+309
+00:23:31,540 --> 00:23:35,960
+ولا فيزيائيpsychophysiological response هيكون صفر
+
+310
+00:23:35,960 --> 00:23:41,660
+لأنه غير مرئي غير مرئي فبالتالي عشان نعرف أثر أي
+
+311
+00:23:41,660 --> 00:23:45,000
+مصدر لازم في الأول أحدد الأطياف الصادرة من هذا
+
+312
+00:23:45,000 --> 00:23:49,950
+المصدر أطوال الموجية الصادرة من هذا المصدر وكلطول
+
+313
+00:23:49,950 --> 00:23:53,070
+مودي each wavelength بنضربها في ال luminous
+
+314
+00:23:53,070 --> 00:23:56,230
+efficacy curve بتاعها بعدين ال responses
+
+315
+00:23:56,230 --> 00:24:00,850
+الاستجابات لكل طيف are summed يعني بيتم جمعها
+
+316
+00:24:00,850 --> 00:24:04,070
+across the visible spectrum to estimate the
+
+317
+00:24:04,070 --> 00:24:08,910
+response of the visual system عشان نقدر جداش ال
+
+318
+00:24:08,910 --> 00:24:11,450
+visual system أو ايش طبيعة الاستجابة بتاعة ال
+
+319
+00:24:11,450 --> 00:24:16,990
+visual system هاي عندنا مثلاالـ luminous efficacy
+
+320
+00:24:16,990 --> 00:24:21,030
+هذا المصباح اللي اخترعه اديسون في البداية اديسون
+
+321
+00:24:21,030 --> 00:24:25,770
+light bulb ال luminous efficacy طبعا في ال 1880
+
+322
+00:24:25,770 --> 00:24:29,350
+هذا مصباح من سنة ال 1880 ال luminous efficacy
+
+323
+00:24:29,350 --> 00:24:35,490
+بتاعته منخفضة جدا اعلى منه يعني بمجال كبير تمام
+
+324
+00:24:35,490 --> 00:24:38,950
+طبعا ال luminous efficacy تقاس بال لومن لكل وطة
+
+325
+00:24:38,950 --> 00:24:42,870
+بال لومن لكل وطة هنا تقريبا اتنين لومن لكل وطة هنا
+
+326
+00:24:43,680 --> 00:24:47,940
+عشر أضعافه اللي هي ال incandescent lamp اللي هي
+
+327
+00:24:47,940 --> 00:24:53,080
+ابن اعرفها كلنا تقريبا عشرين او تمانتاشر لومن لكل
+
+328
+00:24:53,080 --> 00:24:57,670
+وات هنا ال compact fluorescent lampاللي المصابيح
+
+329
+00:24:57,670 --> 00:25:01,970
+المعتادة عندنا و اللي هي تقدر تقريبا ما يقرب من
+
+330
+00:25:01,970 --> 00:25:07,670
+الستين ستين لومن لكل وقت هنا ال neon اللي هو light
+
+331
+00:25:07,670 --> 00:25:12,810
+linear fluorescent lamp تقريبا فوق السبعين اخر
+
+332
+00:25:12,810 --> 00:25:15,890
+حاجة ال led اللي هي light emitting diode ال
+
+333
+00:25:15,890 --> 00:25:19,490
+luminous efficacy بتاعته اعلى تقريبا تقترب من متين
+
+334
+00:25:19,490 --> 00:25:24,730
+لومن يعني مئة ضعف اللي هي مصباح اديسون فبالتالي
+
+335
+00:25:24,730 --> 00:25:31,550
+حسب الأضيافاللي صادرة من كل مصدر كام .. كام طياف
+
+336
+00:25:31,550 --> 00:25:39,190
+مرئي و هذه الأطياف كل واحد منهابدو ينضرب في ال
+
+337
+00:25:39,190 --> 00:25:43,530
+luminous efficacy curve بتاعه ونجمع أثرها كلها على
+
+338
+00:25:43,530 --> 00:25:47,610
+النظام البصري لعين الإنسان على النظام البصري لعين
+
+339
+00:25:47,610 --> 00:25:51,110
+الإنسان كتير من الناس اللي بيشتغلوا في المجال
+
+340
+00:25:51,110 --> 00:25:55,050
+الطبي بيتلخبطوا في قضية انه يفرجوا بين ال
+
+341
+00:25:55,050 --> 00:25:57,730
+radiometric و ال photometric units طبعا ال
+
+342
+00:25:57,730 --> 00:26:01,570
+photometric units بتقيس النشاط أو بتقيس الكمية
+
+343
+00:26:01,570 --> 00:26:08,520
+الإشعاعية اللي بتحدث أثرعلى أثر نفسي فيزيائي على
+
+344
+00:26:08,520 --> 00:26:11,820
+عين الإنسان أو على النظام البصري بتاع الإنسان أو
+
+345
+00:26:11,820 --> 00:26:16,040
+على الإنسان ككل يعني احنا بنحكي عن قياس في المجال
+
+346
+00:26:16,040 --> 00:26:20,820
+المرئي بينما ال radiometric measurements اللي هي
+
+347
+00:26:20,820 --> 00:26:24,360
+القياس الإشعاعي في ال range اللي حكيناه و اللي
+
+348
+00:26:24,360 --> 00:26:28,300
+بتروح من ال microwave لغاية ال soft x-ray هيك
+
+349
+00:26:28,300 --> 00:26:32,100
+بتنتهي المحاضرة و يعطيكم العافية والسلام عليكم
+
+350
+00:26:32,100 --> 00:26:33,620
+ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80_raw.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6f385d622c6c0ec29af79136c9979af7c5728961
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uiL5XqE1Z80_raw.srt
@@ -0,0 +1,1400 @@
+1
+00:00:02,580 --> 00:00:05,460
+بسم الله الرحمن الرحيم بنكمل مع محاضرات ال
+
+2
+00:00:05,460 --> 00:00:09,720
+physical optics ووصلنا لعنوان ال radiometry and
+
+3
+00:00:09,720 --> 00:00:14,520
+photometry يعني القياس الإشعاعي و القياس الإضائي
+
+4
+00:00:14,520 --> 00:00:18,120
+عشان نعرف إيش الفرق بين القياس الإشعاعي اللي هو ال
+
+5
+00:00:18,120 --> 00:00:22,840
+radiometryوالقياس الإضاءي اللي هو ال photometry
+
+6
+00:00:22,840 --> 00:00:27,880
+بدنا نعطي بعض المقدمات البسيطة بنقول it is
+
+7
+00:00:27,880 --> 00:00:31,580
+necessary at times to measure the amount of light
+
+8
+00:00:31,580 --> 00:00:36,320
+produced by a source or illuminating a surface
+
+9
+00:00:36,320 --> 00:00:40,120
+يعني في بعض الأحيان بنحتاج أن نعرف كمية الضوء
+
+10
+00:00:40,120 --> 00:00:45,480
+الصادرة من مصدر ماء أو كمية الضوء اللي أضاءت سطح
+
+11
+00:00:45,480 --> 00:00:50,450
+ماء مثال على ذلك الرسم هاي بتوضحهعندي هاي مصدر
+
+12
+00:00:50,450 --> 00:00:54,970
+ضوء، هذا المصباح الكهربائي بيصدر ضوء أحيانا بنحتاج
+
+13
+00:00:54,970 --> 00:01:00,710
+نعرف قداش كمية الضوء اللي بيصدرها هذا المصدر الضوء
+
+14
+00:01:01,220 --> 00:01:04,680
+أيضا أحيانا بيكون احنا مش معنين بكمية الضوء
+
+15
+00:01:04,680 --> 00:01:09,240
+الصادرة من مصدر ما، ولكن كمية الضوء الصادقة على
+
+16
+00:01:09,240 --> 00:01:14,160
+سطح ما جداش مثلا للمتر المربع أو لصنتيمتر المربع
+
+17
+00:01:14,160 --> 00:01:18,620
+أو لوحدة المساحة جداش بيصلها إضاءة، إما الضوء
+
+18
+00:01:18,620 --> 00:01:22,420
+الصادر جداش كميته أو الضوء الصاقط اللي هو
+
+19
+00:01:22,420 --> 00:01:26,420
+illuminating a surface جداش كميته، إذا في بعض
+
+20
+00:01:26,420 --> 00:01:32,000
+الأحيان نحتاج لقياس أي واحد من الشيءينمثال على ذلك
+
+21
+00:01:32,000 --> 00:01:35,180
+يعني إيش الحاجة؟ يعني لماذا نحتاج أحياناً لقياس
+
+22
+00:01:35,180 --> 00:01:40,320
+الضوء الصادر من سطحنا أو الضوء الصاقط على سطحنا؟
+
+23
+00:01:40,320 --> 00:01:40,420
+نقول
+
+24
+00:02:01,410 --> 00:02:06,250
+جهاز ال perimeter هو جهاز فحص الساحة البصرية أو
+
+25
+00:02:06,250 --> 00:02:12,250
+الحقل البصري أو ال visual field هاي أن أمثل هذا
+
+26
+00:02:12,250 --> 00:02:17,730
+الجهاز .. هاي الجهاز عبارة عن بويلحوب يعني جاي
+
+27
+00:02:17,730 --> 00:02:22,230
+بشكل عمودي هنا هذه القطعة بيسموها chin rest المريض
+
+28
+00:02:22,230 --> 00:02:28,130
+بيحط ذقنه عليها هذه بيسموها head restبي .. بيحط ال
+
+29
+00:02:28,130 --> 00:02:31,470
+.. جبينه عليها، إذا الرأس المريض بتكون على ال head
+
+30
+00:02:31,470 --> 00:02:34,290
+rest و ذقن المريض بتكون على ال chin rest و هو
+
+31
+00:02:34,290 --> 00:02:38,150
+بيكون مواجه .. وجهه مواجه لل bowel أو الحوض .. لل
+
+32
+00:02:38,150 --> 00:02:43,470
+bowel أو الحوض الآن بتم إغلاق عين واحدة أو عمل
+
+33
+00:02:43,470 --> 00:02:47,430
+patching .. تسكير لعين واحدة عشان نفحص حق للإبصار
+
+34
+00:02:47,990 --> 00:02:52,250
+لأ العين الأخرى كيف يفحص حق .. حق للإبصار يفحص بإن
+
+35
+00:02:52,250 --> 00:02:55,630
+المريض بيطلب منه أنه يركز على نقطة مركزية بيكون
+
+36
+00:02:55,630 --> 00:03:00,650
+إلها إضاءة بلون معين و هذا البول في نقاط أخرى
+
+37
+00:03:00,650 --> 00:03:05,010
+بالضيق يعني بطريقة عشوائية مرة في المكان هذا مرة
+
+38
+00:03:05,010 --> 00:03:07,810
+في المكان هذا مرة في المكان هذا مرة في المكان هذا
+
+39
+00:03:07,810 --> 00:03:12,180
+مرة في المكان هذا الآن ضروري المريضيعني يركز بعينه
+
+40
+00:03:12,180 --> 00:03:15,660
+على ال central point اللي هو ال fixating point وما
+
+41
+00:03:15,660 --> 00:03:21,340
+يحرك عينه بتاتا وإنما بيمسك في إيده يعني مكبس أو
+
+42
+00:03:21,340 --> 00:03:25,380
+.. أو زر ولمّا بي .. هو مركز في النقطة المركزية
+
+43
+00:03:25,380 --> 00:03:30,500
+إذا أيضه ظهر في الأطرافبيضغط يعني بمعنى انه شايف
+
+44
+00:03:30,500 --> 00:03:34,680
+هذا الضوء يعني هذا السهم الأصفر بيأشر لنقطة مضيئة
+
+45
+00:03:34,680 --> 00:03:37,660
+طبعا المريض ما بيتطلع على هذه النقطة وانما هو
+
+46
+00:03:37,660 --> 00:03:41,840
+بيتطلع على النقطة المركزية اذا هذه النقطة سقطت على
+
+47
+00:03:41,840 --> 00:03:44,840
+ال peripheral retina بتاعته وشافها معناته بيدغط
+
+48
+00:03:44,840 --> 00:03:50,100
+وبالتالي الجهاز بيسجل ان المنطقة هذهضمن حقل
+
+49
+00:03:50,100 --> 00:03:54,340
+الإبصار المرئي بالنسبة لهذه العين جهاز visual
+
+50
+00:03:54,340 --> 00:03:57,560
+field أحدث أيضا نفس القضية بس الأمر بيكون
+
+51
+00:03:57,560 --> 00:04:01,080
+computerized هذه ال .. ال .. ال .. ال .. ال ..
+
+52
+00:04:01,400 --> 00:04:05,960
+المقبس أو الزر اللى بيضغط عليه المريض لما يشوف
+
+53
+00:04:05,960 --> 00:04:11,300
+النقطة اللى تم إضاءتها له في هذا الـ bowel القصد
+
+54
+00:04:11,300 --> 00:04:15,420
+علاقة هذا الفحص عشان هذا الفحص يكون دقيق هذا الفحص
+
+55
+00:04:15,420 --> 00:04:20,580
+فحص ال visual field أو الساحة البصرية بيفحص في
+
+56
+00:04:20,580 --> 00:04:25,470
+العديد من الأمراض ولكنيعني من أكتر الأمراض اللى
+
+57
+00:04:25,470 --> 00:04:28,210
+بيفحص فيها ال visual field مرض لجليكوما اللى هو
+
+58
+00:04:28,210 --> 00:04:32,990
+ارتفاع ضغط العين ارتفاع ضغط العين لأنه بيتلف العصب
+
+59
+00:04:32,990 --> 00:04:40,220
+البصري وبالتاليبيصير مناطق من ال retina يعني ما
+
+60
+00:04:40,220 --> 00:04:44,920
+بتشوف لأنه الألياف بتاعتها اللي بتشارك في تكوين
+
+61
+00:04:44,920 --> 00:04:48,680
+العصب البصري بتكون ماتت بسبب ال glucoma فبالتالي
+
+62
+00:04:48,680 --> 00:04:53,020
+بتصير هذه المناطق، مناطق يعني خارج ال visual field
+
+63
+00:04:53,020 --> 00:04:55,960
+أو مناطق سوداء في ال visual field يعني مناطق
+
+64
+00:04:55,960 --> 00:04:57,960
+انعدام الرؤية
+
+65
+00:05:00,050 --> 00:05:04,790
+ضروري جدا عشان يكون الفحص تقيق لازم أعمل الفحص
+
+66
+00:05:04,790 --> 00:05:09,570
+يعني في مرات عديدة، يعني ممكن أعمل الفحص للمريض
+
+67
+00:05:09,570 --> 00:05:14,010
+اليوم، بعد تلت شهور، بعد ست شهور، بعد سنة، بعد
+
+68
+00:05:14,010 --> 00:05:16,810
+سنتين، إلى آخر، عشان أتابع هل الجلوكومة
+
+69
+00:05:16,810 --> 00:05:22,210
+progressive، يعني بتتطور للأسوأ، ولا stable، يعني
+
+70
+00:05:22,210 --> 00:05:28,160
+مستقرة ومستجيبة للعلاج اللي بتم إعطاهطيب عشان يكون
+
+71
+00:05:28,160 --> 00:05:31,160
+الفحص دقيق ضروري ال illumination ال background
+
+72
+00:05:31,160 --> 00:05:35,240
+illumination الإضاءة الأساسية للجهاز مش إضاءة
+
+73
+00:05:35,240 --> 00:05:39,280
+النقطة هى هذا الجهاز فيه إله إضاءة أساسية يعني زي
+
+74
+00:05:39,280 --> 00:05:43,460
+ما أنتم لاحظين انبين مضيق بس النقطة هتكون إضاءتها
+
+75
+00:05:43,460 --> 00:05:46,920
+أعلى منه ولكن هو إله إضاءة أساسية بسمها ال
+
+76
+00:05:46,920 --> 00:05:50,500
+background illumination إذا أنا اجيت فحصت المريض
+
+77
+00:05:50,500 --> 00:05:56,510
+سين ال background illumination اليوميعني إله مقدار
+
+78
+00:05:56,510 --> 00:06:00,490
+معين إضاءة معينة ثم عند ال follow-up يعني في
+
+79
+00:06:00,490 --> 00:06:05,610
+المراجعة بعد تلت شهور أو ست شهور فحصته بإضاءة أقل
+
+80
+00:06:05,610 --> 00:06:09,590
+أو أكتر background illumination أكتر أو أقل بيكون
+
+81
+00:06:09,590 --> 00:06:12,650
+مفحص غير دقيق ضروري إن ال illumination بتاع البو
+
+82
+00:06:12,650 --> 00:06:16,790
+يكون ثابت عشان نقدر نعمل comparison عشان نقدر نعمل
+
+83
+00:06:16,790 --> 00:06:21,500
+comparison إذا for examplethe power of a perimeter
+
+84
+00:06:21,500 --> 00:06:26,480
+حوض ال perimeter حوض جهاز فحص الساحة البصرية must
+
+85
+00:06:26,480 --> 00:06:30,920
+be accurately illuminated لابد من إضاءته بشكل دقيق
+
+86
+00:06:30,920 --> 00:06:36,020
+و ثابت in order عشان أقدر for any comparisons of
+
+87
+00:06:36,020 --> 00:06:39,320
+visual field measurements performed on different
+
+88
+00:06:39,320 --> 00:06:42,780
+instruments سواء المريض عمل عند الفحص أو عمل عند
+
+89
+00:06:42,780 --> 00:06:46,820
+أي من الزملاء الآخرين في أي من المراكز الطبيةعشان
+
+90
+00:06:46,820 --> 00:06:50,220
+نقدر نقول أو نقدر نقارن بين الفحص الأول والتاني
+
+91
+00:06:50,220 --> 00:06:53,300
+والتالت والرابع ضروري ال background illumination
+
+92
+00:06:53,300 --> 00:06:57,700
+بتاعة ال bowel بتاعة الحوض بتاعة ال perimeter انه
+
+93
+00:06:57,700 --> 00:07:02,620
+تكون ثابتة ومش متغيرة لان هذا هيأثر على استجابة
+
+94
+00:07:02,620 --> 00:07:12,210
+المريض اذا هذا يعني لي انهالضوء الصادر من الباول
+
+95
+00:07:12,210 --> 00:07:16,950
+لازم يكون قياسه دقيقة يعني كميته موحدة كميته موحدة
+
+96
+00:07:16,950 --> 00:07:19,690
+احنا بنقول كالقاتي عشان ال visual field
+
+97
+00:07:19,690 --> 00:07:23,270
+measurements performed on different instruments او
+
+98
+00:07:23,270 --> 00:07:26,170
+on the same instruments at different times to be
+
+99
+00:07:26,170 --> 00:07:30,070
+meaningful عشان اقدر اقارن بينهم بنشوف مثال بنقول
+
+100
+00:07:30,070 --> 00:07:33,690
+هذا ال baseline visual field مريض اجا انعمله ال
+
+101
+00:07:33,690 --> 00:07:36,750
+visual field واضح المناطق السوداء هي انه مابيشوفش
+
+102
+00:07:36,750 --> 00:07:41,040
+فيهاهذه ال visual field ككل المناطق هاي ما بيشوفش
+
+103
+00:07:41,040 --> 00:07:45,060
+فيها بعد سنة انعمل الفحص بعد سنة أخرى انعمل الفحص
+
+104
+00:07:45,060 --> 00:07:49,740
+واضح ان المناطق بتزداد بعد تلت سنين من ال baseline
+
+105
+00:07:49,740 --> 00:07:54,820
+test انعمل الفحص و بعد أربع سنين عشان أقدر أقارن
+
+106
+00:07:54,820 --> 00:07:58,140
+أقول إن والله فيه progression يعني زي ما هذا الصوت
+
+107
+00:07:58,140 --> 00:08:02,380
+ضروري ال illumination بتاع ال .. بتاع ال .. ال
+
+108
+00:08:02,380 --> 00:08:05,920
+bowel بتاع ال perimeter أنه يكون ثابت ومش مرة أحط
+
+109
+00:08:05,920 --> 00:08:11,470
+مثلاكم معين و مرة تانية كم آخر و مرة تالتة كم تالت
+
+110
+00:08:11,470 --> 00:08:15,370
+.. ساعتها مش أقدر أعمل المقارنات طبعا هذه ممكن
+
+111
+00:08:15,370 --> 00:08:19,050
+تكون للعين اليمين و هذه للعين الشمال أيضا بعد سنة
+
+112
+00:08:19,050 --> 00:08:22,050
+.. بعد سنتين .. بعد تلاتة .. بعد أربع .. لو أجينا
+
+113
+00:08:22,050 --> 00:08:25,870
+نقول بعد أربع سنوات شايفين المناطق .. مناطق
+
+114
+00:08:25,870 --> 00:08:28,650
+بيسموها scotoma يعني منطقة انعدام الرؤية اللي
+
+115
+00:08:28,650 --> 00:08:33,010
+باللون الأسود و هنا ال scotoma طبعاواضح من الصور
+
+116
+00:08:33,010 --> 00:08:37,870
+انه في progression يعني المرض بيزداد سوءًا طب لو
+
+117
+00:08:37,870 --> 00:08:43,210
+احنا أخدنا معلومة انه ال background illumination
+
+118
+00:08:43,210 --> 00:08:46,690
+ماكانش موحد اذا كل المقارنة هذه لا فائدة منها لابد
+
+119
+00:08:46,690 --> 00:08:50,930
+للمريض منه نقم يعيد هذا ال test background
+
+120
+00:08:50,930 --> 00:08:55,410
+illumination موحد background illumination موحد
+
+121
+00:08:55,410 --> 00:08:59,370
+نيجي
+
+122
+00:08:59,370 --> 00:09:06,310
+نحكي عن القياس الإشعاعيالراديومتري القياس الإشعائي
+
+123
+00:09:06,310 --> 00:09:17,750
+هو ان انا
+
+124
+00:09:17,750 --> 00:09:21,150
+اجيس الـ electromagnetic radiation بين هدول
+
+125
+00:09:21,150 --> 00:09:25,490
+الترددين نشوف مع بعض ايش هدول الترددين نطلع على
+
+126
+00:09:25,490 --> 00:09:31,420
+المنظر المكبرهي عندي 10 اقص 11 وهي انا عندي 10 اقص
+
+127
+00:09:31,420 --> 00:09:36,060
+16 يعني هنا بيشمل عندي ال .. شوية من ال microwave
+
+128
+00:09:36,060 --> 00:09:40,100
+شوية من ال infrared و ال visible light و ال
+
+129
+00:09:40,100 --> 00:09:44,120
+ultraviolet و بداية ال إيش ال x-ray إذا هذا ال
+
+130
+00:09:44,120 --> 00:09:48,800
+range لما أجيسه لما أجيس الكمية ال electromagnetic
+
+131
+00:09:48,800 --> 00:09:53,540
+radiation كمية الإشعاع الصادرة من مصدرنا بصدرلي
+
+132
+00:09:53,540 --> 00:09:57,710
+هذه ال radiation بسميهاأنا بكون عملت radiometry
+
+133
+00:09:57,710 --> 00:10:02,790
+radiometry يعني لو تصورنا أن في جهاز بيصدر إشعاعات
+
+134
+00:10:02,790 --> 00:10:06,730
+بيصدر electromagnetic waves وهذه ال
+
+135
+00:10:06,730 --> 00:10:09,810
+electromagnetic waves اللي بيصدرها هذا الجهاز
+
+136
+00:10:09,810 --> 00:10:15,210
+ترددها بتراوح بين عشرة تلاتة في عشرة أُس إحداش
+
+137
+00:10:15,210 --> 00:10:20,410
+لتلاتة في عشرة أُس ستة عشر هيرتز ذبذبه معناته هو
+
+138
+00:10:20,410 --> 00:10:24,680
+هذا الجهاز بيصدر ليه microwavesبصدرلي infrared
+
+139
+00:10:24,680 --> 00:10:29,260
+بصدر visible light و بصدر ultraviolet و بصدر قليل
+
+140
+00:10:29,260 --> 00:10:33,900
+بيسموها ال soft x-ray بيسموها ال soft x-ray ليه
+
+141
+00:10:33,900 --> 00:10:37,760
+ترددها قريب من تردد ال ultraviolet إذا هذا الجهاز
+
+142
+00:10:37,760 --> 00:10:41,980
+بيصدر كل هذه ال electromagnetic radiation لما بجيس
+
+143
+00:10:41,980 --> 00:10:45,900
+الإشعاع اللي صادر من هذا الجهاز هذه العملية تسمى
+
+144
+00:10:45,900 --> 00:10:50,090
+radiometryإذا الـ Radiometry is the measurement هو
+
+145
+00:10:50,090 --> 00:10:56,130
+قياس الـ electromagnetic radiation إشعاع الموجات
+
+146
+00:10:56,130 --> 00:11:01,090
+الكهرومغناطسية اللي ذبذبتها بتتراوح بين 3 في 10
+
+147
+00:11:01,090 --> 00:11:07,830
+أقصى 11 هيرتز ذبذبة ل 3 في 10 أقصى 16 هيرتز هذا ال
+
+148
+00:11:07,830 --> 00:11:11,990
+range corresponding to wavelengths من 10 نانومتر ل
+
+149
+00:11:11,990 --> 00:11:19,790
+1 ملي متر10 nanometer أقل من 400 nanometer و أقل
+
+150
+00:11:19,790 --> 00:11:23,750
+من 700 nanometer يعني من 400 ل 700 nanometer جاية
+
+151
+00:11:23,750 --> 00:11:27,310
+بين العشرة للواحد ملي متر يعني ال visible light
+
+152
+00:11:27,310 --> 00:11:30,970
+جاية ضمن هذا ال range و ايضا ال infrared جاية و ال
+
+153
+00:11:30,970 --> 00:11:36,500
+ultraviolet جاية و شوية microwave و شويةx-ray إذا
+
+154
+00:11:36,500 --> 00:11:41,320
+therefore radiometry spans the microwave infrared
+
+155
+00:11:41,320 --> 00:11:46,180
+visible light ultraviolet and soft x-ray regions
+
+156
+00:11:46,180 --> 00:11:50,740
+of the electromagnetic spectrum يعني أي مصدر أي
+
+157
+00:11:50,740 --> 00:11:56,260
+مصدر بيصدرلي هذه الذبذبات من هذا ال range لعند هذا
+
+158
+00:11:56,260 --> 00:12:01,890
+ال range هذا قياس ال ..الموجات الكهرومغناطسية
+
+159
+00:12:01,890 --> 00:12:05,990
+الصادرة من هذا المصدر يسمى عملية الـ Radiometry
+
+160
+00:12:05,990 --> 00:12:11,970
+القياس الإشعاعي غالبا احنا بنحتاجش .. بنحتاجش ان
+
+161
+00:12:11,970 --> 00:12:16,510
+نقيس كل هذا القياس يعني عندي مصدر صحيح بيصدر كل
+
+162
+00:12:16,510 --> 00:12:19,390
+هذه الأنواع من الموجات بيصدرلي microwave و
+
+163
+00:12:19,390 --> 00:12:23,090
+infrared و visible و ultraviolet إلى آخرى أحيانا
+
+164
+00:12:23,090 --> 00:12:29,210
+بركز القياس على نوع معينفقط من كل هذه الموجات اللي
+
+165
+00:12:29,210 --> 00:12:34,330
+بصدرها هذا المصدر إذا ركزت قياسي على نوع معين هذا
+
+166
+00:12:34,330 --> 00:12:39,090
+بتسمى Spectral Radiometry Spectral Radiometry
+
+167
+00:12:39,090 --> 00:12:44,170
+فبالتالي هذه القضية ضرورية إحنا نفهمها often such
+
+168
+00:12:44,170 --> 00:12:47,890
+broad measurements هذا يعتبر قياس عريض ليش؟ لأن
+
+169
+00:12:47,890 --> 00:12:52,870
+أنا أخدت من عند ال microwave ووصلت لل soft x-ray
+
+170
+00:12:52,870 --> 00:12:57,320
+يعني أخدت شملت حاجات كتيرةفهذا عادة القياس مش
+
+171
+00:12:57,320 --> 00:13:00,820
+ضروري، مش ضروري، إذا often such broad measurements
+
+172
+00:13:00,820 --> 00:13:06,100
+are not necessary، هذه القياسات اللي هي العريضة
+
+173
+00:13:06,100 --> 00:13:10,060
+اللي بتشمل موجات، أنواع موجات كتيرة، غالبا مش لازم
+
+174
+00:13:11,130 --> 00:13:14,990
+فبالتالي بدل ما نعمل Radiometry بنعمل Spectral
+
+175
+00:13:14,990 --> 00:13:20,150
+Radiometry يعني الإشعاع الطيفي أو قياس الإشعاع
+
+176
+00:13:20,150 --> 00:13:24,230
+الطيفي يعني بركز على طيف معين أو Spectrum معين إذا
+
+177
+00:13:24,230 --> 00:13:28,110
+Spectral Radiometry is used instead to measure a
+
+178
+00:13:28,110 --> 00:13:32,740
+narrow portion of the electromagnetic spectrumهذا
+
+179
+00:13:32,740 --> 00:13:37,340
+بالنسبة لقياس الإشعاعي، الآن القياس الإضائي الـ
+
+180
+00:13:37,340 --> 00:13:41,780
+photometry هو نوع من أنواع القياس الإشعاعي، بس
+
+181
+00:13:41,780 --> 00:13:46,340
+طالما يقولنا photometry معناته إحنا بنقصد فيه قياس
+
+182
+00:13:46,340 --> 00:13:50,320
+الإشعاعات في مجال الضوء المرئي، إذا photometry
+
+183
+00:13:50,320 --> 00:13:54,420
+measures the human visual systems psychological
+
+184
+00:13:54,420 --> 00:14:00,220
+response to light، إذاالـ photometry بتجيثني
+
+185
+00:14:00,220 --> 00:14:05,280
+استجابة النظام البصري بتاع الإنسان الاستجابة
+
+186
+00:14:05,280 --> 00:14:10,500
+النفسية ال psychological response بتاع عين الإنسان
+
+187
+00:14:10,500 --> 00:14:13,560
+أو psychological response بتاع ال human visual
+
+188
+00:14:13,560 --> 00:14:16,740
+system لل light و لما بنقول لل light معناته احنا
+
+189
+00:14:16,740 --> 00:14:22,450
+بنقصد فقط الضوء المرئيBasically ال photometry is a
+
+190
+00:14:22,450 --> 00:14:26,730
+type of radiometry عشان نكون دقيقين ال photometry
+
+191
+00:14:26,730 --> 00:14:30,690
+نوع من أنواع ال radiometry لأنها بتجيس ليه بتجيس
+
+192
+00:14:30,690 --> 00:14:36,230
+ليه الموجات المرئية واللي هي تعتبر جزء من الطيف
+
+193
+00:14:36,230 --> 00:14:40,470
+الكهرومغناطيسيطيب إذا ال photometry is a type of
+
+194
+00:14:40,470 --> 00:14:43,850
+radiometry بس لو حد سؤالني .. سألني قاللي ال
+
+195
+00:14:43,850 --> 00:14:47,690
+radiometry تعتبر نوع من أنواع ال photometry؟
+
+196
+00:14:47,690 --> 00:14:52,990
+بنقوله لأ ال photometryالـ photometry is a type of
+
+197
+00:14:52,990 --> 00:14:56,630
+radiometry but radiometry is not a type of
+
+198
+00:14:56,630 --> 00:15:01,190
+photometry لأن ال radiometry عبارة عن قياس أوسع ال
+
+199
+00:15:01,190 --> 00:15:06,590
+radiometry من ال microwave لعين ال soft x-ray ال
+
+200
+00:15:06,590 --> 00:15:10,970
+photometry أثر هذا الجزء من الطيف الكهرومغناطيسي
+
+201
+00:15:10,970 --> 00:15:15,350
+أثر نفسي على العين أثر نفسي أو ال psychology على
+
+202
+00:15:15,840 --> 00:15:18,820
+العين، يعني هو هيسقط على العين على مساحة من
+
+203
+00:15:18,820 --> 00:15:23,980
+الشبكية ثم ينقل عبر ال visual system ويعطي شعور
+
+204
+00:15:23,980 --> 00:15:29,000
+معين عند الإنسان، شعور معين عند الإنسان فبالتالي
+
+205
+00:15:29,000 --> 00:15:36,000
+هذه لما بنجيس هذا الشعور أو بنجيسالأثر .. بنجيس ال
+
+206
+00:15:36,000 --> 00:15:38,680
+.. الأثر النفسي الـ psychological أو الـ
+
+207
+00:15:38,680 --> 00:15:42,500
+psychophysical response توليد بنكون احنا بنعمل
+
+208
+00:15:42,500 --> 00:15:46,380
+عملية ال photometry إذا basically photometry is a
+
+209
+00:15:46,380 --> 00:15:50,300
+type of radiometry هي نوع من أنواع ال radiometry
+
+210
+00:15:50,300 --> 00:15:54,140
+بس إيش بتختلف عنها؟that takes into account the
+
+211
+00:15:54,140 --> 00:15:57,360
+varying sensitivity of the eye to different
+
+212
+00:15:57,360 --> 00:16:01,080
+wavelengths اللي بتاخد الفوتومتري بتاخد في حسابها
+
+213
+00:16:01,080 --> 00:16:07,320
+ان العين البشرية حساسة بطريقة مختلفة حسب ال
+
+214
+00:16:07,320 --> 00:16:11,940
+wavelength الساقطة عليها حساسة بطريقة مختلفة حسب
+
+215
+00:16:11,940 --> 00:16:14,480
+ال wavelength الساقطة عليها
+
+216
+00:16:16,940 --> 00:16:21,320
+مثال على ذلك لما بسقط infrared wavelength مافيش ..
+
+217
+00:16:21,320 --> 00:16:26,500
+مافيش أي شعور عند الإنسان بيتولد لأنه غير مريض لما
+
+218
+00:16:26,500 --> 00:16:32,060
+بسقط blue في شعور باللون الأزرق لما بسقط ال green
+
+219
+00:16:32,060 --> 00:16:36,120
+في شعور باللون الأخضر و هكذا .. إذا في اختلاف في
+
+220
+00:16:36,120 --> 00:16:39,460
+الشعور .. في اختلاف في الشعور هذا الاختلاف في
+
+221
+00:16:39,460 --> 00:16:43,200
+الشعور نادج عن اختلاف الطول الموجي الصابط على
+
+222
+00:16:43,200 --> 00:16:48,990
+مساحة ما من الشبكيةهجوا العلماء قالوا الأمر هذا
+
+223
+00:16:48,990 --> 00:16:56,510
+بده يعني وضع ضمن قواعد، ليش بده وضع ضمن قواعد؟ ال
+
+224
+00:16:56,510 --> 00:17:03,300
+photometryطبعا العالم لازال ينتج مصادر ضوئية بعدد
+
+225
+00:17:03,300 --> 00:17:08,520
+هائل قد يكون عدد لا يمكن الحصول مصابيح كهربائية
+
+226
+00:17:08,520 --> 00:17:14,500
+أدوات إضاءة أدوات اللي هي الشاشات الذكية اللي
+
+227
+00:17:14,500 --> 00:17:19,400
+بتصدر إضاءات مختلفة وما إلى ذلك إذا في مصادر
+
+228
+00:17:19,400 --> 00:17:25,620
+إضائية تصنع مختلفة ومتنوعةوغالبيتها العظمة بيصدر
+
+229
+00:17:25,620 --> 00:17:30,600
+.. بيصدر electromagnetic waves في ال range بتاع
+
+230
+00:17:30,600 --> 00:17:37,440
+الضوء المرقية فعشان ما نجيش احنا عند كل اختراع
+
+231
+00:17:37,440 --> 00:17:44,510
+اداة تصدر ضوءعلى سبيل المثال تم اختراع جوال ويله
+
+232
+00:17:44,510 --> 00:17:50,010
+شاشة معينة هاتف نقال ويله شاشة معينة بتصدر إضاءة
+
+233
+00:17:50,010 --> 00:17:56,130
+بطريقة معينة أو مكونة من أطياف معينة يعني نفرض 650
+
+234
+00:17:56,130 --> 00:18:01,470
+نانومتر 550 نانومتر 547 نانومتر يعني بتصدر خليط من
+
+235
+00:18:01,470 --> 00:18:05,630
+الأطوال الموجية المرئية بدل ما احنا نجري دراسات
+
+236
+00:18:05,630 --> 00:18:12,680
+على الناس كل ما بنصنعمصدر طوئي كل ما بنصنع مصدر
+
+237
+00:18:12,680 --> 00:18:15,800
+طوئي بدل ما نعمل دراسات على الناس اجوا عملوا
+
+238
+00:18:15,800 --> 00:18:21,780
+دراسات موسعة على البشر عشان يعرفوا .. عشان يعرفوا
+
+239
+00:18:21,780 --> 00:18:26,080
+أثر الأطوال الموجية المختلفة الأثر النفسي
+
+240
+00:18:26,080 --> 00:18:31,040
+الفيزيائي للأطوال الموجية المختلفة على عيون البشر
+
+241
+00:18:31,040 --> 00:18:35,850
+بمعنى based on datafrom measurements of numerous
+
+242
+00:18:35,850 --> 00:18:40,530
+people, weighting factors presented graphically as
+
+243
+00:18:40,530 --> 00:18:44,070
+luminous efficacy curves have been developed for
+
+244
+00:18:44,070 --> 00:18:47,450
+each wavelength across the visible spectrum نفهم
+
+245
+00:18:47,450 --> 00:18:52,890
+هذا الموضوع، هاي ال visible spectrum بتكون من
+
+246
+00:18:52,890 --> 00:18:57,510
+الأحمر، البرتقالي، الأصفر، الأخضر، الأزرق، النيلي،
+
+247
+00:18:57,510 --> 00:19:02,440
+البنفسكيجابوا مجموعة هائلة من الناس وعرضوا أعينهم
+
+248
+00:19:02,440 --> 00:19:07,640
+لضوء أحمر بشدة إضاءة معينة، زودوا شدة الإضاءة،
+
+249
+00:19:07,640 --> 00:19:10,260
+زودوا شدة الإضاءة، وشافوا الـ response تعادوا
+
+250
+00:19:10,260 --> 00:19:15,020
+للناس وعملوا curve لللون الأحمر، اسمه الـ luminous
+
+251
+00:19:15,020 --> 00:19:20,040
+efficacy curveكل ما زدنا شدة ال luminosity تاعت
+
+252
+00:19:20,040 --> 00:19:23,560
+هذا المصدر اللي بيعطيني الضوء الأحمر كيف بيكون ال
+
+253
+00:19:23,560 --> 00:19:26,660
+response تاع أعين الناس لكتير اللي أجرينا عليهم
+
+254
+00:19:26,660 --> 00:19:30,960
+التجربة و هذا ال curve صار هو المعدل أو المتوسط أو
+
+255
+00:19:30,960 --> 00:19:34,900
+ال standard بتاعنا الآن هذه التجربة أجريت لللون
+
+256
+00:19:34,900 --> 00:19:38,960
+الأحمر لللون البرتقالي و لللون الأصفر و كل واحد
+
+257
+00:19:38,960 --> 00:19:45,060
+أصبح له curve بيسموه luminous efficacy curve بمعنى
+
+258
+00:19:45,060 --> 00:19:51,900
+آخرلما بنصنع مصباح كهربائي أو أداة تصدر ضوء بنيجي
+
+259
+00:19:51,900 --> 00:19:57,500
+بنقول هذه الأداة أول حاجة إيش بدنا نقيمها وقداش
+
+260
+00:19:57,500 --> 00:20:02,360
+متوقع تأثر على عين
+
+261
+00:20:02,360 --> 00:20:06,720
+الإنسان احنا أنتجنا أداة وبنعرف قداش بتأثر على عين
+
+262
+00:20:06,720 --> 00:20:11,460
+الإنسان أول حاجة أول خطوة في التصنيع spectral
+
+263
+00:20:11,460 --> 00:20:15,550
+characteristics of light source are determinedيعني
+
+264
+00:20:15,550 --> 00:20:20,230
+بنقول هذا ال light source scene صنعنا light source
+
+265
+00:20:20,230 --> 00:20:23,950
+مصدر ضوئي سميناه scene إيش ال spectral
+
+266
+00:20:23,950 --> 00:20:27,010
+characteristics إله؟ إيش عن ال spectral
+
+267
+00:20:27,010 --> 00:20:29,250
+characteristics يعني؟ إيش الأطوال الموجية اللي
+
+268
+00:20:29,250 --> 00:20:33,670
+بصدر؟ نفرض إنه بصدر طول الموج الأحمر والأخضر
+
+269
+00:20:33,670 --> 00:20:36,810
+والأصفر فقط، بصدرش الأزرق، طب ماشي إذا أنا عرفنا
+
+270
+00:20:36,810 --> 00:20:42,300
+بصدر الأحمر والأخضر والأصفر فقطبنجي بنقول الأحمر
+
+271
+00:20:42,300 --> 00:20:46,520
+بنضربه في ال luminous efficacy curve بتاعه يعني في
+
+272
+00:20:46,520 --> 00:20:49,640
+شدة إضاءة معينة جداش بيأثر في شدة إضاءة معينة جداش
+
+273
+00:20:49,640 --> 00:20:53,600
+بيأثر الأخضر نفس الاشي والأصفر نفس الاشي ساعتها
+
+274
+00:20:54,570 --> 00:20:58,850
+الاستجابات المتوقعة كلها تجمع وبنقول هذا المصدر
+
+275
+00:20:58,850 --> 00:21:04,050
+الضوءي بيأثر على العين بالشكل التالي تمام فبالتالي
+
+276
+00:21:04,050 --> 00:21:08,650
+بنقدر نعرف أي مصدر ضوءي أثره ال psycho physical
+
+277
+00:21:08,650 --> 00:21:12,810
+أثره النفسي الفيزيائي على ال visual system بتاع
+
+278
+00:21:12,810 --> 00:21:17,010
+العين بدون ما نعيد إجراء التجربة لأن كل واحدة من
+
+279
+00:21:17,010 --> 00:21:21,680
+الأطوال الموجية المرئيةلها luminous efficacy curve
+
+280
+00:21:21,680 --> 00:21:26,240
+بيقول لإنه عند شدة إضاءة معينة من هذا اللون بيكون
+
+281
+00:21:26,240 --> 00:21:30,180
+أثر على العين كذا عند شدة إضاءة أخرى من نفس اللون
+
+282
+00:21:30,180 --> 00:21:34,220
+بيكون كذا طيب هذا ال curve خاص بالأحمر وفيه curve
+
+283
+00:21:34,220 --> 00:21:37,080
+خاص بالأخضر وفيه curve خاص بالأزرق وفيه curve خاص
+
+284
+00:21:37,080 --> 00:21:43,410
+بالبنفس دي و هكذا طيب عندي مصدر بيصدر نوعين منال
+
+285
+00:21:43,410 --> 00:21:48,410
+.. ال .. ال electromagnetic waves مثلا البرتقالي و
+
+286
+00:21:48,410 --> 00:21:52,830
+الأزرق على سبيل المثال بنشوف قداش بيصدر شدة إضاءة
+
+287
+00:21:52,830 --> 00:21:56,690
+برتقالي و شدة إضاءة أزرق و بنضربهم في ال luminous
+
+288
+00:21:56,690 --> 00:22:00,670
+efficacy curve بتلع ال response لكل واحد منهم
+
+289
+00:22:00,670 --> 00:22:03,770
+بنجمعهم بتلع ال response العام لهذا المصدر بنقول
+
+290
+00:22:03,770 --> 00:22:08,330
+هذا المصدر هيأثر كذا كذا كذا على هذا فبالتالي هذه
+
+291
+00:22:08,330 --> 00:22:13,780
+القضية اللي في ال photometry احنا بنعملهاطيب إذا
+
+292
+00:22:13,780 --> 00:22:18,540
+ما الذي نصنعه؟
+
+293
+00:22:18,540 --> 00:22:22,800
+different luminous efficacy curves are used to
+
+294
+00:22:22,800 --> 00:22:26,240
+assist vision under photopic and scoptopic
+
+295
+00:22:26,240 --> 00:22:29,580
+lighting conditions وهذه القضية اللي احنا عملناها
+
+296
+00:22:29,580 --> 00:22:33,480
+بنجريها يعني في .. في luminous efficacy curve
+
+297
+00:22:33,480 --> 00:22:40,410
+للطيف الأحمر والعين في النهار وفي نفسLuminous
+
+298
+00:22:40,410 --> 00:22:44,890
+efficacy curve آخر للأحمر أيضا أثناء العين و هي في
+
+299
+00:22:44,890 --> 00:22:48,470
+الظلام فساعتها احنا بنقدر نقول جداش هذا المصدر
+
+300
+00:22:48,470 --> 00:22:54,090
+الضوء ايه بي .. بيأثر على العين .. بيأثر على العين
+
+301
+00:22:54,090 --> 00:23:00,950
+طيب بدنا نشوف example بسيط example بسيط انه في
+
+302
+00:23:00,950 --> 00:23:05,650
+عندي light source مصدر ضوء بس بيصدر فقط
+
+303
+00:23:05,650 --> 00:23:10,740
+ultraviolet lightهذا المصدر الضوء اللي بيصدر فقط
+
+304
+00:23:10,740 --> 00:23:15,360
+ultraviolet light has radiometric intensity، إله
+
+305
+00:23:15,360 --> 00:23:19,900
+شدة إشعاع، بس ال luminous intensity عنده صفر، ليش؟
+
+306
+00:23:19,900 --> 00:23:23,980
+لأنه غير مر إيه، مهما زادت الإشعاع بتاعه، لو
+
+307
+00:23:23,980 --> 00:23:28,120
+حطيناه على أقوى إشعاع من ال ultraviolet ممكن،
+
+308
+00:23:28,120 --> 00:23:31,540
+وإنسان واقف أمامه، لن يحدث عنده أثر لا psychology
+
+309
+00:23:31,540 --> 00:23:35,960
+ولا فيزيائيpsychophysiological response هيكون صفر
+
+310
+00:23:35,960 --> 00:23:41,660
+لأنه غير مرئي غير مرئي فبالتالي عشان نعرف أثر أي
+
+311
+00:23:41,660 --> 00:23:45,000
+مصدر لازم في الأول أحدد الأطياف الصادرة من هذا
+
+312
+00:23:45,000 --> 00:23:49,950
+المصدر أطوال الموجية الصادرة من هذا المصدر وكلطول
+
+313
+00:23:49,950 --> 00:23:53,070
+مودي each wavelength بنضربها في ال luminous
+
+314
+00:23:53,070 --> 00:23:56,230
+efficacy curve بتاعها بعدين ال responses
+
+315
+00:23:56,230 --> 00:24:00,850
+الاستجابات لكل طيف are summed يعني بيتم جمعها
+
+316
+00:24:00,850 --> 00:24:04,070
+across the visible spectrum to estimate the
+
+317
+00:24:04,070 --> 00:24:08,910
+response of the visual system عشان نقدر جداش ال
+
+318
+00:24:08,910 --> 00:24:11,450
+visual system أو ايش طبيعة الاستجابة بتاعة ال
+
+319
+00:24:11,450 --> 00:24:16,990
+visual system هاي عندنا مثلاالـ luminous efficacy
+
+320
+00:24:16,990 --> 00:24:21,030
+هذا المصباح اللي اخترعه اديسون في البداية اديسون
+
+321
+00:24:21,030 --> 00:24:25,770
+light bulb ال luminous efficacy طبعا في ال 1880
+
+322
+00:24:25,770 --> 00:24:29,350
+هذا مصباح من سنة ال 1880 ال luminous efficacy
+
+323
+00:24:29,350 --> 00:24:35,490
+بتاعته منخفضة جدا اعلى منه يعني بمجال كبير تمام
+
+324
+00:24:35,490 --> 00:24:38,950
+طبعا ال luminous efficacy تقاس بال لومن لكل وطة
+
+325
+00:24:38,950 --> 00:24:42,870
+بال لومن لكل وطة هنا تقريبا اتنين لومن لكل وطة هنا
+
+326
+00:24:43,680 --> 00:24:47,940
+عشر أضعافه اللي هي ال incandescent lamp اللي هي
+
+327
+00:24:47,940 --> 00:24:53,080
+ابن اعرفها كلنا تقريبا عشرين او تمانتاشر لومن لكل
+
+328
+00:24:53,080 --> 00:24:57,670
+وات هنا ال compact fluorescent lampاللي المصابيح
+
+329
+00:24:57,670 --> 00:25:01,970
+المعتادة عندنا و اللي هي تقدر تقريبا ما يقرب من
+
+330
+00:25:01,970 --> 00:25:07,670
+الستين ستين لومن لكل وقت هنا ال neon اللي هو light
+
+331
+00:25:07,670 --> 00:25:12,810
+linear fluorescent lamp تقريبا فوق السبعين اخر
+
+332
+00:25:12,810 --> 00:25:15,890
+حاجة ال led اللي هي light emitting diode ال
+
+333
+00:25:15,890 --> 00:25:19,490
+luminous efficacy بتاعته اعلى تقريبا تقترب من متين
+
+334
+00:25:19,490 --> 00:25:24,730
+لومن يعني مئة ضعف اللي هي مصباح اديسون فبالتالي
+
+335
+00:25:24,730 --> 00:25:31,550
+حسب الأضيافاللي صادرة من كل مصدر كام .. كام طياف
+
+336
+00:25:31,550 --> 00:25:39,190
+مرئي و هذه الأطياف كل واحد منهابدو ينضرب في ال
+
+337
+00:25:39,190 --> 00:25:43,530
+luminous efficacy curve بتاعه ونجمع أثرها كلها على
+
+338
+00:25:43,530 --> 00:25:47,610
+النظام البصري لعين الإنسان على النظام البصري لعين
+
+339
+00:25:47,610 --> 00:25:51,110
+الإنسان كتير من الناس اللي بيشتغلوا في المجال
+
+340
+00:25:51,110 --> 00:25:55,050
+الطبي بيتلخبطوا في قضية انه يفرجوا بين ال
+
+341
+00:25:55,050 --> 00:25:57,730
+radiometric و ال photometric units طبعا ال
+
+342
+00:25:57,730 --> 00:26:01,570
+photometric units بتقيس النشاط أو بتقيس الكمية
+
+343
+00:26:01,570 --> 00:26:08,520
+الإشعاعية اللي بتحدث أثرعلى أثر نفسي فيزيائي على
+
+344
+00:26:08,520 --> 00:26:11,820
+عين الإنسان أو على النظام البصري بتاع الإنسان أو
+
+345
+00:26:11,820 --> 00:26:16,040
+على الإنسان ككل يعني احنا بنحكي عن قياس في المجال
+
+346
+00:26:16,040 --> 00:26:20,820
+المرئي بينما ال radiometric measurements اللي هي
+
+347
+00:26:20,820 --> 00:26:24,360
+القياس الإشعاعي في ال range اللي حكيناه و اللي
+
+348
+00:26:24,360 --> 00:26:28,300
+بتروح من ال microwave لغاية ال soft x-ray هيك
+
+349
+00:26:28,300 --> 00:26:32,100
+بتنتهي المحاضرة و يعطيكم العافية والسلام عليكم
+
+350
+00:26:32,100 --> 00:26:33,620
+ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uyFVwbm4HE8.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uyFVwbm4HE8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4d701fd516e9baf5be68c817477563f7d6513482
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uyFVwbm4HE8.srt
@@ -0,0 +1,1530 @@
+1
+00:00:01,370 --> 00:00:04,330
+بسم الله الرحمن الرحيم بنواصل مع محاضرات ال
+
+2
+00:00:04,330 --> 00:00:11,870
+physical optics ووصلنا عند موضوع يعني شيق ومهم
+
+3
+00:00:11,870 --> 00:00:16,550
+اللي هو imaging and point spread function وحقيقة
+
+4
+00:00:16,550 --> 00:00:20,610
+هذا الموضوع تم نقشه في مساق ال geometric optics
+
+5
+00:00:20,610 --> 00:00:24,750
+وحنناقشه اليوم في مساق ال physical optics بس من
+
+6
+00:00:24,750 --> 00:00:31,130
+وجهة نظر مختلفة Two different but closely related
+
+7
+00:00:31,130 --> 00:00:34,530
+approaches exist to understand the image formation
+
+8
+00:00:34,530 --> 00:00:40,050
+process يعني في طريقتين مختلفات عشان نفهم عملية
+
+9
+00:00:40,050 --> 00:00:44,390
+تكون الصور بواسطة ال optical system هدول الطريقين
+
+10
+00:00:44,390 --> 00:00:48,990
+عشان نفهم طرق تكون أو كيف تتكون الصورة بواسطة
+
+11
+00:00:48,990 --> 00:00:52,970
+optical system مختلفات بس في بينهم relation يعني
+
+12
+00:00:52,970 --> 00:00:57,750
+في بينهم علاقة بتربطهم مع بعض .. مع بعضهم البعض
+
+13
+00:00:57,750 --> 00:01:01,470
+ممكن الإنسان يرجع لل geometric optics لنقاش ال
+
+14
+00:01:01,470 --> 00:01:05,310
+image formation بواسطة العدسات والمرايا وال pin
+
+15
+00:01:05,310 --> 00:01:08,880
+hole وما إلى ذلك طيب إيش الطريقين اللي احنا
+
+16
+00:01:08,880 --> 00:01:12,820
+بنستخدمهم أو اللي ممكن عن طريقهم ندرس ال image
+
+17
+00:01:12,820 --> 00:01:15,980
+formation process عملية تكوين الصورة بوسطة ال
+
+18
+00:01:15,980 --> 00:01:19,740
+optical system الطريق الأولى أو ال first approach
+
+19
+00:01:19,740 --> 00:01:23,740
+is the basis for aberration theory يعني الطريق
+
+20
+00:01:23,740 --> 00:01:29,720
+الأولى هي طريق فهم الصورة من منطلق نظرية ال
+
+21
+00:01:29,720 --> 00:01:36,140
+aberration أو الزيغ في تكوين صورة الشيء بواسطة
+
+22
+00:01:36,140 --> 00:01:41,100
+optical system ال aberration theory يعني ليش
+
+23
+00:01:41,100 --> 00:01:49,260
+الصورة فيها زيغ عن أنها تصف ال object بشكل حقيقي
+
+24
+00:01:49,820 --> 00:01:54,240
+بينما الطريق الثاني لفهم تكون الصورة إيه له علاقة
+
+25
+00:01:54,240 --> 00:01:57,760
+بال contrast sensitivity وإيه هذا هنحكيه في
+
+26
+00:01:57,760 --> 00:02:02,140
+محاضرة خاصة فيها and the measurement of image 
+
+27
+00:02:02,140 --> 00:02:05,880
+quality اللي هي جودة الصورة واللي هي أحد صفات
+
+28
+00:02:05,880 --> 00:02:06,920
+الصورة
+
+29
+00:02:11,250 --> 00:02:14,790
+الـ aberration theory أو الطريق الأول عشان نفهم
+
+30
+00:02:14,790 --> 00:02:19,390
+طريقة تكون الصور بوسط ال optical system in the
+
+31
+00:02:19,390 --> 00:02:22,630
+first approach an object is regarded as a
+
+32
+00:02:22,630 --> 00:02:26,670
+collection of point sources of light يعني في ال ..
+
+33
+00:02:26,670 --> 00:02:30,030
+في ال .. في النظرية الأولى أو حسب ال .. المسار
+
+34
+00:02:30,030 --> 00:02:33,990
+الأول للفهم لو ال aberration theory بيعتبروا ال
+
+35
+00:02:33,990 --> 00:02:38,450
+object العلماء بيعتبروا أي object مكون من عدد كبير
+
+36
+00:02:38,450 --> 00:02:42,570
+جدا من النقاط كل نقطة منهم بيسموها point source of
+
+37
+00:02:42,570 --> 00:02:47,310
+light طيب each of which كل من هذه النقاط radiates
+
+38
+00:02:47,310 --> 00:02:51,650
+light in all directions طيب some of the light
+
+39
+00:02:51,650 --> 00:02:56,070
+traverses the lens and focuses at best to a small
+
+40
+00:02:56,070 --> 00:03:00,510
+irregularly shaped region never to a perfect point
+
+41
+00:03:01,030 --> 00:03:07,750
+بمعنى آخر الضوء بينطلق من كل نقاط ال object نطلع
+
+42
+00:03:07,750 --> 00:03:12,610
+على رسمة مكبرة الضوء بينطلق من كل نقاط ال object و
+
+43
+00:03:12,610 --> 00:03:17,070
+لو احنا أخدنا نقطة واحدة كمثال بنقول الضوء بينتشر
+
+44
+00:03:17,070 --> 00:03:21,330
+من هذه النقطة كمثال وينطبق كلامنا على كل النقاط
+
+45
+00:03:21,330 --> 00:03:27,070
+بينطبق .. بينطلق الضوء radiates in all directions
+
+46
+00:03:27,070 --> 00:03:32,810
+في كل الاتجاهات، الآن حزمة من هذا الضوء اللي انطلق
+
+47
+00:03:32,810 --> 00:03:39,110
+من النقطة بيعدي من خلال ال optical system أو ال
+
+48
+00:03:39,110 --> 00:03:45,530
+lens أو ما شبه وهذه ال lens بتجمع at best في أفضل
+
+49
+00:03:45,530 --> 00:03:51,730
+حالتها في منطقة صغيرة من ضمن ال image هذه المنطقة
+
+50
+00:03:51,730 --> 00:03:57,000
+الصغيرة صغيرة بس أكبر من ال point ومتعرجة الحدود
+
+51
+00:03:57,000 --> 00:04:01,240
+عشان هيك تسمى point spread function point spread
+
+52
+00:04:01,240 --> 00:04:06,440
+function فبالتالي أفضل optical system لا يمكن
+
+53
+00:04:06,440 --> 00:04:13,780
+يعطيني نقطة .. نقطة كصورة للنقطة وبالتالي بيعطيني
+
+54
+00:04:13,780 --> 00:04:17,200
+شيء أوسع من النقطة واللي هو point spread function
+
+55
+00:04:17,200 --> 00:04:22,360
+إذا some of the light traverses the lens and
+
+56
+00:04:22,360 --> 00:04:26,100
+focuses وبتركز .. بتركز العدسة at best في أفضل
+
+57
+00:04:26,100 --> 00:04:30,740
+أوضاعها to a small irregularly shaped region never
+
+58
+00:04:30,740 --> 00:04:36,140
+to a perfect point هذا الكلام صار مع نقطة واحدة طب
+
+59
+00:04:36,140 --> 00:04:40,660
+والنقطة اللي المجاورة إلها أيضاً إلها point split
+
+60
+00:04:40,660 --> 00:04:44,080
+function مجاورة وبينهم تداخل بيجوا على بعض يعني
+
+61
+00:04:44,080 --> 00:04:47,300
+بيغطوا على بعضهم البعض فبالتالي
+
+62
+00:04:53,330 --> 00:04:59,300
+الضوء اللي جاي من نقاط مجاورة partially overlaps
+
+63
+00:04:59,300 --> 00:05:03,900
+and cause a loss of detail in the formed image وكل
+
+64
+00:05:03,900 --> 00:05:08,460
+ما التداخل بين صور النقاط أو بالأصح بين ال point
+
+65
+00:05:08,460 --> 00:05:12,940
+spread functions بتاعت كل النقاط كل ما زاد التداخل
+
+66
+00:05:12,940 --> 00:05:18,220
+كل ما كان جودة الصورة أقل لأنه بيشوشوا في الرؤية
+
+67
+00:05:18,220 --> 00:05:21,200
+على بعضهم البعض يعني الإنسان لما بيطلع على هذه
+
+68
+00:05:21,200 --> 00:05:24,560
+الصورة بسبب التداخل بين ال point spread function
+
+69
+00:05:25,180 --> 00:05:28,040
+تاع النقطة A وال point split function تاعة النقطة
+
+70
+00:05:28,040 --> 00:05:32,780
+B وتاعة C وتاعة D والاخرى فبيتم أن ال quality
+
+71
+00:05:32,780 --> 00:05:37,780
+تاعة ال image بتكون أقل كل ما زاد التداخل إذا
+
+72
+00:05:37,780 --> 00:05:43,500
+overlaps and causes loss of detail in the formed
+
+73
+00:05:43,500 --> 00:05:53,260
+image هاي مثال عندي object object في منه نقطة أخدنا
+
+74
+00:05:53,260 --> 00:05:56,220
+منه نقطة طبعا هي أكبر من نقطة في الصورة بس هذا
+
+75
+00:05:56,220 --> 00:06:00,680
+اللي استطعنا الحصول عليه النقطة صورتها عبارة عن
+
+76
+00:06:00,680 --> 00:06:06,940
+point spread function شيء متعرج .. شيء متعرج مجموع
+
+77
+00:06:06,940 --> 00:06:11,080
+ال point spread function بتاع كل نقاط ال object في
+
+78
+00:06:11,080 --> 00:06:14,780
+مجموعه بيكون ال image طب هل ال image تشبه ال
+
+79
+00:06:14,780 --> 00:06:19,070
+object؟ كان لا .. لا تشبه ال object لأنه في اختلاف
+
+80
+00:06:19,070 --> 00:06:22,870
+كبير أصبحت ال image بالشكل هذا بعد ما ال object
+
+81
+00:06:22,870 --> 00:06:28,230
+كان شكله دائري ومنتظم فبالتالي هذه فكرة ال
+
+82
+00:06:28,230 --> 00:06:32,230
+aberration ال aberration الزيغ يعني .. يعني ما هو
+
+83
+00:06:32,230 --> 00:06:36,670
+مقدار الزيغ عن المنظر الحقيقي اللي المفروض تكون
+
+84
+00:06:36,670 --> 00:06:38,930
+عليه ال image ال image المفروض تشبه ال object
+
+85
+00:06:38,930 --> 00:06:45,220
+بنسبة 100% فهذا الزيغ اللي احنا شايفينه بنسموه ال
+
+86
+00:06:45,220 --> 00:06:49,380
+aberration ال aberration إله علاقة كبيرة بال point
+
+87
+00:06:49,380 --> 00:06:52,440
+spread function بمعنى آخر كل ما كانت ال point
+
+88
+00:06:52,440 --> 00:06:57,960
+spread function أكبر حجمها و more irregular more
+
+89
+00:06:57,960 --> 00:07:03,760
+irregular كل ما كان .. كل ما كان ال quality بتاعة
+
+90
+00:07:03,760 --> 00:07:10,180
+ال image أسوأ وأردأ إذا ال point spread function
+
+91
+00:07:10,180 --> 00:07:15,930
+وال aberration ارتباطهم ارتباط وثيق جدا وال point
+
+92
+00:07:15,930 --> 00:07:18,710
+spread function بتعبر عن ال aberration وال
+
+93
+00:07:18,710 --> 00:07:29,230
+aberration بتعبر عن ال point spread function هاي
+
+94
+00:07:29,230 --> 00:07:35,820
+أيضا أمثلة للـ point spread function بحسب اختلاف
+
+95
+00:07:35,820 --> 00:07:40,040
+ال optical system بأحجامها وبتعريجاتها بتعريجاتها
+
+96
+00:07:40,040 --> 00:07:43,300
+ال major point spread function كل ما كان حجمها
+
+97
+00:07:43,300 --> 00:07:48,760
+أصغر وأقل تعريجا كل ما كان الوضع بيكون أفضل من
+
+98
+00:07:48,760 --> 00:07:52,940
+ناحية ال image quality كل ما كانت أصغر بيكون
+
+99
+00:07:52,940 --> 00:07:56,320
+تداخلها مع ال point spread function المجاورة لصور
+
+100
+00:07:56,320 --> 00:08:01,020
+النقاط الأخرى بيكون أقل فبالتالي جودة الصورة
+
+101
+00:08:01,020 --> 00:08:04,720
+بتكون أعلى جودة الصورة بتكون أعلى ل quality لـ ال
+
+102
+00:08:04,720 --> 00:08:07,360
+image وكل ما كانت أكبر بيكون الوضع أسوأ لأن
+
+103
+00:08:07,360 --> 00:08:11,800
+التداخل هيزيد طبعا كل ما كانت تعريج أكثر معناته ال
+
+104
+00:08:11,800 --> 00:08:15,820
+aberration أكثر ال aberration الزيغ عن الوضع
+
+105
+00:08:15,820 --> 00:08:20,150
+الحقيقي بيكون أكثر .. بيكون أكثر .. إذا هذه قضية
+
+106
+00:08:20,150 --> 00:08:23,430
+اللي هي ال point spread function وال aberration
+
+107
+00:08:23,430 --> 00:08:27,910
+إذا ال light from nearby point sources partially
+
+108
+00:08:27,910 --> 00:08:32,330
+overlaps and causes a loss of detail in the formed
+
+109
+00:08:32,330 --> 00:08:32,730
+image
+
+110
+00:08:36,240 --> 00:08:41,500
+although no lens focus أو focuses perfectly, some
+
+111
+00:08:41,500 --> 00:08:45,280
+focus better than others and produce more detail
+
+112
+00:08:45,280 --> 00:08:49,900
+in the resulting image طبعا مافيش optical system
+
+113
+00:08:49,900 --> 00:08:54,280
+أو lens بتعمل perfect focus لكل النقاط، إيش يعني
+
+114
+00:08:54,280 --> 00:08:58,670
+perfect focus؟ يعني النقطة إيه؟ صورتها A شرطة في ال
+
+115
+00:08:58,670 --> 00:09:02,770
+image عبارة عن نقطة مش أكبر من نقطة النقطة B أيضا
+
+116
+00:09:02,770 --> 00:09:06,870
+عبارة عن نقطة النقطة C يعني صورة النقطة تساوي نقطة
+
+117
+00:09:06,870 --> 00:09:10,810
+مش point spread function طبعا مافي optical system
+
+118
+00:09:10,810 --> 00:09:15,930
+يعطيني perfect image أو perfect focus لكل نقاط ال
+
+119
+00:09:15,930 --> 00:09:19,570
+object ولكن في optical system أفضل من optical
+
+120
+00:09:19,570 --> 00:09:23,530
+system آخر بمعنى آخر لو احنا رجعنا هنا للعرض
+
+121
+00:09:23,530 --> 00:09:29,070
+المكبر وقلنا الـ point spread function هذه أنتجها
+
+122
+00:09:29,070 --> 00:09:33,410
+optical system A مثلا والـ point spread function
+
+123
+00:09:33,410 --> 00:09:37,470
+هذه أنتجها ال optical system B طبعا بنقول أيهما
+
+124
+00:09:37,470 --> 00:09:40,710
+أفضل بنقول A أفضل طب ليش حكمنا على ال optical
+
+125
+00:09:40,710 --> 00:09:44,370
+system أو العدسة A أنها أفضل من B لأن ال point
+
+126
+00:09:44,370 --> 00:09:49,090
+spread function بتاعتها أصغر حجما وأقل تعريجا .. و
+
+127
+00:09:49,090 --> 00:09:53,110
+أقل تعريجا فبالتالي هذا .. لو عندي optical system
+
+128
+00:09:53,110 --> 00:09:55,730
+يعطيني هذه ال .. ال .. ال point spread function
+
+129
+00:09:55,730 --> 00:09:58,330
+بيكون أفضل وأفضل ولو كان عندي optical system
+
+130
+00:09:58,330 --> 00:10:02,770
+يعطيني حجم أصغر وأقل تعريجا معناته كل ما صغرت ال
+
+131
+00:10:02,770 --> 00:10:05,750
+point spread function معناته ال focus أفضل، ال
+
+132
+00:10:05,750 --> 00:10:09,450
+quality أفضل، ال optical system أفضل ال optical
+
+133
+00:10:09,450 --> 00:10:13,030
+system أفضل فبالتالي هذه القضية ضروري تكون واضحة
+
+134
+00:10:14,300 --> 00:10:18,400
+الـ point spread function هي عبارة عن إيش؟ ال
+
+135
+00:10:18,400 --> 00:10:23,120
+point spread function هي صورة أي نقطة طب بدنا
+
+136
+00:10:23,120 --> 00:10:26,480
+تفصيل أكثر في هذا الموضوع بنقول ال point spread
+
+137
+00:10:26,480 --> 00:10:33,640
+function تصف .. تصف how light from a single point
+
+138
+00:10:33,640 --> 00:10:39,060
+source is distributed in an image and completely
+
+139
+00:10:39,060 --> 00:10:42,360
+describes the imaging characteristics of an
+
+140
+00:10:42,360 --> 00:10:46,430
+optical system يعني ال point spread function أو
+
+141
+00:10:46,430 --> 00:10:51,430
+دالة انتشار النقطة أو بالأصح دالة انتشار الضوء
+
+142
+00:10:51,430 --> 00:10:55,630
+القادم من النقطة بتوصف لي كيف الضوء اللي إيجى من
+
+143
+00:10:55,630 --> 00:11:00,350
+single point في ال object كيف توزع في ال image
+
+144
+00:11:00,350 --> 00:11:06,760
+نشوف الصورة هاي single point هاي الضوء اللي إيجى منه
+
+145
+00:11:06,760 --> 00:11:09,780
+وراح على ال lens دخل في ال lens وال lens جمعته
+
+146
+00:11:09,780 --> 00:11:14,260
+توزع في سطح ال image نفرض هذا اللوح الأسود ال
+
+147
+00:11:14,260 --> 00:11:17,940
+image يشغل كل اللوح الأسود بس هذه المنطقة اللي
+
+148
+00:11:17,940 --> 00:11:22,860
+بالأبيض هي المنطقة اللي انتشر فيها الضوء اللي قدم
+
+149
+00:11:22,860 --> 00:11:25,860
+من نقطة واحد اللي جاء من نقطة واحد اللي هي النقطة
+
+150
+00:11:25,860 --> 00:11:30,000
+A إذا ما الطريقة اللي توزع فيها هذا الضوء القادم
+
+151
+00:11:30,000 --> 00:11:34,100
+من A فقط مش من كل .. مش من كل نقاط ال object هذه
+
+152
+00:11:34,100 --> 00:11:36,720
+هي الشكل اللي هو اللي توزع فيه هذا ال point spread
+
+153
+00:11:36,720 --> 00:11:42,120
+function بتاع النقطة A أو صورة النقطة A أو A شرطة
+
+154
+00:11:42,120 --> 00:11:46,500
+زي ما احنا يعني بنسميها تمام؟ إذا ال point spread
+
+155
+00:11:46,500 --> 00:11:54,400
+function تصف .. تصف كيف توزع الضوء القادم من
+
+156
+00:11:54,400 --> 00:11:59,290
+single point how it is distributed in an image
+
+157
+00:11:59,290 --> 00:12:03,790
+مجموع الـ point spread function بتاع كل نقاط ال
+
+158
+00:12:03,790 --> 00:12:08,570
+object completely describes بشكل كامل the imaging
+
+159
+00:12:08,570 --> 00:12:12,130
+characteristics of an optical system يعني هذا ال
+
+160
+00:12:12,130 --> 00:12:16,780
+optical system هيعطيني image .. هذا ال optical
+
+161
+00:12:16,780 --> 00:12:20,660
+system .. هيعطيني image كيف ال quality بتاعتها ..
+
+162
+00:12:20,660 --> 00:12:23,580
+كيف ال quality بتاعتها .. عالية ولا متوسطة ولا
+
+163
+00:12:23,580 --> 00:12:26,940
+راضية .. عالية ولا متوسطة .. يعني ال imaging
+
+164
+00:12:26,940 --> 00:12:29,740
+characteristic ولا إذا كان هذا ال optical system
+
+165
+00:12:30,400 --> 00:12:35,500
+بيعطيني point spread function صغيرة جدا ومش متعرجة
+
+166
+00:12:35,500 --> 00:12:38,400
+كثير معناته ال quality تاعة ال image عالية ليش؟
+
+167
+00:12:38,400 --> 00:12:42,620
+لأنه صغيرة جدا، إذا A شرطة بتتداخلش مع B شرطة
+
+168
+00:12:42,620 --> 00:12:46,780
+ومع C شرطة ومع D شرطة وما إلى ذلك والله إذا هذا
+
+169
+00:12:46,780 --> 00:12:49,520
+ال optical system أعطاني point spread function
+
+170
+00:12:49,520 --> 00:12:53,540
+متعرجة كثير ومساحتها كبيرة لكل point spread
+
+171
+00:12:53,540 --> 00:12:56,540
+function معناته التداخل كثير وال quality رديئة
+
+172
+00:12:56,540 --> 00:13:01,800
+للغاية إذا هذا بالنسبة لل point spread function و
+
+173
+00:13:01,800 --> 00:13:08,600
+ال aberration طيب إذا ننتقل الآن لتصنيع optical
+
+174
+00:13:08,600 --> 00:13:14,260
+system أو lens بس قبل تصنيعه المفروض نناقش موضوع
+
+175
+00:13:14,260 --> 00:13:18,280
+يعني تخيل إحنا في مصنع بده ينتج عدسات أو optical
+
+176
+00:13:18,280 --> 00:13:23,310
+systems لغرض معين قبل ما ننتج العدسات أو ال optical
+
+177
+00:13:23,310 --> 00:13:27,670
+systems لهذا الغرض اللي احنا ناوين أنه نصنع له
+
+178
+00:13:27,670 --> 00:13:32,410
+العدسات مفروض نعمل حساب لل point spread function
+
+179
+00:13:32,410 --> 00:13:36,990
+يعني بدي أنا optical system يعطيني point spread
+
+180
+00:13:36,990 --> 00:13:43,510
+function أصغر ما يكون وأقل تعريجا ممكن أقل ما يمكن
+
+181
+00:13:43,510 --> 00:13:48,250
+من التعريج وأصغر ما يمكن من الحجم وإذا قدرت أصل أن
+
+182
+00:13:48,250 --> 00:13:52,210
+هذا ال optical system اللي أنا ناوي أصنعه لسه ما
+
+183
+00:13:52,210 --> 00:13:58,080
+صنعته إذا بيعطيني نقطة لكل نقطة في ال object معناته
+
+184
+00:13:58,080 --> 00:14:03,140
+أنا وصلت لـ perfect optical system يعطيني stigmatic
+
+185
+00:14:03,140 --> 00:14:08,260
+image طيب عشان نحسب ال point spread function بشكل
+
+186
+00:14:08,260 --> 00:14:14,020
+معادلات رياضية لازم ناخد بالنا من عدة أمور هذا ال
+
+187
+00:14:14
+
+201
+00:15:13,680 --> 00:15:19,520
+بينهم يعني حواجز وفي الحواجز في مثلا فتحات يعني في
+
+202
+00:15:19,520 --> 00:15:22,480
+الحواجز ممكن يعملي diffraction بدي أحسب الـ
+
+203
+00:15:22,480 --> 00:15:27,860
+diffraction بس لأ طيب تداخل الضوء تداخل الموجات
+
+204
+00:15:27,860 --> 00:15:30,920
+الضوئية the interference هل هو constructive ولا
+
+205
+00:15:30,920 --> 00:15:35,680
+destructive the polarization تاعة الضوء هل اتجاه ال
+
+206
+00:15:35,680 --> 00:15:40,540
+polarization عمودي ولا أفقي ولا oblique ولا
+
+207
+00:15:40,540 --> 00:15:45,520
+circularly polarized ولا elliptically polarized؟
+
+208
+00:15:45,520 --> 00:15:50,660
+أيضا بدي أحسب قضية أنه لو في أي شغلة في ال .. في
+
+209
+00:15:50,660 --> 00:15:55,540
+الإجاز عملت scattering لل light scattering لل light
+
+210
+00:15:55,540 --> 00:16:02,500
+أو في ال media بما فيها الهواء اللي موجودة في مكان
+
+211
+00:16:02,500 --> 00:16:07,080
+التصوير بمعنى اه ف أنا بدي استخدم هذه الكاميرا اللي
+
+212
+00:16:07,080 --> 00:16:10,980
+بدي أصنعها في studio فبدي أحسب ال scattering لل
+
+213
+00:16:10,980 --> 00:16:14,930
+light أيضا بدي أحسب ال dispersion .. dispersion
+
+214
+00:16:14,930 --> 00:16:21,250
+اللي هو بالضبط كأنه بيمرّ الضوء في ثمك معين من
+
+215
+00:16:21,250 --> 00:16:25,350
+الزجاج كأنه بيمرّ في ال prism و بيتحلل للألوان
+
+216
+00:16:25,350 --> 00:16:30,150
+الطيفية the spectral colors فكل هذه الشغلات عشان
+
+217
+00:16:30,150 --> 00:16:35,950
+أحسب ال point spread function بشكل دقيق لابد أن آخذ
+
+218
+00:16:35,950 --> 00:16:39,130
+في اعتباری الأشياء اللي احنا ذكرناها و اللي أنا 
+
+219
+00:16:39,130 --> 00:16:42,670
+بيُعطيها هنا في ال slide ألوان مختلفة نأخذ بالنا
+
+220
+00:16:42,670 --> 00:16:45,150
+أول حاجة من ال Refraction اللي هيعمل ليها ال
+
+221
+00:16:45,150 --> 00:16:48,270
+optical system أو ال lens اللي بدي أصنعها ال
+
+222
+00:16:48,270 --> 00:16:51,610
+reflection ال diffraction هي تلاتة ال interference
+
+223
+00:16:51,610 --> 00:16:55,770
+أربعة ال polarization خمسة ال scattering ستة ال
+
+224
+00:16:55,770 --> 00:16:59,370
+dispersion سبعة عشان نحسب ال point spread function
+
+225
+00:16:59,370 --> 00:17:05,270
+بشكل دقيق و نحاول نصل في التصنيع لأفضل point spread
+
+226
+00:17:05,270 --> 00:17:09,450
+function يعني لأفضل optical system ممكن لازم آخذ
+
+227
+00:17:09,450 --> 00:17:16,190
+بالي من هذه الأشياء السبعة، الآن عند النقطة high
+
+228
+00:17:16,190 --> 00:17:21,270
+بنقول أن الموضوع صعب للغاية حساب ال point spread
+
+229
+00:17:21,270 --> 00:17:23,930
+function حتى لو استخدمنا computer
+
+230
+00:17:26,580 --> 00:17:30,680
+للحسابات the point spread function even using a
+
+231
+00:17:30,680 --> 00:17:34,400
+computer calculating a point spread function that
+
+232
+00:17:34,400 --> 00:17:38,100
+accounts for all optical variables is difficult
+
+233
+00:17:38,100 --> 00:17:42,320
+هذه كلها كانت تُسمى the optical variables يعني ضروري
+
+234
+00:17:42,320 --> 00:17:46,080
+آخذ بالي منها كلها عشان كل الأمور هتكون كويسة يعني
+
+235
+00:17:46,080 --> 00:17:49,060
+يكون ال reflection ممتاز ال reflection أقل ما يمكن
+
+236
+00:17:49,060 --> 00:17:53,040
+ال diffraction يكون قليل ال interference ما ..
+
+237
+00:17:53,040 --> 00:17:57,660
+ما يكونش destructive يكون constructive interference
+
+238
+00:17:57,660 --> 00:18:01,320
+ال polarization يكون مناسب ال scattering يكون أقل
+
+239
+00:18:01,320 --> 00:18:04,580
+ما يمكن عشان ما يُشوش على الصورة ال dispersion
+
+240
+00:18:04,580 --> 00:18:08,700
+برضه يكون أقل ما يمكن يعني كل هذه المتغيرات عشان
+
+241
+00:18:09,330 --> 00:18:13,190
+آخذها في الحسبان حتى لو استعمال الكمبيوتر يحسب لي
+
+242
+00:18:13,190 --> 00:18:17,430
+ال point spread function و تطلع لي خصائص لهذه
+
+243
+00:18:17,430 --> 00:18:22,270
+الأشياء السبعة تكون ممتازة بيكون عندي difficult
+
+244
+00:18:22,270 --> 00:18:27,250
+process difficult process حتى باستعمال الكمبيوتر
+
+245
+00:18:27,250 --> 00:18:33,550
+طب إيش نعمل؟ بعض العلماء اقترح بس أنا جايب .. جايب
+
+246
+00:18:33,550 --> 00:18:36,390
+ما نقول إيش نعمل؟ أنا بدي أطلع على ال net and goal
+
+247
+00:18:37,220 --> 00:18:42,960
+يعني كشيء بسيط جدا نقول calculating the
+
+248
+00:18:42,960 --> 00:18:47,760
+point spread function و نشوف إيش المعادلات اللي
+
+249
+00:18:47,760 --> 00:18:59,720
+ممكن تطلع معنا يعني
+
+250
+00:18:59,720 --> 00:19:04,640
+لو احنا أخذنا منظر هذه
+
+251
+00:19:05,930 --> 00:19:09,690
+calculation لل point spread function هذه
+
+252
+00:19:09,690 --> 00:19:15,210
+calculation لل point spread function لل point
+
+253
+00:19:15,210 --> 00:19:19,530
+spread function فبالتالي احنا الوضع حقيقة صعب و
+
+254
+00:19:19,530 --> 00:19:26,990
+معقد و معادلات كثيرة اللي بتخلي العلماء يعني يعني
+
+255
+00:19:26,990 --> 00:19:30,670
+يشوفوها شغل صعب حتى باستعمال ال computer
+
+256
+00:19:34,360 --> 00:19:39,840
+بعض العلماء اقترح أن نقوم بأمر عكسي أول شيء نصنع ال
+
+257
+00:19:39,840 --> 00:19:44,830
+lens و بعد ما نصنع ال lens ندرس الأشياء السبعة هذه
+
+258
+00:19:44,830 --> 00:19:48,310
+هل ال lens اللي احنا صنعناها بتعمل reflection كويس
+
+259
+00:19:48,310 --> 00:19:52,030
+reflection, diffraction, interference يعني مقبول و
+
+260
+00:19:52,030 --> 00:19:54,990
+ال diffraction مقبول يعني الأشياء هذه يعني نرجعها
+
+261
+00:19:54,990 --> 00:19:59,710
+بعد ما نكون بتصنيع ال lens بعد ما نكون بتصنيع ال
+
+262
+00:19:59,710 --> 00:20:03,270
+lens if the point spread function of a lens can
+
+263
+00:20:03,270 --> 00:20:06,490
+be measured نقدر نجيسها after it is manufactured
+
+264
+00:20:06,490 --> 00:20:09,590
+بعد ما نصنع ال lens نجيس ال point spread function
+
+265
+00:20:09,590 --> 00:20:15,280
+بتاعتها بس في عندي مشكلة doing so is a time
+
+266
+00:20:15,280 --> 00:20:19,580
+-consuming and costly task requiring specialized
+
+267
+00:20:19,580 --> 00:20:25,000
+equipment and expertise أول شيء هذه القضية بتستهلك
+
+268
+00:20:25,000 --> 00:20:28,760
+وقت ليش بتستهلك وقت صنعنا lens و حسبنا ال point
+
+269
+00:20:28,760 --> 00:20:31,240
+spread function أو جسنا ال point spread function
+
+270
+00:20:31,240 --> 00:20:34,330
+بتاعتها يعني .. يعني .. يعني ال point spread
+
+271
+00:20:34,330 --> 00:20:37,790
+function بتاعة نقاط الضوء اللي أو .. أو نقاط الضوء
+
+272
+00:20:37,790 --> 00:20:40,950
+بتاعة ال object أو النقاط بتاعة ال object اللي
+
+273
+00:20:40,950 --> 00:20:43,670
+مررنا الضوء من هذه ال lens اللي صنعناها طب افرض
+
+274
+00:20:43,670 --> 00:20:46,390
+ما عجبتناش ال point spread function أو طلعت رديئة
+
+275
+00:20:47,600 --> 00:20:51,860
+بنضطر نصنع عدسة ثانية و ما عجبتناش برضه بتطلع ..
+
+276
+00:20:51,860 --> 00:20:55,220
+فبالتالي هذا ال time consuming يعني بيستهلك للوقت
+
+277
+00:20:55,220 --> 00:20:59,940
+و طالما أيضا ممكن يعني هيكلفنا تصنيع عدة عدسات عشان
+
+278
+00:20:59,940 --> 00:21:04,040
+بالنهاية نصل ل .. لعدسة .. للعدسة المطلوبة أيضا
+
+279
+00:21:04,040 --> 00:21:10,500
+costly task يعني شيء مكلف بتطلب يعني أدوات يعني
+
+280
+00:21:10,500 --> 00:21:17,010
+معينة و بتطلب خبرة معينة إيش نعمل معناته؟ كيف نحل
+
+281
+00:21:17,010 --> 00:21:20,330
+مشكلة ال point spread function؟ أنا مش قادر أحسبها
+
+282
+00:21:20,330 --> 00:21:24,890
+قبل التصنيع لأن بدنا نحسب variables كثيرة، هاي
+
+283
+00:21:24,890 --> 00:21:28,850
+نقطة، نقطة ثانية لو صنعت بعدين جيسنا ممكن أخطئ مرة
+
+284
+00:21:28,850 --> 00:21:31,890
+في الصناعة و مرة ثانية و مرة ثالثة و مرة رابعة،
+
+285
+00:21:31,890 --> 00:21:36,970
+برضه هتكون مكلفة و يعني يستهلك الوقت، طب إيش نعمل؟
+
+286
+00:21:37,470 --> 00:21:42,250
+حقيقة اللي عمل بسيط جدا fortunately لحسن الحظ most
+
+287
+00:21:42,250 --> 00:21:46,550
+image characteristics such as location الموقع بتاع
+
+288
+00:21:46,550 --> 00:21:49,590
+ال image و ال size اللي هو ال magnification و ال
+
+289
+00:21:49,590 --> 00:21:52,010
+orientation اللي هي above ولا below the optical
+
+290
+00:21:52,010 --> 00:21:55,830
+axis and the brightness can be calculating or
+
+291
+00:21:55,830 --> 00:21:58,510
+measured without considering the point spread
+
+292
+00:21:58,510 --> 00:22:02,300
+function هذه الأشياء و هذه الصفات بقدر أجيسها بدون
+
+293
+00:22:02,300 --> 00:22:06,280
+ما أحسب ال point spread function حدودها حدود ال
+
+294
+00:22:06,280 --> 00:22:11,000
+point spread function كيف؟ بطريقة استعمال قوانين
+
+295
+00:22:11,000 --> 00:22:14,200
+ال geometric optics مش ال physical optics if the
+
+296
+00:22:14,200 --> 00:22:17,600
+field of geometric optics greatly simplifies
+
+297
+00:22:17,600 --> 00:22:22,500
+calculations of image characteristics by ignoring
+
+298
+00:22:22,500 --> 00:22:25,400
+most of light's physical characteristics
+
+299
+00:22:25,400 --> 00:22:31,100
+especially diffraction طيب ال .. ال geometric
+
+300
+00:22:31,100 --> 00:22:36,200
+optics علم مبني على ال approximations المقاربات
+
+301
+00:22:36,200 --> 00:22:41,380
+و أول approximation في ال geometric optics بيقول ..
+
+302
+00:22:41,380 --> 00:22:45,080
+بيقول أو بينص على .. أول مقاربات في ال geometric
+
+303
+00:22:45,080 --> 00:22:50,760
+optics بينص على ignore image quality لا تهتم بال
+
+304
+00:22:50,760 --> 00:22:54,000
+image quality لأن اهتمامك بال image quality هيؤدي
+
+305
+00:22:54,000 --> 00:22:58,560
+أنك أنت لازم تدرس ال point spread function فعلم الـ
+
+306
+00:22:58,560 --> 00:23:02,320
+Geometric Optics بيهمل ال point spread function
+
+307
+00:23:02,320 --> 00:23:06,280
+لأن مش معني بدراسة ال image quality بقدر ما هو
+
+308
+00:23:06,280 --> 00:23:09,580
+معني بدراسة الصفات الأخرى إيش هي الصفات الأخرى ال
+
+309
+00:23:09,580 --> 00:23:12,020
+location يعني موقع ال image بالنسبة لل optical
+
+310
+00:23:12,020 --> 00:23:16,120
+system أو بالأحرى ال image distance ال size ال
+
+311
+00:23:16,120 --> 00:23:19,020
+magnification مكبرة مسافرة كم مرة بالنسبة لل
+
+312
+00:23:19,020 --> 00:23:22,640
+object ال orientation يعني فوق ال optical axis
+
+313
+00:23:22,640 --> 00:23:27,580
+مُعتدلة ولا below ال optical axis يعني مقلوبة و ال
+
+314
+00:23:27,580 --> 00:23:31,780
+brightness يعني قد إيش كمية الإضاءة اللي فيها إذا
+
+315
+00:23:31,780 --> 00:23:35,760
+the field of geometric optics it greatly simplify
+
+316
+00:23:35,760 --> 00:23:40,060
+.. simplifies calculations يُبسط لعلم ال geometric
+
+317
+00:23:40,060 --> 00:23:45,540
+optics بشكل كبير الحسابات حسابات إيش؟ حسابات ال
+
+318
+00:23:45,540 --> 00:23:49,980
+image characteristics كيف يُبسطها by ignoring most
+
+319
+00:23:49,980 --> 00:23:54,560
+of lights physical characteristics كل أو الغالبية
+
+320
+00:23:54,560 --> 00:23:58,760
+العظمى من الصفات الفيزيائية بتاعة الضوء بتهملها ال
+
+321
+00:23:58,760 --> 00:24:01,780
+geometric optics بتهملها ال geometric optics
+
+322
+00:24:01,780 --> 00:24:06,280
+بالذات ال geometric optics بتهمل ال diffraction طب
+
+323
+00:24:06,280 --> 00:24:10,120
+إيش ال .. أو كيف بنصل لباقي الصفات بنستعمل إيش يعني
+
+324
+00:24:10,120 --> 00:24:13,520
+إيش الحسابات اللي بنستعملها عشان نصل لل location و
+
+325
+00:24:13,520 --> 00:24:16,900
+ال size و ال orientation بنستعمل القوانين اللي هي
+
+326
+00:24:17,880 --> 00:24:21,040
+قانون السريان المستقيم، the law of rectilinear
+
+327
+00:24:21,040 --> 00:24:27,040
+propagation قانون ال refraction قانون الانكسار هو
+
+328
+00:24:27,040 --> 00:24:32,520
+Snell's law و قانون الانعكاس هو قانون الانعكاس إذا
+
+329
+00:24:32,520 --> 00:24:35,480
+using only the three laws of rectilinear
+
+330
+00:24:35,480 --> 00:24:39,000
+propagation و ال refraction و ال reflection image
+
+331
+00:24:39,000 --> 00:24:43,040
+characteristics can be determined with sufficient
+
+332
+00:24:43,040 --> 00:24:47,470
+accuracy for most users بقدر أحدد صفات ال image
+
+333
+00:24:47,470 --> 00:24:52,430
+و بدقة عالية كتير في .. في معظم وليس في كل .. في
+
+334
+00:24:52,430 --> 00:24:56,730
+معظم الحالات باستعمال هذه القوانين، في معظم
+
+335
+00:24:56,730 --> 00:25:01,660
+الحالات باستعمال هذه القوانين، طيب لما في عندي بعض
+
+336
+00:25:01,660 --> 00:25:06,400
+الحالات بيكون فيها diffraction كتير بيكون فيها ال
+
+337
+00:25:06,400 --> 00:25:10,540
+interference كتير بيكون فيه بعض الصفات الفيزيائية
+
+338
+00:25:10,540 --> 00:25:14,680
+للضوء مهمة ساعتها the image quality it is necessary
+
+339
+00:25:14,680 --> 00:25:18,680
+to use calculations from physical optics يعني
+
+340
+00:25:18,680 --> 00:25:22,180
+ضروري ساعتها ندخل في التعقيدات وطبعا تعيين الفيزياء
+
+341
+00:25:22,180 --> 00:25:28,450
+هم أو متخصصي الفيزياء هم اللي ساعتها بيحسبوا ال
+
+342
+00:25:28,450 --> 00:25:31,510
+image characteristics باعتماد ال physical أو
+
+343
+00:25:31,510 --> 00:25:34,730
+باعتبار .. باعتماد ال physical laws أو القوانين
+
+344
+00:25:34,730 --> 00:25:38,730
+الفيزيائية لديه، إذا only و ال diffraction و ال
+
+345
+00:25:38,730 --> 00:25:44,070
+interference و other some physical property is a
+
+346
+00:25:44,070 --> 00:25:48,070
+significant factor يعني إيش .. يعني مهمة لأن ال
+
+347
+00:25:48,070 --> 00:25:51,920
+diffraction في بعض ال optical system مهم يعني بعض
+
+348
+00:25:51,920 --> 00:25:54,680
+ال optical system لا يمكن تجاهل ال diffraction
+
+349
+00:25:54,680 --> 00:25:59,200
+فيها في الغالبية العظمى من ال optical systems ممكن
+
+350
+00:25:59,200 --> 00:26:02,760
+أتجاهل ال diffraction طيب في بعض ال optical
+
+351
+00:26:02,760 --> 00:26:06,200
+systems في .. في أغراض علمية أو أغراض صناعية أو
+
+352
+00:26:06,200 --> 00:26:10,260
+مشابه لا يمكن تجاهل ال diffraction ولا يمكن تجاهل
+
+353
+00:26:10,260 --> 00:26:12,820
+ال interference ولا يمكن تجاهل بعض الصفات
+
+354
+00:26:12,820 --> 00:26:16,620
+الفيزيائية للضوء زي ال polarization و زي الشغلات
+
+355
+00:26:16,620 --> 00:26:20,850
+اللي هي زي هيك ساعتها لما بيشكلولي significant
+
+356
+00:26:20,850 --> 00:26:25,470
+factor in image quality it is necessary to use
+
+357
+00:26:25,470 --> 00:26:30,690
+calculations from physical optics فضروري ساعتها ما
+
+358
+00:26:30,690 --> 00:26:36,340
+أكتفي بقوانين ال geometric optics The point spread
+
+359
+00:26:36,340 --> 00:26:39,900
+function is required only for the analysis of
+
+360
+00:26:39,900 --> 00:26:44,540
+image quality, which in most cases is dominated by
+
+361
+00:26:44,540 --> 00:26:49,100
+aberrations or diffraction ما معنى هذا الكلام؟
+
+362
+00:26:49,100 --> 00:26:53,920
+بنقول كالتالي ال point spread function بتلزمنا فقط
+
+363
+00:26:53,920 --> 00:26:59,260
+لتحليل ال image quality لما أنا بتكلم عن ال image
+
+364
+00:26:59,260 --> 00:27:03,380
+quality بدي أعرف ال image quality جودة الصورة
+
+365
+00:27:03,380 --> 00:27:07,680
+و قد إيش الصورة بتشبه ال object ساعتها أنا مضطر لازم
+
+366
+00:27:07,680 --> 00:27:12,200
+أبحث أشوف حدود ال point spread function لكل نقطة
+
+367
+00:27:12,200 --> 00:27:16,040
+من نقاط ال object كيف الحدود كيف التعريج بتاعها
+
+368
+00:27:16,040 --> 00:27:20,360
+وين انتهى الضوء اللي انطلق من نقطة إيه و الخريطة
+
+369
+00:27:20,360 --> 00:27:23,790
+بتاعة ال point spread function يعني الحدود
+
+370
+00:27:23,790 --> 00:27:28,650
+المتعرجة لازم أعرفها بالتفصيل عشان أعرف ال image
+
+371
+00:27:28,650 --> 00:27:32,290
+quality عشان أعرف ال image quality إذا أنا بدي
+
+372
+00:27:32,290 --> 00:27:36,330
+أعرف ال image quality طيب ال image quality اللي
+
+373
+00:27:36,330 --> 00:27:41,070
+بتحكم في التعريج هذا صفات كثيرة فيزيائية لبطولة
+
+374
+00:27:41,070 --> 00:27:46,670
+اللي بتحكم في التعريج هذا اللي بتحكم في التعريج
+
+375
+00:27:46,670 --> 00:27:51,450
+هذا لل point spread function اللي بتحكم في التعريج
+
+376
+00:27:51,450 --> 00:27:56,630
+هذا ربما الصورة هي أوضح صورة لأنها يعني التعريج
+
+377
+00:27:56,630 --> 00:28:00,090
+فيها واضح جدا نمشي مع رأس السهم بتاع ال mouse
+
+378
+00:28:00,090 --> 00:28:05,430
+التعريج هذا اللي بتحكم فيه أشياء كثيرة بس أهم
+
+379
+00:28:05,430 --> 00:28:12,170
+شيئين بتحكموا في التعريج و في حدود في الحدود بتاعة
+
+380
+00:28:12,170 --> 00:28:15,190
+ال point spread function هم ال aberration و ال
+
+381
+00:28:15,190 --> 00:28:18,450
+diffraction هم ال aberration و ال diffraction
+
+382
+00:28:18,450 --> 00:28:23,710
+فبالتالي ال point spread function بتحكم فيها كثيرا
+
+383
+00:28:23,710 --> 00:28:28,570
+صفات فيزيائية بس أكثر شيء dominant في الصفات
+
+384
+00:28:28,570 --> 00:28:31,510
+الفيزيائية اللي بتؤثر اللي بت
+
+401
+00:29:54,620 --> 00:29:59,320
+آخر، لو تصورنا إنه في عندي diffraction كتير بس ال
+
+402
+00:29:59,320 --> 00:30:03,940
+aberration zero هتكون صورة النقطة A عبارة عن ..
+
+403
+00:30:03,940 --> 00:30:11,770
+النقطة A هتكون صورتها عبارة عن دائرة في الـ diffraction
+
+404
+00:30:11,770 --> 00:30:14,950
+يعني في مساحة كبيرة بس فيش aberration يعني فيش 
+
+405
+00:30:14,950 --> 00:30:18,590
+تعريج يعني عبارة عن دائرة فبالتالي هذه القضية
+
+406
+00:30:18,590 --> 00:30:24,010
+ضرورية جدا تكون واضحة إن شاء الله تعالى طيب كيف
+
+407
+00:30:24,010 --> 00:30:28,830
+ندرس الـ point spread function عشان نوصل للـ image
+
+408
+00:30:28,830 --> 00:30:32,550
+quality بدنا ندرس الـ diffraction لحال و الـ
+
+409
+00:30:32,550 --> 00:30:36,350
+aberration لحال بدنا ندرس الـ diffraction لحال و الـ
+
+410
+00:30:36,350 --> 00:30:39,970
+aberration لحال و هذا اللي هنتعرف عليه إن شاء الله
+
+411
+00:30:39,970 --> 00:30:45,110
+في ملحق المحاضرة هاي و يعطيكم العافية و السلام
+
+412
+00:30:45,110 --> 00:30:47,230
+عليكم و رحمة الله و بركة 
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uyFVwbm4HE8_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uyFVwbm4HE8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..15c458fba2a958276044db9e48318817f160e43d
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/uyFVwbm4HE8_postprocess.srt
@@ -0,0 +1,1648 @@
+1
+00:00:01,370 --> 00:00:04,330
+بسم الله الرحمن الرحيم بنواصل مع محاضرات ال
+
+2
+00:00:04,330 --> 00:00:11,870
+physical optics ووصلنا عند موضوع يعني شيق ومهم
+
+3
+00:00:11,870 --> 00:00:16,550
+اللي هو imaging and point spread function وحقيقة
+
+4
+00:00:16,550 --> 00:00:20,610
+هذا الموضوع تم نقشته في مساق ال geometric optics
+
+5
+00:00:20,610 --> 00:00:24,750
+وحنناقشه اليوم في مساق ال physical optics بس من
+
+6
+00:00:24,750 --> 00:00:31,130
+وجهة نظر مختلفةTwo different but closely related
+
+7
+00:00:31,130 --> 00:00:34,530
+approaches exist to understand the image formation
+
+8
+00:00:34,530 --> 00:00:40,050
+process يعني في طريقتين مختلفات عشان نفهم عملية
+
+9
+00:00:40,050 --> 00:00:44,390
+تكون الصور بواسطة ال optical system هدول الطريقين
+
+10
+00:00:44,390 --> 00:00:48,990
+عشان نفهم طرق تكونأو كيف تتكون الصورة بواسطة
+
+11
+00:00:48,990 --> 00:00:52,970
+optical system مختلفات بس في بينهم relation يعني
+
+12
+00:00:52,970 --> 00:00:57,750
+في بينهم علاقة بتربطهم مع بعض .. مع بعضهم البعض
+
+13
+00:00:57,750 --> 00:01:01,470
+ممكن الإنسان يرجع لل geometric optics لنقاش ال
+
+14
+00:01:01,470 --> 00:01:05,310
+image formation بواسطة العدسات و المرايا و ال pin
+
+15
+00:01:05,310 --> 00:01:08,880
+hole و ما إلى ذلكطيب إيش الطريقين اللي احنا
+
+16
+00:01:08,880 --> 00:01:12,820
+بنستخدمهم أو اللي ممكن عن طريقهم ندرس ال image
+
+17
+00:01:12,820 --> 00:01:15,980
+formation process عملية تكوين الصورة بوسطة ال
+
+18
+00:01:15,980 --> 00:01:19,740
+optical system الطريق الأولى أو ال first approach
+
+19
+00:01:19,740 --> 00:01:23,740
+is the basis for aberration theory يعني الطريق
+
+20
+00:01:23,740 --> 00:01:29,720
+الأولى هي طريقفهم الصورة من منطلق نظرية ال
+
+21
+00:01:29,720 --> 00:01:36,140
+aberration أو الزير في تكوين صورة الشيء بواسطة
+
+22
+00:01:36,140 --> 00:01:41,100
+optical system ال aberration theory يعني جداش
+
+23
+00:01:41,100 --> 00:01:49,260
+الصورة فيها زير عن أنها تصف ال object بشكل حقيقي
+
+24
+00:01:49,820 --> 00:01:54,240
+بينما الطريق التاني لفهم تكون الصورة إيه له علاقة
+
+25
+00:01:54,240 --> 00:01:57,760
+بال contrast sensitivity و إيه هذا هنحكيه في
+
+26
+00:01:57,760 --> 00:02:02,140
+محاضرة خاصة فيها and the measurement of image
+
+27
+00:02:02,140 --> 00:02:05,880
+quality اللي هي جودة الصورة و اللي هي أحد صفات
+
+28
+00:02:05,880 --> 00:02:06,920
+الصورة
+
+29
+00:02:11,250 --> 00:02:14,790
+الـ aberration theory أو الطريق الأول عشان نفهم
+
+30
+00:02:14,790 --> 00:02:19,390
+طريقة تكون الصور بوسط ال optical system in the
+
+31
+00:02:19,390 --> 00:02:22,630
+first approach an object is regarded as a
+
+32
+00:02:22,630 --> 00:02:26,670
+collection of point sources of light يعني في ال ..
+
+33
+00:02:26,670 --> 00:02:30,030
+في ال .. في النظرية الأولى أو حسب ال .. المسار
+
+34
+00:02:30,030 --> 00:02:33,990
+الأول للفهملو ال aberration theory بيعتبروا ال
+
+35
+00:02:33,990 --> 00:02:38,450
+object العلماء بيعتبروا أي object مكون من عدد كبير
+
+36
+00:02:38,450 --> 00:02:42,570
+جدا من النقاط كل نقطة منهم بيسموها point source of
+
+37
+00:02:42,570 --> 00:02:47,310
+light طيب each of which كل من هذه النقاط radiates
+
+38
+00:02:47,310 --> 00:02:51,650
+light in all directions طيب some of the light
+
+39
+00:02:51,650 --> 00:02:56,070
+traverses the lens and focuses at best to a small
+
+40
+00:02:56,070 --> 00:03:00,510
+irregularly shaped region never to a perfect point
+
+41
+00:03:01,030 --> 00:03:07,750
+بمعنى آخر الضوء بينطلق من كل نقاط ال object نطلع
+
+42
+00:03:07,750 --> 00:03:12,610
+على رسمة مكبرة الضوء بينطلق من كل نقاط ال object و
+
+43
+00:03:12,610 --> 00:03:17,070
+لو احنا أخدنا نقطة واحدة كمثال بنقول الضوء بينتشر
+
+44
+00:03:17,070 --> 00:03:21,330
+من هذه النقطة كمثال و ينطبق كلامنا على كل النقاط
+
+45
+00:03:21,330 --> 00:03:27,070
+بينطبق .. بينطلق الضوء radiates in all directions
+
+46
+00:03:27,070 --> 00:03:32,810
+في كلالاتجاهات، الآن حزمة من هذا الضوء اللي انطلق
+
+47
+00:03:32,810 --> 00:03:39,110
+من النقطة بيعدي من خلال ال optical system أو ال
+
+48
+00:03:39,110 --> 00:03:45,530
+lens أو ما شبه وهذه ال lens بتجمع at best في أفضل
+
+49
+00:03:45,530 --> 00:03:51,730
+حالتها في منطقة صغيرة من ضمن ال image هذه المنطقة
+
+50
+00:03:51,730 --> 00:03:57,000
+الصغيرة صغيرة بس أكبر من ال pointو متعرجة الحدود
+
+51
+00:03:57,000 --> 00:04:01,240
+عشان هيك تسمى point spread function point spread
+
+52
+00:04:01,240 --> 00:04:06,440
+function فبالتالي أفضل optical system لا يمكن
+
+53
+00:04:06,440 --> 00:04:13,780
+يعطيني نقطة .. نقطة كصورة للنقطة وبالتالي بيعطيني
+
+54
+00:04:13,780 --> 00:04:17,200
+شيء أوسع من النقطة واللي هو point spread function
+
+55
+00:04:17,200 --> 00:04:22,360
+إذا some of the light traverses the lensand
+
+56
+00:04:22,360 --> 00:04:26,100
+focuses و بتركز .. بتركز العدسة at best في أفضل
+
+57
+00:04:26,100 --> 00:04:30,740
+أوضاعها to a small irregularly shaped region never
+
+58
+00:04:30,740 --> 00:04:36,140
+to a perfect point هذا الكلام صار مع نقطة واحدة طب
+
+59
+00:04:36,140 --> 00:04:40,660
+و النقطة اللي المجاورة إلها أيضاً إلها point split
+
+60
+00:04:40,660 --> 00:04:44,080
+function مجاورة و بينهم تداخل بيجوا على بعض يعني
+
+61
+00:04:44,080 --> 00:04:47,300
+بيغطوا على بعضهم البعض فبالتالي
+
+62
+00:04:53,330 --> 00:04:59,300
+الضوء اللي جاي من نقاط مجاورةpartially overlaps
+
+63
+00:04:59,300 --> 00:05:03,900
+and cause a loss of detail in the formed image وكل
+
+64
+00:05:03,900 --> 00:05:08,460
+ما التداخل بين صور النقاط أو بالأصح بين ال point
+
+65
+00:05:08,460 --> 00:05:12,940
+spread functions بتاعت كل النقاط كل ما زاد التداخل
+
+66
+00:05:12,940 --> 00:05:18,220
+كل ما كان جودة الصورة أقل لأنه بيشوشوا في الرؤية
+
+67
+00:05:18,220 --> 00:05:21,200
+على بعضهم البعض يعني الإنسان لما بيطلع على هذه
+
+68
+00:05:21,200 --> 00:05:24,560
+الصورة بسبب التداخل بين ال point spread function
+
+69
+00:05:25,180 --> 00:05:28,040
+تاع النقطة A و ال point split function تاعة النقطة
+
+70
+00:05:28,040 --> 00:05:32,780
+B و تاعة C و تاعة D و الاخرى فبيتم ان ال quality
+
+71
+00:05:32,780 --> 00:05:37,780
+تاعة ال image بتكون أقل كل ما زاد التداخل اذا
+
+72
+00:05:37,780 --> 00:05:43,500
+overlaps and causes loss of detail in the formed
+
+73
+00:05:43,500 --> 00:05:53,260
+image هاي مثال عندي object object في منه نقطةأخدنا
+
+74
+00:05:53,260 --> 00:05:56,220
+منه نقطة طبعا هي أكبر من نقطة في الصورة بس هذا
+
+75
+00:05:56,220 --> 00:06:00,680
+اللي استطعنا الحصول عليه النقطة صورتها عبارة عن
+
+76
+00:06:00,680 --> 00:06:06,940
+point spread function شيء متعرش .. شيء متعرش مجموع
+
+77
+00:06:06,940 --> 00:06:11,080
+ال point spread function بتاع كل نقاط ال object في
+
+78
+00:06:11,080 --> 00:06:14,780
+مجموعه بيكون ال image طب هل ال image تشبه ال
+
+79
+00:06:14,780 --> 00:06:19,070
+object؟كان لا .. لا تشبه ال object لأنه في اختلاف
+
+80
+00:06:19,070 --> 00:06:22,870
+كبير أصبحت ال image بالشكل هذا بعد ما ال object
+
+81
+00:06:22,870 --> 00:06:28,230
+كان شكله دائري ومنتظر فبالتالي هذه فكرة ال
+
+82
+00:06:28,230 --> 00:06:32,230
+aberration ال aberration الزيغ يعني .. يعني ما هو
+
+83
+00:06:32,230 --> 00:06:36,670
+مقدار الزيغ عن المنظر الحقيقي اللي المفروض تكون
+
+84
+00:06:36,670 --> 00:06:38,930
+عليه ال image ال image المفروض تشبه ال object
+
+85
+00:06:38,930 --> 00:06:45,220
+بنسبة 100% فهذا الزيغ اللي احنا شايفينهبسموه ال
+
+86
+00:06:45,220 --> 00:06:49,380
+aberration ال aberration إله علاقة كبيرة بال point
+
+87
+00:06:49,380 --> 00:06:52,440
+spread function بمعنى آخر كل ما كانت ال point
+
+88
+00:06:52,440 --> 00:06:57,960
+spread function أكبر حجمها و more irregular more
+
+89
+00:06:57,960 --> 00:07:03,760
+irregular كل ما كان .. كل ما كان ال quality بتاعة
+
+90
+00:07:03,760 --> 00:07:10,180
+ال image أسوأ و أردب إذا ال point spread function
+
+91
+00:07:10,180 --> 00:07:15,930
+و ال aberration ارتباطهمإرتباط وثيق جدا و ال point
+
+92
+00:07:15,930 --> 00:07:18,710
+spread function بتعبر عن ال aberration و ال
+
+93
+00:07:18,710 --> 00:07:29,230
+aberration بتعبر عن ال point spread function هاي
+
+94
+00:07:29,230 --> 00:07:35,820
+أيضا أمثلةلأ ال point spread function بحسب اختلاف
+
+95
+00:07:35,820 --> 00:07:40,040
+ال optical system بأحجامها و بتعريجاتها بتعريجاتها
+
+96
+00:07:40,040 --> 00:07:43,300
+ال major point spread function كل ما كان حجمها
+
+97
+00:07:43,300 --> 00:07:48,760
+أصغر وأقل تعريجا كل ما كان الوضع بيكون أفضل من
+
+98
+00:07:48,760 --> 00:07:52,940
+ناحية ال image qualityكل ما كانت أصغر بيكون
+
+99
+00:07:52,940 --> 00:07:56,320
+تداخلها مع ال point spread function المجاورة تحت
+
+100
+00:07:56,320 --> 00:08:01,020
+صور النقاط الأخرى بيكون أقل فبالتالي جودة الصورة
+
+101
+00:08:01,020 --> 00:08:04,720
+بتكون أعلى جودة الصورة بتكون أعلى ل quality تحت ال
+
+102
+00:08:04,720 --> 00:08:07,360
+image وكل ما كانت أكبر بيكون الوضع أسوأ لأن
+
+103
+00:08:07,360 --> 00:08:11,800
+التداخل هيزيد طبعا كل ما كانت تعريج أكتر معناته ال
+
+104
+00:08:11,800 --> 00:08:15,820
+aberration أكتر ال aberration الزيغ عن الوضع
+
+105
+00:08:15,820 --> 00:08:20,150
+الحقيقي بيكون أكتر .. بيكون أكتر .. إذاهذه قضية
+
+106
+00:08:20,150 --> 00:08:23,430
+اللي هي ال point spread function و ال aberration
+
+107
+00:08:23,430 --> 00:08:27,910
+إذا ال light from nearby point sources partially
+
+108
+00:08:27,910 --> 00:08:32,330
+overlaps and causes a lot of detail in the formed
+
+109
+00:08:32,330 --> 00:08:32,730
+image
+
+110
+00:08:36,240 --> 00:08:41,500
+although no lens focus أو focuses perfectly, some
+
+111
+00:08:41,500 --> 00:08:45,280
+focus better than others and produce more detail
+
+112
+00:08:45,280 --> 00:08:49,900
+in the resulting image طبعا مافيش optical system
+
+113
+00:08:49,900 --> 00:08:54,280
+أو lens بتعمل perfect focus لكل النقاط، إيش يعني
+
+114
+00:08:54,280 --> 00:08:58,670
+perfect focus؟ يعني النقطة إيه؟صورتها A شرطة في ال
+
+115
+00:08:58,670 --> 00:09:02,770
+image عبارة عن نقطة مش أكبر من نقطة النقطة B أيضا
+
+116
+00:09:02,770 --> 00:09:06,870
+عبارة عن نقطة النقطة C يعني صورة النقطة تساوي نقطة
+
+117
+00:09:06,870 --> 00:09:10,810
+مش point spread function طبعا مافي optical system
+
+118
+00:09:10,810 --> 00:09:15,930
+يعطيني perfect image أو perfect focus لكل نقاط ال
+
+119
+00:09:15,930 --> 00:09:19,570
+object ولكن في optical system أفضل من optical
+
+120
+00:09:19,570 --> 00:09:23,530
+system آخر بمعنى آخر لو احنا رجعنا هنا للعرض
+
+121
+00:09:23,530 --> 00:09:29,070
+المكبر وقلناالـ point spread function هذه أنتجها
+
+122
+00:09:29,070 --> 00:09:33,410
+optical system A مثلا والـ point spread function
+
+123
+00:09:33,410 --> 00:09:37,470
+هذه أنتجها ال optical system B طبعا بنقول أيهما
+
+124
+00:09:37,470 --> 00:09:40,710
+أفضل بنقول A أفضل طب ليش حكمنا على ال optical
+
+125
+00:09:40,710 --> 00:09:44,370
+system أو العدسة A أنها أفضل من B لأن ال point
+
+126
+00:09:44,370 --> 00:09:49,090
+spread function بتاعتها أصغر حجماو أقل تعريجا .. و
+
+127
+00:09:49,090 --> 00:09:53,110
+أقل تعريجا فبالتالي هذا .. لو عندي optical system
+
+128
+00:09:53,110 --> 00:09:55,730
+يعطيني هذه ال .. ال .. ال point spread function
+
+129
+00:09:55,730 --> 00:09:58,330
+بيكون أفضل و أفضل و لو كان عندي optical system
+
+130
+00:09:58,330 --> 00:10:02,770
+يعطيني حجم أصغر و أقل تعريجا معناته كل ما صغرت ال
+
+131
+00:10:02,770 --> 00:10:05,750
+point spread function معناته ال focus أفضل، ال
+
+132
+00:10:05,750 --> 00:10:09,450
+quality أفضل، ال optical system أفضل ال optical
+
+133
+00:10:09,450 --> 00:10:13,030
+system أفضل فبالتالي هذه القضية ضروري تكون واضحة
+
+134
+00:10:14,300 --> 00:10:18,400
+الـ point spread function هي عبارة عن إيش؟ ال
+
+135
+00:10:18,400 --> 00:10:23,120
+point spread function هي صورة أي مقطة طب بدنا
+
+136
+00:10:23,120 --> 00:10:26,480
+تفصيل أكتر في هذا الموضوع بنقول ال point spread
+
+137
+00:10:26,480 --> 00:10:33,640
+function تصف .. تصف how light from a single point
+
+138
+00:10:33,640 --> 00:10:39,060
+source is distributed in an image and completely
+
+139
+00:10:39,060 --> 00:10:42,360
+describes the imaging characteristics of an
+
+140
+00:10:42,360 --> 00:10:46,430
+optical systemيعني ال point spread function أو
+
+141
+00:10:46,430 --> 00:10:51,430
+دالة انتشار النقطة أو بالأصحى دالة انتشار الضوء
+
+142
+00:10:51,430 --> 00:10:55,630
+القادم من النقطة بتوصف لي كيف الضوء اللي إيجا من
+
+143
+00:10:55,630 --> 00:11:00,350
+single point في ال object كيف توزع في ال image
+
+144
+00:11:00,350 --> 00:11:06,760
+نشوف الصورةهاي single point هاي الضوء اللي إجا منه
+
+145
+00:11:06,760 --> 00:11:09,780
+و راح على ال lens دخل في ال lens و ال lens جمعته
+
+146
+00:11:09,780 --> 00:11:14,260
+اتوزع في سطح ال image نفرض هذا اللوح الأسود ال
+
+147
+00:11:14,260 --> 00:11:17,940
+image تشغل كل اللوح الأسود بس هذه المنطقة اللي
+
+148
+00:11:17,940 --> 00:11:22,860
+بالأبيض هي المنطقة اللي انتشر فيها الضوء اللي قدم
+
+149
+00:11:22,860 --> 00:11:25,860
+من نقطة واحد اللي جاء من نقطة واحد اللي هي النقطة
+
+150
+00:11:25,860 --> 00:11:30,000
+ايهإذا ما الطريقة اللي توزع فيها هذا الضوء القادم
+
+151
+00:11:30,000 --> 00:11:34,100
+من a فقط مش من كل .. مش من كل نقاط ال object هذه
+
+152
+00:11:34,100 --> 00:11:36,720
+هي الشكل اللي هو اللي توزع فيه هذا ال point spread
+
+153
+00:11:36,720 --> 00:11:42,120
+function بتاع النقطة a أو صورة النقطة a أو a شرطة
+
+154
+00:11:42,120 --> 00:11:46,500
+زي ما احنا يعني بنسميها تمام؟ إذا ال point spread
+
+155
+00:11:46,500 --> 00:11:54,400
+function تصف .. تصف كيف توزع الضوء القادم من
+
+156
+00:11:54,400 --> 00:11:59,290
+single pointhow it is distributed in an image
+
+157
+00:11:59,290 --> 00:12:03,790
+مجموع الـ point spread function بتاع كل نقاط ال
+
+158
+00:12:03,790 --> 00:12:08,570
+object completely describes بشكل كامل the imaging
+
+159
+00:12:08,570 --> 00:12:12,130
+characteristics of an optical system يعني هذا ال
+
+160
+00:12:12,130 --> 00:12:16,780
+optical systemهيعطيني image .. هذا ال optical
+
+161
+00:12:16,780 --> 00:12:20,660
+system .. هيعطيني image كيف ال quality بتاعتها ..
+
+162
+00:12:20,660 --> 00:12:23,580
+كيف ال quality بتاعتها .. عالية ولا متوسطة ولا
+
+163
+00:12:23,580 --> 00:12:26,940
+راضية .. عالية ولا متوسطة .. يعني ال imaging
+
+164
+00:12:26,940 --> 00:12:29,740
+characteristic ولا إذا كان هذا ال optical system
+
+165
+00:12:30,400 --> 00:12:35,500
+بيعطيني point spread function صغيرة جدا ومش متعرجة
+
+166
+00:12:35,500 --> 00:12:38,400
+كتير معناته ال quality تاعة ال image عالية ليش؟
+
+167
+00:12:38,400 --> 00:12:42,620
+لأنه صغيرة جدا، اذا اي شرطة بتتدافلش مع بي شرطة
+
+168
+00:12:42,620 --> 00:12:46,780
+ومع سي شرطة ومع دي شرطة وما إلى ذلك والله إذا هذا
+
+169
+00:12:46,780 --> 00:12:49,520
+ال optical system أعطاني point spread function
+
+170
+00:12:49,520 --> 00:12:53,540
+متعرجة كتير ومساحتها كبيرة لكل point spread
+
+171
+00:12:53,540 --> 00:12:56,540
+function معناته التدافل كتير و ال quality رديقة
+
+172
+00:12:56,540 --> 00:13:01,800
+للغايةإذا هذا بالنسبة لل point spread function و
+
+173
+00:13:01,800 --> 00:13:08,600
+ال aberration طيب إذا ننتقل الآن لتصنيع optical
+
+174
+00:13:08,600 --> 00:13:14,260
+system أو lens بس قبل تصنيعه المفروض نناقش موضوع
+
+175
+00:13:14,260 --> 00:13:18,280
+يعني تخيل إحنا في مصنع بده ينتج عدسات أو optical
+
+176
+00:13:18,280 --> 00:13:23,310
+systems لغرض معينقبل ما ننتج العدسات او ال optical
+
+177
+00:13:23,310 --> 00:13:27,670
+systems لهذا الغرض اللي احنا نويين انه نصنع له
+
+178
+00:13:27,670 --> 00:13:32,410
+العدسات مفروض نعمل حساب لل point spread function
+
+179
+00:13:32,410 --> 00:13:36,990
+يعني بدي انا optical system يعطيني point spread
+
+180
+00:13:36,990 --> 00:13:43,510
+function أصغر ما يكونوأقل تعريجا ممكن أقل ما يمكن
+
+181
+00:13:43,510 --> 00:13:48,250
+من التعريج وأصغر ما يمكن من الحجم وإذا قدرت أصل أن
+
+182
+00:13:48,250 --> 00:13:52,210
+هذا ال optical system اللي أنا ناوي أصنعه لسه ما
+
+183
+00:13:52,210 --> 00:13:58,080
+صنعته إذا بيعطيني نقطةلكل نقطة في ال object معناته
+
+184
+00:13:58,080 --> 00:14:03,140
+انا وصلت ل perfect optical system يعطيني stigmatic
+
+185
+00:14:03,140 --> 00:14:08,260
+image طيب عشان نحسب ال point spread function بشكل
+
+186
+00:14:08,260 --> 00:14:14,020
+معادلات رياضية لازم ناخد بالنا من عدة أمور هذا ال
+
+187
+00:14:14,020 --> 00:14:17,640
+optical system اللي انا هصنعه بدى يعمللي
+
+188
+00:14:17,640 --> 00:14:23,430
+refraction للضوء هذا واحد تاني حاجةالجزء من الضوء
+
+189
+00:14:23,430 --> 00:14:26,330
+اللي ساقط عليه من ال object هيصير له reflection
+
+190
+00:14:26,330 --> 00:14:30,770
+وهذا كلام معروف جدا ان الضوء لما بسقط على السطح
+
+191
+00:14:30,770 --> 00:14:34,990
+فاصل بين مادتين هذه الضوء يسري في الهواء وهذه مادة
+
+192
+00:14:34,990 --> 00:14:39,950
+ال lens اللي هي الجزاز ووصل حزمة ضوئية نفرض مائة
+
+193
+00:14:39,950 --> 00:14:44,340
+ألف شعاع هينعكس منهم مثلا الفو هينكسر منهم يعني
+
+194
+00:14:44,340 --> 00:14:49,300
+يمر منهم تسعة و تسعين ألف اذا جزء هينعكس وجزء
+
+195
+00:14:49,300 --> 00:14:53,180
+هينكسر اذا لازم في حساب ال point spread function
+
+196
+00:14:53,180 --> 00:14:57,900
+بده احسب جديش مره صارله reflection وجديش صارله
+
+197
+00:14:57,900 --> 00:15:01,820
+reflection وايضا عشان نحسب ال point spread
+
+198
+00:15:01,820 --> 00:15:05,200
+function بشكل دقيقة الجزء من ال light اللي صارله
+
+199
+00:15:05,200 --> 00:15:08,880
+diffraction diffraction يعني اذا هذا ال .. ال ..
+
+200
+00:15:08,880 --> 00:15:13,680
+ال ..الـ optical system عبارة عن عدة عدسات وفي
+
+201
+00:15:13,680 --> 00:15:19,520
+بينهم يعني حواجز وفي الحواجز في مثلا فتحات يعني في
+
+202
+00:15:19,520 --> 00:15:22,480
+الحواجز ممكن يعملي diffraction بدا أحسب الـ
+
+203
+00:15:22,480 --> 00:15:27,860
+diffraction بس لأ طيب تداخل الضوء تداخل الموجات
+
+204
+00:15:27,860 --> 00:15:30,920
+الضوئية ال interference هل هو constructive ولا
+
+205
+00:15:30,920 --> 00:15:35,680
+destructive ال polarization تاعة الضوءهل اتجاه ال
+
+206
+00:15:35,680 --> 00:15:40,540
+polarization عمودي ولا أفقي ولا oblique ولا
+
+207
+00:15:40,540 --> 00:15:45,520
+circularly polarized ولا elliptically polarized؟
+
+208
+00:15:45,520 --> 00:15:50,660
+أيضا بدي أحسب قضية أنه لو في أي شغلة في ال .. في
+
+209
+00:15:50,660 --> 00:15:55,540
+الإجاز عملت scattering لل lightscattering لل light
+
+210
+00:15:55,540 --> 00:16:02,500
+او في ال media بما فيها الهواء اللي موجودة في مكان
+
+211
+00:16:02,500 --> 00:16:07,080
+التصوير بمعنى اه فانا بدي استخدم هذه الكاميرا اللي
+
+212
+00:16:07,080 --> 00:16:10,980
+بدي صنعها في studio فبدي احسب ال scattering لل
+
+213
+00:16:10,980 --> 00:16:14,930
+lightأيضا بدي أحسب ال dispersion .. dispersion
+
+214
+00:16:14,930 --> 00:16:21,250
+اللي هو بالظبط كأنه بيمروا الضوء في ثمك معين من
+
+215
+00:16:21,250 --> 00:16:25,350
+الزجاج كأنه بيمروا في ال prism و بيتحلل للألوان
+
+216
+00:16:25,350 --> 00:16:30,150
+الطيفية ال spectral colors فكل هذه الشغلات عشان
+
+217
+00:16:30,150 --> 00:16:35,950
+أحسب ال point spread function بشكل دقيقلابد ان اخد
+
+218
+00:16:35,950 --> 00:16:39,130
+في اعتباري الاشياء اللي احنا ذكرناها و اللي انا
+
+219
+00:16:39,130 --> 00:16:42,670
+بيعطيها هنا في ال slide ألوان مختلفة بناخد بالنا
+
+220
+00:16:42,670 --> 00:16:45,150
+اول حاجة من الـ Refraction اللي هيعمل ليها ال
+
+221
+00:16:45,150 --> 00:16:48,270
+optical system او ال lens اللي بده اصنعها ال
+
+222
+00:16:48,270 --> 00:16:51,610
+reflection ال diffraction هي تلاتة ال interference
+
+223
+00:16:51,610 --> 00:16:55,770
+أربعة ال polarization خمسة ال scattering ستة ال
+
+224
+00:16:55,770 --> 00:16:59,370
+dispersion سبعة عشان نحسب ال point spread function
+
+225
+00:16:59,370 --> 00:17:05,270
+بشكل دقيق و نحاول نصل في التصنيعلأفضل point spread
+
+226
+00:17:05,270 --> 00:17:09,450
+function يعني لأفضل optical system ممكن لازم أخد
+
+227
+00:17:09,450 --> 00:17:16,190
+بالي من هذه الأشياء السبعة، الآن عند النقطة high
+
+228
+00:17:16,190 --> 00:17:21,270
+بنقول أن الموضوع صعب للغاية حساب ال point spread
+
+229
+00:17:21,270 --> 00:17:23,930
+function حتى لو استخدمنا computer
+
+230
+00:17:26,580 --> 00:17:30,680
+للحسابات ال point spread function even using a
+
+231
+00:17:30,680 --> 00:17:34,400
+computer calculating a point spread function that
+
+232
+00:17:34,400 --> 00:17:38,100
+accounts for all optical variables is difficult
+
+233
+00:17:38,100 --> 00:17:42,320
+هذه كلها كانت تسمى ال optical variables يعني ضروري
+
+234
+00:17:42,320 --> 00:17:46,080
+أخد بالي منها كلها عشان كل الأمور هتكونكويسة يعني
+
+235
+00:17:46,080 --> 00:17:49,060
+يكون ال reflection ممتاز ال reflection أقل ما يمكن
+
+236
+00:17:49,060 --> 00:17:53,040
+ال diffraction يكون قليل ال interference ما ..
+
+237
+00:17:53,040 --> 00:17:57,660
+مايكونش destructive يكون constructive interference
+
+238
+00:17:57,660 --> 00:18:01,320
+ال polarization يكون مناسب ال scattering يكون أقل
+
+239
+00:18:01,320 --> 00:18:04,580
+ما يمكن عشان ما يشوشش على الصورة ال dispersion
+
+240
+00:18:04,580 --> 00:18:08,700
+برضه يكون أقل ما يمكن يعني كل هذه المتغيرات عشان
+
+241
+00:18:09,330 --> 00:18:13,190
+أخدها في الحسبان حتى لو استعمال الكمبيوتر يحسبلي
+
+242
+00:18:13,190 --> 00:18:17,430
+ال point spread function و تطلعلي خصائص لهذه
+
+243
+00:18:17,430 --> 00:18:22,270
+الأشياء السبعة تكون ممتازة بيكون عندي difficult
+
+244
+00:18:22,270 --> 00:18:27,250
+process difficult process حتى باستعمال الكمبيوتر
+
+245
+00:18:27,250 --> 00:18:33,550
+طب إيش نعمل؟ بعض العلماء اقترح بس أنا جابل .. جابل
+
+246
+00:18:33,550 --> 00:18:36,390
+ما نقول إيش نعمل؟ أنا بدي أطلع على ال net and goal
+
+247
+00:18:37,220 --> 00:18:42,960
+يعني كشيء بسيط جدا نقول calculating ال
+
+248
+00:18:42,960 --> 00:18:47,760
+point spread function ونشوف ايش المعادلات اللي
+
+249
+00:18:47,760 --> 00:18:59,720
+ممكن تطلع معانا يعني
+
+250
+00:18:59,720 --> 00:19:04,640
+لو احنا أخدنا منظر هذه
+
+251
+00:19:05,930 --> 00:19:09,690
+calculation لل point spread function هذه
+
+252
+00:19:09,690 --> 00:19:15,210
+calculation لل point spread function لل point
+
+253
+00:19:15,210 --> 00:19:19,530
+spread function فبالتالي احنا الوضع حقيقة صعب و
+
+254
+00:19:19,530 --> 00:19:26,990
+معقد و معادلات كثيرة اللي بتخلي العلماء يعني يعني
+
+255
+00:19:26,990 --> 00:19:30,670
+يشوفوها شغل صعب حتى باستعمال ال computer
+
+256
+00:19:34,360 --> 00:19:39,840
+بعض العلماء اقترح ان نقوم بامر عكسي اول اش نصنع ال
+
+257
+00:19:39,840 --> 00:19:44,830
+lensوبعد ما نصنع ال lens ندرس الأشياء السابعة هذه
+
+258
+00:19:44,830 --> 00:19:48,310
+هل ال lens اللي احنا صنعناها بتعمل reflection كويس
+
+259
+00:19:48,310 --> 00:19:52,030
+reflection, diffraction, interference يعني مقبول و
+
+260
+00:19:52,030 --> 00:19:54,990
+ال diffraction مقبول يعني الأشياء هذه يعني نرجعها
+
+261
+00:19:54,990 --> 00:19:59,710
+بعد ما نكون بتصنيع ال lens بعد ما نكون بتصنيع ال
+
+262
+00:19:59,710 --> 00:20:03,270
+lens اذا the point spread function of a lens can
+
+263
+00:20:03,270 --> 00:20:06,490
+be measured نقدر نجيسها after it is manufactured
+
+264
+00:20:06,490 --> 00:20:09,590
+بعد ما نصنع ال lens نجيس ال point spread function
+
+265
+00:20:09,590 --> 00:20:15,280
+بتاعتهابس في عندي مشكلة doing so is a time
+
+266
+00:20:15,280 --> 00:20:19,580
+-consuming and costly task requiring specialized
+
+267
+00:20:19,580 --> 00:20:25,000
+equipment and expertise أولش هذا القضية بتستهلك
+
+268
+00:20:25,000 --> 00:20:28,760
+وقت ليش بتستهلك وقت صنعنا lens و حسبنا ال point
+
+269
+00:20:28,760 --> 00:20:31,240
+spread function أو جسنا ال point spread function
+
+270
+00:20:31,240 --> 00:20:34,330
+بتاعهايعني .. يعني .. يعني ال point spread
+
+271
+00:20:34,330 --> 00:20:37,790
+function بتاع نقاط الضوء اللي أو .. أو نقاط الضوء
+
+272
+00:20:37,790 --> 00:20:40,950
+بتاعة ال object أو النقاط بتاعة ال object اللي
+
+273
+00:20:40,950 --> 00:20:43,670
+مررنا الضوء من هذه ال lens اللي صنعناها طب افرض
+
+274
+00:20:43,670 --> 00:20:46,390
+ماعجبتناش ال point spread function أو طلعت رديقة
+
+275
+00:20:47,600 --> 00:20:51,860
+بنضطر نصنع عدسة تانية وما عجبتناش برضه بتطلع ..
+
+276
+00:20:51,860 --> 00:20:55,220
+فبتالي هذا ال time consuming يعني بيستهلك للوقت
+
+277
+00:20:55,220 --> 00:20:59,940
+وطالما أيضا ممكن يعني هيكلفنا تصنيع عدة عدسات عشان
+
+278
+00:20:59,940 --> 00:21:04,040
+بالنهاية نصل ل .. لعدسة .. للعدسة المطلوبة أيضا
+
+279
+00:21:04,040 --> 00:21:10,500
+costly task يعني شيء مكلف بتطلب يعني أدوات يعني
+
+280
+00:21:10,500 --> 00:21:17,010
+معينة و بتطلب خبرة معينةإيش نعمل معناته؟ كيف نحل
+
+281
+00:21:17,010 --> 00:21:20,330
+مشكلة ال point spread function؟ أنا مش قادر أحسبها
+
+282
+00:21:20,330 --> 00:21:24,890
+قبل التصنيع لأنه بدنا نحسب variables كتيرة، هاي
+
+283
+00:21:24,890 --> 00:21:28,850
+نقطة، نقطة تانية لو صنعت بعدين جستا ممكن أخطق مرة
+
+284
+00:21:28,850 --> 00:21:31,890
+في الصناعة و مرة تانية و مرة تالتة و مرة رابعة،
+
+285
+00:21:31,890 --> 00:21:36,970
+برضه أدم مكلف و يعني يستهلك الوقت، طب إيش نعمل؟
+
+286
+00:21:37,470 --> 00:21:42,250
+حقيقة اللي عمل بسيط جدا fortunately لحسن الحظ most
+
+287
+00:21:42,250 --> 00:21:46,550
+image characteristics such as location الموقع بتاع
+
+288
+00:21:46,550 --> 00:21:49,590
+ال image و ال size اللي هو ال magnification و ال
+
+289
+00:21:49,590 --> 00:21:52,010
+orientation اللي هي above ولا below the optical
+
+290
+00:21:52,010 --> 00:21:55,830
+axis and the brightness can be calculating or
+
+291
+00:21:55,830 --> 00:21:58,510
+measured without considering ال point spread
+
+292
+00:21:58,510 --> 00:22:02,300
+functionهذه الأشياء و هذه الصفات بقدر أجيسها بدون
+
+293
+00:22:02,300 --> 00:22:06,280
+ما أحسب ال point spread function حدودها حدود ال
+
+294
+00:22:06,280 --> 00:22:11,000
+point spread function كيف؟ بطريقة استعمال قوانين
+
+295
+00:22:11,000 --> 00:22:14,200
+ال geometric optics مش ال physical optics إذا the
+
+296
+00:22:14,200 --> 00:22:17,600
+field of geometric optics greatly simplifies
+
+297
+00:22:17,600 --> 00:22:22,500
+calculations of image characteristics by ignoring
+
+298
+00:22:22,500 --> 00:22:25,400
+most of light's physical characteristics
+
+299
+00:22:25,400 --> 00:22:31,100
+especially diffraction طيبال .. ال geometric
+
+300
+00:22:31,100 --> 00:22:36,200
+optics علم مبني على ال approximations المقاربات
+
+301
+00:22:36,200 --> 00:22:41,380
+وأول approximation في ال geometric optics بيقول ..
+
+302
+00:22:41,380 --> 00:22:45,080
+بيقول أو بينص على .. أول مقاربات في ال geometric
+
+303
+00:22:45,080 --> 00:22:50,760
+optics بينص على ignore image quality لا تهتم بال
+
+304
+00:22:50,760 --> 00:22:54,000
+image quality لأن اهتمامك بال image quality هيقدّي
+
+305
+00:22:54,000 --> 00:22:58,560
+انك انت لازم تدرس ال point spread functionفعلم الـ
+
+306
+00:22:58,560 --> 00:23:02,320
+Geometric Optics بيهمل ال point spread function
+
+307
+00:23:02,320 --> 00:23:06,280
+لأنه مش معنى بدراسة ال image quality بقدر ما هو
+
+308
+00:23:06,280 --> 00:23:09,580
+معنى بدراسة الصفات الأخرى إيش هي الصفات الأخرى ال
+
+309
+00:23:09,580 --> 00:23:12,020
+location يعني موقع ال image بالنسبة لل optical
+
+310
+00:23:12,020 --> 00:23:16,120
+system أو بالأحرى ال image distance ال size ال
+
+311
+00:23:16,120 --> 00:23:19,020
+magnification مكبرة مسافرة كام مرة بالنسبة لل
+
+312
+00:23:19,020 --> 00:23:22,640
+object ال orientation يعني فوق ال optical axis
+
+313
+00:23:22,640 --> 00:23:27,580
+معتدلا ولاbelow ال optical axis يعني مقلوبة و ال
+
+314
+00:23:27,580 --> 00:23:31,780
+brightness يعني قداش كمية الإضاءة اللي فيها اذا
+
+315
+00:23:31,780 --> 00:23:35,760
+the field of geometric optics it greatly simplify
+
+316
+00:23:35,760 --> 00:23:40,060
+.. simplifies calculation ببسط لعلم ال geometric
+
+317
+00:23:40,060 --> 00:23:45,540
+optics بشكل كبير الحسابات حسابات ايش حسابات ال
+
+318
+00:23:45,540 --> 00:23:49,980
+image characteristics كيف ببسطها by ignoring most
+
+319
+00:23:49,980 --> 00:23:54,560
+of lights physical characteristicsكل أو الغالبية
+
+320
+00:23:54,560 --> 00:23:58,760
+العظمة من الصفات الفيزيائية بتاعة الضوء بتهملها ال
+
+321
+00:23:58,760 --> 00:24:01,780
+geometric optics بتهملها ال geometric optics
+
+322
+00:24:01,780 --> 00:24:06,280
+بالذات ال geometric optics بتهمل ال diffraction طب
+
+323
+00:24:06,280 --> 00:24:10,120
+ايش ال .. او كيف بنصل لباقي الصفات بستعمل ايش يعني
+
+324
+00:24:10,120 --> 00:24:13,520
+ايش الحسابات اللي بستعملها عشان نصل لل location و
+
+325
+00:24:13,520 --> 00:24:16,900
+ال size و ال orientation نستعمل القوانين اللي هي
+
+326
+00:24:17,880 --> 00:24:21,040
+قانون السرايان المستقيم، law of rectilinear
+
+327
+00:24:21,040 --> 00:24:27,040
+propagation قانون الـ refraction قانون الانكسار هو
+
+328
+00:24:27,040 --> 00:24:32,520
+Snell's law وقانون الانعكاس هو قانون الانعكس إذا
+
+329
+00:24:32,520 --> 00:24:35,480
+using only the three laws of rectilinear
+
+330
+00:24:35,480 --> 00:24:39,000
+propagation والrefraction والreflection image
+
+331
+00:24:39,000 --> 00:24:43,040
+characteristics can be determined with sufficient
+
+332
+00:24:43,040 --> 00:24:47,470
+accuracy for most usersبقدر أحدد صفات ال image
+
+333
+00:24:47,470 --> 00:24:52,430
+وبدقة عالية كتير في .. في معظم وليس في كل .. في
+
+334
+00:24:52,430 --> 00:24:56,730
+معظم الحالات باستعمال هذه القوانين، في معظم
+
+335
+00:24:56,730 --> 00:25:01,660
+الحالات باستعمال هذه القوانين، طيبلما في عندى بعض
+
+336
+00:25:01,660 --> 00:25:06,400
+الحالات بيكون فيها diffraction كتير بيكون فيها ال
+
+337
+00:25:06,400 --> 00:25:10,540
+interference كتير بيكون فيه بعض الصفات الفيزيائية
+
+338
+00:25:10,540 --> 00:25:14,680
+للضوء مهمة ساعتها ال image quality it is necessary
+
+339
+00:25:14,680 --> 00:25:18,680
+to use calculations from physical optics يعني
+
+340
+00:25:18,680 --> 00:25:22,180
+ضروري ساعتها ندخل في التعقيدات وطبعا تعيين الفيزيا
+
+341
+00:25:22,180 --> 00:25:28,450
+هم او متخصصي الفيزياهم اللي ساعتها بيحسبوا ال
+
+342
+00:25:28,450 --> 00:25:31,510
+image characteristics باعتماد ال physical أو
+
+343
+00:25:31,510 --> 00:25:34,730
+باعتبار .. باعتماد ال physical laws أو القوانين
+
+344
+00:25:34,730 --> 00:25:38,730
+الفيزيائية لدّو، إذا only و ال diffraction و ال
+
+345
+00:25:38,730 --> 00:25:44,070
+interference و other some physical property is a
+
+346
+00:25:44,070 --> 00:25:48,070
+significant factor يعني إيش .. يعني مهمة لأن ال
+
+347
+00:25:48,070 --> 00:25:51,920
+diffraction في بعض ال optical system مهميعني بعض
+
+348
+00:25:51,920 --> 00:25:54,680
+ال optical system لا يمكن تجاهل ال diffraction
+
+349
+00:25:54,680 --> 00:25:59,200
+فيها في الغالبية العظمة من ال optical systems ممكن
+
+350
+00:25:59,200 --> 00:26:02,760
+أتجاهل ال diffraction طيب في بعض ال optical
+
+351
+00:26:02,760 --> 00:26:06,200
+systems في .. في أغراض علمية أو أغراض صناعية أو
+
+352
+00:26:06,200 --> 00:26:10,260
+مشابه لا يمكن تجاهل ال diffraction ولا يمكن تجاهل
+
+353
+00:26:10,260 --> 00:26:12,820
+ال interference ولا يمكن تجاهل بعض الصفات
+
+354
+00:26:12,820 --> 00:26:16,620
+الفيزيائية للضوء زي ال polarization و زي الشغلات
+
+355
+00:26:16,620 --> 00:26:20,850
+اللي هي زي هيك ساعتهالما بيشكلولي significant
+
+356
+00:26:20,850 --> 00:26:25,470
+factor in image quality it is necessary to use
+
+357
+00:26:25,470 --> 00:26:30,690
+calculations from physical optics فضروري ساعتها ما
+
+358
+00:26:30,690 --> 00:26:36,340
+اكتفي بقوانين ال geometric opticsThe point spread
+
+359
+00:26:36,340 --> 00:26:39,900
+function is required only for the analysis of
+
+360
+00:26:39,900 --> 00:26:44,540
+image quality, which in most cases is dominated by
+
+361
+00:26:44,540 --> 00:26:49,100
+aberrations or diffraction ما معنى هذا الكلام؟
+
+362
+00:26:49,100 --> 00:26:53,920
+بنقول كالقادر ال point spread function بتلزمنا فقط
+
+363
+00:26:53,920 --> 00:26:59,260
+لتحليل ال image qualityلما انا بتكلم عن ال image
+
+364
+00:26:59,260 --> 00:27:03,380
+quality بدي اعرف ال image quality جودة الصورة
+
+365
+00:27:03,380 --> 00:27:07,680
+وقداش الصورة بتشبه ال object ساعتها انا مضطر لازم
+
+366
+00:27:07,680 --> 00:27:12,200
+ابحث اشوف حدود ال point spread function لكل نقطة
+
+367
+00:27:12,200 --> 00:27:16,040
+من نقاط ال object كيف الحدود كيف التعريش بتاعها
+
+368
+00:27:16,040 --> 00:27:20,360
+وين انتهى الضوء اللي انطلق من نقطة ايه و الخريطة
+
+369
+00:27:20,360 --> 00:27:23,790
+بتاعةالـ point spread function يعني الحدود
+
+370
+00:27:23,790 --> 00:27:28,650
+المتعرجتها لازم أعرفها بالتفصيل عشان أعرف ال image
+
+371
+00:27:28,650 --> 00:27:32,290
+equality عشان أعرف ال image equality إذا أنا بدي
+
+372
+00:27:32,290 --> 00:27:36,330
+أعرف ال image equality طيب ال image equality اللي
+
+373
+00:27:36,330 --> 00:27:41,070
+بتحكم في التعريج هذا صفات كتير فيزيائية لبطولة
+
+374
+00:27:41,070 --> 00:27:46,670
+اللي بتحكم في التعريج هذا اللي بتحكم في التعريج
+
+375
+00:27:46,670 --> 00:27:51,450
+هذا لل point spread functionاللي بتحكم في التعريج
+
+376
+00:27:51,450 --> 00:27:56,630
+هذا ربما الصورة هي أوضح صورة لإنها يعني التعريج
+
+377
+00:27:56,630 --> 00:28:00,090
+فيها واضح جدا نمشي مع رأس السهم بتاع ال mouse
+
+378
+00:28:00,090 --> 00:28:05,430
+التعريج هذا اللي بتحكم فيه أشياء كتيرة بس أهم
+
+379
+00:28:05,430 --> 00:28:12,170
+شيئين بتحكموا في التعريج وفي حدود في الحدود بتاعة
+
+380
+00:28:12,170 --> 00:28:15,190
+ال point split function هم ال aberration و ال
+
+381
+00:28:15,190 --> 00:28:18,450
+diffraction هم ال aberration و ال diffraction
+
+382
+00:28:18,450 --> 00:28:23,710
+فبالتاليالـ point spread function بتحكم فيها كتير
+
+383
+00:28:23,710 --> 00:28:28,570
+صفات فيزيائية بس أكتر إشي dominant في الصفات
+
+384
+00:28:28,570 --> 00:28:31,510
+الفيزيائية اللي بتضوب اللي بتحكملي في ال point
+
+385
+00:28:31,510 --> 00:28:35,030
+spread function هي ال aberrations التعريج وال
+
+386
+00:28:35,030 --> 00:28:38,690
+diffraction والانتشار إيش يعني التعريج وإيش يعني
+
+387
+00:28:38,690 --> 00:28:49,490
+الانتشار يعني نرجع للصورة بنقول كالقاتل هذه
+
+388
+00:28:49,490 --> 00:28:57,050
+نقطةوهي صورتها إذا مساحة الصورة كبيرة اللي هو
+
+389
+00:28:57,050 --> 00:29:00,250
+البياض هذا اللي هو صورة النقطة إيه إذا المساحة
+
+390
+00:29:00,250 --> 00:29:05,510
+كبيرة معناته الـ diffraction كتير طيب إذا التعريج
+
+391
+00:29:05,510 --> 00:29:09,050
+في الحدود كتير معناته ال aberration كتير يعني ال
+
+392
+00:29:09,050 --> 00:29:13,770
+aberration مسئولة عن التعريج و ال diffraction
+
+393
+00:29:13,770 --> 00:29:18,050
+مسئولة عن مساحة النقطة مساحة النقطة إذا
+
+394
+00:29:22,170 --> 00:29:27,090
+بنعيد عشان ندرس ال image quality لازم ندرس ال
+
+395
+00:29:27,090 --> 00:29:31,030
+point spread function ال point spread function في
+
+396
+00:29:31,030 --> 00:29:36,110
+أشياء فيزيائية كتيرة بتتحكم فيها وفي حدودها وفي
+
+397
+00:29:36,110 --> 00:29:40,230
+مساحتها بس أكتر شيئين بيأثروا على ال point spread
+
+398
+00:29:40,230 --> 00:29:44,830
+function ال aberrations و ال diffraction ال
+
+399
+00:29:44,830 --> 00:29:49,780
+aberrations مسئولة عن تعريج الحدودوالـ diffraction
+
+400
+00:29:49,780 --> 00:29:54,620
+مسؤول عن مساحة الـ point spread function بمعنى
+
+401
+00:29:54,620 --> 00:29:59,320
+آخر، لو تصورنا إنه في عندي diffraction كتير بس ال
+
+402
+00:29:59,320 --> 00:30:03,940
+aberration zero هتكون صورة النقطة A عبارة عن ..
+
+403
+00:30:03,940 --> 00:30:11,770
+النقطة A هتكون صورتها عبارة عن دائرةفي diffraction
+
+404
+00:30:11,770 --> 00:30:14,950
+يعني في مساحة كبيرة بس فيش aberration يعني فيش
+
+405
+00:30:14,950 --> 00:30:18,590
+تعريج يعني عبارة عن دائرة فبالتالي هذه القضية
+
+406
+00:30:18,590 --> 00:30:24,010
+ضرورية جدا تكون واضحة ان شاء الله تعالى طيب كيف
+
+407
+00:30:24,010 --> 00:30:28,830
+ندرسالـ point spread function عشان نوصل لل image
+
+408
+00:30:28,830 --> 00:30:32,550
+quality بدنا ندرس ال diffraction لحال و ال
+
+409
+00:30:32,550 --> 00:30:36,350
+aberration لحال بدنا ندرس ال diffraction لحال و ال
+
+410
+00:30:36,350 --> 00:30:39,970
+aberration لحال و هذا اللي هنتعرف عليه ان شاء الله
+
+411
+00:30:39,970 --> 00:30:45,110
+في ملحق المحاضرة هاي و يعطيكم العافية و السلام
+
+412
+00:30:45,110 --> 00:30:47,230
+عليكم و رحمة الله و بركة
+
diff --git a/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ySXoTncBiWM_postprocess.srt b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ySXoTncBiWM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..acbbf350f79af73e0ecc531f059bb2e12f86ce7e
--- /dev/null
+++ b/PL9fwy3NUQKwYL4S5-iKy7cLnxO4VAOVnL/ySXoTncBiWM_postprocess.srt
@@ -0,0 +1,1408 @@
+1
+00:00:01,640 --> 00:00:05,400
+بسم الله الرحمن الرحيم بنواصل محاضرات ال physical
+
+2
+00:00:05,400 --> 00:00:10,160
+optics واتوقفنا عن موضوع حقيقة مهم للغاية ويستعمل
+
+3
+00:00:10,160 --> 00:00:17,240
+كثير جدا في مجال العيون اللي هو موضوع ال lasers ال
+
+4
+00:00:17,240 --> 00:00:23,760
+laser أو ضوء ال laser كيف فكرته وكيف بيعمل وكيف
+
+5
+00:00:23,760 --> 00:00:26,860
+الاستفادة منه يعني هنبدأ نحكي في المحاضرة هذه
+
+6
+00:00:26,860 --> 00:00:31,360
+والمحاضرة التالية عن هذا الموضوعبنقول an electron
+
+7
+00:00:31,360 --> 00:00:34,560
+may stay in metastable state for minutes or longer
+
+8
+00:00:34,560 --> 00:00:39,180
+يعني بعض الإلكترونات في بعض الظرات لما بتصعد
+
+9
+00:00:39,180 --> 00:00:43,040
+لمدارات طاقة أعلى .. لمدارات طاقة أعلى من اللي هي
+
+10
+00:00:43,040 --> 00:00:47,170
+أصلا موجود فيهابتضلها في حالة بنسميها meta stable
+
+11
+00:00:47,170 --> 00:00:51,750
+state، يعني حالة استقرار نوعًا ما، يعني في مدارتها
+
+12
+00:00:51,750 --> 00:00:55,530
+الجديدة اللي هي أعلى في الطاقة، بتكون مستقرة وليست
+
+13
+00:00:55,530 --> 00:01:00,650
+يعني بمجرد ما تصعد بعد اكتسابها طاقة، بتروح فقد
+
+14
+00:01:00,650 --> 00:01:06,250
+هذه الطاقة بشكل فوري و بتهبط لمدارتها الأساسية،
+
+15
+00:01:06,250 --> 00:01:09,970
+وإنما بتضلها في meta stable state، بمعنى بتضلها في
+
+16
+00:01:09,970 --> 00:01:15,330
+المدارات الجديدة في وضع نوعًا ما مستقرHowever, a
+
+17
+00:01:15,330 --> 00:01:18,690
+photon of appropriate frequency passing near such
+
+18
+00:01:18,690 --> 00:01:21,590
+an electron will stimulate the electron
+
+19
+00:01:21,590 --> 00:01:26,310
+immediately to drop to a lower state and radiate
+
+20
+00:01:26,310 --> 00:01:30,310
+an identical photon ما معنى هذا الكلام؟ هذا الكلام
+
+21
+00:01:30,310 --> 00:01:35,650
+بيتطرنا للرجوع لرسمة سابقة عساس توضيح هذه القضية
+
+22
+00:01:35,650 --> 00:01:41,250
+بنقول electron إجاله فوتون إجاله حصة من الطاقةهذه
+
+23
+00:01:41,250 --> 00:01:44,530
+الحصة من الطاقة خلّت الـ Electron يطلع أو يصعد
+
+24
+00:01:44,530 --> 00:01:50,330
+لمدار أعلى، الآن بعد ما صعد لمدار أعلى من الطاقة،
+
+25
+00:01:50,330 --> 00:01:57,260
+ضال فيها مستقر نوعا ما فترة ماهذه الفترة و هو في
+
+26
+00:01:57,260 --> 00:02:01,280
+المدار الأعلى من الطاقة إجى فوتون إله frequency
+
+27
+00:02:01,280 --> 00:02:05,940
+مناسبة مر جنب هذا الإلكترون، هيخليه يفقد الطاقة
+
+28
+00:02:05,940 --> 00:02:11,860
+اللي اكتسبها و يرجع يعود لمداره الرئيسي، إذا فوتون
+
+29
+00:02:11,860 --> 00:02:15,840
+آخر غير الفوتون اللي اكتسبه الإلكترون عشان يصعد
+
+30
+00:02:16,550 --> 00:02:20,310
+فوتون آخر مر جنب الإلكترون و هو في المداري الأعلى
+
+31
+00:02:20,310 --> 00:02:26,050
+فجعله يفقد كمية الطاقة اللي اكتسبها و يرسل فوتون
+
+32
+00:02:26,050 --> 00:02:31,150
+لي حصة من الطاقة هذه الحصة من الطاقة مماثلة جدا
+
+33
+00:02:31,150 --> 00:02:35,310
+للفوتون المحفز للفوتون المحفز وهذا الكلام ضروري
+
+34
+00:02:35,310 --> 00:02:40,530
+نرجع أيها هذه الرسمة بنقول الرسمة Cالرسمة C او ال
+
+35
+00:02:40,530 --> 00:02:45,410
+part C من الرسمة بنقول ان الاكترون كان في المدار
+
+36
+00:02:45,410 --> 00:02:54,090
+E0 و اتساعد بفعل طاقة معينة ل E1 لمدار اعلى اصبح
+
+37
+00:02:54,090 --> 00:02:58,890
+الان مستقر نوعا ما في المدار الاعلى اجا فوتون
+
+38
+00:02:58,890 --> 00:03:04,800
+طاقته H في Vالو طاقة معينة HPV مر جنب هذا
+
+39
+00:03:04,800 --> 00:03:10,460
+الالكترون هيحفظه انه يطلق حصة من الطاقة يطلق فوتون
+
+40
+00:03:10,460 --> 00:03:15,440
+اخر وينزل للمدار الاصلي الفوتون الاخر اللي اطلق من
+
+41
+00:03:15,440 --> 00:03:22,160
+الالكترون تماما مماثل في ال frequency ل الفوتون
+
+42
+00:03:22,160 --> 00:03:24,880
+المحفظ يعني هذا الفوتون المحفظ اللي هو طاقة
+
+43
+00:03:24,880 --> 00:03:31,980
+مقدارها HPV والالكترون اللي صدرهيكون طقته ايضا H
+
+44
+00:03:31,980 --> 00:03:37,280
+في V فاتنين مع بعض هيكونوا اتنين H في V الغريب او
+
+45
+00:03:37,280 --> 00:03:41,160
+الاشي المميز لهذا الفوتون اللي صدر عن الالكترون
+
+46
+00:03:41,160 --> 00:03:48,070
+انه طقته مماثلة تماما مماثلة تمامالطاقة الفوتون
+
+47
+00:03:48,070 --> 00:03:54,370
+المحفز هدولة two photons totally identical يعني
+
+48
+00:03:54,370 --> 00:03:58,250
+طولهم الموجي واحد بمعنى ال frequency واحد و
+
+49
+00:03:58,250 --> 00:04:02,430
+totally in phase بمعنى القمة مع القمة و القاع مع
+
+50
+00:04:02,430 --> 00:04:06,050
+القاع فبالتالي هدولة يعني
+
+51
+00:04:09,270 --> 00:04:15,290
+الفوتونين متماثلين تماما هذه الفكرة بنية عليها عمل
+
+52
+00:04:15,290 --> 00:04:19,590
+الليزر بنية عليها عمل الليزر زي ما هنحكي بعد قليل
+
+53
+00:04:19,590 --> 00:04:23,830
+وبالتالي بنرجع بنقول لكلام اللي حكيناه قبل شوية
+
+54
+00:04:23,830 --> 00:04:30,830
+إنه إذا كان في هندي فوتون أو إلكترون عفوا موجود في
+
+55
+00:04:30,830 --> 00:04:36,760
+higher energy stateفي higher energy state إذا كان
+
+56
+00:04:36,760 --> 00:04:41,580
+هذا الإلكترون مستقر في higher energy state ومر
+
+57
+00:04:41,580 --> 00:04:45,820
+جنبه فوتون إله appropriate frequency ضروري يكون
+
+58
+00:04:45,820 --> 00:04:52,940
+إله طاقة مناسبة passing near such an electronهيحفظ
+
+59
+00:04:52,940 --> 00:04:58,320
+ال electron انه to drop to a lower state وانه يشعل
+
+60
+00:04:58,320 --> 00:05:02,480
+an identical photon identical photon لمين؟ للفوتون
+
+61
+00:05:02,480 --> 00:05:05,780
+المحفظ يعني الفوتون اللي أطلق ال electron و
+
+62
+00:05:05,780 --> 00:05:12,020
+الفوتون المحفظ متماثلين تماما متماثلين في الطول
+
+63
+00:05:12,020 --> 00:05:16,050
+الموجي وبالتالي متماثلين في ال frequencyو أيضًا
+
+64
+00:05:16,050 --> 00:05:19,930
+totally in phase يعني القمة مع القمة و القاع مع
+
+65
+00:05:19,930 --> 00:05:25,050
+القاع such stimulated emission هذا الإنبعاث المحفظ
+
+66
+00:05:25,050 --> 00:05:29,710
+الإنبعاث لأن الإنبعاث عندي فوتون الإلكترون أرسل أو
+
+67
+00:05:29,710 --> 00:05:34,870
+شع أشع فوتون طبعًا ليش أشع فوتون بعد ما .. ما ..
+
+68
+00:05:34,870 --> 00:05:37,550
+ما الفوتون اللي إيجا يعمله stimulation إذا هذه
+
+69
+00:05:37,550 --> 00:05:42,970
+stimulated emission يعنيالإشعاع المحفظ is the
+
+70
+00:05:42,970 --> 00:05:47,390
+basis of light emission in lasers، هذه الفكرة، هذه
+
+71
+00:05:47,390 --> 00:05:51,430
+الطريقة، بهذه الطريقة ينتج ال laser، بهذه الطريقة
+
+72
+00:05:51,430 --> 00:05:55,450
+ينتج ال laser ولا توجد طريقة أخرى لإنتاج ال laser
+
+73
+00:05:55,450 --> 00:05:59,650
+اللي هي سواء ال stimulated emission، ال stimulated
+
+74
+00:05:59,650 --> 00:06:04,130
+emissionالإلكترون موجود في مدار طاقة أعلى صار له
+
+75
+00:06:04,130 --> 00:06:08,150
+stimulation بواسطة فوتون خارجي، هذا الفوتون
+
+76
+00:06:08,150 --> 00:06:11,630
+الخارجي لما عمل stimulation للإلكترون، الإلكترون
+
+77
+00:06:11,630 --> 00:06:15,870
+هبط لمدار أدنى وأطلق فوتون من عنده، يعني حصة من
+
+78
+00:06:15,870 --> 00:06:20,100
+الطاقةالفوتون اللى تم إشعاعه من الإلكترون والفوتون
+
+79
+00:06:20,100 --> 00:06:24,680
+المحفز ميزتهم إن هم مماثلين لبعض من البعض تماما
+
+80
+00:06:24,680 --> 00:06:29,920
+اول حاجة لهم نفس الطول الموجي نفس ال frequency
+
+81
+00:06:29,920 --> 00:06:34,660
+التردد و totally in phase يعني لهم نفس الحالة إنه
+
+82
+00:06:34,660 --> 00:06:40,140
+القمة على القمة و القاع على القى و القاع على القى
+
+83
+00:06:41,350 --> 00:06:45,910
+إذا بيجي سؤال سواء في الامتحان أو بنسأل من أي يعني
+
+84
+00:06:45,910 --> 00:06:51,110
+شخص أو في مقابلة إنه إيش الطريقة اللي بينتج فيها
+
+85
+00:06:51,110 --> 00:06:55,530
+الليزر بطريقة ال stimulated emission stimulated
+
+86
+00:06:55,530 --> 00:07:00,370
+emission يعني الإشعاع المحفز الإشعاع المحفز أو
+
+87
+00:07:00,370 --> 00:07:07,320
+الانبعاث المحفزو من هنا أخد ال laser اسمه كلمة
+
+88
+00:07:07,320 --> 00:07:10,920
+laser هي اختصار هي light amplification
+
+89
+00:07:13,820 --> 00:07:18,540
+by stimulated emission of radiation يعني تقوية
+
+90
+00:07:18,540 --> 00:07:23,680
+الضوء وتضخيم الضوء وزيادة قوة الضوء بطريقة ال
+
+91
+00:07:23,680 --> 00:07:27,820
+stimulated emission of radiation بطريقة انبعاث
+
+92
+00:07:27,820 --> 00:07:33,220
+الطاقة المحفظ انبعاث الطاقة المحفظ المحفظ بالطريقة
+
+93
+00:07:33,220 --> 00:07:39,270
+اللي حكينا عنها اذا الكلمة laserاختصار ل light
+
+94
+00:07:39,270 --> 00:07:43,270
+amplification خدنا حرف ال L وحرف ال A by
+
+95
+00:07:43,270 --> 00:07:48,630
+stimulated خدنا حرف ال S صار عندي لاز emission E
+
+96
+00:07:48,630 --> 00:07:53,170
+of radiation R أصبح عندي laser إذا تقوية الضوء
+
+97
+00:07:53,170 --> 00:07:58,940
+بواسطةالانبعاث المحفز للطاقة الانبعاث المحفز
+
+98
+00:07:58,940 --> 00:08:03,580
+للطاقة lasers use an active medium ضروري يكون في
+
+99
+00:08:03,580 --> 00:08:06,920
+عندي مادة معينة أنتج منها ال laser هذه المادة
+
+100
+00:08:06,920 --> 00:08:10,440
+المعينة بيسموها ال active medium هي اللي هتحفز
+
+101
+00:08:10,440 --> 00:08:16,400
+ذراتها اللي هتحفز ذراتها عشان تطلع لمدارات أعلى من
+
+102
+00:08:16,400 --> 00:08:19,480
+الطاقة هذه عندي ال active medium باللون الأصفر
+
+103
+00:08:19,480 --> 00:08:25,650
+داخل الأنبوب هذه الذرات مرسومة باللون الأزرقطبعا
+
+104
+00:08:25,650 --> 00:08:31,070
+ملايين ومليارات الذرات في هذه المنطقة بتكون، بس
+
+105
+00:08:31,070 --> 00:08:35,510
+احنا يعني او الرسمة فيها القليل من الذرات لتوضيح
+
+106
+00:08:35,510 --> 00:08:41,050
+الفكرة، هذه الذرات بتم تحفيز إلكتروناتها عشان تصعد
+
+107
+00:08:41,050 --> 00:08:46,550
+لمدارات أعلى من الطاقةتمام؟ بعد ما تصعد لمدارات
+
+108
+00:08:46,550 --> 00:08:51,890
+أعلى من الطاقة أول شيء هيحصل عندى أنه واحدة من
+
+109
+00:08:51,890 --> 00:08:56,930
+الذرات electron هينزل لوحده بدون ما حد يعني يحفظه
+
+110
+00:08:56,930 --> 00:09:01,750
+أنه ينزل و هيطلق فوتون تمام؟ spontaneous emission
+
+111
+00:09:01,750 --> 00:09:05,530
+.. spontaneous emission ماننساش أنه عندى في تلت
+
+112
+00:09:05,530 --> 00:09:09,510
+ظواهر بتصير مع قضية ال laser نرجع للرسمة الأولى
+
+113
+00:09:11,460 --> 00:09:22,660
+واللي هتفيد في توضيح الفكرة الرسم
+
+114
+00:09:22,660 --> 00:09:29,440
+الأولى أو الرسم رقم اتنين lobbyفي حاجة بسموها
+
+115
+00:09:29,440 --> 00:09:34,160
+spontaneous emission إلكترون صعد اكتسب طاقة وصعد
+
+116
+00:09:34,160 --> 00:09:38,840
+لمدار أعلى بعدين فقدها لوحده فقد حصة من الطاقة
+
+117
+00:09:38,840 --> 00:09:45,520
+بشكل فوتون تردده HPV أو الطاقة بتاعته HPV هذا
+
+118
+00:09:45,520 --> 00:09:48,940
+بسموه spontaneous emission هذا مش هينتج ال laser
+
+119
+00:09:48,940 --> 00:09:52,820
+بس هذا هيبدأ العملية زي ما هنشرح بعد قليل اللي
+
+120
+00:09:52,820 --> 00:09:56,860
+هينتج ال laserاللي هنحكيه بعد شوية اللي هي ال
+
+121
+00:09:56,860 --> 00:10:06,000
+stimulated emission ال stimulated emission بنقول
+
+122
+00:10:06,000 --> 00:10:10,200
+كالقادة أول
+
+123
+00:10:10,200 --> 00:10:15,840
+شيء هيتيم عندي يعني ضخ طاقة نوع من الطاقة طاقة
+
+124
+00:10:15,840 --> 00:10:20,560
+ضوئية طاقة كهربائية طاقة حرارية بحيث ان معظم
+
+125
+00:10:20,560 --> 00:10:24,900
+الذرات بتاعة المادةالنشطة اللي هي ال active medium
+
+126
+00:10:24,900 --> 00:10:29,580
+معظم الذرات إلكترونات هتصعد لمدارات أعلى من الطاقة
+
+127
+00:10:29,580 --> 00:10:34,760
+طيب بمجرد ما تصعد لمدارات أعلى من الطاقة هيبدأ
+
+128
+00:10:34,760 --> 00:10:39,460
+العملية ذرة واحدة إنه إلكترون هبط لوحده عمل
+
+129
+00:10:39,460 --> 00:10:44,800
+spontaneous emissionانبعاث تلقائي لحصة من الطاقة
+
+130
+00:10:44,800 --> 00:10:48,260
+عشان الالكترون يرجع للمدار اللي اجا منه هذا
+
+131
+00:10:48,260 --> 00:10:52,940
+الفوتون اللي اطلق من الذره الاوله هيصطدم بالكترون
+
+132
+00:10:52,940 --> 00:10:59,180
+في ذره تانيه موجود في مدار اعلى فهيجبره او هيحفظه
+
+133
+00:10:59,180 --> 00:11:04,690
+هيعمله stimulation انه يطلق فوتونلأ عشان ينزل و
+
+134
+00:11:04,690 --> 00:11:07,530
+هدول الفوتونين الفوتون المحفز اللي إيجا من الذر
+
+135
+00:11:07,530 --> 00:11:11,510
+الأولى و الفوتون المحفز اللي أطلق من الالكترون رقم
+
+136
+00:11:11,510 --> 00:11:17,740
+اتنين أصبح عندي فوتونين هدول الفوتونينالهم نفس
+
+137
+00:11:17,740 --> 00:11:22,020
+التردد و totally in phase هدول الفوتينين هيحفظوا
+
+138
+00:11:22,020 --> 00:11:26,280
+.. هيحفظوا ذرتين من ال active medium هيصير عندى
+
+139
+00:11:26,280 --> 00:11:29,180
+أربع فوتونات و الأربعة هيصيروا تمانية و التمانية
+
+140
+00:11:29,180 --> 00:11:32,560
+هيصيروا ستة عشر و الستة عشر هيصيروا اتنين و تلاتين
+
+141
+00:11:32,560 --> 00:11:37,980
+و هكذا و كل الفوتونات الناتجةالها نفس ال frequency
+
+142
+00:11:37,980 --> 00:11:42,680
+الها نفس التردد و totally in phase الان العلماء
+
+143
+00:11:42,680 --> 00:11:47,480
+حطوا reflecting mirrors يعني مرايا عاكسة على نهاية
+
+144
+00:11:47,480 --> 00:11:51,400
+الأنبوب هذا الانبوب بيسموه ال optical cavity او ال
+
+145
+00:11:51,400 --> 00:11:55,260
+laser cavity التجويف او ال .. ال .. ال .. ال انبوب
+
+146
+00:11:55,260 --> 00:12:00,340
+تاع ال laser تاع إنتاج ال laser حطوا مرايا عاكسة
+
+147
+00:12:00,340 --> 00:12:05,100
+عشان الفوتوناتالفوتونات اللي هي الضوء أو الطاقة
+
+148
+00:12:05,100 --> 00:12:09,820
+لما توصل للمراية تنعكس وترجع تمر على الذرات مرة
+
+149
+00:12:09,820 --> 00:12:14,140
+تانية عشان تطلق منها فوتونات أخرى عشان تطلق منها
+
+150
+00:12:14,140 --> 00:12:20,390
+فوتونات أخرى ممكن يقول طيب احنا لماالفوتونات عدت
+
+151
+00:12:20,390 --> 00:12:24,330
+على الذرات خلت الإلكترونات تهبط للمدارات الأساسية
+
+152
+00:12:24,330 --> 00:12:27,770
+يعني ماضلش عند الإلكترونات طاقة زيادة تتنبعث بنقول
+
+153
+00:12:27,770 --> 00:12:32,090
+مظبوط هذا الكلام صحيح ولكن بمجرد ما توصل و ترجع
+
+154
+00:12:32,090 --> 00:12:36,110
+بيكون ال pumping source أو الطاقة اللي بنمد فيها
+
+155
+00:12:36,110 --> 00:12:39,510
+الذرات سواء طاقة كهربائية أو حرارية أو ضوئية
+
+156
+00:12:39,510 --> 00:12:45,770
+خارجية بيكون رفعت الإلكترونات مرة أخرى لمدارات
+
+157
+00:12:45,770 --> 00:12:51,980
+أعلى والعملية بتتكررو بتصير عدد الفوتونات تزيد و
+
+158
+00:12:51,980 --> 00:12:55,960
+الفوتونات بتنقس بين المرأتين بين ال two mirrors
+
+159
+00:12:55,960 --> 00:13:01,920
+لغاية ما يصل القضية للحظة معينة و واحدة من ال
+
+160
+00:13:01,920 --> 00:13:07,320
+mirrors يتم يعني فتحها جزئيا طبعا بوسطة الضغط على
+
+161
+00:13:07,320 --> 00:13:12,020
+زر الليزر و بالتالي حزمة الليزر تنبعث و هذا الكلام
+
+162
+00:13:12,020 --> 00:13:16,420
+يعني هنشوفهفي .. ب .. ب simulation مناسب ان شاء
+
+163
+00:13:16,420 --> 00:13:21,760
+الله تعالى بنقول lasers use an active medium يعني
+
+164
+00:13:21,760 --> 00:13:25,720
+ال laser بنستعمل في إنتاجه مادة بيسموها المادة
+
+165
+00:13:25,720 --> 00:13:28,140
+النشطة أو ال active medium اللي منها هننتج ال
+
+166
+00:13:28,140 --> 00:13:33,220
+laser with an appropriate metastable state يعني في
+
+167
+00:13:33,220 --> 00:13:37,910
+الهاMeta-stable state مناسبة يعني مدار معين له
+
+168
+00:13:37,910 --> 00:13:42,490
+طاقة معينة والمدار اللي تحته بيفرج عنه ثرج معين في
+
+169
+00:13:42,490 --> 00:13:46,630
+الطاقة هو المطلوب للحصول على فوتونات يعني بطاقة
+
+170
+00:13:46,630 --> 00:13:51,090
+معينة أو laser بطاقة معينة أو بلون معين Energy is
+
+171
+00:13:51,090 --> 00:13:55,050
+introduced into the active medium in a variety of
+
+172
+00:13:55,050 --> 00:13:58,010
+ways يعني أنا بقدر أحفظ الذرار تاعت ال active
+
+173
+00:13:58,010 --> 00:14:03,020
+mediumبطرق متعددة زي ما قلنا بواسطة إما الطاقة
+
+174
+00:14:03,020 --> 00:14:06,240
+الكهربائية أو الحرارية أو الضوء يعني في وسائل
+
+175
+00:14:06,240 --> 00:14:12,160
+عديدة للتهفيز في وسائل عديدة للتهفيز هاي عندنا
+
+176
+00:14:12,160 --> 00:14:17,170
+صورة لجهاز ال laserالـ Optical Cavity أو الـ Laser
+
+177
+00:14:17,170 --> 00:14:20,850
+Cavity اللي هيتم في داخله إنتاج الـ Laser الـ
+
+178
+00:14:20,850 --> 00:14:23,950
+Active Medium هي الـ Atoms بتاعتها الذرات بتاعتها
+
+179
+00:14:23,950 --> 00:14:27,530
+الـ Pumping Source المرسوم باللون الأحمر اللي هو
+
+180
+00:14:27,530 --> 00:14:31,550
+عبارة عن مصدر لتحفيز الذرات عشان تطلع إلكتروناتها
+
+181
+00:14:31,550 --> 00:14:35,270
+تكتسب طاقة و تطلع لمدارات أعلى عشان بعد هيك يتم
+
+182
+00:14:35,270 --> 00:14:39,370
+إسقاطها لمداراتها الأساسية و أخذ الفوتونات منها
+
+183
+00:14:39,370 --> 00:14:40,950
+بطريق التحفيز
+
+184
+00:14:43,120 --> 00:14:46,620
+على سبيل المثال، الـ Optical Pumping يستخدم مصادر
+
+185
+00:14:46,620 --> 00:14:50,200
+الإضاءات الإضاءات المظهرية لإشعال عدد كبير من
+
+186
+00:14:50,200 --> 00:14:54,200
+الإلكترونات إلى مصادر الـ Stable State طبعاً في
+
+187
+00:14:54,200 --> 00:14:56,620
+حاجة بيسموها الـ Optical Pumping هنا عند الـ
+
+188
+00:14:56,620 --> 00:14:59,640
+Pumping Source في Electrical Pumping في Optical
+
+189
+00:14:59,640 --> 00:15:03,190
+Pumpingفي حالة ما أنا بستعمل optical pumping يعني
+
+190
+00:15:03,190 --> 00:15:07,330
+أنا بستعمل طاقة ضوئية incoherent light light عادي
+
+191
+00:15:07,330 --> 00:15:12,690
+عادي مش coherent زي .. زي ال .. الضوء المعتاد بس
+
+192
+00:15:12,690 --> 00:15:17,650
+بقوة عالية بستعمل bright incoherent light يعني
+
+193
+00:15:17,650 --> 00:15:23,030
+براق جدا او مشع جدا ضوء عاديSource to excite large
+
+194
+00:15:23,030 --> 00:15:28,430
+number of electrons يعني بد أحفظ عدد ضخم جدا من
+
+195
+00:15:28,430 --> 00:15:32,830
+الإلكترونات في ذرات ال active medium عشان تصعد ل
+
+196
+00:15:32,830 --> 00:15:37,060
+ال meta stable state لل higher energy levelthe
+
+197
+00:15:37,060 --> 00:15:40,100
+activity .. the active medium is inside a
+
+198
+00:15:40,100 --> 00:15:43,780
+resonator cavity طبعا ال active medium .. ال
+
+199
+00:15:43,780 --> 00:15:48,220
+active medium في داخل optical cavity أو ممكن أسميه
+
+200
+00:15:48,220 --> 00:15:52,520
+laser cavity أو ممكن أسميه resonator cavity ليش؟
+
+201
+00:15:52,520 --> 00:15:56,100
+ال resonance معناه هرنين أو التردد ليش resonator
+
+202
+00:15:56,100 --> 00:15:59,660
+cavity؟ لأنه في مرايا في نهاية هذا ال cavity
+
+203
+00:15:59,660 --> 00:16:03,960
+الإلكترونات أو الفوتونات عفوا اللي أطلقت بواسطة ال
+
+204
+00:16:03,960 --> 00:16:09,340
+stimulated emissionبتتردد بين ال two mirrors جيئة
+
+205
+00:16:09,340 --> 00:16:13,180
+و ذهابا مرة و مرة و مرة و مرة و اها كذا ليش هذه
+
+206
+00:16:13,180 --> 00:16:16,600
+القضية مراد انه يصير resonance يعني تردد و ان ال
+
+207
+00:16:16,600 --> 00:16:20,280
+.. الفوتونات ما بتوصل لمرأة الأولى تعكسها باتجاه
+
+208
+00:16:20,280 --> 00:16:24,320
+المرئات التانية عشان يتكرر عدد مرور الفوتونات على
+
+209
+00:16:24,320 --> 00:16:28,680
+الذرات و تحفيز فوتونات أخرى تطلقها الإلكترونات و
+
+210
+00:16:28,680 --> 00:16:32,970
+تهبطلهاLower energy state و بعدين بواسطة ال
+
+211
+00:16:32,970 --> 00:16:37,370
+pumping source يتم تحفيزها مرة تانية و هكذا و هكذا
+
+212
+00:16:37,370 --> 00:16:41,290
+فبالتالي عشان العملية تتكرر و يتم تقوية للضوء انا
+
+213
+00:16:41,290 --> 00:16:45,650
+وصل عندى ست عشر فوتون هنا رجعوا اخدوا معاهم كمان
+
+214
+00:16:45,650 --> 00:16:49,860
+ست عشر صار و اصل عندى اتنين و تلاتين فوتون32 فوتون
+
+215
+00:16:49,860 --> 00:16:53,120
+عدوا مرة تانية عدد الذرات اللي بتكون حفزت بواسطة
+
+216
+00:16:53,120 --> 00:16:58,440
+ال pumping source 32 فوتون أصبحوا 64 ال 64 أصبحوا
+
+217
+00:16:58,440 --> 00:17:04,180
+128 و هكذا يعني بتتم تقوية و amplification للضوء
+
+218
+00:17:04,180 --> 00:17:08,260
+بواسطة ال stimulated emission وهذا معناه كلمة
+
+219
+00:17:08,260 --> 00:17:12,160
+laser light amplification by stimulated emission
+
+220
+00:17:12,160 --> 00:17:16,020
+of radiationالوسيلة المشتركة في داخل محطة
+
+221
+00:17:16,020 --> 00:17:20,080
+الاريزوناتور التي عادةً تحتوي على مراعاة مفهوم
+
+222
+00:17:20,080 --> 00:17:25,500
+مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم
+
+223
+00:17:25,500 --> 00:17:25,640
+مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم
+
+224
+00:17:25,640 --> 00:17:26,020
+مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم
+
+225
+00:17:26,020 --> 00:17:26,180
+مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم
+
+226
+00:17:26,180 --> 00:17:26,420
+مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم مفهوم
+
+227
+00:17:26,420 --> 00:17:30,190
+مفهوم مفهوم مفهوم مفهوم مفهوم مفواحدة بتكون ..
+
+228
+00:17:30,190 --> 00:17:34,370
+واحدة بتكون totally reflecting بتعكس بنسبة مائة
+
+229
+00:17:34,370 --> 00:17:37,570
+بالمائة كل ما بيصلها من الفوتونات والتانية
+
+230
+00:17:37,570 --> 00:17:41,550
+partially reflecting بتعكس جزء كبير من الفوتونات
+
+231
+00:17:41,550 --> 00:17:46,430
+وبتنفذ جزء آخر عشان يسمح لل laser beam لحزمة ال
+
+232
+00:17:46,430 --> 00:17:50,030
+laser إنها تخرج وإلا لو كانوا ال two mirrors كلهم
+
+233
+00:17:50,030 --> 00:17:55,790
+totally reflecting سيبقى ال laser داخل اللي هو ال
+
+234
+00:17:55,790 --> 00:18:00,080
+cavity ومش هيتمكن من إنهيخرج للخارج ومش هنتمكن من
+
+235
+00:18:00,080 --> 00:18:05,540
+أننا نستفيد منه، اذا this design causes light to
+
+236
+00:18:05,540 --> 00:18:08,680
+make numerous passes through the active medium
+
+237
+00:18:08,680 --> 00:18:12,660
+producing more photons by stimulated emission with
+
+238
+00:18:12,660 --> 00:18:18,220
+each pass، هذا التركيبة أو هذا التصميم بيسمح بأنه
+
+239
+00:18:18,220 --> 00:18:25,050
+الضوء يتقوىبوسط انعكاسه بين المرقاتين و هيعمل كذا
+
+240
+00:18:25,050 --> 00:18:31,510
+pass يعني كذا مرة و كذا دورة من الروحة و العودة و
+
+241
+00:18:31,510 --> 00:18:36,590
+ال photo net بيتضاعف عددها اربعة تمانية ستاشر
+
+242
+00:18:36,590 --> 00:18:39,530
+اتنين و تلاتين اربع و ستين مية و تمانية عشرين و
+
+243
+00:18:39,530 --> 00:18:43,950
+هكذا و بالتالي لما بيخرج ال laser من ال partial
+
+244
+00:18:43,950 --> 00:18:49,190
+reflecting mirror بيكون في اندي حزمة قوية منالضوء
+
+245
+00:18:49,190 --> 00:18:54,150
+او من ضوء الليزر من ضوء الليزر ب .. فبالتلكيب هاي
+
+246
+00:18:54,150 --> 00:18:58,870
+طبعا بيسمح بالانعكاس داخل ال cavity بواسطة ال two
+
+247
+00:18:58,870 --> 00:19:01,730
+mirrors و في نفس الوجد بيسمح لإن في واحدة منهم
+
+248
+00:19:01,730 --> 00:19:06,930
+partial reflecting بيسمح بمرور الضوء عبر ال
+
+249
+00:19:06,930 --> 00:19:10,570
+partial reflecting mirror اللي هو ضوء الليزر طبعا
+
+250
+00:19:10,570 --> 00:19:15,320
+انهي ال laser cavity .. هي ال laser cavity ال
+
+251
+00:19:15,320 --> 00:19:19,820
+laser medium هنا في .. في هذه ال .. ال .. ال laser
+
+252
+00:19:19,820 --> 00:19:23,540
+medium او ال .. ال active medium مستخدمين ال Ruby
+
+253
+00:19:23,540 --> 00:19:26,640
+ال Ruby اللي هو الياقوت .. اللي هو الياقوت هنا
+
+254
+00:19:26,640 --> 00:19:30,740
+fully reflecting mirrorوهنا partial reflecting
+
+255
+00:19:30,740 --> 00:19:34,480
+mirror الذرات بتاعة الياقوت بتم تحفيزها بالإفلاق
+
+256
+00:19:34,480 --> 00:19:38,820
+في .. في .. بواسطة يعني pumping source pumping
+
+257
+00:19:38,820 --> 00:19:42,860
+source سواء optical pumping أو electrical pumping
+
+258
+00:19:42,860 --> 00:19:47,970
+أو heat pumping إلى آخرينو بتتم الفوتونات بتنعكس
+
+259
+00:19:47,970 --> 00:19:51,630
+between the two mirrors جيئة و ذهبا بتحفز
+
+260
+00:19:51,630 --> 00:19:55,450
+الإلكترونات تانية أنها تطلق تعمل stimulation هنا
+
+261
+00:19:55,450 --> 00:19:59,810
+للإلكترونات عشان تعمل radiation وبالتالي بتكون
+
+262
+00:19:59,810 --> 00:20:03,290
+عندى ضوء الليزر وفي النهاية ضوء الليزر بيسمح له
+
+263
+00:20:03,290 --> 00:20:07,470
+بالمرور كحزمة من ال partial reflecting mirror من
+
+264
+00:20:07,470 --> 00:20:12,710
+ال partial reflecting mirror ايضا هنا رسمة تمثلية
+
+265
+00:20:14,800 --> 00:20:18,600
+لجهاز ال laser جهاز ال laser اللي هو ال active
+
+266
+00:20:18,600 --> 00:20:22,090
+medium بتكون داخلهداخل ال laser cavity أو ال
+
+267
+00:20:22,090 --> 00:20:25,690
+resonator cavity ال pumping source سواء electrical
+
+268
+00:20:25,690 --> 00:20:29,150
+pumping أو optical pumping بواسطة ضوء قوي
+
+269
+00:20:29,150 --> 00:20:34,710
+incoherent light أو heat pumping إلى آخرهم و في
+
+270
+00:20:34,710 --> 00:20:39,270
+عندي في أطراف ال laser cavity في عندي two mirrors
+
+271
+00:20:39,270 --> 00:20:43,170
+hundred percent reflecting mirror بتعكس مية في
+
+272
+00:20:43,170 --> 00:20:46,330
+المية كل ما يصلى من الفوتونات عشان مرة تانية تنعكس
+
+273
+00:20:46,330 --> 00:20:50,040
+الفوتوناتوتمر على الذرات هي تاخد منها فوتونات
+
+274
+00:20:50,040 --> 00:20:54,460
+تانية و هنا partially reflecting mirror أيضا بتعكس
+
+275
+00:20:54,460 --> 00:20:59,200
+جزء كبير طبعا هنا أقل من 100% طبعا مش شرط تكون 50%
+
+276
+00:20:59,200 --> 00:21:04,420
+يعني ممكن تكون بتعكس 80% و بتمرر 20% وهذا يكفي
+
+277
+00:21:04,420 --> 00:21:10,520
+ليه؟انه بتعكس كام من الفوتونات يعني اللي يبقى
+
+278
+00:21:10,520 --> 00:21:14,580
+الفوتونات داخل ال laser cavity بكمية كبيرة عشان
+
+279
+00:21:14,580 --> 00:21:18,500
+تحفظ إلكترونات تانية انها تطلق فوتونات والعملية
+
+280
+00:21:18,500 --> 00:21:25,080
+تستمر والعملية تستمر طيب الآن بدنا نحاول نشوف هذه
+
+281
+00:21:25,080 --> 00:21:30,020
+الفكرة بشكل ال simulation عشان توضح معانا الرؤية
+
+282
+00:21:30,020 --> 00:21:35,500
+احنا بنقول لو عندنا كالقاتلإننا نفرض ذرّة واحدة
+
+283
+00:21:35,500 --> 00:21:45,820
+هذه الذرّة موجودة في مدارها الأساسي بدها يمر عليها
+
+284
+00:21:45,820 --> 00:21:50,700
+طاقة ضوئية هذه الطاقة المحفزة هذا cavity و تخيل
+
+285
+00:21:50,700 --> 00:21:55,060
+إنها ذرّة واحدة ل active mediumإذا كان اصطدم فيها
+
+286
+00:21:55,060 --> 00:21:58,360
+فوتون بيصعد بمجرد ما نشوف الدائرة الحمرا معناته
+
+287
+00:21:58,360 --> 00:22:03,120
+الإلكترون صعد لمدار أعلى اللي هو هنا يعني يمثل هذا
+
+288
+00:22:03,120 --> 00:22:08,460
+المدار بعدين إذا ملاحظين صعد الآن إيجا فوتون تاني
+
+289
+00:22:08,460 --> 00:22:14,460
+أصبح فوتونين أطلقوا صعد أطلق فوتونين بنفس التردد
+
+290
+00:22:14,460 --> 00:22:18,420
+الفوتون المحفز أيوة و الفوتون اللي أطلقوا
+
+291
+00:22:18,420 --> 00:22:21,660
+الإلكترون لما أطلقوا بيرجع هذا هذه باسمها
+
+292
+00:22:21,660 --> 00:22:25,800
+stimulated emissionهذا بيسموه absorption، الآن
+
+293
+00:22:25,800 --> 00:22:27,700
+stimulated emission، two photons
+
+294
+00:22:40,170 --> 00:22:44,090
+Spontaneous absorption Emission Spontaneous
+
+295
+00:22:44,090 --> 00:22:49,310
+absorption لاحظين فوتونين المحفز والمحفز لما بيحفز
+
+296
+00:22:49,310 --> 00:22:53,050
+بتطفى الدائرة الحمراء يعني الإلكترون هبط الإلكترون
+
+297
+00:22:53,050 --> 00:22:57,950
+هبط فقد فقد فوتون بنفس الطاقة ونفس التردد بنفس
+
+298
+00:22:57,950 --> 00:23:01,530
+الطاقة ونفس التردد هذا في حالة ذرع واحدة طب لو
+
+299
+00:23:01,530 --> 00:23:04,970
+احنا عندنا هذا ال cavity مليان ب active medium
+
+300
+00:23:04,970 --> 00:23:09,190
+مليان ب active medium خلينا احنا هنرجع من البداية
+
+301
+00:23:10,160 --> 00:23:21,000
+ونشوف إحنا إيش هيصير معنا في ال laser cavity هاي
+
+302
+00:23:21,000 --> 00:23:27,860
+عندنا إحنا الوضع هي الأساسية مافيش عندي طاقة محفزة
+
+303
+00:23:27,860 --> 00:23:34,580
+هاي الذرات بتاعة ال active mediumهذه الذرات تاعت
+
+304
+00:23:34,580 --> 00:23:37,420
+ال active medium مافيش عندي طاقة ال intensity تاعت
+
+305
+00:23:37,420 --> 00:23:43,260
+الطاقة المحفزة ال pumping source صفر صفر الان بدي
+
+306
+00:23:43,260 --> 00:23:47,080
+اعطي طاقة لهذه الذرات عشان تصعد لمدارات اعلى
+
+307
+00:23:47,080 --> 00:23:53,240
+metastable state وبالتالي يتم عندي إنتاج ال laser
+
+308
+00:23:53,240 --> 00:24:00,700
+يتم عندي إنتاج ال laser وفق طبعاشروط معينة وقاليات
+
+309
+00:24:00,700 --> 00:24:05,000
+معينة اول حاجة اذا انا بضل بدون mirrors بدون
+
+310
+00:24:05,000 --> 00:24:08,320
+mirrors معناته انا عندي فيه مشكلة لانه كل
+
+311
+00:24:08,320 --> 00:24:11,180
+الفوتونات هتفقد زي ما انتوا شايفين هي enable
+
+312
+00:24:11,180 --> 00:24:15,580
+mirrors الان
+
+313
+00:24:15,580 --> 00:24:24,560
+هيتم الانعكاس بتاعة الطاقة بشكل هتبدأ
+
+314
+00:24:24,560 --> 00:24:29,370
+بقى بين ال mirrorsتتكون هذه القضية .. تتكون هذه
+
+315
+00:24:29,370 --> 00:24:39,550
+القضية زي
+
+316
+00:24:39,550 --> 00:24:51,810
+ما احنا شايفين لازال
+
+317
+00:24:51,810 --> 00:24:54,910
+احنا في مرحلة تكوين ال laser
+
+318
+00:25:00,250 --> 00:25:04,830
+هي بدت .. بدت الطاقة الداخلية ال internal power
+
+319
+00:25:04,830 --> 00:25:10,390
+تصير كافية احنا هنا لحتى الآن لازم يكون عندي عشان
+
+320
+00:25:10,390 --> 00:25:13,430
+اسرع في الموضوع اول اشي hundred percent reflecting
+
+321
+00:25:13,430 --> 00:25:17,010
+mirror ال ten ten hundred percent اللي احنا جينا
+
+322
+00:25:17,010 --> 00:25:20,470
+في دائرة انه ممكن اعطي laser لان ممكن اعطي laser
+
+323
+00:25:20,470 --> 00:25:24,010
+لان الان بده اخلي واحدة من ال mirror ال
+
+324
+00:25:24,010 --> 00:25:27,030
+reflectivity بتاعتها اقل هى بده ضوء ال laser يطلع
+
+325
+00:25:27,030 --> 00:25:32,900
+عنديبدأ ضوء الليزر يطلع عندى بالشكل طبعا هذه 100%
+
+326
+00:25:32,900 --> 00:25:37,620
+reflectivity تاعت ال mirror وهذه 71% زي ما بتقشر
+
+327
+00:25:37,620 --> 00:25:43,540
+طبعا ممكن اقلل اقلل هذه ضوء الليزر عندى لازال ال
+
+328
+00:25:43,540 --> 00:25:47,220
+photonات بتتردد بين ال two mirrors بعضها بمركض ضوء
+
+329
+00:25:47,220 --> 00:25:52,400
+ليزر للخارج اللي احنا بنشوفه وبعضها بظل يعني داخل
+
+330
+00:25:52,400 --> 00:25:54,780
+الادامة ممكن انا هذه ال photonات اشوفها بطريقة
+
+331
+00:25:54,780 --> 00:26:00,400
+wavesبطريقة ال waves اللي هو ضوء الليزر اللي انا
+
+332
+00:26:00,400 --> 00:26:04,340
+يعني انتجته بواسطة ال laser cavity هذا ال laser
+
+333
+00:26:04,340 --> 00:26:09,440
+cavity هذه الذرات اللي تحفز لما درات اعلى ثم
+
+334
+00:26:09,440 --> 00:26:14,980
+بواسطة ال stimulation بفوتونات مرت جنبها بتطلق
+
+335
+00:26:14,980 --> 00:26:19,860
+يعني فوتونات identical photons بيسموها ذرات ال
+
+336
+00:26:19,860 --> 00:26:24,000
+active medium زي ما احنا شايفين في هذه القضية الان
+
+337
+00:26:24,000 --> 00:26:29,530
+لو حبيت انا اشوفالمنظر الحقيقي للليزر هاي المنظر
+
+338
+00:26:29,530 --> 00:26:34,530
+الحقيقي للليزر هي ال laser cavityهي ال laser
+
+339
+00:26:34,530 --> 00:26:38,430
+cavity اللي هو الأنبوبة الزجاجية هاي هنا total
+
+340
+00:26:38,430 --> 00:26:41,790
+reflecting mirror وهنا partially reflecting mirror
+
+341
+00:26:41,790 --> 00:26:45,450
+اللي خرج منها ال laser سايفين partially reflecting
+
+342
+00:26:45,450 --> 00:26:50,930
+يعني تمانية وتسعين في المية بتعكس و بتمرر اتنين في
+
+343
+00:26:50,930 --> 00:26:55,450
+المية عشان يتظل ال photo net تتردد between the two
+
+344
+00:26:55,450 --> 00:27:01,360
+mirrors وبالتالي يظل عندى اناإنتاج الليزر مستمر ..
+
+345
+00:27:01,360 --> 00:27:04,580
+إنتاج الليزر مستمر واضح أنه عندي الفوتونات هنا
+
+346
+00:27:04,580 --> 00:27:08,880
+بتتردد between the two mirrors وعندي هنا
+
+347
+00:27:08,880 --> 00:27:16,380
+reflectivity 82% يعني بمر 18% ممكن أخليها هنا مثلا
+
+348
+00:27:16,380 --> 00:27:21,930
+90%وهي ال laser أيضا بيصعد وبالتالي لازالت العملية
+
+349
+00:27:21,930 --> 00:27:27,510
+مستمرة لازالت العملية مستمرة وهنا احنا بنتوقف عند
+
+350
+00:27:27,510 --> 00:27:31,390
+هذه النقطة بنرجع بس لل power point هنحكي المرة
+
+351
+00:27:31,390 --> 00:27:34,430
+القادمة ان شاء الله عن خصائص ال laser ويعطيكم
+
+352
+00:27:34,430 --> 00:27:37,890
+العافية والسلام عليكم ورحمة الله وبركاته
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5abe77d536d2539e0f07a0b8a33952d83e4fa579
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/0Tykoh4qs08.srt
@@ -0,0 +1,1654 @@
+1
+00:00:00,000 --> 00:00:01,300
+موسيقى
+
+2
+00:00:19,070 --> 00:00:23,390
+بسم الله الرحمن الرحيم نعود إلى محاضرة الفترة 
+
+3
+00:00:23,390 --> 00:00:27,430
+الصباحية طبعا ما بدأنا بالinverse Laplace 
+
+4
+00:00:27,430 --> 00:00:31,430
+transform عطينا تعريف لـ inverse Laplace transform
+
+5
+00:00:31,430 --> 00:00:36,850
+وعطينا على ذلك مثالا واحدا وهذا هو المثال رقم 2
+
+6
+00:00:37,480 --> 00:00:40,220
+يبقى المثال اللي بقول find the function that has
+
+7
+00:00:40,220 --> 00:00:44,600
+Laplace transform F of S يساوي S على S زائد واحد
+
+8
+00:00:44,600 --> 00:00:48,820
+لكل تربيع زائد أربعة بالشكل اللي قدامنا هنا
+
+9
+00:01:07,560 --> 00:01:11,840
+اللي هو بيعطيه هنا هذا أو اللي بيجينا في قائمة فيه
+
+10
+00:01:11,840 --> 00:01:17,800
+مع أسئلة الامتحان تمام طب بقول لك كويس هذا لو في
+
+11
+00:01:17,800 --> 00:01:23,340
+عندي S زائد واحد في الـ bus ليش؟ لأن عندي هنا S
+
+12
+00:01:23,340 --> 00:01:28,060
+زائد واحد كان قضيتي محلولة ومنتهية تماما إذا أنا
+
+13
+00:01:28,060 --> 00:01:33,340
+بروح أخلك في الـ bus S زائد واحد والله ناقص واحد 
+
+14
+00:01:33,340 --> 00:01:39,660
+خليني أتأكد هذه S وين راحت؟ S زائد واحد يبقى بدي S
+
+15
+00:01:39,660 --> 00:01:44,240
+زائد واحد يبقى بناء عليه مشان هيك ما عنديش partial
+
+16
+00:01:44,240 --> 00:01:48,700
+fraction حتى أقول partial fraction و أنا قلت الصبح
+
+17
+00:01:48,700 --> 00:01:52,740
+أول خطوة بدي أعمل partial fraction مش كل مثل بقدر
+
+18
+00:01:52,740 --> 00:01:56,570
+أعمله partial هدف فيه لـ partial fraction ما لهاش
+
+19
+00:01:56,570 --> 00:02:02,390
+يبقى هذه جاهزة وخالصة تمام؟ إذا أنا بدي أحول هذه 
+
+20
+00:02:02,390 --> 00:02:07,750
+إلى شكل من الأشكال اللي موجودة في الجدول إذا بقدر
+
+21
+00:02:07,750 --> 00:02:14,630
+أقول الـ F of S اللي هي تساوي لو روحت قلت S زائد
+
+22
+00:02:14,630 --> 00:02:20,370
+واحد ناقص واحد على S زائد واحد لكل تربيع زائد 
+
+23
+00:02:20,370 --> 00:02:26,360
+أربعة عملت حاجة؟ أضفت واحد و طرحت واحد بدي أفصل هذا
+
+24
+00:02:26,360 --> 00:02:33,060
+إلى مقدارين يبقى المقدار الأول هو S زائد واحد على 
+
+25
+00:02:33,060 --> 00:02:41,400
+S زائد واحد لكل تربيع زائد أربعة ناقص واحد على S
+
+26
+00:02:41,400 --> 00:02:49,170
+زائد واحد لكل تربيع زائد أربعة  الترم الأول صار
+
+27
+00:02:49,170 --> 00:02:53,390
+ما عنديش مشكلة لو روحت للجدول بلاقي عند وين في
+
+28
+00:02:53,390 --> 00:02:59,390
+الجدول هذا لسه لا يزال فيه مشكلة المشكلة أنه بده
+
+29
+00:02:59,390 --> 00:03:03,890
+اتنين هنا مدام هذه أربعة بدي الجذر تبعها يكون وين
+
+30
+00:03:03,890 --> 00:03:11,370
+فور إذا بقدر أقول الـ F of S بده يساوي الـ S زائد
+
+31
+00:03:11,370 --> 00:03:18,350
+واحد على S زائد واحد لكل تربيع زائد أربعة ناقص نصف 
+
+32
+00:03:18,350 --> 00:03:24,830
+في اتنين على S زائد واحد لكل تربيع زائد أربعة
+
+33
+00:03:24,830 --> 00:03:32,500
+هيك  الكلام صحيح الآن أنا بدي الـ F of T  F of T هي لـ
+
+34
+00:03:32,500 --> 00:03:38,280
+plus inverse لـ F of S يبقى الـ F of T اللي أنا بدور
+
+35
+00:03:38,280 --> 00:03:47,020
+عليها الـ F of T هي لـ plus inverse لـ capital F of S
+
+36
+00:03:47,390 --> 00:03:54,250
+واللي هي بدها تساوي لـ plus inverse لمين؟ لـ S plus 
+
+37
+00:03:54,250 --> 00:04:02,470
+one على الـ S plus one square plus four ناقص نصف في
+
+38
+00:04:02,470 --> 00:04:08,690
+الـ plus inverse لـ الإتنين على S plus one لكل
+
+39
+00:04:08,690 --> 00:04:14,050
+square plus four بالشكل اللي عندنا هنا يبقى الـ F
+
+40
+00:04:14,050 --> 00:04:19,760
+of T تساوي بدي آجي على الـ dialogue هادي و باجي على 
+
+41
+00:04:19,760 --> 00:04:26,020
+الجدول اللي عندنا يبقى الجدول بدي أدور على الشكل
+
+42
+00:04:26,020 --> 00:04:30,880
+اللي الـ S زائد واحد S زائد واحد لكل تربيع زائد
+
+43
+00:04:30,880 --> 00:04:32,400
+تربيع
+
+44
+00:04:34,010 --> 00:04:39,950
+طبعا لو جيت نظرت لهذا الجدول بلاحظ أن عندي هذا
+
+45
+00:04:39,950 --> 00:04:48,250
+الكلام موجود في النقطة رقم عشرة النقطة رقم عشرة
+
+46
+00:04:48,250 --> 00:04:56,040
+بتقول ليس نقص الـ A على S نقص الـ A لكل تربيع زي B 
+
+47
+00:04:56,040 --> 00:05:01,440
+تربيع يعني بيفرق بس بإشارة مين؟ إشارة السالف لكن هذه
+
+48
+00:05:01,440 --> 00:05:08,310
+لو رجعت للأصل تبعها بلاقي E أس A T Cos بت يبقى 
+
+49
+00:05:08,310 --> 00:05:12,550
+معناه هذا الكلام أن الـ a اللي عندي هنا بإشارة بس a
+
+50
+00:05:12,550 --> 00:05:18,430
+سالبة يبقى لو جيت على الجدول من part عشرة هذا
+
+51
+00:05:18,430 --> 00:05:25,110
+الكلام بدي أساوي a أس الـ a عندي هنا بقداش؟ بواحد
+
+52
+00:05:25,110 --> 00:05:33,030
+يبقى E أس ناقص T في cosine بت هذا بي تربيع يبقى
+
+53
+00:05:33,030 --> 00:05:37,300
+بيه بقداش؟ باتنين لأن بي تربيع تساوي 4 وأنت بي
+
+54
+00:05:37,300 --> 00:05:46,180
+باتنين يبقى E أس ناقص T في من؟ في Cos 2T اللي بعدها
+
+55
+00:05:46,180 --> 00:05:52,220
+ناقص نصف بدي آجي لهذه لو رجعت لخط و لجاب الخلف اللي
+
+56
+00:05:52,220 --> 00:05:57,620
+هو النقطة التاسعة بلاقي عندي P على S ناقص L كل
+
+57
+00:05:57,620 --> 00:06:04,650
+تربيع زائد P تربيع يبقى هذه بي هيب اتنين هي بي
+
+58
+00:06:04,650 --> 00:06:10,350
+تربيع بـ 4 زائد يبقى الـ a بس بمين؟ بسالب واحد
+
+59
+00:06:10,350 --> 00:06:18,530
+يبقى باجي بناقص نصف في E أس سالب T لـ sin اتنين T 
+
+60
+00:06:18,530 --> 00:06:23,570
+انتهت مسألتنا يبقى كله اعتماد على الجدول كيف أطلع 
+
+61
+00:06:23,570 --> 00:06:30,680
+من الجدول Laplace transform للدوال المختلفة مثال
+
+62
+00:06:30,680 --> 00:06:35,700
+ثلاثة
+
+63
+00:06:35,700 --> 00:06:43,740
+مثال ثلاثة بيقول ما يأتي بدنا
+
+64
+00:06:43,740 --> 00:06:48,720
+نجد مفعول
+
+65
+00:06:48,720 --> 00:06:53,460
+f of t with
+
+66
+00:06:55,610 --> 00:07:06,170
+اللي هو it's a type with Laplace transform
+
+67
+00:07:09,400 --> 00:07:15,960
+اللي لابلاس ترانسفورم إلها اللي هو capital F of S 
+
+68
+00:07:15,960 --> 00:07:25,280
+بده يساوي تلاتة S ناقص اتنين على S تربيع ناقص
+
+69
+00:07:25,280 --> 00:07:28,680
+اتنين S زائد عشرة 
+
+70
+00:07:33,040 --> 00:07:38,760
+بقول كويس اللي قال لو روحت على الجدول تابعنا هذا و
+
+71
+00:07:38,760 --> 00:07:46,560
+بلاقيش ولا term بهالشكل هذا لكن بده إعادة ايه؟ ترتيب
+
+72
+00:07:46,560 --> 00:07:51,460
+هذا الterm كيف نعمل ترتيبه؟ بده أشوف المقام،
+
+73
+00:07:51,460 --> 00:07:56,000
+ما عنديش شغمة زي هيك كله بلاقي S زي واحد الكل تربيع 
+
+74
+00:07:56,000 --> 00:08:01,440
+S نقص اتنين الكل تربيع زي رقم هنا رقم هنا S إلى
+
+75
+00:08:01,440 --> 00:08:06,100
+آخرين إذا بدي أعيد كتابة هذه الـ function بطريقة
+
+76
+00:08:06,100 --> 00:08:12,260
+ثانية إذا بقدر أقول هذا الكلام يساوي تلاتة S ناقص
+
+77
+00:08:12,260 --> 00:08:18,980
+اتنين على هذا S تربيع ناقص اتنين S إذا هذا لازم 
+
+78
+00:08:18,980 --> 00:08:24,660
+أعمله ايه؟ مربع كامل مشان أعمل هذا مربع كامل قديش 
+
+79
+00:08:24,660 --> 00:08:31,340
+بده S تربيع ازيد اتنين S قديش بده رقم مشان يصير مربع
+
+80
+00:08:31,340 --> 00:08:40,770
+كامل 2S ناقص
+
+81
+00:08:40,770 --> 00:08:47,170
+معامل X على أربع أمثال معامل X تربيع يبقى هنا بقول
+
+82
+00:08:47,170 --> 00:08:55,850
+زائد 2S يبقى مش هين أحول بذكر مرتين و تلتة و عشرين
+
+83
+00:08:56,440 --> 00:09:02,060
+بدي أعمل اكمال المربع بضيف للطرفين و بطرح مربع
+
+84
+00:09:02,060 --> 00:09:07,200
+معامل X على اربع امثال معامل X تربيع أعطيتها لكم
+
+85
+00:09:07,200 --> 00:09:12,900
+في calculus P و يا محل نبع يبقى مربع معامل X على 
+
+86
+00:09:12,900 --> 00:09:17,440
+اربع امثال معامل X تربيع يعني مربع معامل F على 
+
+87
+00:09:17,440 --> 00:09:22,840
+اربع امثال معامل S تربيع يبقى هنا بيبقى قديش؟ بواحد
+
+88
+00:09:22,840 --> 00:09:27,940
+يبقى زائد اتنين اس زائد واحد الواحد موجود عند
+
+89
+00:09:27,940 --> 00:09:34,940
+الجيران عشرة باخد منها واحد بيبقى تسعة يبقى زائد
+
+90
+00:09:34,940 --> 00:09:43,110
+تسعة يبقى هذا الكلام يساوي المقام اللي عندنا هذا 
+
+91
+00:09:43,110 --> 00:09:48,950
+الآنصار مربع كامل صح؟ يبقى هذا بقدر أقول اللي هو الـ
+
+92
+00:09:48,950 --> 00:09:58,580
+S ناقص واحد لكل تربيع زائد تسعة أيوة إذن الـ bus هذا
+
+93
+00:09:58,580 --> 00:10:05,160
+بيدخلك في مين؟ S ناقص واحد بيدخلك في كاف S ناقص أما
+
+94
+00:10:05,160 --> 00:10:09,920
+هو تلاتة S ناقص اتنين الجثة بسيطة خالص بضيف سالب
+
+95
+00:10:09,920 --> 00:10:15,020
+واحد و بطرح واحد يعني بضيف واحد و بطرح سالب واحد
+
+96
+00:10:15,020 --> 00:10:21,200
+يبقى هذا لو حطيت سالب واحد كده بصير؟ بقدر آخد تلاتة
+
+97
+00:10:21,200 --> 00:10:25,360
+عامل مشترك و بظل S ناقص واحد بيكون خلصت مسألة اتنين
+
+98
+00:10:25,360 --> 00:10:32,220
+إذا البسط هذا بقدر أكتب تلاتة S ناقص تلاتة زائد
+
+99
+00:10:32,220 --> 00:10:38,700
+واحد يبقى أضفت سالب واحد وكذلك واحد يعني أضفت صفر
+
+100
+00:10:38,700 --> 00:10:45,760
+ما غيرتش ولا حاجة يبقى بناء عليه أصبح شكل الـ F of S
+
+101
+00:10:45,760 --> 00:10:54,100
+على الشكل التالي هذه تلاتة في S ناقص واحد خدته
+
+102
+00:10:54,100 --> 00:11:02,020
+معامل مشترك و هنا زائد واحد على مين؟ على S على S
+
+103
+00:11:02,020 --> 00:11:09,470
+ناقص واحد لكل تربيع زائد تسعة ممكن هذه أفصلها إلى
+
+104
+00:11:09,470 --> 00:11:18,670
+جزئين من الجزئين هاي تلاتة في S ناقص واحد S ناقص
+
+105
+00:11:18,670 --> 00:11:27,390
+واحد لكل تربيع زائد تسعة ضال عندي زائد واحد على S 
+
+106
+00:11:27,390 --> 00:11:33,350
+ناقص واحد لكل تربيع زائد تسعة أظن صارت شبيهة
+
+107
+00:11:33,350 --> 00:11:40,390
+بمسألة هذه قبل قليل صح؟ و هذه شبيهة ابها بالضبط 
+
+108
+00:11:40,390 --> 00:11:46,670
+تماماً يبقى تعال نشوف كيف نسوي يبقى أنا هذه هاه
+
+109
+00:11:46,670 --> 00:11:52,550
+بدها بس فوق كده شمنها قديش؟ تلاتة ممتاز يبقى بدي 
+
+110
+00:11:52,550 --> 00:11:58,350
+اضرب في تلاتة و اجسم على تلاتة إذا بقدر أقول هذا
+
+111
+00:11:58,350 --> 00:12:05,190
+الكلام تلاتة في اس ناقص واحد على من؟ على اس ناقص
+
+112
+00:12:05,190 --> 00:12:12,690
+واحد الكل تربيع زائد تسعة زائد تلت في تلاتة على اس
+
+113
+00:12:12,690 --> 00:12:20,530
+ناقص واحد الكل تربيع زائد تسعة يبقى الـ F of T هي
+
+114
+00:12:20,530 --> 00:12:25,670
+Laplace inverse للطرفين يبقى تلاتة في Laplace 
+
+115
+00:12:25,670 --> 00:12:32,870
+inverse لـ S ناقص واحد S ناقص واحد لكل تربيع زائد
+
+116
+00:12:32,870 --> 00:12:40,930
+تسعة زائد تلت Laplace inverse لتلاتة S ناقص واحد
+
+117
+00:12:40,930 --> 00:12:48,960
+لكل تربيع زائد تسعة يبقى أصبح شكل الـ F of T بيساوي
+
+118
+00:12:48,960 --> 00:12:56,240
+ثلاثة فيه نرجع بالذاكرة الوراء للجدول قبل قليل
+
+119
+00:12:56,240 --> 00:13:04,700
+كذلك إلى النقطة العاشرة بلاحظ عندي S ناقص A S ناقص
+
+120
+00:13:04,700 --> 00:13:10,560
+A لكل تربيع زائد B تربيع يبقى الأصل تبعها E أس AT 
+
+121
+00:13:10,560 --> 00:13:20,600
+Cos BT قديش الـ A عندي هنا؟ الـ A بواحد طب و الـ B؟ تلاتة
+
+122
+00:13:20,600 --> 00:13:28,100
+لأن هذه بي تربيع يبقى بناء عليه تلاتة E of T بدون 
+
+123
+00:13:28,100 --> 00:13:35,060
+زائد تمام فاهمين في cosine تلاتة T هذا الterm
+
+124
+00:13:35,060 --> 00:13:43,420
+الأول زائد طول هذه بنفس الطريقة E of T sine تلاتة 
+
+125
+00:13:43,420 --> 00:13:48,120
+T يبقى هذه الـ function اللي مطلوبة اللي عندنا 
+
+126
+00:13:55,990 --> 00:14:00,830
+بنعطي كمان مثال مثال
+
+127
+00:14:00,830 --> 00:14:04,570
+تلاتة أو example أربعة
+
+128
+00:14:09,370 --> 00:14:16,690
+بيقول لي نفس القصة capital F of S بده يساوي E أس
+
+129
+00:14:16,690 --> 00:14:25,390
+ناقص S على S ناقص اتنين لكل تربيع و بده مين؟ بده
+
+130
+00:14:25,390 --> 00:14:30,580
+نوجد لنا place transform اللي هالمعكوز تبعه بقول له 
+
+131
+00:14:30,580 --> 00:14:35,340
+بسيطة جدا قبل ما توجد لبلاس ترانسفورم حاول ترتبها
+
+132
+00:14:35,340 --> 00:14:44,620
+بقول له يعني هذه لو كتبتها E أس ناقص S في واحد على 
+
+133
+00:14:44,620 --> 00:14:52,860
+S ناقص اتنين لكل تربيع عملنا حاجة طيب ايش رأيك
+
+134
+00:14:52,860 --> 00:14:57,800
+الواحد هذا لو كتبت واحد factorial الشكل اللي عندنا
+
+135
+00:14:57,800 --> 00:14:58,020
+هذا
+
+136
+00:15:03,450 --> 00:15:09,810
+يبقى باجي بقول الـ F of T اللي أنا بدور عليها هي
+
+137
+00:15:09,810 --> 00:15:17,810
+Laplace transform بالمعكوس تبعها لـ capital F of S
+
+138
+00:15:17,810 --> 00:15:24,110
+و يساوي Laplace transform لـ E أص ناقص S
+
+139
+00:15:39,210 --> 00:15:43,410
+يبقى الـ F of T تساوي
+
+140
+00:15:52,230 --> 00:15:59,670
+طيب من فوق لتحت exponential exponential عندي رقم
+
+141
+00:15:59,670 --> 00:16:05,690
+اتنين exponential على اس أنا عندي على اس ناقص كذا
+
+142
+00:16:06,430 --> 00:16:14,490
+طيب أنا بلاحظ عندي الرقم تلاتة الرقم تلاتة اللي هو
+
+143
+00:16:14,490 --> 00:16:25,780
+E أس ناقص CS في capital F of S capital F of S هذا 
+
+144
+00:16:25,780 --> 00:16:32,100
+الأصل تبعها الأصل تبعها ده الـ step function u C of
+
+145
+00:16:32,100 --> 00:16:39,260
+T فالـ F of T ناقص من؟ ناقص الـ C لكن لو رجعنا
+
+146
+00:16:39,260 --> 00:16:46,700
+للخاصية رقم 5 من section 9 3 تحيلي section 9 3
+
+147
+00:16:46,700 --> 00:16:48,040
+الخاصية رقم 5
+
+148
+00:16:50,690 --> 00:16:53,670
+يعني إذا عرفت تجيبيها من الجدول و كرمها و ما عرفتش 
+
+149
+00:16:53,670 --> 00:17:00,490
+برجع للأصل هذه تبعها طلع لي مشان أكتب هذه الدالة 
+
+150
+00:17:00,490 --> 00:17:08,850
+باجي للدالة بين القوسين هذه هي الـ F of S قولي G 
+
+151
+00:17:08,850 --> 00:17:15,490
+of S يساوي واحد factorial على S ناقص اتنين لكل
+
+152
+00:17:15,490 --> 00:17:20,650
+تربيع بقدر أجيب الأصل تبعها مين الأصل تبعها يا بنات
+
+153
+00:17:20,650 --> 00:17:26,510
+G of T يساوي هذه لو روحت جبت الأصل تبعها يبقى
+
+154
+00:17:26,510 --> 00:17:33,070
+الأصل تبعها هو عبارة عن T في E أس اتنين T طبعا 
+
+155
+00:17:33,070 --> 00:17:38,830
+من الجدول T في E أس اتنين T لو روحت للخاصية رقم 
+
+156
+00:17:38,830 --> 00:17:45,450
+خمسة اللي عندك بدي أعمل لهذه الدالة shift بمقدار
+
+157
+00:17:46,670 --> 00:17:52,430
+قديش؟ اتنين مش عندك هنا اتنين هذا اتنين أنت بقى
+
+158
+00:17:52,430 --> 00:17:56,710
+الـ exponential يبقى بدي أعمله shift بمقدار عفوا
+
+159
+00:17:56,710 --> 00:18:06,530
+بمقدار اللي هو الاتنين بمقدار الواحد
+
+160
+00:18:06,530 --> 00:18:13,450
+و ليس الاتنين طيب كيف ده؟ جت كالتالي فباجي بقول يبقى
+
+161
+00:18:13,450 --> 00:18:20,110
+الـ plus inverse لها يساوي أحد أمرين يا إما صفر لما
+
+162
+00:18:20,110 --> 00:18:26,490
+الـ T أكبر من الـ 0 أقل من واحد يا إما T ناقص 
+
+163
+00:18:26,490 --> 00:18:34,630
+واحد E أس اتنين في T ناقص واحد والـ T أكبر من
+
+164
+00:18:34,630 --> 00:18:35,430
+الواحد
+
+165
+00:18:38,640 --> 00:18:46,220
+خاصية رقم خمسة الخاصية رقم خمسة من سكتشن تسعة تلاتة
+
+166
+00:18:48,480 --> 00:18:53,280
+خاصية رقم خمسة اللي بيقول لي small q of t بدي أساوي 
+
+167
+00:18:53,280 --> 00:18:56,860
+صفر لما t محصورة بين الـ 0 و الـ c أو f of t
+
+168
+00:18:56,860 --> 00:19:02,140
+ناقص الـ c لما t أكبر من الـ c يبقى لبلاي الـ
+
+169
+00:19:02,140 --> 00:19:08,240
+transform اللي هي E اص ناقص CS في capital F of S
+
+170
+00:19:08,240 --> 00:19:14,760
+يعني بدنا نجيب الـ F of S للدلة اللي عندنا وين الـ F
+
+171
+00:19:14,760 --> 00:19:23,510
+of S هي مظ
+
+201
+00:22:46,480 --> 00:22:47,040
+مثال
+
+202
+00:22:53,540 --> 00:23:02,900
+معرفة مفهوم f*)g
+
+203
+00:23:02,900 --> 00:23:06,980
+كمفهوم من f
+
+204
+00:23:12,860 --> 00:23:22,700
+الـ F of T بدها تساوي الـ E أس T والـ G of T بدها تساوي E أس
+
+205
+00:23:22,700 --> 00:23:23,980
+اتنين T
+
+206
+00:23:59,030 --> 00:24:03,430
+بنجي لتعريف الـ convolution لـ الـ two functions ايش
+
+207
+00:24:03,430 --> 00:24:07,750
+بيقول دي؟ الـ function f star g as a function of t
+
+208
+00:24:07,750 --> 00:24:12,710
+بنسميها الـ convolution of الـ function اللي هي الـ
+
+209
+00:24:12,710 --> 00:24:16,710
+main of الـ function f and g convolution في اللغة
+
+210
+00:24:16,710 --> 00:24:22,130
+العربية معناه التفاف يعني كأنه بيعمل التفاف يعني
+
+211
+00:24:22,130 --> 00:24:27,550
+لـ دالة f ممكن اعمل لـ دالة g والتانية تظهر
+
+212
+00:24:27,550 --> 00:24:32,270
+زي ما هي بدون مشاكل من هنا سمينا convolution لـ مين
+
+213
+00:24:32,270 --> 00:24:37,690
+لـ تو functions بهمني هذا جدّاش بيساوي لإن أنا هذا هو
+
+214
+00:24:37,690 --> 00:24:42,290
+اللي بشتغل عليه إذا بدي أقول لـ دالة f star g أو f
+
+215
+00:24:42,290 --> 00:24:46,690
+convolution g as a function of t يتكوّن من zero إلى
+
+216
+00:24:46,690 --> 00:24:52,610
+T يا باجي على الـ F اللي عنها دي بكتبها أو بشيل كل
+
+217
+00:24:52,610 --> 00:24:59,030
+T بحط بدلها T ناقص U , U real number  ها يبقى F of T
+
+218
+00:24:59,030 --> 00:25:08,270
+ناقص الـ U في الـ G of U في الـ DU يبقى كوني الآن أخدت
+
+219
+00:25:08,270 --> 00:25:14,950
+الـ DU يعني U هي اشتقاق وكأن الـ T أنا ثبتها كأنه
+
+220
+00:25:14,950 --> 00:25:18,430
+خليت الـ T مقدار ثابت لأن أنا كامل بالنسبة لـ U إذا
+
+221
+00:25:18,430 --> 00:25:24,020
+الـ T ايش تعتبر مقدارا ثابتا أريد أن أثبت الـ U
+
+222
+00:25:24,020 --> 00:25:28,580
+فأقول F of U يبقى الـ G فأقول G of T ناقص الـ U في
+
+223
+00:25:28,580 --> 00:25:33,380
+الـ DU وحسب الـ Definition هذه ستساوي عملت لهذه G
+
+224
+00:25:33,380 --> 00:25:39,300
+وهذه ثبتت فأقول G star F يبقى بناء عليه الـ F star
+
+225
+00:25:39,300 --> 00:25:46,500
+G هو G star F كلها as a function of T كلها كدالة
+
+226
+00:25:46,500 --> 00:25:50,200
+في T يبقى هذه والله هذه عملت للدالة الأولى والله
+
+227
+00:25:50,200 --> 00:25:55,120
+الدالة التانية الاتنين are the same طب لو بدّه يجيب
+
+228
+00:25:55,120 --> 00:25:59,900
+Laplace transform لل convolution بقول Laplace
+
+229
+00:25:59,900 --> 00:26:05,040
+لـ دالة الأولى ضرب ضرب عادية Laplace لـ دالة التانية
+
+230
+00:26:05,040 --> 00:26:10,180
+هيها dot مضروبة ضرب فيها دي تمام؟ بدنا نروح نطبق
+
+231
+00:26:10,180 --> 00:26:14,790
+هذا الكلام بمثال جالي هاتلي الدالة هادي إذا كانت الـ
+
+232
+00:26:14,790 --> 00:26:19,610
+F of T بدها تساوي الـ E of T والـ G of T بدها تساوي من
+
+233
+00:26:19,610 --> 00:26:25,110
+الـ E أس اتنين T إذا لما بداجي أحل بداجي أقوله الـ F
+
+234
+00:26:25,110 --> 00:26:31,830
+star G كله as a function of T يساوي الـ F of T يا
+
+235
+00:26:31,830 --> 00:26:38,130
+بنات اللي هي من E أس T الـ G of T اللي هي E أس
+
+236
+00:26:38,130 --> 00:26:44,170
+اتنين T وها هم function في T طبقا للتعريف اللي فوق
+
+237
+00:26:44,170 --> 00:26:51,050
+يبقى تكامل من zero إلى T تمام عندك هذه الصيغة أو
+
+238
+00:26:51,050 --> 00:26:56,450
+هذه سيّان يبقى الـ F اللي هي الدالة الأولى بدي اعمل
+
+239
+00:26:56,450 --> 00:27:04,810
+لها shift بمقدار جدّاش الـ U يبقى E أس T ناقص الـ U
+
+240
+00:27:04,810 --> 00:27:12,160
+الـ G أبدا بدي أشيل الـ T بس وأكتب مكانها جدّاش U يوم
+
+241
+00:27:12,160 --> 00:27:22,580
+دي U يوم تمام طيب إذا هذا بنيت بقدر أقول تساوي تكامل
+
+242
+00:27:22,580 --> 00:27:31,380
+من zero إلى T لـ مين؟ للـ E أس T ناقص U E أس 
+
+243
+00:27:31,380 --> 00:27:37,570
+اتنين U أظن الـ E أس T مالهاش دعوة بالتكامل لإنّه
+
+244
+00:27:37,570 --> 00:27:42,250
+بيشتقّ بالنسبة لـ مين؟ يبقى بقدر أطلعها برا التكامل
+
+245
+00:27:42,250 --> 00:27:50,610
+يبقى هذه تساوي E أس T تكامل من Zero إلى T للـ E بجمع
+
+246
+00:27:50,610 --> 00:27:56,250
+الأسس لإنّ الأساسات زي بعض يبقى UDU
+
+247
+00:27:57,600 --> 00:28:04,640
+تمام؟ طيب هذا بيصير E أس T فيه تكامل الـ E أس U بالـ
+
+248
+00:28:04,640 --> 00:28:10,480
+E أس U itself يبقى هذه الـ E أس U من وين لوين؟ من
+
+249
+00:28:10,480 --> 00:28:17,800
+Zero لغاية T يبقى هذا الكلام بدّه يساوي اهه اللي هو
+
+250
+00:28:17,800 --> 00:28:26,970
+مين؟ E أس T في مين؟ في الـ E أس T ناقص E أس Zero E 0
+
+251
+00:28:26,970 --> 00:28:34,490
+بيبقى 1 يبقى صار E of T في E of T ناقص 1
+
+252
+00:28:34,490 --> 00:28:42,950
+يبقى E of 2T ناقص E of T إذا الـ convolution اللي
+
+253
+00:28:42,950 --> 00:28:49,150
+حصل لـ two functions F and G يساوي الدالة الأولى
+
+254
+00:28:49,150 --> 00:28:55,550
+الدالة الثانية ناقص الدالة الأولى بالمثل لو أخذت
+
+255
+00:28:55,550 --> 00:29:01,830
+هذه الـ T عملت لها T ناقص الـ U وهذه خليت الـ U
+
+256
+00:29:01,830 --> 00:29:06,670
+كامل فهو بيطلع نفس النتيجة اللي عندنا لحد هنا stop
+
+257
+00:29:06,670 --> 00:29:11,490
+and turn section إلى يكون أرقام المسائل يبقى
+
+258
+00:29:11,490 --> 00:29:20,370
+exercises تسعة أربعة المسائل 1 و 2 و 4 بدأ
+
+259
+00:29:20,370 --> 00:29:30,170
+أخذ الـ A والـ C وسؤال 5 بدي الـ A والـ B الـ A والـ
+
+260
+00:29:30,170 --> 00:29:37,030
+B والـ A والـ F طيب
+
+261
+00:29:37,030 --> 00:29:45,050
+نيجي لآخر section اللي هو 9 5 يبقى 9 5 اللي هو الـ
+
+262
+00:29:45,050 --> 00:29:46,190
+applications
+
+263
+00:29:49,160 --> 00:29:56,180
+applications to differential equations
+
+264
+00:29:58,370 --> 00:30:03,510
+تطبيقات على المعادلات التفاضلية ايش يعني المقصود
+
+265
+00:30:03,510 --> 00:30:07,730
+فيها المقصود استخدام Laplace transform لحل
+
+266
+00:30:07,730 --> 00:30:13,690
+المعادلة التفاضلية أظن حلينالكوا بدل المعادلة التنين
+
+267
+00:30:13,690 --> 00:30:18,730
+مظبوط يبقى أنا باعتمر ما اشتغلتش بالمرة وبدي اشتغل
+
+268
+00:30:18,730 --> 00:30:26,490
+من جديد يبقى هنا بدي أقول to use السؤال بيجي كتابة
+
+269
+00:30:26,490 --> 00:30:42,450
+example توضيحي example use Laplace transform to
+
+270
+00:30:42,450 --> 00:30:45,490
+solve
+
+271
+00:30:45,490 --> 00:30:51,590
+the
+
+272
+00:30:51,590 --> 00:30:54,690
+initial value problem
+
+273
+00:30:57,680 --> 00:31:05,600
+اللي هي الـ x double prime زائد أربعة x بدها تساوي
+
+274
+00:31:05,600 --> 00:31:13,320
+ثمانية sin الـ T والـ x عند الـ zero بدها تساوي zero
+
+275
+00:31:13,320 --> 00:31:20,440
+والـ x prime عند الـ zero بدها تساوي اثنين solution
+
+276
+00:31:24,890 --> 00:31:28,750
+يبقى مدام أعطاني السؤال من هذا القبيل هو قيدني
+
+277
+00:31:28,750 --> 00:31:32,910
+بطريقة الحل أنا هذه معادلة من الرتبة الثانية إذا
+
+278
+00:31:32,910 --> 00:31:38,110
+لو بدي أرجع للي قبل المعاملات ثوابت ودالة بالـ sin
+
+279
+00:31:38,110 --> 00:31:41,050
+ممكن إذا بحلها بالـ undetermined coefficients بس هو
+
+280
+00:31:41,050 --> 00:31:43,730
+بدّه إياي أحلها بالـ undetermined coefficients بدي
+
+281
+00:31:43,730 --> 00:31:48,130
+إياي أحلها بالـ Laplace transform ويبقى أنا مقيد إذا
+
+282
+00:31:48,130 --> 00:31:52,490
+بالـ Laplace transform إذا بروح آخذ لبلاس ترانسفورم
+
+283
+00:31:52,490 --> 00:31:59,330
+للطرفين يبقى باجي بقول لبلاس ترانسفورم للـ X'' زائد
+
+284
+00:31:59,330 --> 00:32:06,350
+أربعة لبلاس ترانسفورم للـ X بدها تساوي ثمانية لبلاس
+
+285
+00:32:06,350 --> 00:32:12,950
+ترانسفورم لـ sin الـ T؟ إنّ Laplace Transform is a linear
+
+286
+00:32:12,950 --> 00:32:16,390
+function أو linear operator يبقى الـ ثمانية بقدر
+
+287
+00:32:16,390 --> 00:32:25,560
+أطلعها برا بدي أطبق النظرية على هذه يبقى هذه S² X S
+
+288
+00:32:25,560 --> 00:32:39,800
+ناقص S في X عند 0 ناقص X' عند 0 زائد 4X S بدها تساوي
+
+289
+00:32:39,800 --> 00:32:45,890
+8 sin الـ T مظبوط sin الـ T ولا sin 2T يبقى
+
+290
+00:32:45,890 --> 00:32:51,330
+sin الـ T مدام sin الـ T إذا هذه Laplace Transform
+
+291
+00:32:51,330 --> 00:32:58,970
+حسبناها عمليًا يبقى هذا بقدّاش يا بناات بواحد على S²
+
+292
+00:32:58,970 --> 00:33:07,130
+زائد واحد مظبوط طيب يبقى هنيجي طلعيلي لهذه
+
+293
+00:33:07,130 --> 00:33:14,310
+وهذه بقدر آخذ X of S عامل مشترك بيظلّ عندي S²
+
+294
+00:33:14,310 --> 00:33:21,630
+زائد 4 في capital X of S الآن الـ X عندي
+
+295
+00:33:21,630 --> 00:33:25,470
+Zero يبقى
+
+296
+00:33:25,470 --> 00:33:32,970
+ناقص Zero الـ X Prime باثنين يبقى ناقص اثنين يساوي
+
+297
+00:33:32,970 --> 00:33:40,710
+ثمانية على S² زائد واحد أو إن شئتم فقولوا إنّ
+
+298
+00:33:40,710 --> 00:33:48,370
+الـ S² زائد أربعة في capital X of S بدها تساوي
+
+299
+00:33:48,370 --> 00:33:55,790
+ثمانية على S² plus one plus two بدّه واحد
+
+300
+00:33:55,790 --> 00:34:02,690
+المقامات يبقى بيصير S² زائد أربعة في capital
+
+301
+00:34:02,690 --> 00:34:11,050
+X of S يساوي كله على S² plus one وهي ثمانية زي
+
+302
+00:34:11,050 --> 00:34:16,870
+دي اثنين S² زي دي اثنين تمام يبقى بيصير
+
+303
+00:34:16,870 --> 00:34:22,750
+عندنا مين بيصير عندنا S² plus four في
+
+304
+00:34:22,750 --> 00:34:30,970
+capital X of S يساوي اثنين S² زائد عشرة
+
+305
+00:34:30,970 --> 00:34:38,710
+مقسوما على S² plus one طب أنا بدي X of S
+
+306
+00:34:38,710 --> 00:34:46,370
+يبقى الـ X of S بدّه يساوي اثنين S² زائد عشرة
+
+307
+00:34:46,370 --> 00:34:55,610
+على S² plus one في S² plus four لو رحت
+
+308
+00:34:55,610 --> 00:35:01,010
+على الجدول بلاقي شغلة زي هذه في الشمكانية طب كيف
+
+309
+00:35:01,010 --> 00:35:04,870
+نسوي؟ بقول لك بسيطة الـ bus من الدرجة الثانية والـ
+
+310
+00:35:04,870 --> 00:35:11,790
+مقام من الدرجة partial fraction والحمد لله جاهزة
+
+311
+00:35:11,790 --> 00:35:17,550
+يبقى بس أحطها على شكل ايه؟ شكل كسور يبقى هذا الكلام
+
+312
+00:35:17,550 --> 00:35:23,650
+بدّه يساوي هذا كسر وهذا الـ S² plus one وهذا
+
+313
+00:35:23,650 --> 00:35:29,110
+كسر ثاني S² plus four المعادلة من الدرجة
+
+314
+00:35:29,110 --> 00:35:33,790
+الثانية كل واحدة فيهم ولا يمكن تحليلها إذا بدّه أحط
+
+315
+00:35:33,790 --> 00:35:41,210
+فوق معادلة من الدرجة الأولى يبقى باجي بقوله AS زائد
+
+316
+00:35:41,210 --> 00:35:47,910
+B وهنا CS زائد D وبعد هيك بروح أحسب الـ partial
+
+317
+00:35:47,910 --> 00:35:54,030
+fractions يبقى بقوله اثنين S² زائد عشرة بدّه
+
+318
+00:35:54,030 --> 00:36:03,490
+يساوي AS زائد الـ B في مين؟ في الـ S² زائد 4
+
+319
+00:36:03,490 --> 00:36:13,160
+زائد CS زائد دي في الـ S² plus one طبعًا بنفك
+
+320
+00:36:13,160 --> 00:36:19,960
+ونقرر مش هضيع وقت فيها هعطيك النتيجة مباشرة يبقى
+
+321
+00:36:19,960 --> 00:36:27,260
+بتطلع عندك هنا الـ A تساوي Zero الـ A تساوي Zero و
+
+322
+00:36:27,260 --> 00:36:36,660
+الـ B تساوي ناقص تلتين والـ C بتطلع عندك بـ Zero و
+
+323
+00:36:36,660 --> 00:36:45,950
+الـ D بتطلع عندي بـ 8 على 3 بناء عليه أصبحت المسألة
+
+324
+00:36:45,950 --> 00:36:47,770
+على الشكل التالي
+
+325
+00:37:00,950 --> 00:37:07,290
+يبقى أصبحت الـ X of S , X as a function of S على
+
+326
+00:37:07,290 --> 00:37:12,390
+الشكل التالي طلعيها هنا كويسة يبقى بدأت دي أشيل الـ A
+
+327
+00:37:12,390 --> 00:37:18,730
+وأحط مكانها Zero طارت الـ B بدأت أحط بدل سالب تلتين
+
+328
+00:37:18,730 --> 00:37:25,450
+يبقى هاي سالب تلتين ضالّ واحد على S² زائد
+
+329
+00:37:25,450 --> 00:37:31,920
+واحد انتهينا منها الآن الـ C بـ Zero طارت يبقى الـ D بـ
+
+330
+00:37:31,920 --> 00:37:38,320
+ثمانية على ثلاثة زائد ثمانية على ثلاثة في جدّاش؟ في
+
+331
+00:37:38,320 --> 00:37:46,370
+واحد على S² زائد أربعة إذا أنا بدي الـ X as a
+
+332
+00:37:46,370 --> 00:37:52,870
+function of T هي Laplace inverse لـ capital X of S
+
+333
+00:37:52,870 --> 00:37:57,050
+بالشكل اللي عندنا هنا يبقى هذا بدّه يساوي سالب
+
+334
+00:37:57,050 --> 00:38:02,630
+تلتين Laplace inverse للواحد على S² plus
+
+335
+00:38:02,630 --> 00:38:11,680
+one زائد ثمانية على ثلاثة وهنا لابلاس inverse لواحد
+
+336
+00:38:11,680 --> 00:38:18,620
+على S² زائد أربعة يبقى شكل الـ X of T يساوي
+
+337
+00:38:18,620 --> 00:38:26,850
+سالب تلتين مين هذا يا بناات؟ هي مين هذّي؟ الـ sin
+
+338
+00:38:26,850 --> 00:38:33,510
+t يبقى سالب تلتين في sin t زائد ثمانية
+
+339
+00:38:33,510 --> 00:38:41,370
+على ثلاثة في مين كمان هذّي؟ sin 2t هذا ليس ضبط
+
+340
+00:38:41,370 --> 00:38:49,710
+فقط اضرب في 2 واقسم على 2 يبقى بيصير هنا ثمانية
+
+341
+00:38:49,710 --> 00:38:57,070
+على ثلاثة لـ Laplace inverse لـ نصف وهنا اثنين على S
+
+342
+00:38:57,070 --> 00:39:03,030
+² زائد أربعة يعني بدك تظبط مسألتك دائماً وأبداً
+
+343
+00:39:03,030 --> 00:39:08,290
+بيعتمد تكون ما فعلاً لها في صورة الجدول يبقى النتيجة
+
+344
+00:39:08,290 --> 00:39:15,510
+ناقص تلتين sin t النصف بيطلع برا وضَلّ قدّاش عندي؟ أربعة
+
+345
+00:39:15,510 --> 00:39:25,270
+على ثلاثة وهذه اللي هي مين؟ sin 2T هذا هو الحل
+
+346
+00:39:25,270 --> 00:39:32,630
+تبع المعادلة X as a function of T نعطي كمان مثال
+
+347
+00:39:32,630 --> 00:39:40,110
+آخر مثال
+
+348
+00:39:40,110 --> 00:39:48,430
+اثنين بيقول الـ X double prime ناقص X بدها تساوي الـ
+
+349
+00:39:48,430 --> 00:39:56,900
+F of T والـ T أكبر من أو يساوي الـ Zero والـ X عند
+
+350
+00:39:56,900 --> 00:40:02,720
+الـ Zero بدها تساوي واحد والـ X' عند الـ Zero بدّه
+
+351
+00:40:02,720 --> 00:40:10,520
+يساوي Zero وواحد حيث مين هي الـ F of T هذه الـ F of
+
+352
+00:40:10,520 --> 00:40:18,640
+T بدها تساوي يا إما Zero لما T أكبر من Zero أقل من
+
+353
+00:40:18,640 --> 00:40:28,880
+واحد يا إما T ناقص واحد لما T greater than
+
+354
+00:40:28,880 --> 00:40:32,680
+one طيب
+
+355
+00:40:33,610 --> 00:40:39,750
+نبدأ نأخذ Laplace transform للطرفين يبقى solution
+
+356
+00:40:39,750 --> 00:40:46,190
+واضح
+
+357
+00:40:46,190 --> 00:40:49,250
+إنّه ما أقدر أحلها بالـ undetermined coefficients
+
+358
+00:40:49,250 --> 00:40:56,590
+مظبوط؟ بس بدّه إياي ما جاليش قال استخدم Laplace transform
+
+359
+00:40:56,590 --> 00:40:59,370
+لحل هذه المعادلة
+
+360
+00:41:04,040 --> 00:41:08,720
+إذا بدرّح آخذ Laplace للطرفين يبقى Laplace
+
+361
+00:41:08,720 --> 00:41:15,560
+transform للـ X'' as a function of T ناقص
+
+362
+00:41:15,560 --> 00:41:23,480
+Laplace transform للـ X of T بدها تساوي Laplace للـ F
+
+363
+00:41:23,480 --> 00:41:31,160
+of T نعود لهذه الاختصار هذّي S² في capital X of S
+
+364
+00:41:31,160 --> 00:41:39,300
+ناقص S في مين؟ في الـ X عند Zero ناقص X prime of
+
+365
+00:41:39,300 --> 00:41:45,260
+Zero ناقص capital X of S يساوي نحتاج لـ Laplace
+
+366
+00:41:45,260 --> 00:41:51,040
+للدالة هذه تمام؟ نعود لـ مين؟ للخصائص اللي عندنا؟ تبع
+
+367
+00:41:51,040 --> 00:41:53,320
+الـ section تسعة ثلاثة
+
+368
+00:41:55,380 --> 00:42:03,500
+الخاصية رقم خمسة الخاصية رقم خمسة الخاصية رقم خمسة
+
+369
+00:42:03,500 --> 00:42:03,700
+الخاصية رقم خمسة الخاصية رقم خمسة الخاصية رقم خمسة
+
+370
+00:42:03,700 --> 00:42:04,180
+الخاصية رقم خمسة الخاصية رقم خمسة الخاصية رقم خمسة
+
+371
+00:42:04,180
+
+401
+00:45:16,860 --> 00:45:25,340
+زائد واحد، تمام؟ زائد S أو خلّي هذه S ناقص S
+
+402
+00:45:25,340 --> 00:45:33,180
+زي ما هي و بيبقى عندي واحد على S تربيع في S ناقص 
+
+403
+00:45:33,180 --> 00:45:40,740
+واحد في S زائد واحد بالشكل اللي عندنا اه بدنا 
+
+404
+00:45:40,740 --> 00:45:46,080
+partial fraction هذه ولا لأ يبقى بدنا نبدأ نحسب ال
+
+405
+00:45:46,080 --> 00:45:51,120
+part في ال fraction يبقى أخر ما توصلنا إليه هو ال
+
+406
+00:45:51,120 --> 00:45:58,000
+X of S يساوي S على S تربيع ناقص ال one وديك S 
+
+407
+00:45:58,000 --> 00:46:04,070
+تربيع مظبوط تمام مئة مية المية طب خلّينا نشوف هذه
+
+408
+00:46:04,070 --> 00:46:07,330
+اللي هي الأولى نعمل ال partial fraction وبعدين 
+
+409
+00:46:07,330 --> 00:46:12,410
+بنشوف التاني نشوف الكبيرة هذه يبقى واحد على S
+
+410
+00:46:12,410 --> 00:46:19,430
+تربيع في S ناقص ال one في S زائد one يساوي S
+
+411
+00:46:19,430 --> 00:46:27,290
+تربيع يجب لزمنا A S زائد B زائد S ناقص واحد C
+
+412
+00:46:27,290 --> 00:46:37,310
+زائد S زائد واحد يبقى D أحسنت أو الواحد بده يساوي AS
+
+413
+00:46:37,310 --> 00:46:46,130
+زائد ال B ال AS زائد ال B في مين؟ في ال S تربيع
+
+414
+00:46:46,130 --> 00:46:53,550
+ناقص ال one اللي هو حاصل ضربهما زائد C S تربيع
+
+415
+00:46:53,550 --> 00:47:05,210
+في S زائد one زائد D S تربيع في S ناقص ال one طيب
+
+416
+00:47:05,210 --> 00:47:13,130
+هذا الواحد يساوي A تكعيب ناقص ال A S تربيع زائد B
+
+417
+00:47:13,130 --> 00:47:21,250
+تربيع ناقص ال B زائد C تكعيب زائد C تربيع
+
+418
+00:47:21,250 --> 00:47:31,600
+زائد D تكعيب ناقص D تربيع نجمع يبقى هذه فيها
+
+419
+00:47:31,600 --> 00:47:39,440
+تكعيب وهذه تكعيب وهذه تكعيب يبقى A زائد C زائد D
+
+420
+00:47:39,440 --> 00:47:47,440
+كله في ال S تكعيب زائد تعين التربيع يبقى هذه B وهنا
+
+421
+00:47:47,440 --> 00:47:56,560
+C وهنا ناقص D كله في ال S تربيع نجلي فيهم S هنا
+
+422
+00:47:56,560 --> 00:48:03,320
+كله ماعنديش S ماعنديش اللي هاد يتيمة ناقص AS وهنا
+
+423
+00:48:03,320 --> 00:48:10,240
+ناقص B زيهتمام يبقى نعمل مقارنة بين الطرفين يبقى a
+
+424
+00:48:10,240 --> 00:48:18,740
+زيدي ال c زيدي ال d بده يساوي 0 و b زيدي ال c ناقص
+
+425
+00:48:18,740 --> 00:48:26,340
+ال d بده يساوي 0 و ناقص ال a بده يساوي 0 و ناقص ال
+
+426
+00:48:26,340 --> 00:48:31,770
+b يساوي 1 يبقى الاتنين هدول اشباطون يا بنات ان ال a
+
+427
+00:48:31,770 --> 00:48:40,490
+تساوي zero و ال b تساوي سالب واحد يبقى
+
+428
+00:48:40,490 --> 00:48:45,630
+هدف بده يعطينا لو أخدت ال a ب zero بيظل قداش c
+
+429
+00:48:45,630 --> 00:48:51,270
+زائد d يساوي zero و لو أخدت ال b بسالب واحد بيصير
+
+430
+00:48:51,270 --> 00:48:59,510
+ال c ناقص d ساوي واحدمظبوط؟ اجمع هدول مع السلامة
+
+431
+00:48:59,510 --> 00:49:10,130
+يبقى 2C يساوي 1 يبقى C يساوي نص لما C يساوي نص و A
+
+432
+00:49:10,130 --> 00:49:18,870
+ب 0 يبقى D بسالب نص يبقى هيو C بنص يبقى D يساوي
+
+433
+00:49:18,870 --> 00:49:25,610
+سالب نص إذا أصبح ال term اللي عندنا هذا جاهز أيوة
+
+434
+00:49:25,610 --> 00:49:31,370
+بدنا نشوف التاني كمان للتاني على أي حال بدي اكتب
+
+435
+00:49:31,370 --> 00:49:35,490
+النتيجة دغري وانت بدك تروح تعملي partial fraction
+
+436
+00:49:35,490 --> 00:49:41,350
+بسيط انا سويتلك الصعب وخليت البسيط يبقى لو روحنا
+
+437
+00:49:41,350 --> 00:49:49,250
+عملنا بيكون على الشكل التالي يبقى ال X of S بده
+
+438
+00:49:49,250 --> 00:49:56,700
+يساوي ال S على S²-1 هذه لا نريد أن نعملها لها
+
+439
+00:49:56,700 --> 00:50:01,760
+خلّيها زي ما هي مش مشكلة يبقى S على S²-1 مافيهاش
+
+440
+00:50:01,760 --> 00:50:09,360
+مشكلة وهذه زائد E أس ناقص S في قداش في سالب واحد
+
+441
+00:50:09,360 --> 00:50:20,600
+على S² زائد نص في واحد على S ناقص واحد وهنا يبقى
+
+442
+00:50:20,600 --> 00:50:25,980
+هذا ال exponential اللي عندنا طيب اروح نجمع و نشوف
+
+443
+00:50:25,980 --> 00:50:32,320
+وين بدنا نوصلهذه سأتركها كذلك لأنها سهلة و لا يوجد
+
+444
+00:50:32,320 --> 00:50:41,300
+فيها مشكلة يبقى هذه S على S²-1 هذه زائد E أس ناقص S
+
+445
+00:50:41,300 --> 00:50:49,440
+هذه سالب واحد على S تربيع هذول بقدر اخد مين؟ زائد نص
+
+446
+00:50:49,440 --> 00:50:56,260
+عامل مشترك بظل عندنا مين؟ S ناقص واحد في S زائد
+
+447
+00:50:56,260 --> 00:51:03,690
+واحد بصير عندنا هنا S زائد واحد ناقص S زائد واحد
+
+448
+00:51:03,690 --> 00:51:09,670
+شكل لأن هذا أظن هذا كله مش لازم الآن
+
+449
+00:51:21,730 --> 00:51:27,930
+طيب يبقى أصبح شكل ال X as a function of S يساوي
+
+450
+00:51:38,130 --> 00:51:43,590
+هذه البنات بتروح سالب S وموجب S مع السلامة بيظل
+
+451
+00:51:43,590 --> 00:51:48,330
+واحد وواحد اتنين مع المص الله سهل عليه يبقى بيظل
+
+452
+00:51:48,330 --> 00:51:53,530
+عندي قداش بس واحد على S تربيع ناقص واحد يبقى بيظل
+
+453
+00:51:53,530 --> 00:52:01,390
+عندي هنا اللي هو ناقص واحد على S تربيع و هنا زائد
+
+454
+00:52:01,390 --> 00:52:05,110
+واحد على S تربيع ناقص واحد
+
+455
+00:52:09,100 --> 00:52:17,980
+يبقى صرتي النتيجة S على S تربيع ناقص واحد ناقص E
+
+456
+00:52:17,980 --> 00:52:26,060
+أس ناقص S في واحد على S تربيع وهنا زائد E أس ناقص
+
+457
+00:52:26,060 --> 00:52:34,910
+S في واحد على S تربيع ناقص الواحد الآن بقدر اجيب
+
+458
+00:52:34,910 --> 00:52:41,710
+Laplace ل plus المعكوس تبعهم و اشوف كده بده يساوي هذا
+
+459
+00:52:41,710 --> 00:52:49,290
+بيصير ال X of .. بدي ال X of T ال solution X of T
+
+460
+00:52:49,290 --> 00:52:56,730
+يساوي ل plus inverse ل Laplace ل capital X of S و
+
+461
+00:52:56,730 --> 00:53:04,730
+يساوي ل plus inverse ل ال Sعلى S تربيع ناقص واحد
+
+462
+00:53:04,730 --> 00:53:13,630
+ناقص Laplace inverse لمين؟ لل E أس ناقص S في واحد
+
+463
+00:53:13,630 --> 00:53:22,290
+على S تربيع وهنا زائد Laplace inverse لل E أس ناقص
+
+464
+00:53:22,290 --> 00:53:28,490
+S في واحد على S تربيع ناقص واحد بالشكل اللي عندنا
+
+465
+00:53:30,740 --> 00:53:39,060
+هعطيك الجواب النهائي وانت تجيبيه لحالك ها طيب
+
+466
+00:53:39,060 --> 00:53:45,820
+مالكيش بلاش يبقى هذا الكلام يساوي بدالي الآن لل S
+
+467
+00:53:45,820 --> 00:53:51,520
+على S تربيع ناقص واحد حد ممكن تقولي مين هي؟ مين
+
+468
+00:53:51,520 --> 00:53:57,180
+قالك ان ال cosine بالزائد المقام هذا منها cos cos
+
+469
+00:53:57,180 --> 00:54:04,690
+ati و ال a بقدراش بواحد يبقى هذا بقدر اقول هذا t
+
+470
+00:54:04,690 --> 00:54:08,410
+فقط
+
+471
+00:54:08,410 --> 00:54:16,770
+لا غير نيجي لناقص بدي ل plus inverse لل E أُس ناقص
+
+472
+00:54:16,770 --> 00:54:21,150
+S واحد على S تربيع يالا شوفيلي
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/2VZjLKgeRAs_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/2VZjLKgeRAs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..db63faafb4446fc23baa70c31e69acf6a153f8f9
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/2VZjLKgeRAs_postprocess.srt
@@ -0,0 +1,1584 @@
+1
+00:00:19,840 --> 00:00:25,640
+بسم الله الرحمن الرحيم ابتداء من section 5-2 وحتى
+
+2
+00:00:25,640 --> 00:00:31,340
+هذه اللحظة واحنا بنشتغل على معادلة خطية من الرثب
+
+3
+00:00:31,340 --> 00:00:36,680
+النونية بمعاملات ثابتة المعاملات المتغيرة حتى الآن
+
+4
+00:00:36,680 --> 00:00:41,220
+ماعناش علاقة فيهاورحنا فرضنا ان الحل بيكون على
+
+5
+00:00:41,220 --> 00:00:46,440
+صيغة Y تساوي E اصار X ومنها جيبنا المعادلة المميزة
+
+6
+00:00:46,440 --> 00:00:50,560
+لهذه المعادلة فكانت على الشكل التالي قلنا هذه
+
+7
+00:00:50,560 --> 00:00:55,160
+المعادلة لها احدى ثلاث حالاتيمكن أن تكون الجذور
+
+8
+00:00:55,160 --> 00:01:02,440
+حقيقية ومختلفة ويمكن أن تكون الجذور حقيقية ومكررة
+
+9
+00:01:02,440 --> 00:01:07,840
+وقد تكون complex ومكررة والله أعلم كما سنراه ويمكن
+
+10
+00:01:07,840 --> 00:01:13,780
+أن تكون اللي هو complex يبقى يا إما حقيقية ومختلفة
+
+11
+00:01:13,780 --> 00:01:19,260
+يا إما حقيقية ومكررة أو complex ومكررة يا إما
+
+12
+00:01:19,260 --> 00:01:23,940
+complex فقطدراسة في المحاضرة الماضية والمحاضرة
+
+13
+00:01:23,940 --> 00:01:29,640
+السابقة الحالتين الأولين وهي لو كانت الجذور حقيقية
+
+14
+00:01:29,640 --> 00:01:36,240
+ومختلفة وكذلك لو كانت الجذور تخيّلية واليوم بدنا
+
+15
+00:01:36,240 --> 00:01:41,660
+ناخد لو كانت الجذور حقيقية ومكررة أو complex
+
+16
+00:01:41,660 --> 00:01:46,540
+ومكررةفبقى بقول اللى كنا اللى بدنابه الين هو اللى
+
+17
+00:01:46,540 --> 00:01:49,740
+بدنابه المرة اللى فاتت و اللى قبلها فقولنا افترض
+
+18
+00:01:49,740 --> 00:01:53,820
+ان E و Star X هو عبارة عن حل المعادلة لرقم Star
+
+19
+00:01:53,820 --> 00:01:56,840
+جيبنا المشتقة الأولى و التانية و التالتة و الرابعة
+
+20
+00:01:56,840 --> 00:02:00,510
+أنونية و عوضنا في المعادلة و اختصرناوصلنا إلى
+
+21
+00:02:00,510 --> 00:02:03,330
+المعادلة رقم star اللى سميتها ال auxiliary
+
+22
+00:02:03,330 --> 00:02:06,910
+equation المعادلة المساعدة او ال characteristic
+
+23
+00:02:06,910 --> 00:02:13,010
+equation المعادلة المميزة للمعادلة star تمام؟ if
+
+24
+00:02:13,010 --> 00:02:15,590
+the roots of this equation are repeated then we
+
+25
+00:02:15,590 --> 00:02:19,910
+have two cases يبقى إذا الجذور مكررة في عندي
+
+26
+00:02:19,910 --> 00:02:23,870
+حالتين الحالة الأولى حالة ال real repeated والحالة
+
+27
+00:02:23,870 --> 00:02:28,930
+الثانية حالة ال complex repeatedإذا لو كانت الجذور
+
+28
+00:02:28,930 --> 00:02:34,690
+حقيقية ومكررة الحالة الأولى يبقى r1 هيسوي r2 هيسوي
+
+29
+00:02:34,690 --> 00:02:42,330
+r3 هيسوي rn ويساوي rz يبقى الحل الأول E أُس R X
+
+30
+00:02:42,330 --> 00:02:49,310
+الحل الثاني E أُس R Xيبقى أنا بكرر يبقى بضربه بس
+
+31
+00:02:49,310 --> 00:02:55,130
+في X X E أُصار X الحل التالت X تربيه E أُصار X
+
+32
+00:02:55,130 --> 00:02:59,530
+الحل الرابع X تكعيب E أُصار X لو جبت ده جيب الحل
+
+33
+00:02:59,530 --> 00:03:01,850
+طبعا هدول لو روحت حسبهم بلاقيهم كلهم linearly
+
+34
+00:03:01,850 --> 00:03:05,850
+independentيبقى شكل الحل العام في هذه الحالة بيكون
+
+35
+00:03:05,850 --> 00:03:12,570
+على صورة C1 زي C2X زي C3X تربية زي CNX أُس الناقص
+
+36
+00:03:12,570 --> 00:03:17,430
+واحد E أُس R اللي طلعت عند هنا اللي تبعت تقرار
+
+37
+00:03:17,430 --> 00:03:22,050
+يبقى هذا شكل الحل العام لو كانت الجذور حقيقية
+
+38
+00:03:22,050 --> 00:03:27,840
+ومكررةطب لو كانت complex نجي للحالات التانية if
+
+39
+00:03:27,840 --> 00:03:31,780
+the roots are repeated complex conjugate يبقى هي
+
+40
+00:03:31,780 --> 00:03:37,700
+مكررة وفي نفس الوقت complex وقلنا إذا في عندي جذر
+
+41
+00:03:37,700 --> 00:03:42,520
+complex يبقى الجذر المرافق له برضه موجوديبقى حيكون
+
+42
+00:03:42,520 --> 00:03:49,640
+عندي فيه تكرار لكمبليكس والكونجوجت تبعه تمام؟ يبقى
+
+43
+00:03:49,640 --> 00:03:54,760
+ما هو شكل الحل في هذه الحلقة بقول E أُس X في حتة
+
+44
+00:03:54,760 --> 00:03:58,620
+الكمبليكس المرة اللي فاتت قولنا E أُس X C1 Cos X
+
+45
+00:03:58,620 --> 00:04:02,520
+وC2 Sin X مش شكل ال section الماضي طب الأول لما
+
+46
+00:04:02,520 --> 00:04:06,080
+كان عندي تكرار بدي أعمله بمعاملة التكرار اللي
+
+47
+00:04:06,080 --> 00:04:13,210
+أخدناه وياه ال repeatedبعد كتابة الكمبيوتر
+
+48
+00:04:13,210 --> 00:04:22,330
+الاصلية EOSEXEOSEX
+
+49
+00:04:24,230 --> 00:04:28,270
+CS X أُس S ماينس الواحد
+
+50
+00:04:42,570 --> 00:04:46,950
+بقول لك أه ما هم النص هم النص التالي المرافق تمام؟
+
+51
+00:04:46,950 --> 00:04:51,850
+إذا راحت قلت هنا CSX أُس S minus ال one في cosine
+
+52
+00:04:51,850 --> 00:04:58,590
+ال BX زائد برضه polynomial تانية B1 B2 X B3 X
+
+53
+00:04:58,590 --> 00:05:05,770
+تربية لغاية BSX أُس S minus one في sine ال BXيبقى
+
+54
+00:05:05,770 --> 00:05:10,070
+إذا عندي تكرار في ال complex هي الصيغة إذا في عندي
+
+55
+00:05:10,070 --> 00:05:14,630
+تكرار في ال real يبقى الصيغة اللي فوق خلاصنا هيك
+
+56
+00:05:14,630 --> 00:05:17,970
+بيكون غطينا ال section إذا ال rules كانت real and
+
+57
+00:05:17,970 --> 00:05:22,170
+repeated أو complex and repeated كما سنرى الآن من
+
+58
+00:05:22,170 --> 00:05:26,610
+خلال الأمثلة حد فيكم تحب تسأل أسئلة قبل أن ندخل
+
+59
+00:05:26,610 --> 00:05:28,170
+إلى الأمثلة؟
+
+60
+00:05:30,210 --> 00:05:33,850
+طيب نجي للمثال الأول اللي هو السؤال 9 من الكتاب
+
+61
+00:05:33,850 --> 00:05:36,210
+بقول هات لل general solution لل differential
+
+62
+00:05:36,210 --> 00:05:40,110
+equation اللي عندنا هذه بروح تسميتها star يبقى
+
+63
+00:05:40,110 --> 00:05:44,310
+الخطوة الأولى بدي أبدأ زي ما بدأت هنا بدي أقوله
+
+64
+00:05:44,310 --> 00:05:54,030
+let Y تساوي E أُص RX be a solution of the
+
+65
+00:05:54,030 --> 00:05:59,530
+differential equation star then
+
+66
+00:06:02,030 --> 00:06:09,570
+يبقى ثم المعادلة
+
+67
+00:06:09,570 --> 00:06:18,050
+المميزة L هي R تكييب ناقص ستة R تربيع زائد اتناشر
+
+68
+00:06:18,050 --> 00:06:25,500
+R ناقص تمانية يسوى كم؟ يسوى Zeroنحلل هذه المعادلة
+
+69
+00:06:25,500 --> 00:06:29,700
+من الدرجة الثالثة لما نحلل هذه المعادلة من الدرجة
+
+70
+00:06:29,700 --> 00:06:35,320
+الثالثة لما نحلل هذه المعادلة من الدرجة الثالثة
+
+71
+00:06:35,320 --> 00:06:40,460
+لما نحلل هذه المعادلة من الدرجة الثالثة لما نحلل
+
+72
+00:06:40,460 --> 00:06:45,800
+هذه المعادلة
+
+73
+00:06:45,800 --> 00:06:51,400
+من الدرجة الثالثةوإذا وصلت للثانية بكل أمر إيه سهل
+
+74
+00:06:51,400 --> 00:06:56,040
+جدا في هذه الحالة يبقى في الحالة اللي عندها دي لو
+
+75
+00:06:56,040 --> 00:07:01,760
+جيت أخد مثلا R تكيب ناقص تمانية مع بعض في جزء
+
+76
+00:07:01,760 --> 00:07:10,080
+الباقي هذا أخد منه مثلا ناقص ستة R عامل مشترك بضل
+
+77
+00:07:10,080 --> 00:07:16,880
+قداش عندي R ناقص اتنين كله بده يساوي Zeroأخذت ال
+
+78
+00:07:16,880 --> 00:07:21,420
+term الأول والأخر مع بعضهما في قوس و الباقي أخذتهم
+
+79
+00:07:21,420 --> 00:07:25,200
+في قوس ثاني و من القوس التاني أخذت سالب ستة أر
+
+80
+00:07:25,200 --> 00:07:30,090
+عامل مشترك هذا القوس الأول عبارة عن ايه؟فرق بين
+
+81
+00:07:30,090 --> 00:07:34,970
+المكعبين يبقى
+
+82
+00:07:34,970 --> 00:07:42,970
+هاي R ناقص اتنين في R ترابيع زائد اتنين R زائد
+
+83
+00:07:42,970 --> 00:07:49,070
+اربعة ناقص ستة R في R ناقص اتنين كله يساوي Zero
+
+84
+00:07:49,700 --> 00:07:55,340
+ممكن اخد الار ناقص اتنين عامل ومشترك من الكل يبقى
+
+85
+00:07:55,340 --> 00:08:00,920
+ار ناقص اتنين عامل مشترك بيظل ار تربيع زائد اتنين
+
+86
+00:08:00,920 --> 00:08:07,460
+ار زائد اربعة ناقص ستة ار هذا كله يساوي زيرو اذا
+
+87
+00:08:07,460 --> 00:08:15,960
+هذه ار ناقص اتنين في ار تربيع ناقص اربعة ار زائد
+
+88
+00:08:15,960 --> 00:08:23,210
+اربعة كله يساوي زيروهذا معناه ان ر ناقص اتنين وهذه
+
+89
+00:08:23,210 --> 00:08:29,350
+معناته ر ناقص اتنين الكل تربيع يسوى من؟ Zero يبقى
+
+90
+00:08:29,350 --> 00:08:35,450
+معناته ر ناقص اتنين الكل تكييب يسوى قداش؟ Zero إذا
+
+91
+00:08:35,450 --> 00:08:41,230
+صار الجدر اللي عندي حقيقي و الله تخيلي حقيقي مكرر
+
+92
+00:08:41,230 --> 00:08:47,590
+كم مرة؟يبقى بروح بقوله ان هذا بده يعطينا ان ال R
+
+93
+00:08:47,590 --> 00:08:54,570
+تساوي 2 of multiplicity
+
+94
+00:08:54,570 --> 00:08:55,950
+3
+
+95
+00:08:59,930 --> 00:09:06,230
+أو تلاتة مكرر ايه تلات مرات يبقى كويس يبقى انا
+
+96
+00:09:06,230 --> 00:09:11,750
+طالع عندي حقيقي و مكرر اي صيغة الحقيقي و مكرر بروح
+
+97
+00:09:11,750 --> 00:09:17,530
+بقوله the general solution
+
+98
+00:09:38,390 --> 00:09:45,990
+مثال رقم 2 هو
+
+99
+00:09:45,990 --> 00:09:51,880
+سؤال 17 من الكتابيقول لي y to the derivative of IV
+
+100
+00:09:51,880 --> 00:09:58,920
+زائد اتنين y double prime زائد ال y كل هذا بده
+
+101
+00:09:58,920 --> 00:10:08,620
+يساوي كده؟ بده يساوي زيو يبقى solution let
+
+102
+00:10:08,620 --> 00:10:20,330
+y تساوي e قص rx be a solution of theDifferential
+
+103
+00:10:20,330 --> 00:10:25,270
+equation star مين هي ال star اللي هي المعادلة
+
+104
+00:10:25,270 --> 00:10:30,710
+الأصلية اللي عندنا معناته بدي أجيب المعادلة
+
+105
+00:10:30,710 --> 00:10:37,110
+المساعدة the characteristic equation of the
+
+106
+00:10:37,110 --> 00:10:46,240
+equation star is يبقى R أس كذا شبنات هذهIV كده
+
+107
+00:10:46,240 --> 00:10:55,800
+يعني؟ 4 زائد 2 R تربية زائد 1 يساوي 0 اظن هذه
+
+108
+00:10:55,800 --> 00:11:01,740
+عبارة عن مين؟ عبارة عن R تربية زائد 1 لكل تربية
+
+109
+00:11:01,740 --> 00:11:07,740
+يساوي مين؟ يساوي 0 يبقى الجزر الحياة طلع عندي مكرر
+
+110
+00:11:07,740 --> 00:11:15,040
+كم مرة؟ كده؟كم مرة الجدر مكرر؟ مرتين وبتطلع لل أُس
+
+111
+00:11:15,040 --> 00:11:19,680
+اللي عندي قداش عندي أُس قداش عندي عدد مراتي
+
+112
+00:11:19,680 --> 00:11:24,220
+التكرار تمام يبقى بناء عليه بس تعالى نشوف الجدر
+
+113
+00:11:24,220 --> 00:11:29,920
+هذا قداش يبقى هذا ال R تربية زائد واحد يساوي Zero
+
+114
+00:11:29,920 --> 00:11:34,800
+يبقى ال R تربية يساوي سالب واحد يبقى ال R تساوي
+
+115
+00:11:34,800 --> 00:11:45,130
+زائد او ناقص I تمامwith repeated
+
+116
+00:11:45,130 --> 00:11:53,750
+والله that repeated that repeated
+
+117
+00:11:53,750 --> 00:11:57,670
+two times
+
+118
+00:12:00,210 --> 00:12:04,910
+يبقى يا بقول العبارة هذه مكرر مرتين يا بقول
+
+119
+00:12:04,910 --> 00:12:10,170
+العبارة اللي عندنا هذه with multiplicity 3 يبقى
+
+120
+00:12:10,170 --> 00:12:13,730
+صيغة هذه او صيغة هذه لاتنين are the same نفس
+
+121
+00:12:13,730 --> 00:12:19,890
+الصيغة اللي عندنا هذه تمام؟ طيب، الآن يبقى بناء
+
+122
+00:12:19,890 --> 00:12:23,590
+عليه بيصير ال general solution على الشكل التالف
+
+123
+00:12:23,590 --> 00:12:27,770
+يبقى the general solution
+
+124
+00:12:45,370 --> 00:12:51,990
+يبقى بطير الأولى بظل بس ما يأتي هنا مكرر كم مرة
+
+125
+00:12:53,530 --> 00:13:03,930
+يبقى c1 زائد c2x في cosine ال x لأن b عندنا يعني a
+
+126
+00:13:03,930 --> 00:13:14,070
+تساوي zero و b تساوي واحد زائد b1 زايد b2x في sin
+
+127
+00:13:14,070 --> 00:13:21,430
+x بالشكل اللي عندنا هذا example
+
+128
+00:13:21,430 --> 00:13:21,870
+3
+
+129
+00:13:27,460 --> 00:13:36,040
+Y to the derivative of V زائد اربعة Y تكعيب او Y
+
+130
+00:13:36,040 --> 00:13:41,980
+to the derivative of V3 بده يساوي زيلة نفس التكتيك
+
+131
+00:13:41,980 --> 00:13:45,900
+اللي عملته فوق حتى تبقى هنا بالضبط تماما يبقى حاجة
+
+132
+00:13:45,900 --> 00:13:52,400
+اقوله solution بعد ما سمي هذا المعادلة رقم star
+
+133
+00:13:53,240 --> 00:14:03,440
+Assume that the solution of
+
+134
+00:14:04,340 --> 00:14:14,240
+The equation star is y تساوي u star x بناء عليه
+
+135
+00:14:14,240 --> 00:14:24,140
+The characteristic equation is أرقص خمسة زائد
+
+136
+00:14:24,140 --> 00:14:28,640
+أربعة R تكيب زائد أربعة
+
+137
+00:14:31,980 --> 00:14:37,860
+زاد اربعة ار تكييب بده يساوي مين بده يساوي زيرو
+
+138
+00:14:37,860 --> 00:14:41,460
+يبقى
+
+139
+00:14:41,460 --> 00:14:46,360
+بناء عليه لو أخدت ار تكييب عامل مشترك بيظل ار
+
+140
+00:14:46,360 --> 00:14:53,080
+تربيع زاد جداش زاد اربعة بده يساوي زيرو يبقى
+
+141
+00:14:53,080 --> 00:14:58,120
+الأولى مكررة كام مرة وجداش حقيقية ولا complex
+
+142
+00:15:02,290 --> 00:15:12,070
+يبقى هنا R واحد تساوي R اتنين تساوي R تلاتة والله
+
+143
+00:15:12,070 --> 00:15:16,470
+R واحد تساوي
+
+144
+00:15:16,470 --> 00:15:21,910
+Zero of Multiplicity
+
+145
+00:15:21,910 --> 00:15:25,350
+of three and
+
+146
+00:15:26,950 --> 00:15:35,030
+And الـ R تساوي التانية اللي هو زائد او ناقص 2I
+
+147
+00:15:35,030 --> 00:15:39,930
+لما اخد الجدر التربيعي لأ باطلع زائد او ناقص 2I
+
+148
+00:15:39,930 --> 00:15:45,790
+يبقى بناء عليه بده اكتب ال general solution لمن
+
+149
+00:15:45,790 --> 00:15:48,690
+لهذه المعادلة
+
+150
+00:15:57,470 --> 00:16:07,130
+يبقى باجي بقوله the general solution of the
+
+151
+00:16:07,130 --> 00:16:15,770
+differential equation star is y to the seventh
+
+152
+00:16:16,710 --> 00:16:24,930
+الأولى real و مكرر تلت مرات يبقى اش بقوله C1 C2 X
+
+153
+00:16:24,930 --> 00:16:31,550
+C3 X تربية في E أس Zero نفجر دايش بواحد انسى
+
+154
+00:16:31,550 --> 00:16:37,070
+الباقى من Complex يبقى زائد C4
+
+155
+00:16:49,580 --> 00:16:54,960
+المثال الرابع عبارة عن سؤال أتينا به في إحدى
+
+156
+00:16:54,960 --> 00:17:03,400
+الامتحانات بيقول suppose that افترض
+
+157
+00:17:03,400 --> 00:17:05,500
+انه suppose that
+
+158
+00:17:08,290 --> 00:17:21,190
+الـ L of Y بدو يساوي 0 is a homogeneous linear
+
+159
+00:17:21,190 --> 00:17:24,350
+differential
+
+160
+00:17:24,350 --> 00:17:30,370
+equation with
+
+161
+00:17:30,370 --> 00:17:37,450
+constant coefficients with constant
+
+162
+00:17:43,160 --> 00:17:46,180
+بمعاملات ثابتة بمعاملات ثابتة بمعاملات ثابتة of
+
+163
+00:17:46,180 --> 00:17:59,460
+order 11 which has a
+
+164
+00:17:59,460 --> 00:18:01,420
+characteristic equation
+
+165
+00:18:08,660 --> 00:18:20,420
+الـ P of R بدي ساوي R زائد اتنين و R ناقص تلاتة أس
+
+166
+00:18:20,420 --> 00:18:30,400
+أربعة و R ترابيع زائد اتنين R زائد خمسة لكل تكيب
+
+167
+00:18:30,400 --> 00:18:37,820
+هذا الكلام بدي ساوي قداش Zero Find the
+
+168
+00:18:38,660 --> 00:18:50,580
+General solution of the given differential
+
+169
+00:18:50,580 --> 00:18:52,620
+equation
+
+170
+00:19:20,490 --> 00:19:27,810
+السؤال مرتين بقول كل اللي قعدت كتبة تسميهم هنا؟
+
+171
+00:19:27,810 --> 00:19:34,170
+قول كيف اللي جامد كتب و أنت لأ يعني؟ يلا كل أحد
+
+172
+00:19:34,170 --> 00:19:38,030
+اسمه رقم اليامي، اللي ماكتبش تكتب، علي بالك هنا
+
+173
+00:19:39,800 --> 00:19:44,180
+سؤال جلبناه في إحدى الامتحانات يقول ما يأتي طبعا
+
+174
+00:19:44,180 --> 00:19:47,200
+هذا بنشوف هل الطالب أنا بهمنش يجيب المعادلة أنا
+
+175
+00:19:47,200 --> 00:19:50,720
+أعطيته المعادلة بس بده يشوفه بيعرف يجيب الحل ولا
+
+176
+00:19:50,720 --> 00:19:56,580
+لا كاللي أنا عندي معادلة تفاضلية على الشكل L of Y
+
+177
+00:19:56,580 --> 00:19:59,800
+الساوية Zero هذه homogeneously in differential
+
+178
+00:19:59,800 --> 00:20:08,620
+equationو بحيث ال order ايه اللي هيسوي 11 يعني هذه
+
+179
+00:20:08,620 --> 00:20:13,880
+معادلة من الرتبة الحادية عشرة تمام حسبنا ال
+
+180
+00:20:13,880 --> 00:20:16,940
+characteristic equation اللي هي فلجيناها على الشكل
+
+181
+00:20:16,940 --> 00:20:21,260
+R زائد اتنين R نقص تلتة كل قصر اربعة R تربية زائد
+
+182
+00:20:21,260 --> 00:20:26,760
+اتنين R زائد خمسة لكل تكييب يساوي Zero قال لي هتلي
+
+183
+00:20:26,760 --> 00:20:31,040
+حل المعادلة الأصلية ايه ال characteristic equation
+
+184
+00:20:31,040 --> 00:20:36,920
+هذههي تبعدت اللي قدامك. قبل المبدأ حل هل المعادلة
+
+185
+00:20:36,920 --> 00:20:40,780
+هذه من الرتبة الحادية عشرة؟ من الدرجة الحادية
+
+186
+00:20:40,780 --> 00:20:45,920
+عشرة؟ طب كيف؟ هي واحد واربعة وخمسة وثلاثة تمانية
+
+187
+00:20:47,520 --> 00:20:53,620
+هذه complex و ال complex بيكون تلاتة إذا عندي هي
+
+188
+00:20:53,620 --> 00:20:57,920
+من الدرجة التانية يبقى واحد complex والتاني
+
+189
+00:20:57,920 --> 00:21:01,580
+complex conjugate تمام الكلتة كاي بيبقى هذا مكرر
+
+190
+00:21:01,580 --> 00:21:05,540
+تلات مرات و هذا تلات مرات يبقى المجموع ستة وأربعة
+
+191
+00:21:05,540 --> 00:21:11,360
+عشرة واحد احداشر يبقى هيك شغل سليم مئة بالمئةيبقى
+
+192
+00:21:11,360 --> 00:21:17,100
+باجي بقوله الحل انا عند ال R زائدي اتنين في ال R
+
+193
+00:21:17,100 --> 00:21:22,760
+ناقص تلاتة لكل قص اربعة في R تربية زائدي اتنين R
+
+194
+00:21:22,760 --> 00:21:27,300
+زائد خمسة لكل تكريم بيساوي جداش يساوي Zero يبقى
+
+195
+00:21:27,300 --> 00:21:31,760
+بناء عليه ال R الأولى بيبقى تساوي جداش سالي باتنين
+
+196
+00:21:31,760 --> 00:21:37,970
+وال R التانى بيبقى تساوي جداش بس مكررة جداشيبقى
+
+197
+00:21:37,970 --> 00:21:43,770
+هذا of multiplicity
+
+198
+00:21:43,770 --> 00:21:53,310
+four مكره رابع مرات andالاخيرة R تساوي هذا مالناش
+
+199
+00:21:53,310 --> 00:21:58,510
+نحلها بالقانون لإنه لا يمكن تحليلها يبقى ناقص باء
+
+200
+00:21:58,510 --> 00:22:05,290
+زائدة وناقص الجذر التربيعي لباء تربيع ناقص أربعة
+
+201
+00:22:05,290 --> 00:22:12,580
+ألف بواحد جيمب خمسة كله على اتنين في واحديبقى R
+
+202
+00:22:12,580 --> 00:22:18,120
+الأخيرة هذه بدها تساوي سالي باتنين زاد او ناقص
+
+203
+00:22:18,120 --> 00:22:22,740
+اربعة في الخمسة عشرين بالسالب شيل منهم اربعة
+
+204
+00:22:22,740 --> 00:22:29,800
+بالسلب ستاشت تحت الجدر اربعة I يبقى زاد او ناقص
+
+205
+00:22:29,800 --> 00:22:35,700
+اربعة I كله على اتنين يعني ناقص واحد زاد او ناقص
+
+206
+00:22:35,700 --> 00:22:46,310
+اتنين I هذا مكرر كم مرةتلات مرات تمام يبقى الجدر
+
+207
+00:22:46,310 --> 00:22:50,530
+الأول مكرر تلات مرات و ال conjugate تبعه مكرر تلات
+
+208
+00:22:50,530 --> 00:22:58,390
+مرات يبقى هذا is of multiplicity
+
+209
+00:22:58,390 --> 00:23:03,970
+three مدام هيك إذا بقدر أجيب من ال general
+
+210
+00:23:03,970 --> 00:23:10,670
+solution يبقى بروح بقوله the general solution
+
+211
+00:23:12,490 --> 00:23:23,850
+of the equation L of Y بده يستوي Zero as Y تسوى
+
+212
+00:23:25,470 --> 00:23:34,770
+الحل الأول يبقى C1E-2X مالوش داعو هذا بيختلف عن
+
+213
+00:23:34,770 --> 00:23:42,410
+اللي بعده اللي بعده مكرر أربع مرات يبقى زائد C2
+
+214
+00:23:42,410 --> 00:23:54,860
+زائد C3X زائد C4X تربية زائد C5X تكعيدكل هذا مضروف
+
+215
+00:23:54,860 --> 00:24:04,280
+في كده؟ في EOS 3X يبقى هذا ريال مرات أربع مرات
+
+216
+00:24:04,280 --> 00:24:08,340
+خلصنا منه يبقى خلصنا من الريال ضايل عليه لمين؟
+
+217
+00:24:08,340 --> 00:24:15,840
+ضايل علينا ال complex يبقى زائد الآن ال A عندى
+
+218
+00:24:15,840 --> 00:24:24,850
+كده؟مثال بواحد يبقى E أُس ناقص X أفتح يقوس الآن
+
+219
+00:24:24,850 --> 00:24:30,590
+هذا مكرر كده؟ تلات مرات خلصنا السيهات يبقى بقدر
+
+220
+00:24:30,590 --> 00:24:38,470
+أقولهم إيه؟ E واحد زائد E اتنين X زائد E تلاتة X
+
+221
+00:24:38,470 --> 00:24:47,800
+تربيع هي التلاتة في Cos PX كده ال P؟بتنين يبقى
+
+222
+00:24:47,800 --> 00:24:59,020
+اتنين اكس زائد بواحد زائد باتنين اكس زائد بتلاتة
+
+223
+00:24:59,020 --> 00:25:07,940
+اكس تربيع كله هدمين في sign اتنين اكسالشكل اللي
+
+224
+00:25:07,940 --> 00:25:12,460
+عندنا يبقى هذا شكل ال general solution يبقى هذا ما
+
+225
+00:25:12,460 --> 00:25:16,580
+شاء الله جيبليه تلت حالات كلهم بسؤال واحد ليش؟ لأن
+
+226
+00:25:16,580 --> 00:25:21,380
+الأول مختلف عن الجذور المختلفة التاني rear وانقرر
+
+227
+00:25:21,380 --> 00:25:25,950
+أربع مراتهذا الكمبليكس مكرر تلات مرات يبقى هذا
+
+228
+00:25:25,950 --> 00:25:28,530
+السؤال جاب لهذا ال section و ال two sections
+
+229
+00:25:28,530 --> 00:25:34,670
+الماضية كلها بسؤال واحد و لذلك بنيجي نقول انتهى
+
+230
+00:25:34,670 --> 00:25:39,770
+هذا ال section و إلي كنا أرقام المسائل ل exercises
+
+231
+00:25:39,770 --> 00:25:47,990
+5-4 المسائل التالية اللي هو من 1 إلى 25
+
+232
+00:25:50,860 --> 00:25:56,200
+ننتقل الان الى ال section اللى يليه section خمسة
+
+233
+00:25:56,200 --> 00:26:09,080
+خمسة اللى همين كوشي كوشي اويلر equations معدلات
+
+234
+00:26:09,080 --> 00:26:15,960
+كوشي اويلر definition a
+
+235
+00:26:15,960 --> 00:26:20,000
+linear differential
+
+236
+00:26:26,860 --> 00:26:35,040
+الشكل التالي بي نود x to the power n y to the
+
+237
+00:26:35,040 --> 00:26:42,980
+derivative n زاد بيون x أُس n مينوس الوان y to the
+
+238
+00:26:42,980 --> 00:26:49,700
+derivative n مينوس الوانزائد افضل مستمرين لغاية ما
+
+239
+00:26:49,700 --> 00:27:00,260
+نصل الى B N minus one X Y prime زائد B N Y كله بده
+
+240
+00:27:00,260 --> 00:27:09,120
+يساوي Zero هذه المعادلة اللي هي رقم ستة where حيث
+
+241
+00:27:09,120 --> 00:27:15,890
+ال B nodeو ال b1 و لغاية ال bn minus ال one و ال
+
+242
+00:27:15,890 --> 00:27:25,910
+bn هدول كلهم are constants are constants هذه is
+
+243
+00:27:25,910 --> 00:27:33,290
+called بنسميها المعادلة Cauchy-Euler equation يبقى
+
+244
+00:27:33,290 --> 00:27:40,730
+هذه Cauchy-Euler equation
+
+245
+00:27:41,900 --> 00:27:47,200
+معادلة Koshi Euler طب لو حبينا نشوف شكلها في
+
+246
+00:27:47,200 --> 00:27:52,980
+second order كأنه بداخل حلقة خاصة منها in second
+
+247
+00:27:52,980 --> 00:28:07,620
+order in second order the general form الشكل العام
+
+248
+00:28:07,620 --> 00:28:18,210
+of theكوشي اويلر الواقع
+
+249
+00:28:18,210 --> 00:28:28,990
+هو اكس تربيع واي دابل اي برايم زائد الفا اكس واي
+
+250
+00:28:28,990 --> 00:28:33,950
+برايم زائد بيتا واي اكس تربيع اكس تربيع is equal
+
+251
+00:28:33,950 --> 00:28:38,310
+to zero to
+
+252
+00:28:38,310 --> 00:28:40,370
+solve
+
+253
+00:28:42,550 --> 00:28:54,230
+The differential equation is star there are two
+
+254
+00:28:54,230 --> 00:29:00,530
+methods في
+
+255
+00:29:00,530 --> 00:29:09,930
+عندنا طريقتين الطريقة الأولى يبقى first method
+
+256
+00:29:16,350 --> 00:29:29,170
+Change The Differential Equation Into Differential
+
+257
+00:29:29,170 --> 00:29:38,950
+Equation Star Into A
+
+258
+00:29:38,950 --> 00:29:44,450
+Differential Equation With
+
+259
+00:29:47,970 --> 00:29:55,470
+constant coefficients coefficients
+
+260
+00:29:55,470 --> 00:30:03,750
+as follow فالتالي
+
+261
+00:30:03,750 --> 00:30:05,470
+let
+
+262
+00:30:07,020 --> 00:30:14,660
+الـ X بدي يساوي E أُس T هذا بدي لك أنه T تساوي لنا
+
+263
+00:30:14,660 --> 00:30:23,620
+ال X هذا بدي أديلك أنه DT على DX يساوي 1 على X
+
+264
+00:31:05,620 --> 00:31:08,800
+حكينا في ال section اللي فات و اللي جابله و اللي
+
+265
+00:31:08,800 --> 00:31:14,860
+جابله كان في three sections الماضية كله عن مين؟ عن
+
+266
+00:31:14,860 --> 00:31:20,220
+المعادلات اللي المعاملات تبعتها ثوابت بنتقل الآن
+
+267
+00:31:20,220 --> 00:31:26,980
+لو كانت المعادلات المعاملات تبعتها متغيرات و إلها
+
+268
+00:31:26,980 --> 00:31:31,600
+شكل محدد بدنا نعرف مين هو هذا الشكل المحدد و ما هو
+
+269
+00:31:31,600 --> 00:31:36,080
+اسمهفبقول إيش الـ Linear differential equation of
+
+270
+00:31:36,080 --> 00:31:42,120
+the form طلعيلي كويس يبقى هذا ال Xn و Xn-1 و X ..
+
+271
+00:31:42,120 --> 00:31:45,940
+ماكانش موجود في المعادلة السابقة كانوا ال B0 و ال
+
+272
+00:31:45,940 --> 00:31:52,040
+B1 و ال Bn كل هدول ثوابة تمام؟ إذا المعادلة اللي
+
+273
+00:31:52,040 --> 00:31:57,400
+عندي بالشكل هذا X مرفوعة للأس N Y2 نفسي derivative
+
+274
+00:31:57,400 --> 00:32:03,090
+Nوبنبدأ أنزل بي وان X أس وان minus one Y to the
+
+275
+00:32:03,090 --> 00:32:06,970
+derivative of N minus one اللي بعده بي وان X أس
+
+276
+00:32:06,970 --> 00:32:09,710
+وان minus two Y to the derivative of N minus two
+
+277
+00:32:09,710 --> 00:32:13,750
+ضلينا ماشي لغاية ما أوصلنا بي وان minus ال one X
+
+278
+00:32:13,750 --> 00:32:18,730
+أس وان Y prime زائد بي وان ال X صارت أز Zero يعني
+
+279
+00:32:18,730 --> 00:32:25,210
+بواحد بالطير Y تساوي Zero البيهات هدول كلهم ثوابت
+
+280
+00:32:25,360 --> 00:32:29,460
+يبقى اي معادلة على هذا الشكل اللي بسميها Cauchy
+
+281
+00:32:29,460 --> 00:32:33,880
+-Euler equation طب ال Cauchy-Euler equation هذه
+
+282
+00:32:33,880 --> 00:32:38,240
+بدنا نحاول انحلها مش انحلها بدي اقول لو عندي شكل
+
+283
+00:32:38,240 --> 00:32:43,130
+خاص منها لو بدي مثل معادلة من الرتبة الثانيةيبقى
+
+284
+00:32:43,130 --> 00:32:46,650
+باجي يقول المعادلة من الرتبة الثانية شكلها X تربيع
+
+285
+00:32:46,650 --> 00:32:51,230
+و Y W prime المعامل هنا طلع مقداش بواحظ أو كان فيه
+
+286
+00:32:51,230 --> 00:32:55,650
+معامل و جسمنا عليه يبقى صارت X تربيع و Y W prime
+
+287
+00:32:55,650 --> 00:33:00,170
+الدرجة التانية الرتبة الثانية زائد constant اللي
+
+288
+00:33:00,170 --> 00:33:04,090
+هو جسمناه هنا بي وان او بي وان مقسوما على بي نوت
+
+289
+00:33:04,090 --> 00:33:06,450
+سميته Alpha X
+
+290
+00:33:14,840 --> 00:33:20,960
+يبقى كمان هذه المعادلة كوشي اويلر بس من الرتبة ا
+
+291
+00:33:20,960 --> 00:33:26,060
+ثاني تمام الان كيف بنحل المعادلة الأصلية هذه هي
+
+292
+00:33:26,060 --> 00:33:32,690
+starفي اندي هناك طريقتان للحل وحدة الحل بطريقة
+
+293
+00:33:32,690 --> 00:33:38,850
+التعويض التعويض له فائدة ينقل المعادلة من معادلة
+
+294
+00:33:38,850 --> 00:33:44,260
+بمعاملات متغيرة إلى معادلة بمعاملات ثابتةوإذا
+
+295
+00:33:44,260 --> 00:33:48,160
+وصلنا إلى معادلة بمعاملة ثابتة بروح بنحلها بمين؟
+
+296
+00:33:48,160 --> 00:33:51,600
+بالطرق التلاتة اللي فتك complex roots real
+
+297
+00:33:51,600 --> 00:33:55,840
+repeated real and different roots يبقى بأي طريقة
+
+298
+00:33:55,840 --> 00:33:59,520
+من الطرق تلاتة الطريقة الثانية بس نخلص الأولى بصير
+
+299
+00:33:59,520 --> 00:34:03,940
+خير بنروح على تانية طب الطريقة الأولى هذه بقول في
+
+300
+00:34:03,940 --> 00:34:09,350
+أن تعويضة هذه التعويضة بواسطتهابقدر اشيل كل
+
+301
+00:34:09,350 --> 00:34:13,570
+المتغيرات اللى موجودة وين في المعادلة هذه طب ماهي
+
+302
+00:34:13,570 --> 00:34:19,830
+التعويضة هذه؟ مجلبك تحط X يساوي E أس T فقط ده يعني
+
+303
+00:34:19,830 --> 00:34:25,190
+ماذا يترتب على ذلك؟ بقدر أخد لن للطرفين فبصير T
+
+304
+00:34:25,190 --> 00:34:30,190
+تساوي من؟ لن ال X لو جبت DT على DX بصير قداش
+
+305
+00:34:30,190 --> 00:34:35,090
+قيمتها واحدة على X خلّي المعلومة هذه عندك وتعالى
+
+306
+00:34:35,090 --> 00:34:44,770
+لمن؟ للمسألة تبعتناأنا بدي أجيب دي وايعلى DX مش
+
+307
+00:34:44,770 --> 00:34:49,850
+هذه Y' اللي عندنا و بعدين بدي أجيب YW' طبقا لمن؟
+
+308
+00:34:49,850 --> 00:34:54,570
+طبقا للتعويض هذه يعني بدل ما المعادلة كانت بدللة X
+
+309
+00:34:54,570 --> 00:34:59,290
+و Y بدي أخليها بدللة T و Y و أشوف إيش بدي أصير
+
+310
+00:34:59,290 --> 00:35:06,670
+شكلها يبقى هذا الكلام بقدر أقول DY على DT في DT
+
+311
+00:35:06,670 --> 00:35:12,290
+على DXطب ال دي تي على دي إكس بقداش؟ واحد على إكس،
+
+312
+00:35:12,290 --> 00:35:17,630
+يبقى هذا الكلام بده يساوي واحد على إكس في دي واي
+
+313
+00:35:17,630 --> 00:35:24,930
+على دي تيتمام بدنا نجيب المشتقة الثانية يبقى لو
+
+314
+00:35:24,930 --> 00:35:29,790
+جيت أخدت ال D أو ال YW prime هذه اللي هي ال Y
+
+315
+00:35:29,790 --> 00:35:36,310
+prime وهذه ال YW prime يبقى ال YW prime على الشكل
+
+316
+00:35:36,310 --> 00:35:44,190
+التالي اللي هي D square Y على DX square يعني D على
+
+317
+00:35:44,190 --> 00:35:51,360
+DX لDY على DXمش هيك المشتقة التانية خدتها في
+
+318
+00:35:51,360 --> 00:35:57,900
+calculus ايه؟ هذا الكلام بده يساوي دي على دي إكس
+
+319
+00:35:57,900 --> 00:36:01,680
+لمين؟ دي واي على دي إكس هيها جبت من الحالة الأولى
+
+320
+00:36:01,680 --> 00:36:06,180
+ليه جداش؟ واحد على إكس في دي واي على دي تين يبقى
+
+321
+00:36:06,180 --> 00:36:12,780
+واحد على إكس في دي واي على دي تينهذه الأقنعة عبارة
+
+322
+00:36:12,780 --> 00:36:18,340
+عن مشتقة من حاصل ضرب دالتين يبقى مشتقة الأولى في
+
+323
+00:36:18,340 --> 00:36:22,760
+الثانية زايد الأولى في مشتقة الثانية يبقى مشتقة
+
+324
+00:36:22,760 --> 00:36:27,940
+الأولى في جداش سالب واحد على اكس تربيع يبقى هاي
+
+325
+00:36:27,940 --> 00:36:31,800
+سالب واحد على اكس تربيع ليش؟ لأنه بفضلها بالنسبة
+
+326
+00:36:31,800 --> 00:36:36,210
+إلى اكسأنا قاعد أفضلها بالنسبة لـ X في مين؟ في
+
+327
+00:36:36,210 --> 00:36:43,430
+الدالة التانية الـ dy على dt زاد 1 على x كما هي
+
+328
+00:36:43,430 --> 00:36:49,210
+بدي أشتق الدالة التانية اللي هو d على dx اللي
+
+329
+00:36:49,210 --> 00:36:58,230
+عندنا لdy على dtيبقى بناء عليه أصبح عند ال y
+
+330
+00:36:58,230 --> 00:37:05,350
+double prime تساوي اللي هو السالم 1 على x تربيع في
+
+331
+00:37:05,350 --> 00:37:15,350
+dy على dt زائد 1 على x هذي أمانات بقدر أكتبها على
+
+332
+00:37:15,350 --> 00:37:19,210
+الشكل التالي d على dt
+
+333
+00:37:28,420 --> 00:37:34,550
+مظبوط؟الـ D على DX اللي عندنا كتب D على DT في DT
+
+334
+00:37:34,550 --> 00:37:39,710
+على DX D على DT لمين؟ للمقدار اللي عندنا هنا تمام
+
+335
+00:37:39,710 --> 00:37:45,650
+تمام يعني هذه صارت قداش ناقص واحد على X تربيه DY
+
+336
+00:37:45,650 --> 00:37:54,270
+على DT زاد هذه بقداش DT على DX واحد على X إذا بدي
+
+337
+00:37:54,270 --> 00:37:58,730
+أشيل هذه هنا و أحط بدل واحد على X وعندي واحد على X
+
+338
+00:37:59,950 --> 00:38:08,110
+بصير واحد على X تربيع وهذه عبارة عن D²Y على DT²
+
+339
+00:38:08,110 --> 00:38:13,810
+مظبوط يعني كأن المثل واحد على X تربيع خليكي برا
+
+340
+00:38:13,810 --> 00:38:24,830
+وD²Y على DT² ناقص DY على DT مظبوط بنفس الطريقة لو
+
+341
+00:38:24,830 --> 00:38:26,990
+بد المشتاق قد تالتة similarly
+
+342
+00:38:30,730 --> 00:38:36,470
+لو رحت جبت المشتقة التالتة هتساوي اللي هو مين؟
+
+343
+00:38:36,470 --> 00:38:44,870
+واحد على X تكييب فيه اللي هو D تكييب Y على DT
+
+344
+00:38:44,870 --> 00:38:53,450
+تكييب ناقص تلاتة D تربيع Y على DT تربيع زائد اتنين
+
+345
+00:38:53,450 --> 00:38:56,990
+DY على DT
+
+346
+00:39:01,350 --> 00:39:05,850
+طيب استنى شوية لو بدى أجيبه مش هتقرب على بنفس
+
+347
+00:39:05,850 --> 00:39:10,010
+الطريقة أو الخامسة أو السالسة وهلومة جرّع طيب إيش
+
+348
+00:39:10,010 --> 00:39:14,890
+استفدت من هذه؟ انت بتقول هنا هذه التعويضة بدها ضيع
+
+349
+00:39:14,890 --> 00:39:18,290
+لل variable اللي عندنا هذا اللي هو ال X تربيع وال
+
+350
+00:39:18,290 --> 00:39:22,350
+X أو كل ال Xات اللي هنا بتروح لو أعطيكي مثال بسيط
+
+351
+00:39:22,350 --> 00:39:26,890
+خليني مع المعادلة اللي عندنا هذه X تربيع في مين؟
+
+352
+00:39:26,890 --> 00:39:31,250
+في YW prime وين YW prime؟هذا هو الوايضة
+
+353
+00:39:31,250 --> 00:39:35,630
+بالإبراهيم، صح؟ لو كان طلبها فيك السربية، بتروح مع
+
+354
+00:39:35,630 --> 00:39:39,530
+اللي برا، بيظل هذا، يبقى صارة المعادلة with
+
+355
+00:39:45,670 --> 00:39:52,310
+بتحل بيولي المعادلة بمعاملات متغيرة إلى معادلة
+
+356
+00:39:52,310 --> 00:39:57,390
+بمعاملات ثابتة وروح بحل هبمين بالطرق السابقة التي
+
+357
+00:39:57,390 --> 00:40:03,130
+كنت بحل قبها هذه الطريقة الأولىطريقة ثانية برضه
+
+358
+00:40:03,130 --> 00:40:08,070
+بدي اعمل نفس فكرة المعادلة المميزة بس احنا كنا لما
+
+359
+00:40:08,070 --> 00:40:13,430
+كان فش عند X بقولت افترض الحل على صيغة Y تساوي E
+
+360
+00:40:13,430 --> 00:40:20,790
+أُس RX هنا لأ بدي افترض الحل هو Y تساوي X أُس R و
+
+361
+00:40:20,790 --> 00:40:25,330
+بدي اروح اجيب المعادلة المميزة لمين لهذه المعادلة
+
+362
+00:40:25,330 --> 00:40:30,430
+يبقى الحل التاني second solution يبقى second
+
+363
+00:40:34,480 --> 00:40:48,460
+طريقة الثانية بتقول let ال y يساوي x plus r be a
+
+364
+00:40:48,460 --> 00:40:59,760
+solution of the differential equation star on
+
+365
+00:41:01,670 --> 00:41:06,570
+على الفترة من zero لغاية infinity يبقى على x
+
+366
+00:41:06,570 --> 00:41:13,850
+الموجبة فقط then لو بدي y prime يا بنات قدش تزاوي
+
+367
+00:41:13,850 --> 00:41:23,430
+r x أُص r minus ال one لو بدي ال y w primeيبقى R
+
+368
+00:41:23,430 --> 00:41:31,530
+في R-1 في X أُص R-2 لو بدي المشتقة التالتة
+
+369
+00:41:34,070 --> 00:41:45,590
+يجب ان تقوم باستخدام R-1-2-X-R-3 وهلما تجرب اذا
+
+370
+00:41:45,590 --> 00:41:54,530
+جيت للمشتقة النونية او المشتقة رقم M مثلا يجب ان
+
+371
+00:41:54,530 --> 00:42:01,380
+تقوم باستخدامفى R ناقص واحد فى R ناقص اتنين وظل
+
+372
+00:42:01,380 --> 00:42:13,000
+مستمر لوين يا بنات ل R ناقص M زائد واحد اصلا M
+
+373
+00:42:13,000 --> 00:42:17,940
+ناقص واحد وسبقتها اشارة سالف بصير ناقص ال M زائد
+
+374
+00:42:17,940 --> 00:42:26,540
+واحد فى ال X أس R ناقص Mبعد ذلك المعلومات اللي
+
+375
+00:42:26,540 --> 00:42:31,760
+عندي بدي أخدهم و أحوظهم في المعادلة star نحصل على
+
+376
+00:42:31,760 --> 00:42:37,720
+مين؟ على المعادلة المميزة لإيش؟ لأن X أكبر من Zero
+
+377
+00:42:37,720 --> 00:42:43,760
+إذا ما بقدر أقسم ليش كله فيه بيطلع XR و هكذا تمام
+
+378
+00:42:43,760 --> 00:42:56,950
+فبجي بقول من هنا F و سبس تتيود إذا عوضناIn the
+
+379
+00:42:56,950 --> 00:43:08,050
+differential equation A star we get B
+
+380
+00:43:08,050 --> 00:43:16,080
+node Rفى ال R ناقص واحد فى ال R ناقص اتنين ونظل
+
+381
+00:43:16,080 --> 00:43:23,040
+ماشيين لغاية R ناقص ال N زائد ال واحد زائد ضلك
+
+382
+00:43:23,040 --> 00:43:29,780
+ماشي لما توصل لحد قبل الأخير P N ناقص واحد R زائد
+
+383
+00:43:29,780 --> 00:43:35,040
+P N تساوي Zero وهذه المعادلة رقم Star
+
+384
+00:43:39,790 --> 00:43:48,690
+Equation double star is called the
+
+385
+00:43:48,690 --> 00:43:58,010
+characteristic equation of the differential
+
+386
+00:43:58,010 --> 00:44:04,250
+equation star to
+
+387
+00:44:04,250 --> 00:44:06,830
+solve
+
+388
+00:44:09,530 --> 00:44:24,150
+to solve the equation double star we have three
+
+389
+00:44:24,150 --> 00:44:30,850
+cases يبقى هذا يعني الحالة اللي قبل real or
+
+390
+00:44:30,850 --> 00:44:35,130
+different, real repeated او complex بدنا نشوف في
+
+391
+00:44:35,130 --> 00:44:43,120
+كل حالة ما هو شكل الحال اللي عندناCase 1 الحالة
+
+392
+00:44:43,120 --> 00:44:47,500
+الأولى مش
+
+393
+00:44:47,500 --> 00:44:53,120
+هنلعق فبلاش حاضر الجامعه نكمل بس احفظوا المعلومات
+
+394
+00:44:53,120 --> 00:44:58,340
+هذه احصل عليها لإنه بدنا نبني كل شغل عليها تمام
+
+395
+00:44:58,340 --> 00:45:02,780
+يبقى احنا لازلنا في نفس ال section و لنا عودة ان
+
+396
+00:45:02,780 --> 00:45:03,380
+شاء الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..4f6d511f2af31ae11ae48af202d6454975f6eee2
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/6o3WBz-uTLI_raw.json
@@ -0,0 +1 @@
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ما يأتي بدأ أحط سهم و أقول هنا سالب R تلاتة to R اتنين", "tokens": [10721, 8315, 3714, 43020, 5551, 9778, 20292, 34105, 23758, 4018, 4032, 5551, 9778, 20292, 23758, 4018, 7251, 3555, 4587, 7578, 47525, 10721, 5551, 11242, 33911, 31767, 5172, 16712, 6027, 2655, 30731, 31767, 5172, 6024, 104, 7649, 1829, 4724, 9778, 1211, 4587, 4018, 6156, 30543, 7251, 3555, 4587, 7578, 34105, 47525, 8315, 8717, 25957, 1211, 19446, 7251, 10721, 31371, 47525, 10721, 5551, 5016, 9566, 8608, 16095, 4032, 5551, 39648, 34105, 8608, 6027, 3555, 497, 6055, 1211, 9307, 3660, 281, 497, 1975, 2655, 1863, 9957], "avg_logprob": -0.2280506021564915, "compression_ratio": 1.7575757575757576, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 619.51, "end": 619.87, "word": "أنا", "probability": 0.7490234375}, {"start": 619.87, "end": 620.41, "word": " ممكن", "probability": 0.967041015625}, {"start": 620.41, "end": 621.35, "word": " أخلي", "probability": 0.522705078125}, {"start": 621.35, "end": 621.93, "word": 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كمان اضربه في نص و اضيفه للي فوق بالمرة كويس؟", "tokens": [1829, 3555, 4587, 7578, 47525, 7578, 7251, 9381, 13546, 43242, 7578, 19446, 7251, 10721, 31371, 497, 18, 281, 497, 17, 4032, 23758, 13412, 2407, 12602, 10721, 1829, 4117, 9122, 2304, 7649, 1975, 11242, 25513, 3224, 8978, 8717, 9381, 4032, 1975, 11242, 33911, 3224, 5296, 20292, 6156, 30543, 20666, 2304, 25720, 9122, 45865, 3794, 22807], "avg_logprob": -0.32017046213150024, "compression_ratio": 1.296, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 647.63, "end": 648.15, "word": "يبقى", "probability": 0.8438720703125}, {"start": 648.15, "end": 648.49, "word": " بدى", "probability": 0.3656005859375}, {"start": 648.49, "end": 648.75, "word": " يصير", "probability": 0.6991373697916666}, {"start": 648.75, "end": 649.29, "word": " عندى", "probability": 0.785888671875}, {"start": 649.29, "end": 649.53, "word": " ما", "probability": 0.51416015625}, {"start": 649.53, "end": 650.53, "word": " يأتي", "probability": 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هو واحد سالب واحد سالب واحد اتنين Zero الصف التاني هذا صار Zero وهذا ضربته في سالب اتنين بصير هنا Zero وهذا ضربته في سالب اتنين بصير هنا واحد وهنا هذا بصير سالب تلاتة وهذه Zero", "tokens": [20534, 366, 1045, 28242, 3224, 3714, 25720, 36764, 24401, 3660, 7251, 3555, 4587, 7578, 31767, 5172, 16247, 12610, 30767, 1829, 19446, 31439, 36764, 24401, 8608, 6027, 3555, 36764, 24401, 8608, 6027, 3555, 36764, 24401, 1975, 2655, 1863, 9957, 17182, 31767, 5172, 16712, 7649, 1829, 23758, 20328, 9640, 17182, 37037, 15730, 48812, 25513, 47395, 8978, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 4724, 9381, 13546, 34105, 17182, 37037, 15730, 48812, 25513, 47395, 8978, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 4724, 9381, 13546, 34105, 36764, 24401, 37037, 8315, 23758, 4724, 9381, 13546, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 37037, 24192, 17182], "avg_logprob": -0.17585784605905122, "compression_ratio": 2.165714285714286, "no_speech_prob": 1.0728836059570312e-06, "words": [{"start": 2844.48, "end": 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ضربت في سالب تلاتة بصير Zero هذا بصير تلاتة و سالب تلاتة كمان Zero هذا ضربت في سالب تلاتة بصير تلاتة واحد أربعة هذا سالب ستة و سالب ستة بصير سالب أتماشى و هنا Zero", "tokens": [3224, 15730, 48812, 25513, 2655, 8978, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 4724, 9381, 13546, 17182, 23758, 4724, 9381, 13546, 6055, 1211, 9307, 3660, 4032, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 9122, 2304, 7649, 17182, 23758, 48812, 25513, 2655, 8978, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 4724, 9381, 13546, 6055, 1211, 9307, 3660, 36764, 24401, 5551, 25513, 27884, 23758, 8608, 6027, 3555, 8608, 2655, 3660, 4032, 8608, 6027, 3555, 8608, 2655, 3660, 4724, 9381, 13546, 8608, 6027, 3555, 5551, 2655, 2304, 33599, 7578, 4032, 34105, 17182], "avg_logprob": -0.1359374933772617, "compression_ratio": 2.1908396946564888, "no_speech_prob": 0.0, "words": [{"start": 2873.3, "end": 2873.82, "word": "هذا", "probability": 0.76953125}, {"start": 2873.82, "end": 2874.32, "word": " ضربت", "probability": 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سالف اتنين بصير هنا zero وهذا بيصير هنا اتنين وهذا ربطه في سالف اتنين بيصير سالف اربعة يفجر سالف ستة وهنا اتنين وهنا zero اللي ماصارش عندي leading هنا واحد امان طالع صار في أسرار اللي بجهرش أسوي فيها حاجة إذا مداجي على مين؟", "tokens": [2407, 3224, 15730, 4018, 34105, 37037, 15730, 12602, 3555, 9566, 3224, 8978, 8608, 6027, 5172, 1975, 2655, 1863, 9957, 4724, 9381, 13546, 34105, 4018, 37037, 15730, 4724, 1829, 9381, 13546, 34105, 1975, 2655, 1863, 9957, 37037, 15730, 12602, 3555, 9566, 3224, 8978, 8608, 6027, 5172, 1975, 2655, 1863, 9957, 4724, 1829, 9381, 13546, 8608, 6027, 5172, 1975, 25513, 27884, 7251, 5172, 7435, 2288, 8608, 6027, 5172, 8608, 2655, 3660, 37037, 8315, 1975, 2655, 1863, 9957, 37037, 8315, 4018, 13672, 1829, 19446, 9381, 9640, 8592, 18871, 16254, 5775, 34105, 36764, 24401, 1975, 15042, 1863, 23032, 6027, 3615, 20328, 9640, 8978, 5551, 3794, 2288, 9640, 13672, 1829, 4724, 7435, 3224, 2288, 8592, 5551, 3794, 45865, 8978, 11296, 11331, 26108, 3660, 11933, 15730, 3714, 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"probability": 0.95947265625}, {"start": 3217.37, "end": 3217.99, "word": " X", "probability": 0.72607421875}, {"start": 3217.99, "end": 3218.69, "word": " اتنين", "probability": 0.8800048828125}, {"start": 3218.69, "end": 3219.35, "word": " X", "probability": 0.95849609375}, {"start": 3219.35, "end": 3220.21, "word": " تلاتة", "probability": 0.97509765625}, {"start": 3220.21, "end": 3220.71, "word": " X", "probability": 0.95947265625}, {"start": 3220.71, "end": 3222.01, "word": " أربعة", "probability": 0.951171875}, {"start": 3222.01, "end": 3222.91, "word": " أساوية", "probability": 0.715380859375}, {"start": 3222.91, "end": 3223.63, "word": " X", "probability": 0.8876953125}, {"start": 3223.63, "end": 3224.33, "word": " واحد", "probability": 0.98681640625}], "temperature": 1.0}, {"id": 124, "seek": 325299, "start": 3224.71, "end": 3252.99, "text": "اللي هي بقداش طلعناها A زائد الـ B X2 حطناها V X3 ثلاثة A X4 دي A بالشكل اللي عندنا يبقى هذا أصبح الحل طب هل هذا يحتوي على ال trivial solution الإجابة نعم حطيت قيود على A وB", "tokens": [6027, 20292, 39896, 4724, 28543, 33599, 23032, 1211, 3615, 8315, 11296, 316, 30767, 16373, 3215, 2423, 39184, 363, 1783, 17, 11331, 9566, 8315, 11296, 691, 1783, 18, 38637, 1211, 5718, 104, 3660, 316, 1783, 19, 11778, 1829, 316, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 7251, 3555, 4587, 7578, 23758, 5551, 9381, 49628, 21542, 1211, 23032, 3555, 8032, 1211, 23758, 7251, 33753, 45865, 15844, 2423, 26703, 3827, 33688, 7435, 16758, 3660, 8717, 25957, 11331, 9566, 36081, 12174, 1829, 23328, 15844, 316, 4032, 33], "avg_logprob": -0.2786458365264393, "compression_ratio": 1.4659685863874345, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 3224.71, "end": 3225.13, "word": "اللي", "probability": 0.3494873046875}, {"start": 3225.13, "end": 3225.31, "word": " هي", "probability": 0.89697265625}, {"start": 3225.31, "end": 3225.85, "word": " بقداش", "probability": 0.7069498697916666}, {"start": 3225.85, "end": 3226.83, "word": " طلعناها", "probability": 0.93662109375}, {"start": 3226.83, "end": 3228.09, "word": " A", "probability": 0.227783203125}, {"start": 3228.09, "end": 3229.21, "word": " زائد", "probability": 0.5343017578125}, {"start": 3229.21, "end": 3229.57, "word": " الـ", "probability": 0.678466796875}, {"start": 3229.57, "end": 3229.81, "word": " B", "probability": 0.431640625}, {"start": 3229.81, "end": 3231.71, "word": " X2", "probability": 0.7421875}, {"start": 3231.71, "end": 3233.55, "word": " حطناها", "probability": 0.72314453125}, {"start": 3233.55, "end": 3234.03, "word": " V", "probability": 0.342041015625}, {"start": 3234.03, "end": 3235.71, "word": " X3", "probability": 0.90869140625}, {"start": 3235.71, "end": 3237.03, "word": " ثلاثة", "probability": 0.8013427734375}, {"start": 3237.03, "end": 3237.33, "word": " A", "probability": 0.89794921875}, {"start": 3237.33, "end": 3238.91, "word": " X4", "probability": 0.901123046875}, {"start": 3238.91, "end": 3239.85, "word": " دي", "probability": 0.56805419921875}, {"start": 3239.85, "end": 3240.25, "word": " A", "probability": 0.9248046875}, {"start": 3240.25, "end": 3241.17, "word": " بالشكل", "probability": 0.8406575520833334}, {"start": 3241.17, "end": 3241.33, "word": " اللي", "probability": 0.985595703125}, {"start": 3241.33, "end": 3241.81, "word": " عندنا", "probability": 0.876708984375}, {"start": 3241.81, "end": 3242.87, "word": " يبقى", "probability": 0.749755859375}, {"start": 3242.87, "end": 3243.17, "word": " هذا", "probability": 0.92529296875}, {"start": 3243.17, "end": 3243.87, "word": " أصبح", "probability": 0.9718424479166666}, {"start": 3243.87, "end": 3244.69, "word": " الحل", "probability": 0.7301025390625}, {"start": 3244.69, "end": 3245.75, "word": " طب", "probability": 0.77099609375}, {"start": 3245.75, "end": 3246.07, "word": " هل", "probability": 0.973876953125}, {"start": 3246.07, "end": 3246.49, "word": " هذا", "probability": 0.93408203125}, {"start": 3246.49, "end": 3247.13, "word": " يحتوي", "probability": 0.9801432291666666}, {"start": 3247.13, "end": 3247.37, "word": " على", "probability": 0.84814453125}, {"start": 3247.37, "end": 3247.53, "word": " ال", "probability": 0.85888671875}, {"start": 3247.53, "end": 3247.93, "word": " trivial", "probability": 0.470458984375}, {"start": 3247.93, "end": 3249.01, "word": " solution", "probability": 0.95751953125}, {"start": 3249.01, "end": 3250.89, "word": " الإجابة", "probability": 0.8179931640625}, {"start": 3250.89, "end": 3251.21, "word": " نعم", "probability": 0.98046875}, {"start": 3251.21, "end": 3251.81, "word": " حطيت", "probability": 0.8232421875}, {"start": 3251.81, "end": 3252.17, "word": " قيود", "probability": 0.9768880208333334}, {"start": 3252.17, "end": 3252.39, "word": " على", "probability": 0.8349609375}, {"start": 3252.39, "end": 3252.59, "word": " A", "probability": 0.89697265625}, {"start": 3252.59, "end": 3252.99, "word": " وB", "probability": 0.78076171875}], "temperature": 1.0}, {"id": 125, "seek": 328151, "start": 3256.07, "end": 3281.51, "text": "بحصل على حل الصفري اذا صار عندي عدد لنهائي من الحلول system has infinite number of solutions", "tokens": [3555, 5016, 36520, 15844, 11331, 1211, 31767, 5172, 16572, 1975, 15730, 20328, 9640, 18871, 16254, 6225, 3215, 3215, 5296, 1863, 3224, 16373, 1829, 9154, 21542, 1211, 12610, 1185, 575, 13785, 1230, 295, 6547], "avg_logprob": -0.43887867734712716, "compression_ratio": 1.1260504201680672, "no_speech_prob": 0.0, "words": [{"start": 3256.0699999999997, "end": 3257.47, "word": "بحصل", "probability": 0.4536336263020833}, {"start": 3257.47, "end": 3257.65, "word": " على", "probability": 0.845703125}, {"start": 3257.65, "end": 3257.99, "word": " حل", "probability": 0.888916015625}, {"start": 3257.99, "end": 3258.43, "word": " الصفري", "probability": 0.7830403645833334}, {"start": 3258.43, "end": 3262.41, "word": " اذا", "probability": 0.44134521484375}, {"start": 3262.41, "end": 3263.17, "word": " صار", "probability": 0.56829833984375}, {"start": 3263.17, "end": 3263.45, "word": " عندي", "probability": 0.6502685546875}, {"start": 3263.45, "end": 3263.83, "word": " عدد", "probability": 0.9034830729166666}, {"start": 3263.83, "end": 3264.67, "word": " لنهائي", "probability": 0.85185546875}, {"start": 3264.67, "end": 3264.93, "word": " من", "probability": 0.9453125}, {"start": 3264.93, "end": 3265.99, "word": " الحلول", "probability": 0.97900390625}, {"start": 3265.99, "end": 3268.19, "word": " system", "probability": 0.2060546875}, {"start": 3268.19, "end": 3271.39, "word": " has", "probability": 0.340576171875}, {"start": 3271.39, "end": 3274.25, "word": " infinite", "probability": 0.6064453125}, {"start": 3274.25, "end": 3276.61, "word": " number", "probability": 0.923828125}, {"start": 3276.61, "end": 3278.85, "word": " of", "probability": 0.91552734375}, {"start": 3278.85, "end": 3281.51, "word": " solutions", "probability": 0.8828125}], "temperature": 1.0}, {"id": 126, "seek": 330508, "start": 3282.44, "end": 3305.08, "text": "that is this system this system is consistent لازلنا في نفس ال section و لمّا ننتهي بعد للمرة القادمة ان شاء الله تعالى", "tokens": [6780, 307, 341, 1185, 341, 1185, 307, 8398, 5296, 31377, 1211, 8315, 8978, 8717, 36178, 2423, 3541, 4032, 32767, 11703, 995, 8717, 29399, 3224, 1829, 39182, 5296, 19528, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": -0.16367186978459358, "compression_ratio": 1.2954545454545454, "no_speech_prob": 0.0, "words": [{"start": 3282.44, "end": 3282.94, "word": "that", "probability": 0.432861328125}, {"start": 3282.94, "end": 3284.12, "word": " is", "probability": 0.94921875}, {"start": 3284.12, "end": 3286.72, "word": " this", "probability": 0.8583984375}, {"start": 3286.72, "end": 3288.38, "word": " system", "probability": 0.95703125}, {"start": 3288.38, "end": 3290.98, "word": " this", "probability": 0.43212890625}, {"start": 3290.98, "end": 3292.0, "word": " system", "probability": 0.9560546875}, {"start": 3292.0, "end": 3293.86, "word": " is", "probability": 0.7666015625}, {"start": 3293.86, "end": 3294.64, "word": " consistent", "probability": 0.411376953125}, {"start": 3294.64, "end": 3298.6, "word": " لازلنا", "probability": 0.8941650390625}, {"start": 3298.6, "end": 3298.8, "word": " في", "probability": 0.923828125}, {"start": 3298.8, "end": 3299.1, "word": " نفس", "probability": 0.99560546875}, {"start": 3299.1, "end": 3299.24, "word": " ال", "probability": 0.9228515625}, {"start": 3299.24, "end": 3299.6, "word": " section", "probability": 0.91357421875}, {"start": 3299.6, "end": 3299.82, "word": " و", "probability": 0.76220703125}, {"start": 3299.82, "end": 3300.14, "word": " لمّا", "probability": 0.747314453125}, {"start": 3300.14, "end": 3300.86, "word": " ننتهي", "probability": 0.975341796875}, {"start": 3300.86, "end": 3301.3, "word": " بعد", "probability": 0.9287109375}, {"start": 3301.3, "end": 3302.52, "word": " للمرة", "probability": 0.9461263020833334}, {"start": 3302.52, "end": 3303.4, "word": " القادمة", "probability": 0.9874674479166666}, {"start": 3303.4, "end": 3303.76, "word": " ان", "probability": 0.62744140625}, {"start": 3303.76, "end": 3304.08, "word": " شاء", "probability": 0.970458984375}, {"start": 3304.08, "end": 3304.3, "word": " الله", "probability": 0.92578125}, {"start": 3304.3, "end": 3305.08, "word": " تعالى", "probability": 0.9679361979166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3305.8715, "duration_after_vad": 3141.348749999989}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0706ef2c6f529a990e046edf58dc0aac9fa489e3
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_postprocess.srt
@@ -0,0 +1,1532 @@
+1
+00:00:19,390 --> 00:00:23,870
+بسم الله الرحمن الرحيم انتهينا في أول chapter من
+
+2
+00:00:23,870 --> 00:00:27,410
+الجابرة الخاطية و هو chapter 2 والان بنروح لل
+
+3
+00:00:27,410 --> 00:00:31,030
+chapter الثاني من الجابرة الخاطية و هو chapter 3
+
+4
+00:00:31,030 --> 00:00:35,870
+من الكتاب المقرر هذا ال chapter يتحدث عن نقطتين
+
+5
+00:00:35,870 --> 00:00:39,910
+رئيسيتين النقطة الأولى هي ال vector spaces و
+
+6
+00:00:39,910 --> 00:00:43,890
+النقطة الثانية هي ال linear transformations يعني
+
+7
+00:00:43,890 --> 00:00:48,830
+التحويلات الخاطيةموضوعنا اليوم موضوع ال vector
+
+8
+00:00:48,830 --> 00:00:54,070
+spaces وعلى مدار الأيام القادمة كذلك لكننا في هذا
+
+9
+00:00:54,070 --> 00:00:58,550
+ال section فقط سنعطي تعريف لل vector space ونعطي
+
+10
+00:00:58,550 --> 00:01:04,670
+بعض الأمثلة عليه فقط لا غير ومن ثم ننتقل إلى بقية
+
+11
+00:01:04,670 --> 00:01:09,450
+الأجزاء التي تتعلق بال vector spaces يبقى احنا
+
+12
+00:01:09,450 --> 00:01:16,950
+عندنا vector spaces يعني الفضاءات الاتجاهيةبدنا
+
+13
+00:01:16,950 --> 00:01:22,530
+نعطي تعريف للفضاء الاتجاهي ونشوف كيف نطبق التعريف
+
+14
+00:01:22,530 --> 00:01:28,090
+على الأمثلة المختلفةبقول افترض ان capital V عبارة
+
+15
+00:01:28,090 --> 00:01:32,370
+عن non-empty set of objects يبقى انا عندي capital
+
+16
+00:01:32,370 --> 00:01:37,650
+V هي عبارة عن مجموعة وهذه المجموعة تحتوي على عدد
+
+17
+00:01:37,650 --> 00:01:41,750
+من العناصر in which two operations addition and
+
+18
+00:01:41,750 --> 00:01:45,610
+multiplication by scalars are defined وعليها
+
+19
+00:01:45,610 --> 00:01:50,030
+عمليتين معرفتين عملية بنسميها عملية الجمع والثانية
+
+20
+00:01:50,030 --> 00:01:54,650
+عملية الضرب في مقدار قياسي او مقدار ثابت لما نقول
+
+21
+00:01:54,650 --> 00:01:58,930
+vectorيبقى لو ضربناها في رقم نقول هذا هو scalar
+
+22
+00:01:58,930 --> 00:02:04,130
+multiplication يعني ضرب قياسي يبقى احنا في عندنا
+
+23
+00:02:04,130 --> 00:02:08,670
+set V ال V هذا بدأ أضع عليها عمليتين العملية
+
+24
+00:02:08,670 --> 00:02:14,070
+الأولى عملية الجمع بين المتجهات الموجودة في V
+
+25
+00:02:14,070 --> 00:02:18,870
+العملية الثانية أخد رقم من set of real numbers R
+
+26
+00:02:18,870 --> 00:02:25,370
+وضربه في أي من المتجهات تبعات ال vector Vيبقى هاي
+
+27
+00:02:25,370 --> 00:02:28,970
+العمليتين اللي أنا بقول عليهم معرفتين كانوا معرفة
+
+28
+00:02:28,970 --> 00:02:29,550
+ذاتي
+
+29
+00:02:46,650 --> 00:02:52,470
+عملية جمع متجهين من V هو متجه جديد موجود في V
+
+30
+00:02:52,470 --> 00:02:58,210
+عملية ضرب scalar A في U هو بيعطيني متجه جديد هذا
+
+31
+00:02:58,210 --> 00:03:04,030
+المتجه موجود في V كذلك R definedيبقى في هذه الحالة
+
+32
+00:03:04,030 --> 00:03:08,170
+بيقول إن ال V وعليها عملية الجمع وعليها عملية
+
+33
+00:03:08,170 --> 00:03:13,390
+الضرب base color is a vector space أو linear space
+
+34
+00:03:13,390 --> 00:03:16,830
+بعض الكتب بتقول عنه vector space و بعض الكتب بتقول
+
+35
+00:03:16,830 --> 00:03:19,890
+عنه linear space if the following properties are
+
+36
+00:03:19,890 --> 00:03:26,080
+satisfied على Vيبقى إذا تحقق الشروط العشرة التالية
+
+37
+00:03:26,080 --> 00:03:31,540
+على هذه الست بقول الست هذي vector space إذا لم
+
+38
+00:03:31,540 --> 00:03:36,640
+يتحقق ولو شرط واحد يبقى بيبطل يصير vector space
+
+39
+00:03:36,640 --> 00:03:40,520
+يبقى يبين لي أن هذا ما هو واش vector space بيكفي
+
+40
+00:03:40,520 --> 00:03:47,060
+ألغي شرط من الشروط العشرةنأتي للشرط الأول أو
+
+41
+00:03:47,060 --> 00:03:51,080
+الخاصية اللي هو لو أخدت عنصرين من V يبقى حاصل
+
+42
+00:03:51,080 --> 00:03:56,420
+الجمحو مش بده يكون موجود في V وليس خارج V طالع
+
+43
+00:03:56,420 --> 00:04:00,240
+خارج V فبتطل يصير vector space يبقى بد المجموع
+
+44
+00:04:00,240 --> 00:04:05,480
+يكون داخل V ال condition التاني ال U زائد ال V
+
+45
+00:04:05,480 --> 00:04:10,020
+يساوي ال V زائد ال U يعني عملية عملية جمع المنتجات
+
+46
+00:04:10,020 --> 00:04:14,690
+عمليةإبدالية لو ماكنتش إبدالية it is not a vector
+
+47
+00:04:14,690 --> 00:04:19,210
+space طيب الخاصيتين اللي اتنينه اتحققوا بروحنا
+
+48
+00:04:19,210 --> 00:04:23,210
+الخاصية التالتة و هي خاصية ال associativity لو
+
+49
+00:04:23,210 --> 00:04:29,230
+جمعت ال U إلى V زائد ال W تماما كما لو جمعت ال U
+
+50
+00:04:29,230 --> 00:04:34,530
+زائد ال V إلى من إلى ال W و دي بيسميه خاصية الدمج
+
+51
+00:04:34,530 --> 00:04:38,830
+associative law أو associative propertyالان انت
+
+52
+00:04:38,830 --> 00:04:42,630
+حققت الخواص الثلاث بروح لخاصية رابعة الخاصية
+
+53
+00:04:42,630 --> 00:04:46,450
+الرابعة تقول لي في عندك عنصر اللي هو ال zero
+
+54
+00:04:46,450 --> 00:04:51,450
+المطول هذا موجود في Vإذا و الله كان Zero زايد V
+
+55
+00:04:51,450 --> 00:04:57,230
+يسوي V زايد Zero يسوي V لكل ال V يبقى هذا بسميه
+
+56
+00:04:57,230 --> 00:05:01,970
+Zero vector لمين؟ لل vector space V يعني بمعنى أخر
+
+57
+00:05:01,970 --> 00:05:07,070
+أن ال vector space V لازم يحتوي على العنصر الصفري
+
+58
+00:05:07,070 --> 00:05:13,410
+بالنسبة لعملية الجامعيبقى الـ zero هذا vector يبقى
+
+59
+00:05:13,410 --> 00:05:20,130
+مش scalar يعني مش number وإنما هو vector تمام بحيث
+
+60
+00:05:20,130 --> 00:05:24,030
+هذا ال zero vector لو جمعته إلى أي vector آخر من
+
+61
+00:05:24,030 --> 00:05:28,590
+اليمين أو من الشمال بدي يعطيني نفس ال vector هذا
+
+62
+00:05:28,590 --> 00:05:32,850
+ال element بقول عليه ال zero vector خاصية الخامسة
+
+63
+00:05:32,850 --> 00:05:37,470
+لأي u موجود في capital V there exists لازم اللي
+
+64
+00:05:37,470 --> 00:05:42,980
+أجي أسالي بـU موجود في V يعنييعني إذا العنصر أو ال
+
+65
+00:05:42,980 --> 00:05:48,560
+vector موجود في V لازم ألاقي سالب هذا العنصر موجود
+
+66
+00:05:48,560 --> 00:05:54,560
+في V بحيث لو جمعت ال U وسالب U تماما كما لو جمعت
+
+67
+00:05:54,560 --> 00:05:58,740
+سالب U و U لأنه قال هنا commutative وندش بده
+
+68
+00:05:58,740 --> 00:06:02,830
+يعطيناالـ zero vector مش الـ zero scalar لإن احنا
+
+69
+00:06:02,830 --> 00:06:09,790
+بنجمع vectors سالب U هو vector يبقى U زائد ناقص U
+
+70
+00:06:09,790 --> 00:06:14,910
+يسوى تماما ناقص الـ U زائد الـ U بده يسوى من الـ
+
+71
+00:06:14,910 --> 00:06:19,180
+zero vectorهذه الخامسة الخاصية الساسة لو أخدت أي
+
+72
+00:06:19,180 --> 00:06:23,740
+scalar من ال set of real number A أخدت عنصر A من
+
+73
+00:06:23,740 --> 00:06:27,900
+ال set of real number و أخدت ال U vector موجود في
+
+74
+00:06:27,900 --> 00:06:35,880
+V إذا حصل ضرب ل 2A في U بدي يكون موجود في V تماما
+
+75
+00:06:35,880 --> 00:06:40,070
+تحققت الخاصية ده نروح بالخاصية اللي بعدهالو كان
+
+76
+00:06:40,070 --> 00:06:45,170
+الـ A scalar واخدت two vectors من V وروح ضرب كسكلر
+
+77
+00:06:45,170 --> 00:06:51,550
+الـ A ضد الـ U زائد الـ V خضعت هذه لعمليات التوزيع
+
+78
+00:06:51,550 --> 00:06:56,850
+او distributive property خاصية التوزيع صارت هذه A
+
+79
+00:06:56,850 --> 00:07:03,190
+ضد الـ U زائد A ضد الـ Vمش عاجز هك و بس ضرب scalar
+
+80
+00:07:03,190 --> 00:07:08,090
+مع جامعة و vector لأ جامعة و scalars مع ضرب مع مين
+
+81
+00:07:08,090 --> 00:07:12,750
+مع vector الخاصية اللي بعدها لو كان ال a و ال b
+
+82
+00:07:12,750 --> 00:07:16,930
+موجودة في R و ال u موجودة في V يبقى ال a زائد ال b
+
+83
+00:07:16,930 --> 00:07:21,450
+و dot ال u بيسوي a dot ال u زائد ال b dot ال u كل
+
+84
+00:07:21,450 --> 00:07:28,160
+هذا بيكون موجود في Vطبعا يبقى بنجي للخاصية التاسعة
+
+85
+00:07:28,160 --> 00:07:34,580
+لو كان عندي scholar A وعندي scholar B ضربت ال B في
+
+86
+00:07:34,580 --> 00:07:39,000
+ال U والنتج روحت ضربت في A تماما كما لو ضربت ال
+
+87
+00:07:39,000 --> 00:07:43,360
+two scholars من البداية في من في ال vector V بده
+
+88
+00:07:43,360 --> 00:07:48,960
+يطلع عندي vector اسمه A B ضد ال Uوهذا بيكون vector
+
+89
+00:07:48,960 --> 00:07:53,220
+موجود في الـ vector الأصلي طبقًا للخاصية اللي
+
+90
+00:07:53,220 --> 00:07:57,640
+عندنا هذه تمام اتحقق الخاصية التاسعة بيروح الخاصية
+
+91
+00:07:57,640 --> 00:08:02,860
+العاشرة لو أخدت الواحد as a scalar يعني كأنه
+
+92
+00:08:02,860 --> 00:08:08,400
+الخاصية دي حالة خاصة من من اللي فوق أخدت ال U هو
+
+93
+00:08:08,400 --> 00:08:12,180
+vector و أخدت الواحد as a scalar ضربت الواحد في U
+
+94
+00:08:12,180 --> 00:08:18,850
+بيطلع النتج يساوي U اللي هو موجود في Vيبقى إذا
+
+95
+00:08:18,850 --> 00:08:23,930
+تحققت هذه الخواص العشر في هذه الحالة بقول يبقى
+
+96
+00:08:23,930 --> 00:08:28,430
+اللي في عندي هذا ماله vector space بدنا نبدأ نطبق
+
+97
+00:08:28,430 --> 00:08:31,710
+الكلام اللي احنا بنقوله على أرض الواقع بأمثلة
+
+98
+00:08:31,710 --> 00:08:35,950
+مختلفة ونشوف مين ممكن يطلع vector space او ممكن
+
+99
+00:08:35,950 --> 00:08:42,150
+مايطلعش vector space وإذا ماطلعش مين من الخواص لا
+
+100
+00:08:42,150 --> 00:08:46,790
+تحتحقق في هذه الحالة بقيت يصير ما هواش vector
+
+101
+00:08:46,790 --> 00:08:52,980
+spaceجال ياخد المثال الأول افترض ال V كل العناصر
+
+102
+00:08:52,980 --> 00:08:59,700
+ال zero X1 و X2 بها X1 و X2 موجود في R يعني ايش؟
+
+103
+00:08:59,700 --> 00:09:04,700
+يعني بدي اخد كل ال vectors اللي كل vector مكون من
+
+104
+00:09:04,700 --> 00:09:08,560
+ال three components بحيث المركبة الأولى دائما و
+
+105
+00:09:08,560 --> 00:09:12,920
+أبداzero لو ما هي zero إذا مش عندنا برا مالناش
+
+106
+00:09:12,920 --> 00:09:17,560
+علاقة فيها يبقى احنا بدنا نجمع يعني مثلا لو جيت
+
+107
+00:09:17,560 --> 00:09:22,140
+قولت يا بنات هذا كل واحدة فيكو عبارة عن عنصر في ال
+
+108
+00:09:22,140 --> 00:09:26,560
+vector space الشك هذي تمام جيت قولت للبنات السطر
+
+109
+00:09:26,560 --> 00:09:30,930
+هذا كله انتج للناحية التانيةيبقى كأنه انا أخدت
+
+110
+00:09:30,930 --> 00:09:35,490
+حالة خاصة من الأصلية المركبة الأولى كلها zero في
+
+111
+00:09:35,490 --> 00:09:42,390
+كل three tuple تمام؟ بدأت أشوف هل هذا تحت عملية
+
+112
+00:09:42,390 --> 00:09:47,030
+الجمع العادية و تحت عملية الضرب العادية هل هو
+
+113
+00:09:47,030 --> 00:09:52,990
+vector space أم لا طلع هنا كل العناصر اللي المركبة
+
+114
+00:09:52,990 --> 00:09:56,610
+الأولى دائما و أبدا ب zero طب و المركبة التانية و
+
+115
+00:09:56,610 --> 00:10:01,430
+التالتةأش ما كان يكون وما حطيتش عليهم قيود يمكن
+
+116
+00:10:01,430 --> 00:10:06,250
+سالب يمكن موجب يمكن Zero كل أنا مقيد بالمركبة
+
+117
+00:10:06,250 --> 00:10:10,510
+الأولى لازم تكون Zero وقولتك X1 و X2 موجودة في
+
+118
+00:10:10,510 --> 00:10:14,510
+هرموجة بسالب كسر مش عارف أيه Zero ماليش علاقة بيه
+
+119
+00:10:14,510 --> 00:10:17,210
+أش ما يكون شكله ما يكون ان شاء الله يكون جذور
+
+120
+00:10:17,210 --> 00:10:22,210
+تربية وجذور تكييبية لأنها set أي عناصر موجودة في
+
+121
+00:10:22,210 --> 00:10:27,060
+ال set of real number طيبunder the usual addition
+
+122
+00:10:27,060 --> 00:10:33,680
+عملية الجمع العادية تبع ال vectors and the usual
+
+123
+00:10:33,680 --> 00:10:38,040
+multiplication of scalar وعملية الضرب العادي لل
+
+124
+00:10:38,040 --> 00:10:42,280
+vectors في scalar واخدنا سابقا انه عملية لو ضربت
+
+125
+00:10:42,280 --> 00:10:47,160
+element في vector بدربه في جميع ال components مش
+
+126
+00:10:47,160 --> 00:10:51,720
+هيك يبقى ده اسمه الضرب العادي والجمع بجمع
+
+127
+00:10:51,720 --> 00:10:57,070
+component was كل عنصر معاهنظيره بيقول then ال V is
+
+128
+00:10:57,070 --> 00:11:02,490
+a vector space because يبقى هذا اللي فوق تحت عملية
+
+129
+00:11:02,490 --> 00:11:06,010
+الجامعة العادية والضرب العادية دي بيكون vector
+
+130
+00:11:06,010 --> 00:11:10,030
+space ما هو السبب بيقول لو أخدت three vectors
+
+131
+00:11:10,030 --> 00:11:15,770
+موجودات في V طلعي المركبة طلعي كله المركبة الأولى
+
+132
+00:11:15,770 --> 00:11:25,990
+والمركبة الأولىوالمُركّب الأولى كله بأسفار موجودة
+
+133
+00:11:25,990 --> 00:11:31,690
+في V بداية أشوف الخواصة العاشرة هل ال U زائد ال V
+
+134
+00:11:31,690 --> 00:11:37,070
+موجود في V ولا لأ يبقى بداية للخاصية الأولىنمر
+
+135
+00:11:37,070 --> 00:11:42,370
+واحد بيداخد ال U زائد ال V يبقى هذا بده يعطيني
+
+136
+00:11:42,370 --> 00:11:48,130
+Zero و X واحد و X اتنين زائد Zero و Y واحد و Y
+
+137
+00:11:48,130 --> 00:11:55,140
+اتنين و Y ساويأحنا قلنا هذه عملية الجمع عادية لمن؟
+
+138
+00:11:55,140 --> 00:11:59,040
+للـ vectors يبقى عملية الجمع العادية بجمع
+
+139
+00:11:59,040 --> 00:12:08,440
+component y 0 مع 0 بقدرش 0 X1 زائد Y1 X2 زائد Y2
+
+140
+00:12:08,440 --> 00:12:12,630
+موجودة في V ولا يا بنات؟موجود في V ليش؟ لأن الـ
+
+141
+00:12:12,630 --> 00:12:17,290
+element الأول أو المركبة الأولى في كل vector يساوي
+
+142
+00:12:17,290 --> 00:12:23,030
+0 إذا انتحققت الخاصية الأولى بدي أجلال الخاصية
+
+143
+00:12:23,030 --> 00:12:28,750
+التانية نمره 2 بدي أخد ال U زائد ال V يبقى .. بدي
+
+144
+00:12:28,750 --> 00:12:33,970
+أجمعه لغاية يا بناتي يبقى هنا 0 زائد 0 ب0 X1 زائد
+
+145
+00:12:33,970 --> 00:12:44,370
+Y1 X2 زائد Y2 موجود في Vموجودة في V أنا بدّي خاصية
+
+146
+00:12:44,370 --> 00:12:51,790
+الإبدال أليس تهادي تساوي Zero one الآن X واحد زائد
+
+147
+00:12:51,790 --> 00:12:57,030
+Y واحد مش هدول X واحد و Y واحد أعداد موجودة في
+
+148
+00:12:57,030 --> 00:13:01,810
+الست في real numbers عملية جمع الأعداد العاديةهذه
+
+149
+00:13:01,810 --> 00:13:05,210
+عملية إبدالية ولا لا؟ أنا بقول خمسة زائد ستة و
+
+150
+00:13:05,210 --> 00:13:09,030
+الله ستة زائد خمسة ما هي نفس الشيء إذا باجي بقول
+
+151
+00:13:09,030 --> 00:13:16,210
+هذا y واحد زائد x واحد و y اتنين زائد x اتنين اللي
+
+152
+00:13:16,210 --> 00:13:23,350
+بقدر أقول هذه zero و y واحد و y اتنين زائد zero x
+
+153
+00:13:23,350 --> 00:13:28,490
+واحد و x اتنينصحيح ولا لأ؟ يعني فصلت هذا ال vector
+
+154
+00:13:28,490 --> 00:13:32,710
+إلى مجموع two vectors طب الأول مين هو؟ مش V
+
+155
+00:13:32,710 --> 00:13:38,930
+والتاني يبقى V زائد ال U يبقى بدأت ب U زائد ال V
+
+156
+00:13:38,930 --> 00:13:44,130
+وصلت إلى V زائد ال U يبقى اتحققت الخاصية الأولى
+
+157
+00:13:44,130 --> 00:13:48,800
+والخاصية الثانية عندنا بدنا نروح لمين؟للخاصية
+
+158
+00:13:48,800 --> 00:13:54,360
+التالتة يبقى باخد U ذائد V ذائد W
+
+159
+00:13:59,340 --> 00:14:04,300
+و X1 و X2 زائد ال V زائد ال W بدي أجمع على طول
+
+160
+00:14:04,300 --> 00:14:10,640
+الخط هاي عند ال V وهذه ال W بدي أجمعها مباشرة يبقى
+
+161
+00:14:10,640 --> 00:14:22,570
+Zero Y1 زائد Z1 و Y2 زائد Z2الان بدأجي اجمع صار
+
+162
+00:14:22,570 --> 00:14:25,650
+عندى vector وعندى vector تانى بدأ اجمع component
+
+163
+00:14:25,650 --> 00:14:33,650
+twice 00 ب0 يبقى بيصير عندى X واحد زائد Y واحد
+
+164
+00:14:33,650 --> 00:14:46,190
+زائد Z واحد و Xي اتنين زائد Y اتنين زائد Z اتنين
+
+165
+00:14:46,190 --> 00:14:54,460
+بالشكل اللى عندناطيب هذا الكلام بده يساوي بداجي
+
+166
+00:14:54,460 --> 00:14:59,700
+للي وصلتله هذا هدول كلهم real number عملية الجمع
+
+167
+00:14:59,700 --> 00:15:04,160
+على ال real number إدماجية ولا لا يبقى خلاص إذا
+
+168
+00:15:04,160 --> 00:15:09,860
+بقدر أكتب هذه على الشكل التالي هي عبارة عن zero و
+
+169
+00:15:09,860 --> 00:15:17,480
+X واحد زائد Y واحد زائد Z واحد تمامهذا ال term
+
+170
+00:15:17,480 --> 00:15:25,640
+الأول و ال term التاني بقدر اقول x واحد زائد y
+
+171
+00:15:25,640 --> 00:15:30,840
+واحد زائد z واحد وهذه بقول x اتنين زائد y اتنين
+
+172
+00:15:30,840 --> 00:15:39,220
+زائد z اتنينتمام إذا هذه بقدر أقول تساوي بداتي
+
+173
+00:15:39,220 --> 00:15:44,300
+أحطها على شكل مجموع two vectors إذا بقدر أقول هذا
+
+174
+00:15:44,300 --> 00:15:54,100
+zero و X واحد زائد Y واحد و X اتنين زائد Y اتنين
+
+175
+00:15:54,100 --> 00:16:00,580
+زائد ضال عندي zero و ضال عندي Z واحد و ضال عندي Z
+
+176
+00:16:00,580 --> 00:16:07,060
+اتنين تمامبقدر أقول هذا الكلام يساوي هذا عبارة عن
+
+177
+00:16:07,060 --> 00:16:13,520
+مجموع مين يا بنات مش عبارة عن ال U زائد ال V صح
+
+178
+00:16:13,520 --> 00:16:20,560
+ولا لا؟ ودك زائد اللي هو ال W العنصر التالت يبقى
+
+179
+00:16:20,560 --> 00:16:26,460
+صار U زائد V زائد W سوى U زائد V زائد W إذا انتحقت
+
+180
+00:16:26,460 --> 00:16:29,100
+الخاصية رقم تلاتة عنه
+
+181
+00:16:32,920 --> 00:16:38,900
+الان انا بدي
+
+182
+00:16:38,900 --> 00:16:43,700
+اخد العنصر zero اللي موجود في V الان ال zero
+
+183
+00:16:43,700 --> 00:16:49,480
+vector خاصية الرابعة هو من؟ هو العنصر zero و zero
+
+184
+00:16:49,480 --> 00:16:55,590
+و zero موجود في capital V ولا لا؟صح؟ لأن المركبة
+
+185
+00:16:55,590 --> 00:16:59,890
+الأولى عندي هي اللي عليها قايدن تبقى بـ0 و 2 إيش
+
+186
+00:16:59,890 --> 00:17:06,350
+ما كانوا يكونوا الآن بدأت أخدله and بدأ أخدله 0
+
+187
+00:17:06,350 --> 00:17:15,710
+زائد ال U يساوي الـ0 اللي هو 0 و 0 و 0 زائد ال U
+
+188
+00:17:15,710 --> 00:17:22,100
+اللي هو 0 X 1 و X 2 الشكل اللي عندنا هذابتجمع
+
+189
+00:17:22,100 --> 00:17:30,240
+component y يبقى 0 زائد 0 ب0 0 زائد x1 بx1 0 زائد
+
+190
+00:17:30,240 --> 00:17:39,620
+x2 بx2 مش هذا هو ال U نفسه صح ولا لأ يبقى بقى بنفس
+
+191
+00:17:39,620 --> 00:17:48,300
+الطريقة similarly بنفس الطريقة ال U زائد ال 0 بده
+
+192
+00:17:48,300 --> 00:17:49,580
+يساوي ال U
+
+193
+00:17:57,200 --> 00:18:02,520
+الخاصية الخامسة بيقول إذا أي element U موجود في V،
+
+194
+00:18:02,520 --> 00:18:09,700
+ناقص الـU موجود في V، such that المجموعة بيساوي من
+
+195
+00:18:09,700 --> 00:18:14,720
+الـzero vectorالان انا بدي اخد مين؟ بدي اخد U
+
+196
+00:18:14,720 --> 00:18:22,280
+موجود في V الان ال U بده يساوي Zero و X واحد و X
+
+197
+00:18:22,280 --> 00:18:30,080
+اتنينهذا بده يعطيك مين؟ ناقص U احنا كأنه بدي اضرب
+
+198
+00:18:30,080 --> 00:18:35,580
+سالب واحد في U اذا ضرب عادي جدا component loss لإن
+
+199
+00:18:35,580 --> 00:18:40,780
+احنا قولنا ضرب عادي يبقى هذا الكلام بده يساوي سالب
+
+200
+00:18:40,780 --> 00:18:48,400
+واحد في Zero ب Zero سالب X واحد سالب X اتنين مداجي
+
+201
+00:18:48,400 --> 00:18:58,430
+اقوله andبدي ال U زائد سالب U و يساوي ال U له 0 و
+
+202
+00:18:58,430 --> 00:19:10,130
+X1 و X2 زائد 0 سالب X1 سالب X2 تمام نجمع 0 مع 0 ب0
+
+203
+00:19:10,130 --> 00:19:18,110
+X1 و نقص X1 ب0 X2 و نقص X2 ب0 مين هو هذا هذا ال
+
+204
+00:19:18,110 --> 00:19:27,610
+zero vectorSimilarly بنفس الطريقة سالب
+
+205
+00:19:27,610 --> 00:19:33,810
+U زائد U ساوي الـ Zero vector إذا تحققت الخاصية
+
+206
+00:19:33,810 --> 00:19:39,590
+رقم خمسة بدنا نحقق باق الخواص خليني أمسح اللي فوق
+
+207
+00:19:39,590 --> 00:19:45,610
+هذا طيب هذا اللي مالهوش لزوم من هنا و فوق نمسحه
+
+208
+00:19:56,930 --> 00:20:01,810
+خلصنا الخاصية الخامسة وانتجنا الخاصية السادسةخاصية
+
+209
+00:20:01,810 --> 00:20:06,230
+السالسة بيقول لو كان خدت scalar موجود في R و U
+
+210
+00:20:06,230 --> 00:20:11,430
+موجود في V فحصل ضربه مابدى يكون موجود في V يبقى
+
+211
+00:20:11,430 --> 00:20:18,390
+بدى اخد هنا F ال A موجود في R scalar و ال U اللى
+
+212
+00:20:18,390 --> 00:20:25,310
+هي يساوي Zero و X واحد و X اتنين موجودات في V then
+
+213
+00:20:25,310 --> 00:20:33,740
+بدى اخد ال A في ال Uيبقى هذه A بدي أضربها في الـ 0
+
+214
+00:20:33,740 --> 00:20:39,420
+X1 و X2 Y الساوية الـ A في الـ 0 بقداش يا بنات
+
+215
+00:20:39,420 --> 00:20:46,200
+Zero و هنا A X1 و هنا A X2 إيش رأيك في ال vector
+
+216
+00:20:46,200 --> 00:20:50,120
+اللي طلع موجود في V ولا لأ لأن المركبة الأولى
+
+217
+00:20:50,620 --> 00:20:55,820
+والباقية اش مكان يكون يبقى هذا موجود في ال vector
+
+218
+00:20:55,820 --> 00:21:01,020
+space V وبالتالي اتحققت الخاصية السادسة بدنا نروح
+
+219
+00:21:01,020 --> 00:21:05,700
+للخاصية السابعة الخاصية السابعة بيقول لو كان A
+
+220
+00:21:05,700 --> 00:21:13,980
+موجود في R و U و V موجودة في U يبقى هنا Fالـ A
+
+221
+00:21:13,980 --> 00:21:21,940
+موجودة في R and ال U اللي هي Zero Zero و X واحد و
+
+222
+00:21:21,940 --> 00:21:30,080
+X اتنين و ال V Zero و Y واحد و Y اتنين موجودات في
+
+223
+00:21:30,080 --> 00:21:40,020
+V then بدي اخد ال A Dot ال U زائدي ال V يبقى ال A
+
+224
+00:21:40,020 --> 00:21:46,430
+Dotالـ U زائد ال V بدي أجمع component twice يبقى
+
+225
+00:21:46,430 --> 00:21:55,970
+Zero X واحد زائد Y واحد X اتنين زائد Y اتنين بدي
+
+226
+00:21:55,970 --> 00:22:05,350
+أضرب يبقى هاديزيرو و a في x واحد زائد y واحد و a
+
+227
+00:22:05,350 --> 00:22:17,030
+في x اتنين زائد y اتنين ليش ضربتك لأن ضرب عادي طيب
+
+228
+00:22:17,030 --> 00:22:27,330
+هذا الكلام بده يساويبدو يساوي zero اكس واحد زائد
+
+229
+00:22:27,330 --> 00:22:32,650
+اي واحد اكس
+
+230
+00:22:32,650 --> 00:22:39,820
+اتنين زائد اي اتنينهذا صار vector واحد شو رايك
+
+231
+00:22:39,820 --> 00:22:45,900
+ممكن اجزءه الى two vectors ايش ال two vectors يعني
+
+232
+00:22:45,900 --> 00:22:53,700
+ممكن اقول هذا zero و a x واحد و a x اتنين زائد
+
+233
+00:22:53,700 --> 00:23:02,480
+zero و a y واحد و a y اتنين لو جمعتهم بطلع عند هذا
+
+234
+00:23:02,480 --> 00:23:08,260
+مرة تانيةطب بدرجة على خواص الـ scalar أظن بقدر أخد
+
+235
+00:23:08,260 --> 00:23:19,160
+a عامل مشترك من الكل برا بيظل 0 x1 x2 زائد a 0 y1
+
+236
+00:23:19,160 --> 00:23:29,950
+y2يبقى هذا A الأولاني هو الـU والتاني A في الـV
+
+237
+00:23:29,950 --> 00:23:36,290
+الشكل اللي عنها يبقى بناء على A ضد U زائد V يبقى A
+
+238
+00:23:36,290 --> 00:23:44,270
+ضد U زائد A ضد V وبالتالي تحققت الخاصية السابعة
+
+239
+00:23:44,750 --> 00:23:51,810
+بنروح للخاص يمين الثامنة يبقى باجي بقوله تمانية if
+
+240
+00:23:51,810 --> 00:24:00,710
+ال A و ال B موجودة في R and ال U Zero X واحد X
+
+241
+00:24:00,710 --> 00:24:09,870
+اتنين موجودة في V then بدي اخد ال A زائد ال B Dot
+
+242
+00:24:09,870 --> 00:24:20,230
+من Dot ال Uيساوي A زائد B ضات ال U
+
+243
+00:24:26,050 --> 00:24:29,870
+هذا مجموع two real numbers يبقى real number واحد
+
+244
+00:24:29,870 --> 00:24:35,310
+يبقى بدي أضرب جوبه حسب الضرب العادى يبقى هذا بقداش
+
+245
+00:24:35,310 --> 00:24:44,530
+ب zero نجي للي بعدها هذه ا زائد ال B في ال X1 وهنا
+
+246
+00:24:44,530 --> 00:24:51,770
+ا زائد ال B في من؟ في ال X2 وهيقفلنا الجزءهذه بقدر
+
+247
+00:24:51,770 --> 00:24:57,750
+اقول عليها ما يأتي يساوي هاي zero زي مهين وهذه
+
+248
+00:24:57,750 --> 00:25:01,930
+بقدر افكها لان ال X واحد وال X اتنية real number
+
+249
+00:25:01,930 --> 00:25:08,270
+وال A و ال B real number يبقى A X one زائد بي X
+
+250
+00:25:08,270 --> 00:25:18,280
+one فاصلة A X two زائد بي X twoممكن اجزئها الى two
+
+251
+00:25:18,280 --> 00:25:28,180
+vectors يبقى هذه بقدر اقول zero و ax1 و ax2 زائد
+
+252
+00:25:28,180 --> 00:25:39,510
+zero و bx1 و bx2ممكن أخد الـ A برا يبقى الـ A في
+
+253
+00:25:39,510 --> 00:25:50,050
+Zero X واحد و X اتنين زائد B في Zero و X واحد و X
+
+254
+00:25:50,050 --> 00:25:57,030
+اتنين يبقى هذه بدأت تساوي A ضد الـ U زائد B ضد الـ
+
+255
+00:25:57,030 --> 00:26:03,150
+U وبالتالي تحققت الخاصية رقم تمانية يبقى تمانية
+
+256
+00:26:07,780 --> 00:26:18,160
+الخاصية التاسعة يبقى الفرصة
+
+257
+00:26:18,160 --> 00:26:28,520
+التاسعةبدأت أخد F الـ A والـ B موجودة في R and ال
+
+258
+00:26:28,520 --> 00:26:36,780
+U Zero X واحد X اتنين موجودة في V then بدأت أخد ال
+
+259
+00:26:36,780 --> 00:26:46,120
+A في ال B ضد ال U يساوي A فيبضد ال U يبقى بدي اضرب
+
+260
+00:26:46,120 --> 00:26:52,220
+بي في كل عنصر من العاصر اللي عندنا يبقى هاي Zero و
+
+261
+00:26:52,220 --> 00:27:00,280
+بي X one و بي X two الشكل اللي عندنا هنا الان بدي
+
+262
+00:27:00,280 --> 00:27:07,280
+اضرب ال A يبقى هذا الكلام بدي يساوي A في Zero ب
+
+263
+00:27:07,280 --> 00:27:17,690
+Zero يبقى A بي X oneو A B X 2 بالشكل اللي عندنا
+
+264
+00:27:17,690 --> 00:27:24,790
+هنا هذا الكلام بده يساوي الان ال A و ال B و ال X 1
+
+265
+00:27:24,790 --> 00:27:29,830
+كلهم real numbers و كذلك ال A و ال B و ال X 2 كله
+
+266
+00:27:29,830 --> 00:27:36,350
+real numbers يبقى بقدر اقول هذا zero و هذا A B X 1
+
+267
+00:27:36,350 --> 00:27:43,980
+و في نفس الوقت A B X 2بقدر أخد ال a بي برا يبقى
+
+268
+00:27:43,980 --> 00:27:51,160
+هذا a بي برا كله في مين في ال zero x one x two
+
+269
+00:27:51,160 --> 00:27:59,360
+يبقى هذا a بي ضد ال uيبقى تحققت الخاصية رقم 9
+
+270
+00:27:59,360 --> 00:28:07,540
+بنانيج الخاصية رقم 10 الأخيرة بدي 1.tlu يبقى 1
+
+271
+00:28:07,540 --> 00:28:12,520
+.0x1x2y
+
+272
+00:28:13,880 --> 00:28:17,600
+الواحد لما نضربه في زيرو بيبقى ده جمنات بزيرو
+
+273
+00:28:17,600 --> 00:28:23,660
+الواحد في ال X1 بال X1 الواحد في ال X2 بال X2 يبقى
+
+274
+00:28:23,660 --> 00:28:29,940
+هذا أعطاني مين ال U يبقى قلنالك من البداية أن هذا
+
+275
+00:28:29,940 --> 00:28:35,040
+vector space ليش قلنا because وروحنا وجينا العشر
+
+276
+00:28:35,040 --> 00:28:39,660
+خواص كلها محققة يبقى أصبح هذا اللي عندنا اللي هو
+
+277
+00:28:39,660 --> 00:28:45,840
+vector space طبعامش كل ستة بنعطيها لك بتكون vector
+
+278
+00:28:45,840 --> 00:28:51,660
+space و بضروح أبدأ أطبق الخواص العاشرة، تمام؟ يعني
+
+279
+00:28:51,660 --> 00:28:56,840
+ليس بالضرورة إن راح أطول خاصية ماتحققتش، يبقى أروح
+
+280
+00:28:56,840 --> 00:29:00,240
+أدور على الباقي، مدورش على الباقي، خلاص نطب vector
+
+281
+00:29:00,240 --> 00:29:03,940
+space و باسكنلقيت الأولى اتحققت بروح للتانية وما
+
+282
+00:29:03,940 --> 00:29:07,400
+اتحققتش التانية not vector space و بسيب الباقي و
+
+283
+00:29:07,400 --> 00:29:12,520
+هكذا يعني وين خاصية بتتحققش بقول يبقى هذا ماهواش
+
+284
+00:29:12,520 --> 00:29:16,880
+vector space و بنتهيه الدلة تانية الأولى اتحققت
+
+285
+00:29:16,880 --> 00:29:20,680
+انها بروح للتالت بروح للرابع لما إذا اتحققوا
+
+286
+00:29:20,680 --> 00:29:24,400
+العشرة كلهم يبقى هو vector space يبقى إذا اختلت أي
+
+287
+00:29:24,400 --> 00:29:28,320
+خاصية من الخاصة العشر بكون معله ماهواش vector
+
+288
+00:29:28,320 --> 00:29:35,680
+spaceهذا أول مثال على هذا الموضوع، لا يزال عندنا
+
+289
+00:29:35,680 --> 00:29:45,140
+العديد من الأمثلة، دي المثال رقم اتنين هذا
+
+290
+00:29:45,140 --> 00:29:50,320
+إذا طلع vector space، إذا ما طلعش vector space
+
+291
+00:29:50,320 --> 00:29:55,990
+يمكن تسوي خطوة واحدة، ولا لا؟وإذا انت دقيقة نظر
+
+292
+00:29:55,990 --> 00:30:00,090
+وشاطرة في الحسابات ومجرد النظر بتقولي هذه البرشم
+
+293
+00:30:00,090 --> 00:30:04,230
+تنفعش للخاصية الفلانية على طول من دون مجرمي و تروح
+
+294
+00:30:04,230 --> 00:30:09,030
+تكتبي ليها و بتكشف الباقي 100% تمام نعطي المثال
+
+295
+00:30:09,030 --> 00:30:17,970
+رقم اتنين example two هذا سؤال خمسة من الكتاب
+
+296
+00:30:17,970 --> 00:30:20,690
+بيقول little v to sound
+
+297
+00:30:24,960 --> 00:30:34,460
+كل العناصر على الشكل واحد و X و Y بحيث X و Y
+
+298
+00:30:34,460 --> 00:30:39,800
+موجودة في set of real numbers under usual addition
+
+299
+00:30:40,930 --> 00:30:49,930
+under usual addition تحت عملية الجامعة العادية and
+
+300
+00:30:49,930 --> 00:30:57,030
+وفي نفس الوقت usual scalar multiplication usual
+
+301
+00:30:57,030 --> 00:31:03,250
+scalar multiplication
+
+302
+00:31:03,250 --> 00:31:06,370
+تحت
+
+303
+00:31:06,370 --> 00:31:18,190
+عملية الجامعة الدرب والجامعة العادية thenis not
+
+304
+00:31:18,190 --> 00:31:26,430
+a vector space
+
+305
+00:31:32,720 --> 00:31:37,520
+ومجرد النظر هذا ال 6 اللي عندنا هذه تحت عملية
+
+306
+00:31:37,520 --> 00:31:40,760
+الجمع العادية و الضرب العادية ليست في الاقتراضية
+
+307
+00:31:40,760 --> 00:31:44,520
+ليه؟ بدي واحدة تحكي بس واحدة ترفع أيديها و تحكي
+
+308
+00:31:44,520 --> 00:31:49,680
+انا بقول فيش zero element ماعشي الحالة هذا وجهة
+
+309
+00:31:49,680 --> 00:31:55,200
+نظر في وجهة نظر تانية؟ قبل ال zero طب شوفي اللي
+
+310
+00:31:55,200 --> 00:32:01,520
+قبل ال zero اجمع اتنين اجمع لو جمعت اتنين ايش
+
+311
+00:32:01,520 --> 00:32:02,100
+بطلع؟
+
+312
+00:32:06,540 --> 00:32:11,420
+يبقى عمله الجامعة لا تتحقق صحيح ولا لأ بروح بقوله
+
+313
+00:32:11,420 --> 00:32:15,500
+هذا is not a vector space because
+
+314
+00:32:19,270 --> 00:32:26,570
+الـ U بدها تساوي واحد و X واحد و Y واحد و ال V
+
+315
+00:32:26,570 --> 00:32:33,150
+دوسر واحد و X اتنين و Y اتنين موجودة في capital V
+
+316
+00:32:33,150 --> 00:32:42,170
+then ال U زائد ال V بده يساوي اتنين و X واحد زائد
+
+317
+00:32:42,170 --> 00:32:48,860
+X اتنين و X واحدخلّيها بس لسهولة يا فنات خلّيها X
+
+318
+00:32:48,860 --> 00:32:57,060
+واحد و X اتنين و هذي Y واحد و Y اتنين تمام يبقى X
+
+319
+00:32:57,060 --> 00:33:04,800
+واحد زائد Y واحد و X اتنين زائد Y اتنين does not
+
+320
+00:33:04,800 --> 00:33:09,740
+belong to V مش موجودة في V لإن أنا بدى ال
+
+321
+00:33:09,740 --> 00:33:14,550
+component اللي قداش تكونيبقى في حالة الـ zero نفع
+
+322
+00:33:14,550 --> 00:33:18,830
+يصير vector space لكن في حالة الواحد مانفعش يكون
+
+323
+00:33:18,830 --> 00:33:24,230
+vector space ماهواش vector space طيب مثال تلاتة
+
+324
+00:33:24,230 --> 00:33:32,530
+مثال تلاتة له سؤال سبعة من الكتاب كذلك سؤال سبعة
+
+325
+00:33:32,530 --> 00:33:42,530
+بيقول letالـ V تساوي كل المصفوفات A بحيث الـ A is
+
+326
+00:33:42,530 --> 00:33:48,370
+two by two matrix كل المصفوفات اللي نضامها اتنين
+
+327
+00:33:48,370 --> 00:33:56,450
+في اتنين with determinant للـ A لا يساوي Zero
+
+328
+00:33:56,450 --> 00:34:02,970
+under usual
+
+329
+00:34:09,830 --> 00:34:19,150
+addition and scalar multiplication
+
+330
+00:34:19,150 --> 00:34:26,610
+of
+
+331
+00:34:26,610 --> 00:34:38,460
+matrices then ايش رايك؟الـ V مش عارف اكتب هي
+
+332
+00:34:38,460 --> 00:34:42,420
+vector space ولا not vector space نيجي مين هي ال V
+
+333
+00:34:42,420 --> 00:34:51,200
+في الأول ال V كل المصفوفات A اللي نظامها 2 في 2 و
+
+334
+00:34:51,200 --> 00:34:55,760
+اللي محددها ماله لا يساوي 0 اللي محدد فيها لا
+
+335
+00:34:55,760 --> 00:34:59,550
+يساوي 0يبقى كل المصوات اللي نظامها اتنين في اتنين
+
+336
+00:34:59,550 --> 00:35:04,850
+و اللي محددة ولا يساوي تجمعتهم و حطيتهم في 6V عرفت
+
+337
+00:35:04,850 --> 00:35:09,510
+عليها عملية جمع المصوفات العادى وهو جمع component
+
+338
+00:35:09,510 --> 00:35:14,630
+-wise وعرفت عليها ضرب المصوفة في scalar وهو ضرب ال
+
+339
+00:35:14,630 --> 00:35:17,730
+real number في كل عنصر من العناصر المصوفة اللي
+
+340
+00:35:17,730 --> 00:35:21,670
+كانت usual addition and usual multiplication تمام
+
+341
+00:35:21,990 --> 00:35:27,530
+تحت العمليتين الأثنين هدول هل ال V Vector Space أم
+
+342
+00:35:27,530 --> 00:35:35,990
+لا؟ طبعاً لأ أبسط شغلة بدي Zero Matrix هل ال Zero
+
+343
+00:35:35,990 --> 00:35:40,270
+Matrix المحدد تبعها لا يساوي Zero؟ لأ طبعاً يبجد
+
+344
+00:35:40,270 --> 00:35:48,990
+ان ال V is not a vector space because
+
+345
+00:35:54,180 --> 00:36:10,760
+it does not contain the zero matrix since
+
+346
+00:36:15,640 --> 00:36:23,320
+الـ Determinant للمصفوف Zero يبقى Zero يبقى
+
+347
+00:36:23,320 --> 00:36:28,760
+الخاصية تبع الأنصار الصفرية لم تتحقق لذلك هذا ليس
+
+348
+00:36:28,760 --> 00:36:37,320
+Vector Space فبالمثال
+
+349
+00:36:37,320 --> 00:36:47,640
+رقم أربعة بقول Letcapital V كل العناصر على الشكل X
+
+350
+00:36:47,640 --> 00:36:57,480
+و Y و Z بحيث ان ال X و Y و Z موجودة في set of real
+
+351
+00:36:57,480 --> 00:37:03,900
+numbers define addition
+
+352
+00:37:03,900 --> 00:37:07,380
+define
+
+353
+00:37:07,380 --> 00:37:09,780
+addition and
+
+354
+00:37:16,800 --> 00:37:26,020
+multiplication on the by الـ
+
+355
+00:37:26,020 --> 00:37:40,400
+x واحد y واحدو Z1 زائد X2 و Y2 و Z2 بده يساوي اللي
+
+356
+00:37:40,400 --> 00:37:54,760
+هو X1 و Y1 و Z1 و هنا X2 و Y2 و Z2 X1 زائد X2 Y1
+
+357
+00:37:54,760 --> 00:38:06,920
+زائد Y2 و هنا Z1زائد زيت دي اتنين هذا الجامعه and
+
+358
+00:38:06,920 --> 00:38:11,000
+ال
+
+359
+00:38:11,000 --> 00:38:25,540
+a في ال x و ال y و ال z يساوي ax و y و z then ال V
+
+360
+00:38:25,540 --> 00:38:28,580
+is الله أعلم
+
+361
+00:38:40,130 --> 00:38:46,110
+كيف؟ آه بس بنضربها في المركبة الأولى، يعني عملية
+
+362
+00:38:46,110 --> 00:38:50,690
+الجامعة كما هي component-wise والإيه بس بنضربها في
+
+363
+00:38:50,690 --> 00:38:59,410
+المركبة الأولى فقط لا غير، تمام؟يعني إنه هذه ال
+
+364
+00:38:59,410 --> 00:39:07,410
+Sid هي هيك قصيقة .. فاهم
+
+365
+00:39:07,410 --> 00:39:13,190
+يعني هذه ال Sid خاص فيه لأنه .. خاص فيه .. فاهم
+
+366
+00:39:17,540 --> 00:39:21,240
+هل هذا vector space ولا ماهواش vector space بتخيل
+
+367
+00:39:21,240 --> 00:39:28,220
+أنه ماهواش vector space السبق because لو أخدت يبقى
+
+368
+00:39:28,220 --> 00:39:40,920
+هذا is not a vector space because لو
+
+369
+00:39:40,920 --> 00:39:47,910
+أخدت يا مناد a زائد ال b في من؟ في اليوميبقى هذا
+
+370
+00:39:47,910 --> 00:39:57,190
+بيصير a زائد ال b في ال u اللي قلنا له x, y, z
+
+371
+00:39:57,190 --> 00:40:04,850
+يبقى حسب الضرب هذا بيضرب في ال a زائد ال b فقط و
+
+372
+00:40:04,850 --> 00:40:12,400
+ال x, y, z كما هي طب لو جيت أخدتالـ A Dot لـ U
+
+373
+00:40:12,400 --> 00:40:23,820
+زائد الـ B Dot لـ U يبقى هذا يصير A Dot XYZ زائد B
+
+374
+00:40:23,820 --> 00:40:29,140
+Dot XYZ
+
+375
+00:40:29,140 --> 00:40:36,720
+ويساوي حسب الخواصة اللي عندنا يبقى هذا A XYZ
+
+376
+00:40:37,620 --> 00:40:46,580
+زائد هذي بيكس و Y و Z يبقى لو جينا جمعناها هذي بده
+
+377
+00:40:46,580 --> 00:40:57,400
+يصير AX زائد بيكس و اتنين Y و اتنين Z تمام؟ يبقى
+
+378
+00:40:57,400 --> 00:41:03,950
+ايش رأيك؟ هل هذه اللي فوق هي هذه؟طبعا هذه بقدر
+
+379
+00:41:03,950 --> 00:41:10,590
+اقول a زائد ال b في ال x و اتنين y و اتنين z طبعا
+
+380
+00:41:10,590 --> 00:41:17,170
+اللي فوق ماهياش اللي تحت يبقى هنا ال a زائد ال b
+
+381
+00:41:17,170 --> 00:41:27,570
+ضات ال u لا يساوي ال au زائد ال b ال a ضات ال u
+
+382
+00:41:27,570 --> 00:41:32,940
+زائد ال b ضات ال uلا يزال هناك العديد من الأمثلة
+
+383
+00:41:32,940 --> 00:41:36,820
+نتعرض لها المرة القادمة ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..59761f8fa2e2c64501b2540414350930ee245051
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_raw.json
@@ -0,0 +1 @@
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28480, 2655, 9957, 6225, 42213, 10632, 44945, 38251, 1829, 11296, 6225, 42213, 10632, 25724, 2304, 3615, 16070, 12984, 7649, 10632, 6225, 42213, 10632, 6024, 114, 25513, 8978, 3714, 28543, 9640, 12174, 25528, 3794, 1829, 1975, 2407, 3714, 28543, 9640, 38637, 16758, 2655, 5296, 15042, 8717, 39648, 8062], "avg_logprob": -0.13545672882061738, "compression_ratio": 1.7247386759581882, "no_speech_prob": 0.0, "words": [{"start": 85.71, "end": 86.15, "word": "بقول", "probability": 0.76806640625}, {"start": 86.15, "end": 86.61, "word": " افترض", "probability": 0.908447265625}, {"start": 86.61, "end": 86.79, "word": " ان", "probability": 0.85302734375}, {"start": 86.79, "end": 87.27, "word": " capital", "probability": 0.1485595703125}, {"start": 87.27, "end": 87.63, "word": " V", "probability": 0.90576171875}, {"start": 87.63, "end": 88.09, "word": " عبارة", "probability": 0.9649658203125}, {"start": 88.09, "end": 88.35, "word": " عن", "probability": 0.99560546875}, {"start": 88.35, "end": 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100.97, "end": 101.45, "word": " addition", "probability": 0.68408203125}, {"start": 101.45, "end": 101.75, "word": " and", "probability": 0.904296875}, {"start": 101.75, "end": 102.41, "word": " multiplication", "probability": 0.755859375}, {"start": 102.41, "end": 102.91, "word": " by", "probability": 0.8935546875}, {"start": 102.91, "end": 103.45, "word": " scalars", "probability": 0.89453125}, {"start": 103.45, "end": 103.73, "word": " are", "probability": 0.95068359375}, {"start": 103.73, "end": 104.43, "word": " defined", "probability": 0.89599609375}, {"start": 104.43, "end": 105.61, "word": " وعليها", "probability": 0.82965087890625}, {"start": 105.61, "end": 106.43, "word": " عمليتين", "probability": 0.85986328125}, {"start": 106.43, "end": 107.43, "word": " معرفتين", "probability": 0.9808349609375}, {"start": 107.43, "end": 107.87, "word": " عملية", "probability": 0.9562174479166666}, {"start": 107.87, "end": 108.45, "word": " بنسميها", "probability": 0.81695556640625}, {"start": 108.45, "end": 108.89, "word": " عملية", "probability": 0.9866536458333334}, {"start": 108.89, "end": 109.29, "word": " الجمع", "probability": 0.87890625}, {"start": 109.29, "end": 110.03, "word": " والثانية", "probability": 0.939697265625}, {"start": 110.03, "end": 110.87, "word": " عملية", "probability": 0.9724934895833334}, {"start": 110.87, "end": 111.39, "word": " الضرب", "probability": 0.8502604166666666}, {"start": 111.39, "end": 111.81, "word": " في", "probability": 0.96630859375}, {"start": 111.81, "end": 112.61, "word": " مقدار", "probability": 0.9443359375}, {"start": 112.61, "end": 113.11, "word": " قياسي", "probability": 0.9442138671875}, {"start": 113.11, "end": 113.31, "word": " او", "probability": 0.849365234375}, {"start": 113.31, "end": 113.83, "word": " مقدار", "probability": 0.9822591145833334}, {"start": 113.83, "end": 114.21, "word": " ثابت", "probability": 0.9939778645833334}, {"start": 114.21, "end": 114.43, "word": " لما", "probability": 0.88427734375}, {"start": 114.43, "end": 114.65, "word": " نقول", "probability": 0.891357421875}, {"start": 114.65, "end": 115.05, "word": " vector", "probability": 0.83935546875}], "temperature": 1.0}, {"id": 5, "seek": 14435, "start": 115.41, "end": 144.35, "text": "يبقى لو ضربناها في رقم نقول هذا هو scalar multiplication يعني ضرب قياسي يبقى احنا في عندنا set V ال V هذا بدأ أضع عليها عمليتين العملية الأولى عملية الجمع بين المتجهات الموجودة في V العملية الثانية أخد رقم من set of real numbers R وضربه في أي من المتجهات تبعات ال vector V", "tokens": [1829, 3555, 4587, 7578, 45164, 48812, 25513, 8315, 11296, 8978, 12602, 4587, 2304, 8717, 39648, 23758, 31439, 39684, 27290, 37495, 22653, 48812, 25513, 12174, 25528, 3794, 1829, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 8978, 43242, 8315, 992, 691, 2423, 691, 23758, 47525, 10721, 5551, 11242, 3615, 25894, 11296, 6225, 42213, 36081, 9957, 18863, 42213, 10632, 16247, 12610, 7578, 6225, 42213, 10632, 25724, 2304, 3615, 49374, 9673, 2655, 7435, 3224, 9307, 9673, 29245, 23328, 3660, 8978, 691, 18863, 42213, 10632, 6024, 104, 7649, 10632, 5551, 9778, 3215, 12602, 4587, 2304, 9154, 992, 295, 957, 3547, 497, 4032, 11242, 25513, 3224, 8978, 36632, 9154, 9673, 2655, 7435, 3224, 9307, 6055, 3555, 3615, 9307, 2423, 8062, 691], "avg_logprob": -0.17497306368474302, "compression_ratio": 1.822314049586777, "no_speech_prob": 0.0, "words": [{"start": 115.41, "end": 115.79, "word": "يبقى", "probability": 0.75799560546875}, {"start": 115.79, "end": 115.99, "word": " لو", "probability": 0.82275390625}, {"start": 115.99, "end": 116.51, "word": " ضربناها", "probability": 0.9490966796875}, {"start": 116.51, "end": 116.63, "word": " في", "probability": 0.87060546875}, {"start": 116.63, "end": 116.95, "word": " رقم", "probability": 0.9952799479166666}, {"start": 116.95, "end": 117.23, "word": " نقول", "probability": 0.54937744140625}, {"start": 117.23, "end": 117.53, "word": " هذا", "probability": 0.4326171875}, {"start": 117.53, "end": 118.01, "word": " هو", "probability": 0.3779296875}, {"start": 118.01, "end": 118.93, "word": " scalar", "probability": 0.6884765625}, {"start": 118.93, "end": 119.91, "word": " multiplication", "probability": 0.82568359375}, {"start": 119.91, "end": 120.41, "word": " يعني", "probability": 0.854736328125}, {"start": 120.41, "end": 120.91, "word": " ضرب", "probability": 0.855224609375}, {"start": 120.91, "end": 121.73, "word": " قياسي", "probability": 0.9581298828125}, {"start": 121.73, "end": 122.73, "word": " يبقى", "probability": 0.939453125}, {"start": 122.73, "end": 123.05, "word": " احنا", "probability": 0.86962890625}, {"start": 123.05, "end": 123.31, "word": " في", "probability": 0.86083984375}, {"start": 123.31, "end": 124.13, "word": " عندنا", "probability": 0.871826171875}, {"start": 124.13, "end": 124.55, "word": " set", "probability": 0.88720703125}, {"start": 124.55, "end": 125.01, "word": " V", "probability": 0.71875}, {"start": 125.01, "end": 125.55, "word": " ال", "probability": 0.6044921875}, {"start": 125.55, "end": 125.69, "word": " V", "probability": 0.52685546875}, {"start": 125.69, "end": 125.87, "word": " هذا", "probability": 0.609375}, {"start": 125.87, "end": 126.11, "word": " بدأ", "probability": 0.4932861328125}, {"start": 126.11, "end": 126.35, "word": " أضع", "probability": 0.5382486979166666}, {"start": 126.35, "end": 126.75, "word": " عليها", "probability": 0.973388671875}, {"start": 126.75, "end": 127.63, "word": " عمليتين", "probability": 0.8792724609375}, {"start": 127.63, "end": 128.67, "word": " العملية", "probability": 0.9695638020833334}, {"start": 128.67, "end": 129.13, "word": " الأولى", "probability": 0.9599609375}, {"start": 129.13, "end": 129.71, "word": " عملية", "probability": 0.9778645833333334}, {"start": 129.71, "end": 130.39, "word": " الجمع", "probability": 0.9541015625}, {"start": 130.39, "end": 130.87, "word": " بين", "probability": 0.986328125}, {"start": 130.87, "end": 132.41, "word": " المتجهات", "probability": 0.97685546875}, {"start": 132.41, "end": 133.55, "word": " الموجودة", "probability": 0.97265625}, {"start": 133.55, "end": 133.81, "word": " في", "probability": 0.9814453125}, {"start": 133.81, "end": 134.07, "word": " V", "probability": 0.9609375}, {"start": 134.07, "end": 135.13, "word": " العملية", "probability": 0.9637044270833334}, {"start": 135.13, "end": 135.47, "word": " الثانية", "probability": 0.9508056640625}, {"start": 135.47, "end": 136.03, "word": " أخد", "probability": 0.7431640625}, {"start": 136.03, "end": 136.77, "word": " رقم", "probability": 0.9978841145833334}, {"start": 136.77, "end": 137.07, "word": " من", "probability": 0.97998046875}, {"start": 137.07, "end": 137.43, "word": " set", "probability": 0.51806640625}, {"start": 137.43, "end": 137.67, "word": " of", "probability": 0.91455078125}, {"start": 137.67, "end": 137.89, "word": " real", "probability": 0.96826171875}, {"start": 137.89, "end": 138.49, "word": " numbers", "probability": 0.8681640625}, {"start": 138.49, "end": 138.87, "word": " R", "probability": 0.822265625}, {"start": 138.87, "end": 140.17, "word": " وضربه", "probability": 0.888671875}, {"start": 140.17, "end": 140.53, "word": " في", "probability": 0.98486328125}, {"start": 140.53, "end": 140.85, "word": " أي", "probability": 0.65380859375}, {"start": 140.85, "end": 141.45, "word": " من", "probability": 0.9853515625}, {"start": 141.45, "end": 143.03, "word": " المتجهات", "probability": 0.981640625}, {"start": 143.03, "end": 143.55, "word": " تبعات", "probability": 0.78033447265625}, {"start": 143.55, "end": 143.71, "word": " ال", "probability": 0.86328125}, {"start": 143.71, "end": 144.01, "word": " vector", "probability": 0.90625}, {"start": 144.01, "end": 144.35, "word": " V", "probability": 0.9140625}], "temperature": 1.0}, {"id": 6, "seek": 14955, "start": 144.53, "end": 149.55, "text": "يبقى هاي العمليتين اللي أنا بقول عليهم معرفتين كانوا معرفة ذاتي", "tokens": [1829, 3555, 4587, 7578, 8032, 47302, 18863, 42213, 36081, 9957, 13672, 1829, 41850, 4724, 39648, 25894, 16095, 20449, 28480, 2655, 9957, 25961, 14407, 20449, 28480, 3660, 29910, 9307, 1829], "avg_logprob": -0.29244790474573773, "compression_ratio": 1.3647058823529412, "no_speech_prob": 0.0, "words": [{"start": 144.53, "end": 145.15, "word": "يبقى", "probability": 0.8507080078125}, {"start": 145.15, "end": 145.37, "word": " هاي", "probability": 0.4554443359375}, {"start": 145.37, "end": 146.27, "word": " العمليتين", "probability": 0.831787109375}, {"start": 146.27, "end": 146.43, "word": " اللي", "probability": 0.896484375}, {"start": 146.43, "end": 146.59, "word": " أنا", "probability": 0.57861328125}, {"start": 146.59, "end": 146.81, "word": " بقول", "probability": 0.8310546875}, {"start": 146.81, "end": 146.83, "word": " عليهم", "probability": 0.802001953125}, {"start": 146.83, "end": 147.43, "word": " معرفتين", "probability": 0.907958984375}, {"start": 147.43, "end": 148.27, "word": " كانوا", "probability": 0.71826171875}, {"start": 148.27, "end": 148.97, "word": " معرفة", "probability": 0.8186848958333334}, {"start": 148.97, "end": 149.55, "word": " ذاتي", "probability": 0.8004557291666666}], "temperature": 1.0}, {"id": 7, "seek": 18199, "start": 166.65, "end": 181.99, "text": "عملية جمع متجهين من V هو متجه جديد موجود في V عملية ضرب scalar A في U هو بيعطيني متجه جديد هذا المتجه موجود في V كذلك R defined", "tokens": [25957, 1211, 10632, 10874, 2304, 3615, 44650, 7435, 3224, 9957, 9154, 691, 31439, 44650, 7435, 3224, 10874, 16254, 3215, 3714, 29245, 23328, 8978, 691, 6225, 42213, 10632, 48812, 25513, 39684, 316, 8978, 624, 31439, 4724, 40228, 9566, 1829, 22653, 44650, 7435, 3224, 10874, 16254, 3215, 23758, 9673, 2655, 7435, 3224, 3714, 29245, 23328, 8978, 691, 9122, 8848, 23275, 497, 7642], "avg_logprob": -0.1655993793831497, "compression_ratio": 1.5333333333333334, "no_speech_prob": 0.0, "words": [{"start": 166.65, "end": 167.43, "word": "عملية", "probability": 0.8759765625}, {"start": 167.43, "end": 167.85, "word": " جمع", "probability": 0.9422200520833334}, {"start": 167.85, "end": 168.79, "word": " متجهين", "probability": 0.944091796875}, {"start": 168.79, "end": 169.13, "word": " من", "probability": 0.89599609375}, {"start": 169.13, "end": 169.55, "word": " V", "probability": 0.71533203125}, {"start": 169.55, "end": 169.81, "word": " هو", "probability": 0.59375}, {"start": 169.81, "end": 170.41, "word": " متجه", "probability": 0.9890950520833334}, {"start": 170.41, "end": 171.11, "word": " جديد", "probability": 0.9772135416666666}, {"start": 171.11, "end": 171.91, "word": " موجود", "probability": 0.8761393229166666}, {"start": 171.91, "end": 172.15, "word": " في", "probability": 0.978515625}, {"start": 172.15, "end": 172.47, "word": " V", "probability": 0.9287109375}, {"start": 172.47, "end": 173.53, "word": " عملية", "probability": 0.9225260416666666}, {"start": 173.53, "end": 173.91, "word": " ضرب", "probability": 0.9833984375}, {"start": 173.91, "end": 174.45, "word": " scalar", "probability": 0.55517578125}, {"start": 174.45, "end": 175.19, "word": " A", "probability": 0.60888671875}, {"start": 175.19, "end": 175.59, "word": " في", "probability": 0.953125}, {"start": 175.59, "end": 175.99, "word": " U", "probability": 0.97265625}, {"start": 175.99, "end": 176.19, "word": " هو", "probability": 0.8896484375}, {"start": 176.19, "end": 176.61, "word": " بيعطيني", "probability": 0.68994140625}, {"start": 176.61, "end": 177.11, "word": " متجه", "probability": 0.9933268229166666}, {"start": 177.11, "end": 177.71, "word": " جديد", "probability": 0.9930013020833334}, {"start": 177.71, "end": 178.21, "word": " هذا", "probability": 0.77587890625}, {"start": 178.21, "end": 178.81, "word": " المتجه", "probability": 0.9862060546875}, {"start": 178.81, "end": 179.33, "word": " موجود", "probability": 0.9581705729166666}, {"start": 179.33, "end": 179.53, "word": " في", "probability": 0.986328125}, {"start": 179.53, "end": 179.81, "word": " V", 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يبين لي أن هذا ما هو واش vector space بيكفي ألغي شرط من الشروط العشرة", "tokens": [1829, 3555, 4587, 7578, 11933, 15730, 6055, 5016, 4587, 4587, 25124, 32887, 9566, 18863, 8592, 25720, 16712, 6027, 10632, 15844, 29538, 2423, 14851, 4724, 39648, 2423, 14851, 8032, 8848, 1829, 8062, 1901, 11933, 15730, 32767, 7251, 2655, 5016, 4587, 4587, 35525, 2407, 13412, 2288, 9566, 36764, 24401, 7251, 3555, 4587, 7578, 4724, 1829, 3555, 9566, 1211, 7251, 9381, 13546, 8062, 1901, 7251, 3555, 4587, 7578, 7251, 3555, 9957, 32239, 14739, 23758, 19446, 31439, 4032, 33599, 8062, 1901, 4724, 1829, 4117, 41185, 5551, 1211, 17082, 1829, 13412, 2288, 9566, 9154, 25124, 32887, 9566, 18863, 8592, 25720], "avg_logprob": -0.19726562158515057, "compression_ratio": 1.9039548022598871, "no_speech_prob": 0.0, "words": [{"start": 202.18, "end": 202.8, "word": "يبقى", "probability": 0.772491455078125}, {"start": 202.8, "end": 202.98, "word": " إذا", "probability": 0.81298828125}, {"start": 202.98, "end": 203.7, "word": 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vector لو جمعته إلى أي vector آخر من اليمين أو من الشمال بدي يعطيني نفس ال vector هذا ال element بقول عليه ال zero vector خاصية الخامسة لأي u موجود في capital V there exists لازم اللي أجي أسالي بـU موجود في V يعني", "tokens": [1829, 3555, 4587, 7578, 2423, 39184, 4018, 23758, 8062, 7251, 3555, 4587, 7578, 37893, 39684, 37495, 22653, 37893, 1230, 4032, 28814, 1863, 15042, 31439, 8062, 46811, 10943, 4724, 5016, 1829, 12984, 23758, 2423, 4018, 8062, 45164, 10874, 2304, 34268, 3224, 30731, 36632, 8062, 19753, 34740, 9154, 2423, 32640, 9957, 34051, 9154, 25124, 2304, 6027, 4724, 16254, 7251, 3615, 9566, 9957, 1829, 8717, 36178, 2423, 8062, 23758, 2423, 4478, 4724, 39648, 47356, 2423, 4018, 8062, 16490, 33546, 10632, 33962, 10943, 3794, 3660, 5296, 10721, 1829, 344, 3714, 29245, 23328, 8978, 4238, 691, 456, 8198, 5296, 31377, 2304, 13672, 1829, 5551, 7435, 1829, 5551, 3794, 6027, 1829, 4724, 39184, 52, 3714, 29245, 23328, 8978, 691, 37495, 22653], "avg_logprob": -0.24339978037209348, 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"end": 346.2, "word": " سالب", "probability": 0.7809244791666666}, {"start": 346.2, "end": 346.48, "word": " هذا", "probability": 0.9697265625}, {"start": 346.48, "end": 346.94, "word": " العنصر", "probability": 0.994873046875}, {"start": 346.94, "end": 348.56, "word": " موجود", "probability": 0.9689127604166666}, {"start": 348.56, "end": 348.68, "word": " في", "probability": 0.91650390625}, {"start": 348.68, "end": 348.94, "word": " V", "probability": 0.939453125}, {"start": 348.94, "end": 349.8, "word": " بحيث", "probability": 0.84326171875}, {"start": 349.8, "end": 350.46, "word": " لو", "probability": 0.8818359375}, {"start": 350.46, "end": 351.06, "word": " جمعت", "probability": 0.9918619791666666}, {"start": 351.06, "end": 351.28, "word": " ال", "probability": 0.74169921875}, {"start": 351.28, "end": 351.5, "word": " U", "probability": 0.90234375}, {"start": 351.5, "end": 352.4, "word": " وسالب", "probability": 0.8289388020833334}, {"start": 352.4, "end": 352.76, "word": " U", "probability": 0.96923828125}, {"start": 352.76, "end": 353.66, "word": " تماما", "probability": 0.98095703125}, {"start": 353.66, "end": 353.96, "word": " كما", "probability": 0.80419921875}, {"start": 353.96, "end": 354.16, "word": " لو", "probability": 0.990234375}, {"start": 354.16, "end": 354.56, "word": " جمعت", "probability": 0.9939778645833334}, {"start": 354.56, "end": 355.18, "word": " سالب", "probability": 0.9856770833333334}, {"start": 355.18, "end": 355.5, "word": " U", "probability": 0.97998046875}, {"start": 355.5, "end": 355.74, "word": " و", "probability": 0.94775390625}, {"start": 355.74, "end": 356.0, "word": " U", "probability": 0.71240234375}, {"start": 356.0, "end": 356.74, "word": " لأنه", "probability": 0.7239583333333334}, {"start": 356.74, "end": 356.92, "word": " قال", "probability": 0.75732421875}, {"start": 356.92, "end": 357.2, "word": " هنا", "probability": 0.91357421875}, {"start": 357.2, "end": 357.92, "word": " commutative", "probability": 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"compression_ratio": 1.6099290780141844, "no_speech_prob": 0.0, "words": [{"start": 359.69, "end": 360.17, "word": "الـ", "probability": 0.33599853515625}, {"start": 360.17, "end": 360.31, "word": " zero", "probability": 0.302978515625}, {"start": 360.31, "end": 360.75, "word": " vector", "probability": 0.921875}, {"start": 360.75, "end": 361.03, "word": " مش", "probability": 0.437744140625}, {"start": 361.03, "end": 361.27, "word": " الـ", "probability": 0.6522216796875}, {"start": 361.27, "end": 361.41, "word": " zero", "probability": 0.68798828125}, {"start": 361.41, "end": 361.87, "word": " scalar", "probability": 0.9365234375}, {"start": 361.87, "end": 362.63, "word": " لإن", "probability": 0.49853515625}, {"start": 362.63, "end": 362.83, "word": " احنا", "probability": 0.791015625}, {"start": 362.83, "end": 363.37, "word": " بنجمع", "probability": 0.963134765625}, {"start": 363.37, "end": 364.13, "word": " vectors", "probability": 0.83056640625}, {"start": 364.13, "end": 365.07, "word": " سالب", "probability": 0.6993001302083334}, {"start": 365.07, "end": 365.29, "word": " U", "probability": 0.53076171875}, {"start": 365.29, "end": 365.59, "word": " هو", "probability": 0.958984375}, {"start": 365.59, "end": 366.45, "word": " vector", "probability": 0.91748046875}, {"start": 366.45, "end": 367.63, "word": " يبقى", "probability": 0.9737548828125}, {"start": 367.63, "end": 367.97, "word": " U", "probability": 0.9453125}, {"start": 367.97, "end": 368.69, "word": " زائد", "probability": 0.7910970052083334}, {"start": 368.69, "end": 369.33, "word": " ناقص", "probability": 0.933837890625}, {"start": 369.33, "end": 369.79, "word": " U", "probability": 0.982421875}, {"start": 369.79, "end": 370.55, "word": " يسوى", "probability": 0.8131103515625}, {"start": 370.55, "end": 371.13, "word": " تماما", "probability": 0.9822591145833334}, {"start": 371.13, "end": 371.69, "word": " ناقص", "probability": 0.9754638671875}, {"start": 371.69, "end": 371.93, "word": " الـ", "probability": 0.58740234375}, {"start": 371.93, "end": 372.13, "word": " U", "probability": 0.880859375}, {"start": 372.13, "end": 372.73, "word": " زائد", "probability": 0.9695638020833334}, {"start": 372.73, "end": 372.91, "word": " الـ", "probability": 0.895263671875}, {"start": 372.91, "end": 373.05, "word": " U", "probability": 0.90673828125}, {"start": 373.05, "end": 373.33, "word": " بده", "probability": 0.445556640625}, {"start": 373.33, "end": 373.65, "word": " يسوى", "probability": 0.9010009765625}, {"start": 373.65, "end": 373.89, "word": " من", "probability": 0.50732421875}, {"start": 373.89, "end": 374.91, "word": " الـ", "probability": 0.6380615234375}, {"start": 374.91, "end": 375.19, "word": " zero", "probability": 0.60205078125}, {"start": 375.19, "end": 375.95, "word": " vector", "probability": 0.97265625}], "temperature": 1.0}, {"id": 17, "seek": 39906, "start": 376.46, "end": 399.06, "text": "هذه الخامسة الخاصية الساسة لو أخدت أي scalar من ال set of real number A أخدت عنصر A من ال set of real number و أخدت ال U vector موجود في V إذا حصل ضرب ل 2A في U بدي يكون موجود في V تماما تحققت الخاصية ده نروح بالخاصية اللي بعدها", "tokens": [3224, 24192, 33962, 10943, 3794, 3660, 33962, 33546, 10632, 21136, 32277, 3660, 45164, 5551, 9778, 3215, 2655, 36632, 39684, 9154, 2423, 992, 295, 957, 1230, 316, 5551, 9778, 3215, 2655, 18871, 9381, 2288, 316, 9154, 2423, 992, 295, 957, 1230, 4032, 5551, 9778, 3215, 2655, 2423, 624, 8062, 3714, 29245, 23328, 8978, 691, 11933, 15730, 11331, 36520, 48812, 25513, 5296, 568, 32, 8978, 624, 4724, 16254, 7251, 30544, 3714, 29245, 23328, 8978, 691, 46811, 10943, 995, 6055, 5016, 4587, 4587, 2655, 33962, 33546, 10632, 11778, 3224, 8717, 32887, 5016, 20666, 9778, 33546, 10632, 13672, 1829, 39182, 11296], "avg_logprob": -0.22656250152052665, "compression_ratio": 1.7574257425742574, "no_speech_prob": 0.0, "words": [{"start": 376.46, "end": 376.8, "word": "هذه", "probability": 0.6962890625}, {"start": 376.8, "end": 377.28, "word": " الخامسة", "probability": 0.77423095703125}, {"start": 377.28, "end": 377.78, "word": " الخاصية", "probability": 0.96337890625}, {"start": 377.78, "end": 378.22, "word": " الساسة", "probability": 0.6109212239583334}, {"start": 378.22, "end": 378.38, "word": " لو", "probability": 0.5185546875}, {"start": 378.38, "end": 378.84, "word": " أخدت", "probability": 0.8878173828125}, {"start": 378.84, "end": 379.18, "word": " أي", "probability": 0.81884765625}, {"start": 379.18, "end": 379.8, "word": " scalar", "probability": 0.73974609375}, {"start": 379.8, "end": 380.12, "word": " من", "probability": 0.966796875}, {"start": 380.12, "end": 380.28, "word": " ال", "probability": 0.84326171875}, {"start": 380.28, "end": 380.48, "word": " set", "probability": 0.2264404296875}, {"start": 380.48, "end": 380.64, "word": " of", "probability": 0.927734375}, {"start": 380.64, "end": 380.86, "word": " real", "probability": 0.95751953125}, {"start": 380.86, "end": 381.38, "word": " number", 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{"start": 391.78, "end": 392.06, "word": " بدي", "probability": 0.51190185546875}, {"start": 392.06, "end": 392.28, "word": " يكون", "probability": 0.8916015625}, {"start": 392.28, "end": 394.14, "word": " موجود", "probability": 0.96826171875}, {"start": 394.14, "end": 394.3, "word": " في", "probability": 0.7685546875}, {"start": 394.3, "end": 394.78, "word": " V", "probability": 0.83837890625}, {"start": 394.78, "end": 395.88, "word": " تماما", "probability": 0.9798177083333334}, {"start": 395.88, "end": 397.0, "word": " تحققت", "probability": 0.735693359375}, {"start": 397.0, "end": 397.52, "word": " الخاصية", "probability": 0.97265625}, {"start": 397.52, "end": 397.68, "word": " ده", "probability": 0.5006103515625}, {"start": 397.68, "end": 397.82, "word": " نروح", "probability": 0.6411946614583334}, {"start": 397.82, "end": 398.42, "word": " بالخاصية", "probability": 0.950439453125}, {"start": 398.42, "end": 398.6, "word": " اللي", "probability": 0.91552734375}, {"start": 398.6, 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"probability": 0.63262939453125}, {"start": 405.17, "end": 405.49, "word": " الـ", "probability": 0.767578125}, {"start": 405.49, "end": 405.67, "word": " A", "probability": 0.8408203125}, {"start": 405.67, "end": 406.25, "word": " ضد", "probability": 0.94384765625}, {"start": 406.25, "end": 406.59, "word": " الـ", "probability": 0.781982421875}, {"start": 406.59, "end": 406.97, "word": " U", "probability": 0.67236328125}, {"start": 406.97, "end": 407.41, "word": " زائد", "probability": 0.7421875}, {"start": 407.41, "end": 407.63, "word": " الـ", "probability": 0.85302734375}, {"start": 407.63, "end": 407.87, "word": " V", "probability": 0.75146484375}, {"start": 407.87, "end": 408.87, "word": " خضعت", "probability": 0.8767903645833334}, {"start": 408.87, "end": 409.17, "word": " هذه", "probability": 0.921875}, {"start": 409.17, "end": 410.21, "word": " لعمليات", "probability": 0.8302001953125}, {"start": 410.21, "end": 411.55, "word": " التوزيع", "probability": 0.980224609375}, {"start": 411.55, "end": 412.07, "word": " او", "probability": 0.678466796875}, {"start": 412.07, "end": 413.29, "word": " distributive", "probability": 0.6990966796875}, {"start": 413.29, "end": 414.19, "word": " property", "probability": 0.91064453125}, {"start": 414.19, "end": 414.83, "word": " خاصية", "probability": 0.8821614583333334}, {"start": 414.83, "end": 415.45, "word": " التوزيع", "probability": 0.976318359375}, {"start": 415.45, "end": 416.15, "word": " صارت", "probability": 0.8447265625}, {"start": 416.15, "end": 416.49, "word": " هذه", "probability": 0.923828125}, {"start": 416.49, "end": 416.85, "word": " A", "probability": 0.82421875}, {"start": 416.85, "end": 417.25, "word": " ضد", "probability": 0.9873046875}, {"start": 417.25, "end": 417.47, "word": " الـ", "probability": 0.731201171875}, {"start": 417.47, "end": 417.69, "word": " U", "probability": 0.8310546875}, {"start": 417.69, "end": 418.25, "word": " زائد", "probability": 0.958984375}, {"start": 418.25, "end": 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"probability": 0.8411458333333334}, {"start": 653.42, "end": 653.92, "word": " معاه", "probability": 0.8623046875}], "temperature": 1.0}, {"id": 28, "seek": 67717, "start": 654.07, "end": 677.17, "text": "نظيره بيقول then ال V is a vector space because يبقى هذا اللي فوق تحت عملية الجامعة العادية والضرب العادية دي بيكون vector space ما هو السبب بيقول لو أخدت three vectors موجودات في V طلعي المركبة طلعي كله المركبة الأولى والمركبة الأولى", "tokens": [1863, 19913, 13546, 3224, 4724, 1829, 39648, 550, 2423, 691, 307, 257, 8062, 1901, 570, 7251, 3555, 4587, 7578, 23758, 13672, 1829, 6156, 30543, 6055, 33753, 6225, 42213, 10632, 25724, 10943, 27884, 18863, 18513, 10632, 16070, 11242, 25513, 18863, 18513, 10632, 11778, 1829, 4724, 1829, 30544, 8062, 1901, 19446, 31439, 21136, 3555, 3555, 4724, 1829, 39648, 45164, 5551, 9778, 3215, 2655, 1045, 18875, 3714, 29245, 23328, 9307, 8978, 691, 23032, 1211, 3615, 1829, 9673, 31747, 49401, 23032, 1211, 3615, 1829, 28242, 3224, 9673, 31747, 49401, 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659.25, "end": 660.31, "word": " يبقى", "probability": 0.9637451171875}, {"start": 660.31, "end": 660.93, "word": " هذا", "probability": 0.90625}, {"start": 660.93, "end": 661.23, "word": " اللي", "probability": 0.943603515625}, {"start": 661.23, "end": 661.65, "word": " فوق", "probability": 0.978271484375}, {"start": 661.65, "end": 662.03, "word": " تحت", "probability": 0.993408203125}, {"start": 662.03, "end": 662.49, "word": " عملية", "probability": 0.9934895833333334}, {"start": 662.49, "end": 662.91, "word": " الجامعة", "probability": 0.6531575520833334}, {"start": 662.91, "end": 663.33, "word": " العادية", "probability": 0.9879557291666666}, {"start": 663.33, "end": 663.85, "word": " والضرب", "probability": 0.8009440104166666}, {"start": 663.85, "end": 664.47, "word": " العادية", "probability": 0.9440104166666666}, {"start": 664.47, "end": 665.17, "word": " دي", "probability": 0.6361083984375}, {"start": 665.17, "end": 665.65, "word": " بيكون", "probability": 0.9300130208333334}, {"start": 665.65, "end": 666.01, "word": " vector", "probability": 0.927734375}, {"start": 666.01, "end": 666.43, "word": " space", "probability": 0.962890625}, {"start": 666.43, "end": 666.65, "word": " ما", "probability": 0.89453125}, {"start": 666.65, "end": 666.89, "word": " هو", "probability": 0.91845703125}, {"start": 666.89, "end": 667.43, "word": " السبب", "probability": 0.9856770833333334}, {"start": 667.43, "end": 668.21, "word": " بيقول", "probability": 0.8030598958333334}, {"start": 668.21, "end": 668.45, "word": " لو", "probability": 0.92724609375}, {"start": 668.45, "end": 669.05, "word": " أخدت", "probability": 0.9534912109375}, {"start": 669.05, "end": 669.43, "word": " three", "probability": 0.88525390625}, {"start": 669.43, "end": 670.03, "word": " vectors", "probability": 0.96044921875}, {"start": 670.03, "end": 670.75, "word": " موجودات", "probability": 0.90771484375}, {"start": 670.75, "end": 670.93, "word": " في", "probability": 0.896484375}, {"start": 670.93, "end": 671.09, "word": " V", "probability": 0.94482421875}, {"start": 671.09, "end": 671.83, "word": " طلعي", "probability": 0.8773193359375}, {"start": 671.83, "end": 673.13, "word": " المركبة", "probability": 0.6189778645833334}, {"start": 673.13, "end": 673.93, "word": " طلعي", "probability": 0.83026123046875}, {"start": 673.93, "end": 674.35, "word": " كله", "probability": 0.812255859375}, {"start": 674.35, "end": 675.25, "word": " المركبة", "probability": 0.97216796875}, {"start": 675.25, "end": 675.77, "word": " الأولى", "probability": 0.97607421875}, {"start": 675.77, "end": 676.55, "word": " والمركبة", "probability": 0.76556396484375}, {"start": 676.55, "end": 677.17, "word": " الأولى", "probability": 0.98828125}], "temperature": 1.0}, {"id": 29, "seek": 69573, "start": 678.71, "end": 695.73, "text": "والمُركّب الأولى كله بأسفار موجودة في V بداية أشوف الخواصة العاشرة هل ال U زائد ال V موجود في V ولا لأ يبقى بداية للخاصية الأولى", "tokens": [2407, 45340, 10859, 31747, 11703, 3555, 16247, 12610, 7578, 28242, 3224, 4724, 10721, 3794, 5172, 9640, 3714, 29245, 23328, 3660, 8978, 691, 4724, 28259, 10632, 5551, 8592, 38688, 33962, 2407, 33546, 3660, 18863, 33599, 25720, 8032, 1211, 2423, 624, 30767, 16373, 3215, 2423, 691, 3714, 29245, 23328, 8978, 691, 49429, 5296, 10721, 7251, 3555, 4587, 7578, 4724, 28259, 10632, 24976, 9778, 33546, 10632, 16247, 12610, 7578], "avg_logprob": -0.28125001067545874, "compression_ratio": 1.6214285714285714, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 678.71, "end": 679.61, "word": "والمُركّب", "probability": 0.57586669921875}, {"start": 679.61, "end": 680.31, "word": " الأولى", "probability": 0.7919921875}, {"start": 680.31, "end": 680.71, "word": " كله", "probability": 0.759033203125}, {"start": 680.71, "end": 682.31, "word": " بأسفار", "probability": 0.84052734375}, {"start": 682.31, "end": 685.99, "word": " موجودة", "probability": 0.8604736328125}, {"start": 685.99, "end": 686.21, "word": " في", "probability": 0.96337890625}, {"start": 686.21, "end": 686.49, "word": " V", "probability": 0.599609375}, {"start": 686.49, "end": 687.45, "word": " بداية", "probability": 0.52020263671875}, {"start": 687.45, "end": 687.85, "word": " أشوف", "probability": 0.7955729166666666}, {"start": 687.85, "end": 688.53, "word": " الخواصة", "probability": 0.71533203125}, {"start": 688.53, "end": 689.07, "word": " العاشرة", "probability": 0.8416341145833334}, {"start": 689.07, "end": 690.25, "word": " هل", "probability": 0.91552734375}, {"start": 690.25, "end": 690.61, "word": " ال", "probability": 0.80078125}, {"start": 690.61, "end": 690.87, "word": " U", "probability": 0.51513671875}, {"start": 690.87, "end": 691.35, "word": " زائد", "probability": 0.8115234375}, {"start": 691.35, "end": 691.49, "word": " ال", "probability": 0.55712890625}, {"start": 691.49, "end": 691.69, "word": " V", "probability": 0.97705078125}, {"start": 691.69, "end": 692.15, "word": " موجود", "probability": 0.9861653645833334}, {"start": 692.15, "end": 692.37, "word": " في", "probability": 0.94873046875}, {"start": 692.37, "end": 692.61, "word": " V", "probability": 0.98095703125}, {"start": 692.61, "end": 692.85, "word": " ولا", "probability": 0.7783203125}, {"start": 692.85, "end": 693.21, "word": " لأ", "probability": 0.827392578125}, {"start": 693.21, "end": 693.89, "word": " يبقى", "probability": 0.83685302734375}, {"start": 693.89, "end": 694.33, "word": " بداية", "probability": 0.8455403645833334}, {"start": 694.33, "end": 695.19, "word": " للخاصية", "probability": 0.89111328125}, {"start": 695.19, "end": 695.73, "word": " الأولى", "probability": 0.9939778645833334}], "temperature": 1.0}, {"id": 30, "seek": 70949, "start": 696.43, "end": 709.49, "text": "نمر واحد بيداخد ال U زائد ال V يبقى هذا بده يعطيني Zero و X واحد و X اتنين زائد Zero و Y واحد و Y اتنين و Y ساوي", "tokens": [1863, 29973, 36764, 24401, 4724, 25708, 47283, 3215, 2423, 624, 30767, 16373, 3215, 2423, 691, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 37495, 9566, 1829, 22653, 17182, 4032, 1783, 36764, 24401, 4032, 1783, 1975, 2655, 1863, 9957, 30767, 16373, 3215, 17182, 4032, 398, 36764, 24401, 4032, 398, 1975, 2655, 1863, 9957, 4032, 398, 8608, 995, 45865], "avg_logprob": -0.31195175020318283, "compression_ratio": 1.5384615384615385, "no_speech_prob": 0.0, "words": [{"start": 696.43, "end": 697.07, "word": "نمر", "probability": 0.37451171875}, {"start": 697.07, "end": 697.53, "word": " واحد", "probability": 0.77294921875}, {"start": 697.53, "end": 698.23, "word": " بيداخد", "probability": 0.4565277099609375}, {"start": 698.23, "end": 698.45, "word": " ال", "probability": 0.90966796875}, {"start": 698.45, "end": 698.81, "word": " U", "probability": 0.441650390625}, {"start": 698.81, "end": 699.79, "word": " زائد", "probability": 0.7332356770833334}, {"start": 699.79, "end": 700.05, "word": " ال", "probability": 0.8583984375}, {"start": 700.05, "end": 700.37, "word": " V", "probability": 0.966796875}, {"start": 700.37, "end": 701.25, "word": " يبقى", "probability": 0.91162109375}, {"start": 701.25, "end": 701.47, "word": " هذا", "probability": 0.8720703125}, {"start": 701.47, "end": 701.89, "word": " بده", "probability": 0.51617431640625}, {"start": 701.89, "end": 702.37, "word": " يعطيني", "probability": 0.7738037109375}, {"start": 702.37, "end": 702.87, "word": " Zero", "probability": 0.40380859375}, {"start": 702.87, "end": 703.21, "word": " و", "probability": 0.65185546875}, {"start": 703.21, "end": 703.53, "word": " X", "probability": 0.904296875}, {"start": 703.53, "end": 704.05, "word": " واحد", "probability": 0.9111328125}, {"start": 704.05, "end": 704.31, "word": " و", "probability": 0.947265625}, {"start": 704.31, "end": 704.63, "word": " X", "probability": 0.94677734375}, {"start": 704.63, "end": 705.21, "word": " اتنين", "probability": 0.9105224609375}, {"start": 705.21, "end": 706.19, "word": " زائد", "probability": 0.97021484375}, {"start": 706.19, "end": 706.65, "word": " Zero", "probability": 0.9091796875}, {"start": 706.65, "end": 706.87, "word": " و", "probability": 0.327880859375}, {"start": 706.87, "end": 707.07, "word": " Y", "probability": 0.912109375}, {"start": 707.07, "end": 707.67, "word": " واحد", "probability": 0.972900390625}, {"start": 707.67, "end": 707.85, "word": " و", "probability": 0.97021484375}, {"start": 707.85, "end": 708.13, "word": " Y", "probability": 0.94091796875}, {"start": 708.13, "end": 708.63, "word": " اتنين", "probability": 0.970703125}, {"start": 708.63, "end": 708.79, "word": " و", "probability": 0.8193359375}, {"start": 708.79, "end": 708.99, "word": " Y", "probability": 0.89697265625}, {"start": 708.99, "end": 709.49, "word": " ساوي", "probability": 0.618408203125}], "temperature": 1.0}, {"id": 31, "seek": 73034, "start": 710.82, "end": 730.34, "text": "أحنا قلنا هذه عملية الجمع عادية لمن؟ للـ vectors يبقى عملية الجمع العادية بجمع component y 0 مع 0 بقدرش 0 X1 زائد Y1 X2 زائد Y2 موجودة في V ولا يا بنات؟", "tokens": [10721, 5016, 8315, 12174, 1211, 8315, 29538, 6225, 42213, 10632, 25724, 2304, 3615, 6225, 18513, 10632, 5296, 27842, 22807, 24976, 39184, 18875, 7251, 3555, 4587, 7578, 6225, 42213, 10632, 25724, 2304, 3615, 18863, 18513, 10632, 4724, 7435, 2304, 3615, 6542, 288, 1958, 20449, 1958, 4724, 28543, 2288, 8592, 1958, 1783, 16, 30767, 16373, 3215, 398, 16, 1783, 17, 30767, 16373, 3215, 398, 17, 3714, 29245, 23328, 3660, 8978, 691, 49429, 35186, 4724, 8315, 2655, 22807], "avg_logprob": -0.28104441926667567, "compression_ratio": 1.4817073170731707, "no_speech_prob": 0.0, "words": [{"start": 710.82, "end": 711.26, "word": "أحنا", "probability": 0.6936848958333334}, {"start": 711.26, "end": 711.62, "word": " قلنا", "probability": 0.9016927083333334}, {"start": 711.62, "end": 711.96, "word": " هذه", "probability": 0.3798828125}, {"start": 711.96, "end": 712.72, "word": " عملية", "probability": 0.9798177083333334}, {"start": 712.72, "end": 713.2, "word": " الجمع", "probability": 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0.1593017578125}, {"start": 720.54, "end": 720.84, "word": " مع", "probability": 0.75439453125}, {"start": 720.84, "end": 721.24, "word": " 0", "probability": 0.888671875}, {"start": 721.24, "end": 722.04, "word": " بقدرش", "probability": 0.6837158203125}, {"start": 722.04, "end": 722.94, "word": " 0", "probability": 0.1824951171875}, {"start": 722.94, "end": 723.96, "word": " X1", "probability": 0.4786376953125}, {"start": 723.96, "end": 724.48, "word": " زائد", "probability": 0.7616373697916666}, {"start": 724.48, "end": 725.2, "word": " Y1", "probability": 0.97265625}, {"start": 725.2, "end": 726.36, "word": " X2", "probability": 0.92138671875}, {"start": 726.36, "end": 727.54, "word": " زائد", "probability": 0.9680989583333334}, {"start": 727.54, "end": 728.44, "word": " Y2", "probability": 0.995849609375}, {"start": 728.44, "end": 728.98, "word": " موجودة", "probability": 0.958984375}, {"start": 728.98, "end": 729.14, "word": " في", "probability": 0.98779296875}, {"start": 729.14, 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" اتنين", "probability": 0.9693603515625}, {"start": 1550.71, "end": 1551.53, "word": " يبقى", "probability": 0.9775390625}, {"start": 1551.53, "end": 1551.85, "word": " هذه", "probability": 0.626953125}, {"start": 1551.85, "end": 1552.27, "word": " بدأت", "probability": 0.5713704427083334}, {"start": 1552.27, "end": 1552.67, "word": " تساوي", "probability": 0.838134765625}, {"start": 1552.67, "end": 1553.21, "word": " A", "probability": 0.890625}, {"start": 1553.21, "end": 1553.71, "word": " ضد", "probability": 0.6640625}, {"start": 1553.71, "end": 1554.11, "word": " الـ", "probability": 0.674072265625}, {"start": 1554.11, "end": 1554.39, "word": " U", "probability": 0.84912109375}, {"start": 1554.39, "end": 1555.49, "word": " زائد", "probability": 0.9715169270833334}, {"start": 1555.49, "end": 1556.05, "word": " B", "probability": 0.986328125}, {"start": 1556.05, "end": 1556.73, "word": " ضد", "probability": 0.99462890625}, {"start": 1556.73, "end": 1557.03, "word": " الـ", "probability": 0.988525390625}, {"start": 1557.03, "end": 1557.23, "word": " U", "probability": 0.8291015625}, {"start": 1557.23, "end": 1558.35, "word": " وبالتالي", "probability": 0.9439453125}, {"start": 1558.35, "end": 1559.09, "word": " تحققت", "probability": 0.9208984375}, {"start": 1559.09, "end": 1559.81, "word": " الخاصية", "probability": 0.9861653645833334}, {"start": 1559.81, "end": 1560.51, "word": " رقم", "probability": 0.9931640625}, {"start": 1560.51, "end": 1561.75, "word": " تمانية", "probability": 0.8606770833333334}, {"start": 1561.75, "end": 1562.51, "word": " يبقى", "probability": 0.9637451171875}, {"start": 1562.51, "end": 1563.15, "word": " تمانية", "probability": 0.9749348958333334}], "temperature": 1.0}, {"id": 68, "seek": 157906, "start": 1567.78, "end": 1579.06, "text": "الخاصية التاسعة يبقى الفرصة التاسعة", "tokens": [6027, 9778, 33546, 10632, 16712, 32277, 27884, 7251, 3555, 4587, 7578, 27188, 2288, 9381, 3660, 16712, 32277, 27884], "avg_logprob": 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"probability": 0.8681640625}], "temperature": 1.0}, {"id": 80, "seek": 187009, "start": 1840.93, "end": 1870.09, "text": "under usual addition تحت عملية الجامعة العادية and وفي نفس الوقت usual scalar multiplication usual scalar multiplication تحت عملية الجامعة الدرب والجامعة العادية then", "tokens": [6617, 7713, 4500, 6055, 33753, 6225, 42213, 10632, 25724, 10943, 27884, 18863, 18513, 10632, 293, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 7713, 39684, 27290, 7713, 39684, 27290, 6055, 33753, 6225, 42213, 10632, 25724, 10943, 27884, 32748, 25513, 16070, 7435, 10943, 27884, 18863, 18513, 10632, 550], "avg_logprob": -0.1576629046429979, "compression_ratio": 1.8425196850393701, "no_speech_prob": 0.0, "words": [{"start": 1840.93, "end": 1841.59, "word": "under", "probability": 0.2705078125}, {"start": 1841.59, "end": 1843.29, "word": " usual", "probability": 0.80908203125}, {"start": 1843.29, "end": 1845.13, "word": " addition", "probability": 0.900390625}, {"start": 1845.13, "end": 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"compression_ratio": 0.7241379310344828, "no_speech_prob": 0.0, "words": [{"start": 1871.45, "end": 1872.07, "word": "is", "probability": 0.060638427734375}, {"start": 1872.07, "end": 1878.19, "word": " not", "probability": 0.95556640625}, {"start": 1878.19, "end": 1879.85, "word": " a", "probability": 0.89111328125}, {"start": 1879.85, "end": 1880.27, "word": " vector", "probability": 0.9638671875}, {"start": 1880.27, "end": 1886.43, "word": " space", "probability": 0.919921875}], "temperature": 1.0}, {"id": 82, "seek": 192210, "start": 1892.72, "end": 1922.1, "text": "ومجرد النظر هذا ال 6 اللي عندنا هذه تحت عملية الجمع العادية و الضرب العادية ليست في الاقتراضية ليه؟ بدي واحدة تحكي بس واحدة ترفع أيديها و تحكي انا بقول فيش zero element ماعشي الحالة هذا وجهة نظر في وجهة نظر تانية؟ قبل ال zero طب شوفي اللي قبل ال zero اجمع اتنين اجمع لو جمعت اتنين ايش بطلع؟", "tokens": [2407, 2304, 7435, 2288, 3215, 28239, 19913, 2288, 23758, 2423, 1386, 13672, 1829, 43242, 8315, 29538, 6055, 33753, 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ترفع", "probability": 0.9617513020833334}, {"start": 1904.04, "end": 1904.24, "word": " أيديها", "probability": 0.5384114583333334}, {"start": 1904.24, "end": 1904.34, "word": " و", "probability": 0.453857421875}, {"start": 1904.34, "end": 1904.52, "word": " تحكي", "probability": 0.8275146484375}, {"start": 1904.52, "end": 1904.88, "word": " انا", "probability": 0.6068115234375}, {"start": 1904.88, "end": 1905.16, "word": " بقول", "probability": 0.825439453125}, {"start": 1905.16, "end": 1905.44, "word": " فيش", "probability": 0.54022216796875}, {"start": 1905.44, "end": 1905.88, "word": " zero", "probability": 0.5595703125}, {"start": 1905.88, "end": 1908.02, "word": " element", "probability": 0.90087890625}, {"start": 1908.02, "end": 1908.84, "word": " ماعشي", "probability": 0.55816650390625}, {"start": 1908.84, "end": 1909.18, "word": " الحالة", "probability": 0.681884765625}, {"start": 1909.18, "end": 1909.34, "word": " هذا", "probability": 0.6533203125}, {"start": 1909.34, "end": 1909.68, "word": " وجهة", "probability": 0.8875325520833334}, {"start": 1909.68, "end": 1910.34, "word": " نظر", "probability": 0.98876953125}, {"start": 1910.34, "end": 1910.58, "word": " في", "probability": 0.65576171875}, {"start": 1910.58, "end": 1910.88, "word": " وجهة", "probability": 0.98095703125}, {"start": 1910.88, "end": 1911.14, "word": " نظر", "probability": 0.9969075520833334}, {"start": 1911.14, "end": 1912.42, "word": " تانية؟", "probability": 0.8509521484375}, {"start": 1912.42, "end": 1914.14, "word": " قبل", "probability": 0.71240234375}, {"start": 1914.14, "end": 1914.28, "word": " ال", "probability": 0.51171875}, {"start": 1914.28, "end": 1914.52, "word": " zero", "probability": 0.71044921875}, {"start": 1914.52, "end": 1914.74, "word": " طب", "probability": 0.909912109375}, {"start": 1914.74, "end": 1915.04, "word": " شوفي", "probability": 0.8779296875}, {"start": 1915.04, "end": 1915.2, "word": " اللي", "probability": 0.893798828125}, {"start": 1915.2, "end": 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0.6863606770833334}, {"start": 2457.04, "end": 2457.4, "word": " يبقى", "probability": 0.9786376953125}, {"start": 2457.4, "end": 2457.7, "word": " ايش", "probability": 0.623046875}, {"start": 2457.7, "end": 2458.18, "word": " رأيك؟", "probability": 0.82666015625}, {"start": 2458.18, "end": 2458.5, "word": " هل", "probability": 0.9697265625}, {"start": 2458.5, "end": 2458.98, "word": " هذه", "probability": 0.61767578125}, {"start": 2458.98, "end": 2459.2, "word": " اللي", "probability": 0.972900390625}, {"start": 2459.2, "end": 2459.98, "word": " فوق", "probability": 0.66650390625}, {"start": 2459.98, "end": 2461.08, "word": " هي", "probability": 0.81494140625}, {"start": 2461.08, "end": 2461.86, "word": " هذه؟", "probability": 0.841064453125}], "temperature": 1.0}, {"id": 104, "seek": 248979, "start": 2462.55, "end": 2489.79, "text": "طبعا هذه بقدر اقول a زائد ال b في ال x و اتنين y و اتنين z طبعا اللي فوق ماهياش اللي تحت يبقى هنا ال a زائد ال b ضات ال u لا يساوي ال au زائد ال b ال a 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0.9642333984375}, {"start": 2469.41, "end": 2469.79, "word": " z", "probability": 0.9931640625}, {"start": 2469.79, "end": 2470.59, "word": " طبعا", "probability": 0.967529296875}, {"start": 2470.59, "end": 2470.75, "word": " اللي", "probability": 0.768310546875}, {"start": 2470.75, "end": 2470.99, "word": " فوق", "probability": 0.96337890625}, {"start": 2470.99, "end": 2471.51, "word": " ماهياش", "probability": 0.79766845703125}, {"start": 2471.51, "end": 2471.71, "word": " اللي", "probability": 0.987548828125}, {"start": 2471.71, "end": 2472.15, "word": " تحت", "probability": 0.893798828125}, {"start": 2472.15, "end": 2473.23, "word": " يبقى", "probability": 0.88671875}, {"start": 2473.23, "end": 2473.63, "word": " هنا", "probability": 0.96044921875}, {"start": 2473.63, "end": 2474.37, "word": " ال", "probability": 0.27490234375}, {"start": 2474.37, "end": 2475.37, "word": " a", "probability": 0.83984375}, {"start": 2475.37, "end": 2476.37, "word": " زائد", "probability": 0.95947265625}, {"start": 2476.37, "end": 2476.61, "word": " ال", "probability": 0.919921875}, {"start": 2476.61, "end": 2477.17, "word": " b", "probability": 0.9609375}, {"start": 2477.17, "end": 2478.25, "word": " ضات", "probability": 0.481201171875}, {"start": 2478.25, "end": 2478.57, "word": " ال", "probability": 0.9501953125}, {"start": 2478.57, "end": 2478.93, "word": " u", "probability": 0.939453125}, {"start": 2478.93, "end": 2479.71, "word": " لا", "probability": 0.7421875}, {"start": 2479.71, "end": 2480.85, "word": " يساوي", "probability": 0.873046875}, {"start": 2480.85, "end": 2481.57, "word": " ال", "probability": 0.77587890625}, {"start": 2481.57, "end": 2482.31, "word": " au", "probability": 0.5}, {"start": 2482.31, "end": 2484.81, "word": " زائد", "probability": 0.91845703125}, {"start": 2484.81, "end": 2485.53, "word": " ال", "probability": 0.91064453125}, {"start": 2485.53, "end": 2486.07, "word": " b", "probability": 0.93603515625}, {"start": 2486.07, "end": 2486.57, "word": " ال", "probability": 0.452880859375}, {"start": 2486.57, "end": 2486.77, "word": " a", "probability": 0.9677734375}, {"start": 2486.77, "end": 2487.09, "word": " ضات", "probability": 0.89453125}, {"start": 2487.09, "end": 2487.29, "word": " ال", "probability": 0.982421875}, {"start": 2487.29, "end": 2487.57, "word": " u", "probability": 0.99169921875}, {"start": 2487.57, "end": 2488.47, "word": " زائد", "probability": 0.9793294270833334}, {"start": 2488.47, "end": 2488.67, "word": " ال", "probability": 0.93115234375}, {"start": 2488.67, "end": 2488.93, "word": " b", "probability": 0.962890625}, {"start": 2488.93, "end": 2489.39, "word": " ضات", "probability": 0.9755859375}, {"start": 2489.39, "end": 2489.63, "word": " ال", "probability": 0.984375}, {"start": 2489.63, "end": 2489.79, "word": " u", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 105, "seek": 249682, "start": 2490.46, "end": 2496.82, "text": "لا يزال هناك العديد من الأمثلة نتعرض لها المرة القادمة ان شاء الله تعالى", "tokens": [15040, 7251, 11622, 6027, 34105, 4117, 18863, 16254, 3215, 9154, 16247, 2304, 12984, 37977, 8717, 2655, 3615, 43042, 5296, 11296, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 37279, 6027, 7578], "avg_logprob": -0.17613636363636365, "compression_ratio": 1.3936170212765957, "no_speech_prob": 0.0, "words": [{"start": 2490.46, "end": 2490.8, "word": "لا", "probability": 0.490966796875}, {"start": 2490.8, "end": 2491.24, "word": " يزال", "probability": 0.9710286458333334}, {"start": 2491.24, "end": 2491.7, "word": " هناك", "probability": 0.968017578125}, {"start": 2491.7, "end": 2492.14, "word": " العديد", "probability": 0.8956705729166666}, {"start": 2492.14, "end": 2492.28, "word": " من", "probability": 0.9892578125}, {"start": 2492.28, "end": 2492.94, "word": " الأمثلة", "probability": 0.9833984375}, {"start": 2492.94, "end": 2493.88, "word": " نتعرض", "probability": 0.80560302734375}, {"start": 2493.88, "end": 2494.1, "word": " لها", "probability": 0.944580078125}, {"start": 2494.1, "end": 2494.48, "word": " المرة", "probability": 0.947021484375}, {"start": 2494.48, "end": 2495.26, "word": " القادمة", "probability": 0.9951171875}, {"start": 2495.26, "end": 2495.66, "word": " ان", "probability": 0.40966796875}, {"start": 2495.66, "end": 2496.0, "word": " شاء", "probability": 0.96240234375}, {"start": 2496.0, "end": 2496.22, "word": " الله", "probability": 0.9638671875}, {"start": 2496.22, "end": 2496.82, "word": " تعالى", "probability": 0.7517903645833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2497.53825, "duration_after_vad": 2417.6849999999918}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0706ef2c6f529a990e046edf58dc0aac9fa489e3
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/7876uCpWVEQ_raw.srt
@@ -0,0 +1,1532 @@
+1
+00:00:19,390 --> 00:00:23,870
+بسم الله الرحمن الرحيم انتهينا في أول chapter من
+
+2
+00:00:23,870 --> 00:00:27,410
+الجابرة الخاطية و هو chapter 2 والان بنروح لل
+
+3
+00:00:27,410 --> 00:00:31,030
+chapter الثاني من الجابرة الخاطية و هو chapter 3
+
+4
+00:00:31,030 --> 00:00:35,870
+من الكتاب المقرر هذا ال chapter يتحدث عن نقطتين
+
+5
+00:00:35,870 --> 00:00:39,910
+رئيسيتين النقطة الأولى هي ال vector spaces و
+
+6
+00:00:39,910 --> 00:00:43,890
+النقطة الثانية هي ال linear transformations يعني
+
+7
+00:00:43,890 --> 00:00:48,830
+التحويلات الخاطيةموضوعنا اليوم موضوع ال vector
+
+8
+00:00:48,830 --> 00:00:54,070
+spaces وعلى مدار الأيام القادمة كذلك لكننا في هذا
+
+9
+00:00:54,070 --> 00:00:58,550
+ال section فقط سنعطي تعريف لل vector space ونعطي
+
+10
+00:00:58,550 --> 00:01:04,670
+بعض الأمثلة عليه فقط لا غير ومن ثم ننتقل إلى بقية
+
+11
+00:01:04,670 --> 00:01:09,450
+الأجزاء التي تتعلق بال vector spaces يبقى احنا
+
+12
+00:01:09,450 --> 00:01:16,950
+عندنا vector spaces يعني الفضاءات الاتجاهيةبدنا
+
+13
+00:01:16,950 --> 00:01:22,530
+نعطي تعريف للفضاء الاتجاهي ونشوف كيف نطبق التعريف
+
+14
+00:01:22,530 --> 00:01:28,090
+على الأمثلة المختلفةبقول افترض ان capital V عبارة
+
+15
+00:01:28,090 --> 00:01:32,370
+عن non-empty set of objects يبقى انا عندي capital
+
+16
+00:01:32,370 --> 00:01:37,650
+V هي عبارة عن مجموعة وهذه المجموعة تحتوي على عدد
+
+17
+00:01:37,650 --> 00:01:41,750
+من العناصر in which two operations addition and
+
+18
+00:01:41,750 --> 00:01:45,610
+multiplication by scalars are defined وعليها
+
+19
+00:01:45,610 --> 00:01:50,030
+عمليتين معرفتين عملية بنسميها عملية الجمع والثانية
+
+20
+00:01:50,030 --> 00:01:54,650
+عملية الضرب في مقدار قياسي او مقدار ثابت لما نقول
+
+21
+00:01:54,650 --> 00:01:58,930
+vectorيبقى لو ضربناها في رقم نقول هذا هو scalar
+
+22
+00:01:58,930 --> 00:02:04,130
+multiplication يعني ضرب قياسي يبقى احنا في عندنا
+
+23
+00:02:04,130 --> 00:02:08,670
+set V ال V هذا بدأ أضع عليها عمليتين العملية
+
+24
+00:02:08,670 --> 00:02:14,070
+الأولى عملية الجمع بين المتجهات الموجودة في V
+
+25
+00:02:14,070 --> 00:02:18,870
+العملية الثانية أخد رقم من set of real numbers R
+
+26
+00:02:18,870 --> 00:02:25,370
+وضربه في أي من المتجهات تبعات ال vector Vيبقى هاي
+
+27
+00:02:25,370 --> 00:02:28,970
+العمليتين اللي أنا بقول عليهم معرفتين كانوا معرفة
+
+28
+00:02:28,970 --> 00:02:29,550
+ذاتي
+
+29
+00:02:46,650 --> 00:02:52,470
+عملية جمع متجهين من V هو متجه جديد موجود في V
+
+30
+00:02:52,470 --> 00:02:58,210
+عملية ضرب scalar A في U هو بيعطيني متجه جديد هذا
+
+31
+00:02:58,210 --> 00:03:04,030
+المتجه موجود في V كذلك R definedيبقى في هذه الحالة
+
+32
+00:03:04,030 --> 00:03:08,170
+بيقول إن ال V وعليها عملية الجمع وعليها عملية
+
+33
+00:03:08,170 --> 00:03:13,390
+الضرب base color is a vector space أو linear space
+
+34
+00:03:13,390 --> 00:03:16,830
+بعض الكتب بتقول عنه vector space و بعض الكتب بتقول
+
+35
+00:03:16,830 --> 00:03:19,890
+عنه linear space if the following properties are
+
+36
+00:03:19,890 --> 00:03:26,080
+satisfied على Vيبقى إذا تحقق الشروط العشرة التالية
+
+37
+00:03:26,080 --> 00:03:31,540
+على هذه الست بقول الست هذي vector space إذا لم
+
+38
+00:03:31,540 --> 00:03:36,640
+يتحقق ولو شرط واحد يبقى بيبطل يصير vector space
+
+39
+00:03:36,640 --> 00:03:40,520
+يبقى يبين لي أن هذا ما هو واش vector space بيكفي
+
+40
+00:03:40,520 --> 00:03:47,060
+ألغي شرط من الشروط العشرةنأتي للشرط الأول أو
+
+41
+00:03:47,060 --> 00:03:51,080
+الخاصية اللي هو لو أخدت عنصرين من V يبقى حاصل
+
+42
+00:03:51,080 --> 00:03:56,420
+الجمحو مش بده يكون موجود في V وليس خارج V طالع
+
+43
+00:03:56,420 --> 00:04:00,240
+خارج V فبتطل يصير vector space يبقى بد المجموع
+
+44
+00:04:00,240 --> 00:04:05,480
+يكون داخل V ال condition التاني ال U زائد ال V
+
+45
+00:04:05,480 --> 00:04:10,020
+يساوي ال V زائد ال U يعني عملية عملية جمع المنتجات
+
+46
+00:04:10,020 --> 00:04:14,690
+عمليةإبدالية لو ماكنتش إبدالية it is not a vector
+
+47
+00:04:14,690 --> 00:04:19,210
+space طيب الخاصيتين اللي اتنينه اتحققوا بروحنا
+
+48
+00:04:19,210 --> 00:04:23,210
+الخاصية التالتة و هي خاصية ال associativity لو
+
+49
+00:04:23,210 --> 00:04:29,230
+جمعت ال U إلى V زائد ال W تماما كما لو جمعت ال U
+
+50
+00:04:29,230 --> 00:04:34,530
+زائد ال V إلى من إلى ال W و دي بيسميه خاصية الدمج
+
+51
+00:04:34,530 --> 00:04:38,830
+associative law أو associative propertyالان انت
+
+52
+00:04:38,830 --> 00:04:42,630
+حققت الخواص الثلاث بروح لخاصية رابعة الخاصية
+
+53
+00:04:42,630 --> 00:04:46,450
+الرابعة تقول لي في عندك عنصر اللي هو ال zero
+
+54
+00:04:46,450 --> 00:04:51,450
+المطول هذا موجود في Vإذا و الله كان Zero زايد V
+
+55
+00:04:51,450 --> 00:04:57,230
+يسوي V زايد Zero يسوي V لكل ال V يبقى هذا بسميه
+
+56
+00:04:57,230 --> 00:05:01,970
+Zero vector لمين؟ لل vector space V يعني بمعنى أخر
+
+57
+00:05:01,970 --> 00:05:07,070
+أن ال vector space V لازم يحتوي على العنصر الصفري
+
+58
+00:05:07,070 --> 00:05:13,410
+بالنسبة لعملية الجامعيبقى الـ zero هذا vector يبقى
+
+59
+00:05:13,410 --> 00:05:20,130
+مش scalar يعني مش number وإنما هو vector تمام بحيث
+
+60
+00:05:20,130 --> 00:05:24,030
+هذا ال zero vector لو جمعته إلى أي vector آخر من
+
+61
+00:05:24,030 --> 00:05:28,590
+اليمين أو من الشمال بدي يعطيني نفس ال vector هذا
+
+62
+00:05:28,590 --> 00:05:32,850
+ال element بقول عليه ال zero vector خاصية الخامسة
+
+63
+00:05:32,850 --> 00:05:37,470
+لأي u موجود في capital V there exists لازم اللي
+
+64
+00:05:37,470 --> 00:05:42,980
+أجي أسالي بـU موجود في V يعنييعني إذا العنصر أو ال
+
+65
+00:05:42,980 --> 00:05:48,560
+vector موجود في V لازم ألاقي سالب هذا العنصر موجود
+
+66
+00:05:48,560 --> 00:05:54,560
+في V بحيث لو جمعت ال U وسالب U تماما كما لو جمعت
+
+67
+00:05:54,560 --> 00:05:58,740
+سالب U و U لأنه قال هنا commutative وندش بده
+
+68
+00:05:58,740 --> 00:06:02,830
+يعطيناالـ zero vector مش الـ zero scalar لإن احنا
+
+69
+00:06:02,830 --> 00:06:09,790
+بنجمع vectors سالب U هو vector يبقى U زائد ناقص U
+
+70
+00:06:09,790 --> 00:06:14,910
+يسوى تماما ناقص الـ U زائد الـ U بده يسوى من الـ
+
+71
+00:06:14,910 --> 00:06:19,180
+zero vectorهذه الخامسة الخاصية الساسة لو أخدت أي
+
+72
+00:06:19,180 --> 00:06:23,740
+scalar من ال set of real number A أخدت عنصر A من
+
+73
+00:06:23,740 --> 00:06:27,900
+ال set of real number و أخدت ال U vector موجود في
+
+74
+00:06:27,900 --> 00:06:35,880
+V إذا حصل ضرب ل 2A في U بدي يكون موجود في V تماما
+
+75
+00:06:35,880 --> 00:06:40,070
+تحققت الخاصية ده نروح بالخاصية اللي بعدهالو كان
+
+76
+00:06:40,070 --> 00:06:45,170
+الـ A scalar واخدت two vectors من V وروح ضرب كسكلر
+
+77
+00:06:45,170 --> 00:06:51,550
+الـ A ضد الـ U زائد الـ V خضعت هذه لعمليات التوزيع
+
+78
+00:06:51,550 --> 00:06:56,850
+او distributive property خاصية التوزيع صارت هذه A
+
+79
+00:06:56,850 --> 00:07:03,190
+ضد الـ U زائد A ضد الـ Vمش عاجز هك و بس ضرب scalar
+
+80
+00:07:03,190 --> 00:07:08,090
+مع جامعة و vector لأ جامعة و scalars مع ضرب مع مين
+
+81
+00:07:08,090 --> 00:07:12,750
+مع vector الخاصية اللي بعدها لو كان ال a و ال b
+
+82
+00:07:12,750 --> 00:07:16,930
+موجودة في R و ال u موجودة في V يبقى ال a زائد ال b
+
+83
+00:07:16,930 --> 00:07:21,450
+و dot ال u بيسوي a dot ال u زائد ال b dot ال u كل
+
+84
+00:07:21,450 --> 00:07:28,160
+هذا بيكون موجود في Vطبعا يبقى بنجي للخاصية التاسعة
+
+85
+00:07:28,160 --> 00:07:34,580
+لو كان عندي scholar A وعندي scholar B ضربت ال B في
+
+86
+00:07:34,580 --> 00:07:39,000
+ال U والنتج روحت ضربت في A تماما كما لو ضربت ال
+
+87
+00:07:39,000 --> 00:07:43,360
+two scholars من البداية في من في ال vector V بده
+
+88
+00:07:43,360 --> 00:07:48,960
+يطلع عندي vector اسمه A B ضد ال Uوهذا بيكون vector
+
+89
+00:07:48,960 --> 00:07:53,220
+موجود في الـ vector الأصلي طبقًا للخاصية اللي
+
+90
+00:07:53,220 --> 00:07:57,640
+عندنا هذه تمام اتحقق الخاصية التاسعة بيروح الخاصية
+
+91
+00:07:57,640 --> 00:08:02,860
+العاشرة لو أخدت الواحد as a scalar يعني كأنه
+
+92
+00:08:02,860 --> 00:08:08,400
+الخاصية دي حالة خاصة من من اللي فوق أخدت ال U هو
+
+93
+00:08:08,400 --> 00:08:12,180
+vector و أخدت الواحد as a scalar ضربت الواحد في U
+
+94
+00:08:12,180 --> 00:08:18,850
+بيطلع النتج يساوي U اللي هو موجود في Vيبقى إذا
+
+95
+00:08:18,850 --> 00:08:23,930
+تحققت هذه الخواص العشر في هذه الحالة بقول يبقى
+
+96
+00:08:23,930 --> 00:08:28,430
+اللي في عندي هذا ماله vector space بدنا نبدأ نطبق
+
+97
+00:08:28,430 --> 00:08:31,710
+الكلام اللي احنا بنقوله على أرض الواقع بأمثلة
+
+98
+00:08:31,710 --> 00:08:35,950
+مختلفة ونشوف مين ممكن يطلع vector space او ممكن
+
+99
+00:08:35,950 --> 00:08:42,150
+مايطلعش vector space وإذا ماطلعش مين من الخواص لا
+
+100
+00:08:42,150 --> 00:08:46,790
+تحتحقق في هذه الحالة بقيت يصير ما هواش vector
+
+101
+00:08:46,790 --> 00:08:52,980
+spaceجال ياخد المثال الأول افترض ال V كل العناصر
+
+102
+00:08:52,980 --> 00:08:59,700
+ال zero X1 و X2 بها X1 و X2 موجود في R يعني ايش؟
+
+103
+00:08:59,700 --> 00:09:04,700
+يعني بدي اخد كل ال vectors اللي كل vector مكون من
+
+104
+00:09:04,700 --> 00:09:08,560
+ال three components بحيث المركبة الأولى دائما و
+
+105
+00:09:08,560 --> 00:09:12,920
+أبداzero لو ما هي zero إذا مش عندنا برا مالناش
+
+106
+00:09:12,920 --> 00:09:17,560
+علاقة فيها يبقى احنا بدنا نجمع يعني مثلا لو جيت
+
+107
+00:09:17,560 --> 00:09:22,140
+قولت يا بنات هذا كل واحدة فيكو عبارة عن عنصر في ال
+
+108
+00:09:22,140 --> 00:09:26,560
+vector space الشك هذي تمام جيت قولت للبنات السطر
+
+109
+00:09:26,560 --> 00:09:30,930
+هذا كله انتج للناحية التانيةيبقى كأنه انا أخدت
+
+110
+00:09:30,930 --> 00:09:35,490
+حالة خاصة من الأصلية المركبة الأولى كلها zero في
+
+111
+00:09:35,490 --> 00:09:42,390
+كل three tuple تمام؟ بدأت أشوف هل هذا تحت عملية
+
+112
+00:09:42,390 --> 00:09:47,030
+الجمع العادية و تحت عملية الضرب العادية هل هو
+
+113
+00:09:47,030 --> 00:09:52,990
+vector space أم لا طلع هنا كل العناصر اللي المركبة
+
+114
+00:09:52,990 --> 00:09:56,610
+الأولى دائما و أبدا ب zero طب و المركبة التانية و
+
+115
+00:09:56,610 --> 00:10:01,430
+التالتةأش ما كان يكون وما حطيتش عليهم قيود يمكن
+
+116
+00:10:01,430 --> 00:10:06,250
+سالب يمكن موجب يمكن Zero كل أنا مقيد بالمركبة
+
+117
+00:10:06,250 --> 00:10:10,510
+الأولى لازم تكون Zero وقولتك X1 و X2 موجودة في
+
+118
+00:10:10,510 --> 00:10:14,510
+هرموجة بسالب كسر مش عارف أيه Zero ماليش علاقة بيه
+
+119
+00:10:14,510 --> 00:10:17,210
+أش ما يكون شكله ما يكون ان شاء الله يكون جذور
+
+120
+00:10:17,210 --> 00:10:22,210
+تربية وجذور تكييبية لأنها set أي عناصر موجودة في
+
+121
+00:10:22,210 --> 00:10:27,060
+ال set of real number طيبunder the usual addition
+
+122
+00:10:27,060 --> 00:10:33,680
+عملية الجمع العادية تبع ال vectors and the usual
+
+123
+00:10:33,680 --> 00:10:38,040
+multiplication of scalar وعملية الضرب العادي لل
+
+124
+00:10:38,040 --> 00:10:42,280
+vectors في scalar واخدنا سابقا انه عملية لو ضربت
+
+125
+00:10:42,280 --> 00:10:47,160
+element في vector بدربه في جميع ال components مش
+
+126
+00:10:47,160 --> 00:10:51,720
+هيك يبقى ده اسمه الضرب العادي والجمع بجمع
+
+127
+00:10:51,720 --> 00:10:57,070
+component was كل عنصر معاهنظيره بيقول then ال V is
+
+128
+00:10:57,070 --> 00:11:02,490
+a vector space because يبقى هذا اللي فوق تحت عملية
+
+129
+00:11:02,490 --> 00:11:06,010
+الجامعة العادية والضرب العادية دي بيكون vector
+
+130
+00:11:06,010 --> 00:11:10,030
+space ما هو السبب بيقول لو أخدت three vectors
+
+131
+00:11:10,030 --> 00:11:15,770
+موجودات في V طلعي المركبة طلعي كله المركبة الأولى
+
+132
+00:11:15,770 --> 00:11:25,990
+والمركبة الأولىوالمُركّب الأولى كله بأسفار موجودة
+
+133
+00:11:25,990 --> 00:11:31,690
+في V بداية أشوف الخواصة العاشرة هل ال U زائد ال V
+
+134
+00:11:31,690 --> 00:11:37,070
+موجود في V ولا لأ يبقى بداية للخاصية الأولىنمر
+
+135
+00:11:37,070 --> 00:11:42,370
+واحد بيداخد ال U زائد ال V يبقى هذا بده يعطيني
+
+136
+00:11:42,370 --> 00:11:48,130
+Zero و X واحد و X اتنين زائد Zero و Y واحد و Y
+
+137
+00:11:48,130 --> 00:11:55,140
+اتنين و Y ساويأحنا قلنا هذه عملية الجمع عادية لمن؟
+
+138
+00:11:55,140 --> 00:11:59,040
+للـ vectors يبقى عملية الجمع العادية بجمع
+
+139
+00:11:59,040 --> 00:12:08,440
+component y 0 مع 0 بقدرش 0 X1 زائد Y1 X2 زائد Y2
+
+140
+00:12:08,440 --> 00:12:12,630
+موجودة في V ولا يا بنات؟موجود في V ليش؟ لأن الـ
+
+141
+00:12:12,630 --> 00:12:17,290
+element الأول أو المركبة الأولى في كل vector يساوي
+
+142
+00:12:17,290 --> 00:12:23,030
+0 إذا انتحققت الخاصية الأولى بدي أجلال الخاصية
+
+143
+00:12:23,030 --> 00:12:28,750
+التانية نمره 2 بدي أخد ال U زائد ال V يبقى .. بدي
+
+144
+00:12:28,750 --> 00:12:33,970
+أجمعه لغاية يا بناتي يبقى هنا 0 زائد 0 ب0 X1 زائد
+
+145
+00:12:33,970 --> 00:12:44,370
+Y1 X2 زائد Y2 موجود في Vموجودة في V أنا بدّي خاصية
+
+146
+00:12:44,370 --> 00:12:51,790
+الإبدال أليس تهادي تساوي Zero one الآن X واحد زائد
+
+147
+00:12:51,790 --> 00:12:57,030
+Y واحد مش هدول X واحد و Y واحد أعداد موجودة في
+
+148
+00:12:57,030 --> 00:13:01,810
+الست في real numbers عملية جمع الأعداد العاديةهذه
+
+149
+00:13:01,810 --> 00:13:05,210
+عملية إبدالية ولا لا؟ أنا بقول خمسة زائد ستة و
+
+150
+00:13:05,210 --> 00:13:09,030
+الله ستة زائد خمسة ما هي نفس الشيء إذا باجي بقول
+
+151
+00:13:09,030 --> 00:13:16,210
+هذا y واحد زائد x واحد و y اتنين زائد x اتنين اللي
+
+152
+00:13:16,210 --> 00:13:23,350
+بقدر أقول هذه zero و y واحد و y اتنين زائد zero x
+
+153
+00:13:23,350 --> 00:13:28,490
+واحد و x اتنينصحيح ولا لأ؟ يعني فصلت هذا ال vector
+
+154
+00:13:28,490 --> 00:13:32,710
+إلى مجموع two vectors طب الأول مين هو؟ مش V
+
+155
+00:13:32,710 --> 00:13:38,930
+والتاني يبقى V زائد ال U يبقى بدأت ب U زائد ال V
+
+156
+00:13:38,930 --> 00:13:44,130
+وصلت إلى V زائد ال U يبقى اتحققت الخاصية الأولى
+
+157
+00:13:44,130 --> 00:13:48,800
+والخاصية الثانية عندنا بدنا نروح لمين؟للخاصية
+
+158
+00:13:48,800 --> 00:13:54,360
+التالتة يبقى باخد U ذائد V ذائد W
+
+159
+00:13:59,340 --> 00:14:04,300
+و X1 و X2 زائد ال V زائد ال W بدي أجمع على طول
+
+160
+00:14:04,300 --> 00:14:10,640
+الخط هاي عند ال V وهذه ال W بدي أجمعها مباشرة يبقى
+
+161
+00:14:10,640 --> 00:14:22,570
+Zero Y1 زائد Z1 و Y2 زائد Z2الان بدأجي اجمع صار
+
+162
+00:14:22,570 --> 00:14:25,650
+عندى vector وعندى vector تانى بدأ اجمع component
+
+163
+00:14:25,650 --> 00:14:33,650
+twice 00 ب0 يبقى بيصير عندى X واحد زائد Y واحد
+
+164
+00:14:33,650 --> 00:14:46,190
+زائد Z واحد و Xي اتنين زائد Y اتنين زائد Z اتنين
+
+165
+00:14:46,190 --> 00:14:54,460
+بالشكل اللى عندناطيب هذا الكلام بده يساوي بداجي
+
+166
+00:14:54,460 --> 00:14:59,700
+للي وصلتله هذا هدول كلهم real number عملية الجمع
+
+167
+00:14:59,700 --> 00:15:04,160
+على ال real number إدماجية ولا لا يبقى خلاص إذا
+
+168
+00:15:04,160 --> 00:15:09,860
+بقدر أكتب هذه على الشكل التالي هي عبارة عن zero و
+
+169
+00:15:09,860 --> 00:15:17,480
+X واحد زائد Y واحد زائد Z واحد تمامهذا ال term
+
+170
+00:15:17,480 --> 00:15:25,640
+الأول و ال term التاني بقدر اقول x واحد زائد y
+
+171
+00:15:25,640 --> 00:15:30,840
+واحد زائد z واحد وهذه بقول x اتنين زائد y اتنين
+
+172
+00:15:30,840 --> 00:15:39,220
+زائد z اتنينتمام إذا هذه بقدر أقول تساوي بداتي
+
+173
+00:15:39,220 --> 00:15:44,300
+أحطها على شكل مجموع two vectors إذا بقدر أقول هذا
+
+174
+00:15:44,300 --> 00:15:54,100
+zero و X واحد زائد Y واحد و X اتنين زائد Y اتنين
+
+175
+00:15:54,100 --> 00:16:00,580
+زائد ضال عندي zero و ضال عندي Z واحد و ضال عندي Z
+
+176
+00:16:00,580 --> 00:16:07,060
+اتنين تمامبقدر أقول هذا الكلام يساوي هذا عبارة عن
+
+177
+00:16:07,060 --> 00:16:13,520
+مجموع مين يا بنات مش عبارة عن ال U زائد ال V صح
+
+178
+00:16:13,520 --> 00:16:20,560
+ولا لا؟ ودك زائد اللي هو ال W العنصر التالت يبقى
+
+179
+00:16:20,560 --> 00:16:26,460
+صار U زائد V زائد W سوى U زائد V زائد W إذا انتحقت
+
+180
+00:16:26,460 --> 00:16:29,100
+الخاصية رقم تلاتة عنه
+
+181
+00:16:32,920 --> 00:16:38,900
+الان انا بدي
+
+182
+00:16:38,900 --> 00:16:43,700
+اخد العنصر zero اللي موجود في V الان ال zero
+
+183
+00:16:43,700 --> 00:16:49,480
+vector خاصية الرابعة هو من؟ هو العنصر zero و zero
+
+184
+00:16:49,480 --> 00:16:55,590
+و zero موجود في capital V ولا لا؟صح؟ لأن المركبة
+
+185
+00:16:55,590 --> 00:16:59,890
+الأولى عندي هي اللي عليها قايدن تبقى بـ0 و 2 إيش
+
+186
+00:16:59,890 --> 00:17:06,350
+ما كانوا يكونوا الآن بدأت أخدله and بدأ أخدله 0
+
+187
+00:17:06,350 --> 00:17:15,710
+زائد ال U يساوي الـ0 اللي هو 0 و 0 و 0 زائد ال U
+
+188
+00:17:15,710 --> 00:17:22,100
+اللي هو 0 X 1 و X 2 الشكل اللي عندنا هذابتجمع
+
+189
+00:17:22,100 --> 00:17:30,240
+component y يبقى 0 زائد 0 ب0 0 زائد x1 بx1 0 زائد
+
+190
+00:17:30,240 --> 00:17:39,620
+x2 بx2 مش هذا هو ال U نفسه صح ولا لأ يبقى بقى بنفس
+
+191
+00:17:39,620 --> 00:17:48,300
+الطريقة similarly بنفس الطريقة ال U زائد ال 0 بده
+
+192
+00:17:48,300 --> 00:17:49,580
+يساوي ال U
+
+193
+00:17:57,200 --> 00:18:02,520
+الخاصية الخامسة بيقول إذا أي element U موجود في V،
+
+194
+00:18:02,520 --> 00:18:09,700
+ناقص الـU موجود في V، such that المجموعة بيساوي من
+
+195
+00:18:09,700 --> 00:18:14,720
+الـzero vectorالان انا بدي اخد مين؟ بدي اخد U
+
+196
+00:18:14,720 --> 00:18:22,280
+موجود في V الان ال U بده يساوي Zero و X واحد و X
+
+197
+00:18:22,280 --> 00:18:30,080
+اتنينهذا بده يعطيك مين؟ ناقص U احنا كأنه بدي اضرب
+
+198
+00:18:30,080 --> 00:18:35,580
+سالب واحد في U اذا ضرب عادي جدا component loss لإن
+
+199
+00:18:35,580 --> 00:18:40,780
+احنا قولنا ضرب عادي يبقى هذا الكلام بده يساوي سالب
+
+200
+00:18:40,780 --> 00:18:48,400
+واحد في Zero ب Zero سالب X واحد سالب X اتنين مداجي
+
+201
+00:18:48,400 --> 00:18:58,430
+اقوله andبدي ال U زائد سالب U و يساوي ال U له 0 و
+
+202
+00:18:58,430 --> 00:19:10,130
+X1 و X2 زائد 0 سالب X1 سالب X2 تمام نجمع 0 مع 0 ب0
+
+203
+00:19:10,130 --> 00:19:18,110
+X1 و نقص X1 ب0 X2 و نقص X2 ب0 مين هو هذا هذا ال
+
+204
+00:19:18,110 --> 00:19:27,610
+zero vectorSimilarly بنفس الطريقة سالب
+
+205
+00:19:27,610 --> 00:19:33,810
+U زائد U ساوي الـ Zero vector إذا تحققت الخاصية
+
+206
+00:19:33,810 --> 00:19:39,590
+رقم خمسة بدنا نحقق باق الخواص خليني أمسح اللي فوق
+
+207
+00:19:39,590 --> 00:19:45,610
+هذا طيب هذا اللي مالهوش لزوم من هنا و فوق نمسحه
+
+208
+00:19:56,930 --> 00:20:01,810
+خلصنا الخاصية الخامسة وانتجنا الخاصية السادسةخاصية
+
+209
+00:20:01,810 --> 00:20:06,230
+السالسة بيقول لو كان خدت scalar موجود في R و U
+
+210
+00:20:06,230 --> 00:20:11,430
+موجود في V فحصل ضربه مابدى يكون موجود في V يبقى
+
+211
+00:20:11,430 --> 00:20:18,390
+بدى اخد هنا F ال A موجود في R scalar و ال U اللى
+
+212
+00:20:18,390 --> 00:20:25,310
+هي يساوي Zero و X واحد و X اتنين موجودات في V then
+
+213
+00:20:25,310 --> 00:20:33,740
+بدى اخد ال A في ال Uيبقى هذه A بدي أضربها في الـ 0
+
+214
+00:20:33,740 --> 00:20:39,420
+X1 و X2 Y الساوية الـ A في الـ 0 بقداش يا بنات
+
+215
+00:20:39,420 --> 00:20:46,200
+Zero و هنا A X1 و هنا A X2 إيش رأيك في ال vector
+
+216
+00:20:46,200 --> 00:20:50,120
+اللي طلع موجود في V ولا لأ لأن المركبة الأولى
+
+217
+00:20:50,620 --> 00:20:55,820
+والباقية اش مكان يكون يبقى هذا موجود في ال vector
+
+218
+00:20:55,820 --> 00:21:01,020
+space V وبالتالي اتحققت الخاصية السادسة بدنا نروح
+
+219
+00:21:01,020 --> 00:21:05,700
+للخاصية السابعة الخاصية السابعة بيقول لو كان A
+
+220
+00:21:05,700 --> 00:21:13,980
+موجود في R و U و V موجودة في U يبقى هنا Fالـ A
+
+221
+00:21:13,980 --> 00:21:21,940
+موجودة في R and ال U اللي هي Zero Zero و X واحد و
+
+222
+00:21:21,940 --> 00:21:30,080
+X اتنين و ال V Zero و Y واحد و Y اتنين موجودات في
+
+223
+00:21:30,080 --> 00:21:40,020
+V then بدي اخد ال A Dot ال U زائدي ال V يبقى ال A
+
+224
+00:21:40,020 --> 00:21:46,430
+Dotالـ U زائد ال V بدي أجمع component twice يبقى
+
+225
+00:21:46,430 --> 00:21:55,970
+Zero X واحد زائد Y واحد X اتنين زائد Y اتنين بدي
+
+226
+00:21:55,970 --> 00:22:05,350
+أضرب يبقى هاديزيرو و a في x واحد زائد y واحد و a
+
+227
+00:22:05,350 --> 00:22:17,030
+في x اتنين زائد y اتنين ليش ضربتك لأن ضرب عادي طيب
+
+228
+00:22:17,030 --> 00:22:27,330
+هذا الكلام بده يساويبدو يساوي zero اكس واحد زائد
+
+229
+00:22:27,330 --> 00:22:32,650
+اي واحد اكس
+
+230
+00:22:32,650 --> 00:22:39,820
+اتنين زائد اي اتنينهذا صار vector واحد شو رايك
+
+231
+00:22:39,820 --> 00:22:45,900
+ممكن اجزءه الى two vectors ايش ال two vectors يعني
+
+232
+00:22:45,900 --> 00:22:53,700
+ممكن اقول هذا zero و a x واحد و a x اتنين زائد
+
+233
+00:22:53,700 --> 00:23:02,480
+zero و a y واحد و a y اتنين لو جمعتهم بطلع عند هذا
+
+234
+00:23:02,480 --> 00:23:08,260
+مرة تانيةطب بدرجة على خواص الـ scalar أظن بقدر أخد
+
+235
+00:23:08,260 --> 00:23:19,160
+a عامل مشترك من الكل برا بيظل 0 x1 x2 زائد a 0 y1
+
+236
+00:23:19,160 --> 00:23:29,950
+y2يبقى هذا A الأولاني هو الـU والتاني A في الـV
+
+237
+00:23:29,950 --> 00:23:36,290
+الشكل اللي عنها يبقى بناء على A ضد U زائد V يبقى A
+
+238
+00:23:36,290 --> 00:23:44,270
+ضد U زائد A ضد V وبالتالي تحققت الخاصية السابعة
+
+239
+00:23:44,750 --> 00:23:51,810
+بنروح للخاص يمين الثامنة يبقى باجي بقوله تمانية if
+
+240
+00:23:51,810 --> 00:24:00,710
+ال A و ال B موجودة في R and ال U Zero X واحد X
+
+241
+00:24:00,710 --> 00:24:09,870
+اتنين موجودة في V then بدي اخد ال A زائد ال B Dot
+
+242
+00:24:09,870 --> 00:24:20,230
+من Dot ال Uيساوي A زائد B ضات ال U
+
+243
+00:24:26,050 --> 00:24:29,870
+هذا مجموع two real numbers يبقى real number واحد
+
+244
+00:24:29,870 --> 00:24:35,310
+يبقى بدي أضرب جوبه حسب الضرب العادى يبقى هذا بقداش
+
+245
+00:24:35,310 --> 00:24:44,530
+ب zero نجي للي بعدها هذه ا زائد ال B في ال X1 وهنا
+
+246
+00:24:44,530 --> 00:24:51,770
+ا زائد ال B في من؟ في ال X2 وهيقفلنا الجزءهذه بقدر
+
+247
+00:24:51,770 --> 00:24:57,750
+اقول عليها ما يأتي يساوي هاي zero زي مهين وهذه
+
+248
+00:24:57,750 --> 00:25:01,930
+بقدر افكها لان ال X واحد وال X اتنية real number
+
+249
+00:25:01,930 --> 00:25:08,270
+وال A و ال B real number يبقى A X one زائد بي X
+
+250
+00:25:08,270 --> 00:25:18,280
+one فاصلة A X two زائد بي X twoممكن اجزئها الى two
+
+251
+00:25:18,280 --> 00:25:28,180
+vectors يبقى هذه بقدر اقول zero و ax1 و ax2 زائد
+
+252
+00:25:28,180 --> 00:25:39,510
+zero و bx1 و bx2ممكن أخد الـ A برا يبقى الـ A في
+
+253
+00:25:39,510 --> 00:25:50,050
+Zero X واحد و X اتنين زائد B في Zero و X واحد و X
+
+254
+00:25:50,050 --> 00:25:57,030
+اتنين يبقى هذه بدأت تساوي A ضد الـ U زائد B ضد الـ
+
+255
+00:25:57,030 --> 00:26:03,150
+U وبالتالي تحققت الخاصية رقم تمانية يبقى تمانية
+
+256
+00:26:07,780 --> 00:26:18,160
+الخاصية التاسعة يبقى الفرصة
+
+257
+00:26:18,160 --> 00:26:28,520
+التاسعةبدأت أخد F الـ A والـ B موجودة في R and ال
+
+258
+00:26:28,520 --> 00:26:36,780
+U Zero X واحد X اتنين موجودة في V then بدأت أخد ال
+
+259
+00:26:36,780 --> 00:26:46,120
+A في ال B ضد ال U يساوي A فيبضد ال U يبقى بدي اضرب
+
+260
+00:26:46,120 --> 00:26:52,220
+بي في كل عنصر من العاصر اللي عندنا يبقى هاي Zero و
+
+261
+00:26:52,220 --> 00:27:00,280
+بي X one و بي X two الشكل اللي عندنا هنا الان بدي
+
+262
+00:27:00,280 --> 00:27:07,280
+اضرب ال A يبقى هذا الكلام بدي يساوي A في Zero ب
+
+263
+00:27:07,280 --> 00:27:17,690
+Zero يبقى A بي X oneو A B X 2 بالشكل اللي عندنا
+
+264
+00:27:17,690 --> 00:27:24,790
+هنا هذا الكلام بده يساوي الان ال A و ال B و ال X 1
+
+265
+00:27:24,790 --> 00:27:29,830
+كلهم real numbers و كذلك ال A و ال B و ال X 2 كله
+
+266
+00:27:29,830 --> 00:27:36,350
+real numbers يبقى بقدر اقول هذا zero و هذا A B X 1
+
+267
+00:27:36,350 --> 00:27:43,980
+و في نفس الوقت A B X 2بقدر أخد ال a بي برا يبقى
+
+268
+00:27:43,980 --> 00:27:51,160
+هذا a بي برا كله في مين في ال zero x one x two
+
+269
+00:27:51,160 --> 00:27:59,360
+يبقى هذا a بي ضد ال uيبقى تحققت الخاصية رقم 9
+
+270
+00:27:59,360 --> 00:28:07,540
+بنانيج الخاصية رقم 10 الأخيرة بدي 1.tlu يبقى 1
+
+271
+00:28:07,540 --> 00:28:12,520
+.0x1x2y
+
+272
+00:28:13,880 --> 00:28:17,600
+الواحد لما نضربه في زيرو بيبقى ده جمنات بزيرو
+
+273
+00:28:17,600 --> 00:28:23,660
+الواحد في ال X1 بال X1 الواحد في ال X2 بال X2 يبقى
+
+274
+00:28:23,660 --> 00:28:29,940
+هذا أعطاني مين ال U يبقى قلنالك من البداية أن هذا
+
+275
+00:28:29,940 --> 00:28:35,040
+vector space ليش قلنا because وروحنا وجينا العشر
+
+276
+00:28:35,040 --> 00:28:39,660
+خواص كلها محققة يبقى أصبح هذا اللي عندنا اللي هو
+
+277
+00:28:39,660 --> 00:28:45,840
+vector space طبعامش كل ستة بنعطيها لك بتكون vector
+
+278
+00:28:45,840 --> 00:28:51,660
+space و بضروح أبدأ أطبق الخواص العاشرة، تمام؟ يعني
+
+279
+00:28:51,660 --> 00:28:56,840
+ليس بالضرورة إن راح أطول خاصية ماتحققتش، يبقى أروح
+
+280
+00:28:56,840 --> 00:29:00,240
+أدور على الباقي، مدورش على الباقي، خلاص نطب vector
+
+281
+00:29:00,240 --> 00:29:03,940
+space و باسكنلقيت الأولى اتحققت بروح للتانية وما
+
+282
+00:29:03,940 --> 00:29:07,400
+اتحققتش التانية not vector space و بسيب الباقي و
+
+283
+00:29:07,400 --> 00:29:12,520
+هكذا يعني وين خاصية بتتحققش بقول يبقى هذا ماهواش
+
+284
+00:29:12,520 --> 00:29:16,880
+vector space و بنتهيه الدلة تانية الأولى اتحققت
+
+285
+00:29:16,880 --> 00:29:20,680
+انها بروح للتالت بروح للرابع لما إذا اتحققوا
+
+286
+00:29:20,680 --> 00:29:24,400
+العشرة كلهم يبقى هو vector space يبقى إذا اختلت أي
+
+287
+00:29:24,400 --> 00:29:28,320
+خاصية من الخاصة العشر بكون معله ماهواش vector
+
+288
+00:29:28,320 --> 00:29:35,680
+spaceهذا أول مثال على هذا الموضوع، لا يزال عندنا
+
+289
+00:29:35,680 --> 00:29:45,140
+العديد من الأمثلة، دي المثال رقم اتنين هذا
+
+290
+00:29:45,140 --> 00:29:50,320
+إذا طلع vector space، إذا ما طلعش vector space
+
+291
+00:29:50,320 --> 00:29:55,990
+يمكن تسوي خطوة واحدة، ولا لا؟وإذا انت دقيقة نظر
+
+292
+00:29:55,990 --> 00:30:00,090
+وشاطرة في الحسابات ومجرد النظر بتقولي هذه البرشم
+
+293
+00:30:00,090 --> 00:30:04,230
+تنفعش للخاصية الفلانية على طول من دون مجرمي و تروح
+
+294
+00:30:04,230 --> 00:30:09,030
+تكتبي ليها و بتكشف الباقي 100% تمام نعطي المثال
+
+295
+00:30:09,030 --> 00:30:17,970
+رقم اتنين example two هذا سؤال خمسة من الكتاب
+
+296
+00:30:17,970 --> 00:30:20,690
+بيقول little v to sound
+
+297
+00:30:24,960 --> 00:30:34,460
+كل العناصر على الشكل واحد و X و Y بحيث X و Y
+
+298
+00:30:34,460 --> 00:30:39,800
+موجودة في set of real numbers under usual addition
+
+299
+00:30:40,930 --> 00:30:49,930
+under usual addition تحت عملية الجامعة العادية and
+
+300
+00:30:49,930 --> 00:30:57,030
+وفي نفس الوقت usual scalar multiplication usual
+
+301
+00:30:57,030 --> 00:31:03,250
+scalar multiplication
+
+302
+00:31:03,250 --> 00:31:06,370
+تحت
+
+303
+00:31:06,370 --> 00:31:18,190
+عملية الجامعة الدرب والجامعة العادية thenis not
+
+304
+00:31:18,190 --> 00:31:26,430
+a vector space
+
+305
+00:31:32,720 --> 00:31:37,520
+ومجرد النظر هذا ال 6 اللي عندنا هذه تحت عملية
+
+306
+00:31:37,520 --> 00:31:40,760
+الجمع العادية و الضرب العادية ليست في الاقتراضية
+
+307
+00:31:40,760 --> 00:31:44,520
+ليه؟ بدي واحدة تحكي بس واحدة ترفع أيديها و تحكي
+
+308
+00:31:44,520 --> 00:31:49,680
+انا بقول فيش zero element ماعشي الحالة هذا وجهة
+
+309
+00:31:49,680 --> 00:31:55,200
+نظر في وجهة نظر تانية؟ قبل ال zero طب شوفي اللي
+
+310
+00:31:55,200 --> 00:32:01,520
+قبل ال zero اجمع اتنين اجمع لو جمعت اتنين ايش
+
+311
+00:32:01,520 --> 00:32:02,100
+بطلع؟
+
+312
+00:32:06,540 --> 00:32:11,420
+يبقى عمله الجامعة لا تتحقق صحيح ولا لأ بروح بقوله
+
+313
+00:32:11,420 --> 00:32:15,500
+هذا is not a vector space because
+
+314
+00:32:19,270 --> 00:32:26,570
+الـ U بدها تساوي واحد و X واحد و Y واحد و ال V
+
+315
+00:32:26,570 --> 00:32:33,150
+دوسر واحد و X اتنين و Y اتنين موجودة في capital V
+
+316
+00:32:33,150 --> 00:32:42,170
+then ال U زائد ال V بده يساوي اتنين و X واحد زائد
+
+317
+00:32:42,170 --> 00:32:48,860
+X اتنين و X واحدخلّيها بس لسهولة يا فنات خلّيها X
+
+318
+00:32:48,860 --> 00:32:57,060
+واحد و X اتنين و هذي Y واحد و Y اتنين تمام يبقى X
+
+319
+00:32:57,060 --> 00:33:04,800
+واحد زائد Y واحد و X اتنين زائد Y اتنين does not
+
+320
+00:33:04,800 --> 00:33:09,740
+belong to V مش موجودة في V لإن أنا بدى ال
+
+321
+00:33:09,740 --> 00:33:14,550
+component اللي قداش تكونيبقى في حالة الـ zero نفع
+
+322
+00:33:14,550 --> 00:33:18,830
+يصير vector space لكن في حالة الواحد مانفعش يكون
+
+323
+00:33:18,830 --> 00:33:24,230
+vector space ماهواش vector space طيب مثال تلاتة
+
+324
+00:33:24,230 --> 00:33:32,530
+مثال تلاتة له سؤال سبعة من الكتاب كذلك سؤال سبعة
+
+325
+00:33:32,530 --> 00:33:42,530
+بيقول letالـ V تساوي كل المصفوفات A بحيث الـ A is
+
+326
+00:33:42,530 --> 00:33:48,370
+two by two matrix كل المصفوفات اللي نضامها اتنين
+
+327
+00:33:48,370 --> 00:33:56,450
+في اتنين with determinant للـ A لا يساوي Zero
+
+328
+00:33:56,450 --> 00:34:02,970
+under usual
+
+329
+00:34:09,830 --> 00:34:19,150
+addition and scalar multiplication
+
+330
+00:34:19,150 --> 00:34:26,610
+of
+
+331
+00:34:26,610 --> 00:34:38,460
+matrices then ايش رايك؟الـ V مش عارف اكتب هي
+
+332
+00:34:38,460 --> 00:34:42,420
+vector space ولا not vector space نيجي مين هي ال V
+
+333
+00:34:42,420 --> 00:34:51,200
+في الأول ال V كل المصفوفات A اللي نظامها 2 في 2 و
+
+334
+00:34:51,200 --> 00:34:55,760
+اللي محددها ماله لا يساوي 0 اللي محدد فيها لا
+
+335
+00:34:55,760 --> 00:34:59,550
+يساوي 0يبقى كل المصوات اللي نظامها اتنين في اتنين
+
+336
+00:34:59,550 --> 00:35:04,850
+و اللي محددة ولا يساوي تجمعتهم و حطيتهم في 6V عرفت
+
+337
+00:35:04,850 --> 00:35:09,510
+عليها عملية جمع المصوفات العادى وهو جمع component
+
+338
+00:35:09,510 --> 00:35:14,630
+-wise وعرفت عليها ضرب المصوفة في scalar وهو ضرب ال
+
+339
+00:35:14,630 --> 00:35:17,730
+real number في كل عنصر من العناصر المصوفة اللي
+
+340
+00:35:17,730 --> 00:35:21,670
+كانت usual addition and usual multiplication تمام
+
+341
+00:35:21,990 --> 00:35:27,530
+تحت العمليتين الأثنين هدول هل ال V Vector Space أم
+
+342
+00:35:27,530 --> 00:35:35,990
+لا؟ طبعاً لأ أبسط شغلة بدي Zero Matrix هل ال Zero
+
+343
+00:35:35,990 --> 00:35:40,270
+Matrix المحدد تبعها لا يساوي Zero؟ لأ طبعاً يبجد
+
+344
+00:35:40,270 --> 00:35:48,990
+ان ال V is not a vector space because
+
+345
+00:35:54,180 --> 00:36:10,760
+it does not contain the zero matrix since
+
+346
+00:36:15,640 --> 00:36:23,320
+الـ Determinant للمصفوف Zero يبقى Zero يبقى
+
+347
+00:36:23,320 --> 00:36:28,760
+الخاصية تبع الأنصار الصفرية لم تتحقق لذلك هذا ليس
+
+348
+00:36:28,760 --> 00:36:37,320
+Vector Space فبالمثال
+
+349
+00:36:37,320 --> 00:36:47,640
+رقم أربعة بقول Letcapital V كل العناصر على الشكل X
+
+350
+00:36:47,640 --> 00:36:57,480
+و Y و Z بحيث ان ال X و Y و Z موجودة في set of real
+
+351
+00:36:57,480 --> 00:37:03,900
+numbers define addition
+
+352
+00:37:03,900 --> 00:37:07,380
+define
+
+353
+00:37:07,380 --> 00:37:09,780
+addition and
+
+354
+00:37:16,800 --> 00:37:26,020
+multiplication on the by الـ
+
+355
+00:37:26,020 --> 00:37:40,400
+x واحد y واحدو Z1 زائد X2 و Y2 و Z2 بده يساوي اللي
+
+356
+00:37:40,400 --> 00:37:54,760
+هو X1 و Y1 و Z1 و هنا X2 و Y2 و Z2 X1 زائد X2 Y1
+
+357
+00:37:54,760 --> 00:38:06,920
+زائد Y2 و هنا Z1زائد زيت دي اتنين هذا الجامعه and
+
+358
+00:38:06,920 --> 00:38:11,000
+ال
+
+359
+00:38:11,000 --> 00:38:25,540
+a في ال x و ال y و ال z يساوي ax و y و z then ال V
+
+360
+00:38:25,540 --> 00:38:28,580
+is الله أعلم
+
+361
+00:38:40,130 --> 00:38:46,110
+كيف؟ آه بس بنضربها في المركبة الأولى، يعني عملية
+
+362
+00:38:46,110 --> 00:38:50,690
+الجامعة كما هي component-wise والإيه بس بنضربها في
+
+363
+00:38:50,690 --> 00:38:59,410
+المركبة الأولى فقط لا غير، تمام؟يعني إنه هذه ال
+
+364
+00:38:59,410 --> 00:39:07,410
+Sid هي هيك قصيقة .. فاهم
+
+365
+00:39:07,410 --> 00:39:13,190
+يعني هذه ال Sid خاص فيه لأنه .. خاص فيه .. فاهم
+
+366
+00:39:17,540 --> 00:39:21,240
+هل هذا vector space ولا ماهواش vector space بتخيل
+
+367
+00:39:21,240 --> 00:39:28,220
+أنه ماهواش vector space السبق because لو أخدت يبقى
+
+368
+00:39:28,220 --> 00:39:40,920
+هذا is not a vector space because لو
+
+369
+00:39:40,920 --> 00:39:47,910
+أخدت يا مناد a زائد ال b في من؟ في اليوميبقى هذا
+
+370
+00:39:47,910 --> 00:39:57,190
+بيصير a زائد ال b في ال u اللي قلنا له x, y, z
+
+371
+00:39:57,190 --> 00:40:04,850
+يبقى حسب الضرب هذا بيضرب في ال a زائد ال b فقط و
+
+372
+00:40:04,850 --> 00:40:12,400
+ال x, y, z كما هي طب لو جيت أخدتالـ A Dot لـ U
+
+373
+00:40:12,400 --> 00:40:23,820
+زائد الـ B Dot لـ U يبقى هذا يصير A Dot XYZ زائد B
+
+374
+00:40:23,820 --> 00:40:29,140
+Dot XYZ
+
+375
+00:40:29,140 --> 00:40:36,720
+ويساوي حسب الخواصة اللي عندنا يبقى هذا A XYZ
+
+376
+00:40:37,620 --> 00:40:46,580
+زائد هذي بيكس و Y و Z يبقى لو جينا جمعناها هذي بده
+
+377
+00:40:46,580 --> 00:40:57,400
+يصير AX زائد بيكس و اتنين Y و اتنين Z تمام؟ يبقى
+
+378
+00:40:57,400 --> 00:41:03,950
+ايش رأيك؟ هل هذه اللي فوق هي هذه؟طبعا هذه بقدر
+
+379
+00:41:03,950 --> 00:41:10,590
+اقول a زائد ال b في ال x و اتنين y و اتنين z طبعا
+
+380
+00:41:10,590 --> 00:41:17,170
+اللي فوق ماهياش اللي تحت يبقى هنا ال a زائد ال b
+
+381
+00:41:17,170 --> 00:41:27,570
+ضات ال u لا يساوي ال au زائد ال b ال a ضات ال u
+
+382
+00:41:27,570 --> 00:41:32,940
+زائد ال b ضات ال uلا يزال هناك العديد من الأمثلة
+
+383
+00:41:32,940 --> 00:41:36,820
+نتعرض لها المرة القادمة ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOlfMJSH6b4_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOlfMJSH6b4_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..dd778f1cdb61f9252a9f8730ad486eb1080df3dc
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOlfMJSH6b4_postprocess.srt
@@ -0,0 +1,1888 @@
+1
+00:00:19,070 --> 00:00:24,270
+بسم الله الرحمن الرحيم بنرجع نكمل محاضرة الفترة
+
+2
+00:00:24,270 --> 00:00:28,470
+الصباحية و بدأنا في كلام جديد اللي هو linear
+
+3
+00:00:28,470 --> 00:00:32,430
+transformation بدي أذكر عفوا بال linear
+
+4
+00:00:32,430 --> 00:00:35,590
+combination بدي أذكر الان بال two definitions
+
+5
+00:00:35,590 --> 00:00:39,050
+تبعات الصبح في نهاية المحاضرةثم نبدأ في ال
+
+6
+00:00:39,050 --> 00:00:43,150
+definition الجديد و النظرية اللى بين إيدنا ال
+
+7
+00:00:43,150 --> 00:00:46,890
+definition تابعة الصبح ال definition ما قبل الأخير
+
+8
+00:00:46,890 --> 00:00:51,010
+قال لو كان ال V هو vector of space واخدت منه
+
+9
+00:00:51,010 --> 00:00:56,450
+مجموعة من ال vectors هدولولاقيت ان واحد من ال
+
+10
+00:00:56,450 --> 00:01:00,750
+vectors V من تعات ال vector space V قدرت اكتبه على
+
+11
+00:01:00,750 --> 00:01:05,710
+صورة Linear Combination من هدول كاف يعني يعني قدرت
+
+12
+00:01:05,710 --> 00:01:11,290
+اكتب ال V هو C1 في V1 زي تكون أسطن تاني في V2 زي
+
+13
+00:01:11,290 --> 00:01:16,990
+تكون أسطن تاني في V3 زي تكون أسطن CM في VM لقيت ال
+
+14
+00:01:16,990 --> 00:01:21,460
+vector هو مجموعهميبقى بقول إن الـ vector V هو
+
+15
+00:01:21,460 --> 00:01:28,200
+linear combination من الـ V1 و V2 و V3 و VM وهذا
+
+16
+00:01:28,200 --> 00:01:33,160
+ما ذكرناه في الفترة الصباحية نجلن التعريف الثاني
+
+17
+00:01:33,740 --> 00:01:39,720
+بقول إذا كان كل عنصر فيه V هو linear combination
+
+18
+00:01:39,720 --> 00:01:46,460
+من ال vectors هذا بقول إن ال V يولد بهذه العناصر
+
+19
+00:01:46,460 --> 00:01:50,980
+أو هذه العناصر بتجيب لمين؟ بتجيب لل vector space V
+
+20
+00:01:50,980 --> 00:01:57,600
+يعني بتجيب لكل عناصر V بلا ستة نايبقى إذا كان كل
+
+21
+00:01:57,600 --> 00:02:02,520
+عنصر في ال vector V بقدر أكتبه على صيغة linear
+
+22
+00:02:02,520 --> 00:02:07,180
+combination من ال vectors اللي عندنا هدول يبقى في
+
+23
+00:02:07,180 --> 00:02:11,000
+هذه الحالة بقول ال vector space V يولد بهذه
+
+24
+00:02:11,000 --> 00:02:15,800
+العناصر أو هذه العناصر Spain V بتولد لل vector
+
+25
+00:02:15,800 --> 00:02:20,040
+space V هذا ما تكلمنا عنه في الفترة الصباحية
+
+26
+00:02:20,040 --> 00:02:24,630
+الجديد هو التعريف اللي بين إيدينا هذابقول لو كان
+
+27
+00:02:24,630 --> 00:02:29,710
+الـU1 وU2 وUK are any k elements of a vector space
+
+28
+00:02:29,710 --> 00:02:34,730
+V يعني هدول vectors في ال vector space V وإذا كان
+
+29
+00:02:34,730 --> 00:02:38,810
+الـU the set of all linear combinations من الـU1
+
+30
+00:02:38,810 --> 00:02:44,970
+وU2 وUK then الـU is defined by يعني كيف؟ احنا
+
+31
+00:02:44,970 --> 00:02:49,550
+عندنا vector space V تمام؟أتخذت اي مجموعة من
+
+32
+00:02:49,550 --> 00:02:54,150
+العناصر تلاتة اربعة خمسة عشرة جد ما يكون و روحت
+
+33
+00:02:54,150 --> 00:02:58,730
+العناصر هدول جيبت كل ال linear combinations تبعتهم
+
+34
+00:02:58,730 --> 00:03:03,750
+ان اعبر عن هذا الكلام رياضيا بالشكل التالي بقول ال
+
+35
+00:03:03,750 --> 00:03:10,610
+Uهو الـ span تبع من U1 ل UK يعني مين يعني كل عنصر
+
+36
+00:03:10,610 --> 00:03:15,970
+اللي على شكل linear combination بهذا الشكل كل عنصر
+
+37
+00:03:15,970 --> 00:03:20,310
+فيه بقدر اكتبه على صيغة linear combination بهذا
+
+38
+00:03:20,310 --> 00:03:27,690
+الشكل C1U1 زي C2U2 زي زي CKUK بحيث الـ CI موجودة
+
+39
+00:03:27,690 --> 00:03:32,140
+في الارحيبجات كل الصيغات اللي عندها موجودةفي R
+
+40
+00:03:32,140 --> 00:03:38,090
+والـ I من واحد لغاية الـ Kتمام يبقى انا ايش اللي
+
+41
+00:03:38,090 --> 00:03:46,170
+حصل عندى يبقى كوانت ست جديدة الست جديدة هي التي
+
+42
+00:03:46,170 --> 00:03:52,390
+تولد بالعناصر U1 و U2 و UK هل هي كل ال vector
+
+43
+00:03:52,390 --> 00:03:58,270
+space فيه قد يكون و قد لا يكون ليش ان انا ماخدتش
+
+44
+00:03:58,270 --> 00:04:01,550
+ان هذا العنصر بولدولي ال vector space كله اخدت
+
+45
+00:04:01,550 --> 00:04:05,690
+حيال العناصر من مكان يكونوايبقى انا روحت جبت كل ال
+
+46
+00:04:05,690 --> 00:04:11,830
+linear combinations اللي هم سميتها 6U يبقى U هي ال
+
+47
+00:04:11,830 --> 00:04:17,050
+span تبع ال vectors اللي عندنا هدول تمام؟ طيب هذا
+
+48
+00:04:17,050 --> 00:04:20,930
+التعريف اللي أنا اش بتقول النظريةيقول اللي جيبتها
+
+49
+00:04:20,930 --> 00:04:26,050
+هذه هي subspace من ال vector space الأساسي V يعني
+
+50
+00:04:26,050 --> 00:04:31,890
+هذه ممكن يجيبلي V كله و ممكن يجيبلي جزء منه مش كله
+
+51
+00:04:31,890 --> 00:04:37,390
+على أي حال إن كانت كله فهي subspace لأن any set is
+
+52
+00:04:37,390 --> 00:04:41,850
+a subset of itself ويمكن ما تجيبش بتبقى subset
+
+53
+00:04:41,850 --> 00:04:46,580
+عادية من ال vector space اللي عندنايبقى أنا بدأ
+
+54
+00:04:46,580 --> 00:04:51,240
+أروح أثبت له أن الـ U اللي جيبناها بهذا الشكل هي
+
+55
+00:04:51,240 --> 00:04:56,640
+مين هي sub space من ال vector space الأصلي بدنا
+
+56
+00:04:56,640 --> 00:05:01,460
+نروح نبرهن صحة هذا الكلام مشان نبرهن صحة هذا
+
+57
+00:05:01,460 --> 00:05:06,560
+الكلام بدأ أروح أثبت مينتلات نقاط ان ال set U is
+
+58
+00:05:06,560 --> 00:05:10,520
+non-empty لو أخدت element اسكرال و element منها
+
+59
+00:05:10,520 --> 00:05:14,500
+ضربت اتنين في بعض بدلجيه في ال set هذه لو أخدت two
+
+60
+00:05:14,500 --> 00:05:19,820
+elements منها وجمعتهم بدلجيه في هذه ال set أول شيء
+
+61
+00:05:19,820 --> 00:05:24,620
+بدي أثبت له ان ال U هذه is non-empty يعني على
+
+62
+00:05:24,620 --> 00:05:32,260
+الأقل بدلجي فيها ولو عنصر واحدة تمام يبقى باجي
+
+63
+00:05:32,260 --> 00:05:41,850
+بقوله هناالـ U is not empty يعني
+
+64
+00:05:41,850 --> 00:05:47,610
+أنا أدعي أنها ليست فارغة أو ليست فاية بقى بدك
+
+65
+00:05:47,610 --> 00:05:52,730
+تجيبلي و لو عنصر و عادي لأن لو لجيت vector قدرت
+
+66
+00:05:52,730 --> 00:05:58,680
+أكتبه بدلالة هدوليبقى هذا ال element موجود فيه
+
+67
+00:05:58,680 --> 00:06:02,520
+صحيح ولا لأ؟ لأن هذه مكتوبة على صيغة linear
+
+68
+00:06:02,520 --> 00:06:06,860
+combination بالشكل هذا والصيغات هذه موجودة في R
+
+69
+00:06:06,860 --> 00:06:11,760
+ماعنديش قيود عليهم يبقى سالي بموجة بصفر ماعندي
+
+70
+00:06:11,760 --> 00:06:16,640
+مشكلة في هذه الحالة يبقى أنا بدعي أن هذه non-empty
+
+71
+00:06:16,640 --> 00:06:21,920
+بدي أروح أجيب و لو عنصر واحد فقط موجود في هذه ال
+
+72
+00:06:21,920 --> 00:06:27,870
+set بقول له اه becauseالـ zero موجود في ال U
+
+73
+00:06:27,870 --> 00:06:33,410
+معقول؟ معقول ال zero vector موجود في ال U؟ اه
+
+74
+00:06:33,410 --> 00:06:38,130
+معقول، معقول كيف؟ لو جدرها اكتب ال zero على صيغة
+
+75
+00:06:38,130 --> 00:06:42,890
+linear compilation من هدول بيكبر كلامي صح؟ مظبوط
+
+76
+00:06:42,890 --> 00:06:51,620
+يبقى باجي بقوله because sinceلأن الـ zero هه ..
+
+77
+00:06:51,620 --> 00:06:58,280
+بقدر اقول scalar zero في U1 scalar zero تاني في ال
+
+78
+00:06:58,280 --> 00:07:06,340
+U2 زائد scalar zero في ال UKصحيح ولا لا يبقى كتبت
+
+79
+00:07:06,340 --> 00:07:11,940
+الـ zero على صيغة linear combination من U1 و U2 و
+
+80
+00:07:11,940 --> 00:07:16,940
+لغاية UK و ال scholars كلهم أخدتهم بأصفر حتى دي
+
+81
+00:07:16,940 --> 00:07:20,760
+يبقى كلامي صحيح يبقى سعر ال U empty ولا ال non
+
+82
+00:07:20,760 --> 00:07:26,120
+-empty non-empty بهاي جبت في عنصر ولو العنصر
+
+83
+00:07:26,120 --> 00:07:31,740
+الصفرينتمام؟ يبقى هذا أول نقطة طب انت ليش بتختار
+
+84
+00:07:31,740 --> 00:07:35,540
+العنصر الصفري دايما؟ مش شاك سؤال؟ سؤال يطرح ليش
+
+85
+00:07:35,540 --> 00:07:38,940
+انت بتختار العنصر الصفري؟ بقولك اه ما هو ال
+
+86
+00:07:38,940 --> 00:07:43,840
+subspace أصلا vector space صحيح ولا لأ؟ ومن خواص
+
+87
+00:07:43,840 --> 00:07:48,150
+لل vector space أنه يحتوي على العنصر الصفرييبقى
+
+88
+00:07:48,150 --> 00:07:53,690
+أنا بختاره متعمد انه دائما اثبت ان العنصر الصفري
+
+89
+00:07:53,690 --> 00:07:57,530
+موجود في هذا ال vector space هذا ال condition
+
+90
+00:07:57,530 --> 00:08:04,570
+الأول ال condition التاني بدي اخد element من عرس
+
+91
+00:08:04,570 --> 00:08:09,610
+color و element menu و اشوف هل موجود ولا لا يبقى
+
+92
+00:08:09,610 --> 00:08:20,510
+باجي بقوله F ال A موجود في R andالـ U موجود في
+
+93
+00:08:20,510 --> 00:08:29,170
+كابتة U then الـ U يستوي الـ U يا بنات موجود في U
+
+94
+00:08:29,170 --> 00:08:34,010
+وهذا الـ Uبقدر اكتبه على صيغة linear combination
+
+95
+00:08:34,010 --> 00:08:39,990
+بهذا الشكل صحيح ولا لا يبقى بقدر اكتبه اللي هو c1
+
+96
+00:08:39,990 --> 00:08:50,610
+u1 زائد c2 u2 زائد زائد ck uk و ال ci موجودة في r
+
+97
+00:08:50,610 --> 00:08:56,350
+و ال I أكبر من أو تساوي واحد و أقل من أو تساوي k
+
+98
+00:08:57,770 --> 00:09:03,690
+طيب بدي أخد حاصل ضربهما يبقى بدي أخد ال a في ال u
+
+99
+00:09:03,690 --> 00:09:16,770
+يبقى بده يساوي يبقى a في c1u1 زائد a في c2u2
+
+100
+00:09:16,770 --> 00:09:21,730
+زائد
+
+101
+00:09:21,730 --> 00:09:25,490
+ونظل ماشيين لغاية a في ck
+
+102
+00:09:28,600 --> 00:09:35,510
+Okay بالشكل اللي عندناطيب هذا الكلام يساوي بدا
+
+103
+00:09:35,510 --> 00:09:40,750
+ارجع لخواص ال vector space من ضمن خواص ال vector
+
+104
+00:09:40,750 --> 00:09:45,430
+space لو كان ال a ليش ان ال u1 و ال u2 و ال un
+
+105
+00:09:45,430 --> 00:09:49,610
+هدول عناصر في v الأصلي صحيح ان هم موجودات في u لكن
+
+106
+00:09:49,610 --> 00:09:52,970
+هدول أصلا وين في ال vector space الأصلي اذا من
+
+107
+00:09:52,970 --> 00:09:58,050
+خواص ال vector space انه عملية ضرب associative على
+
+108
+00:09:58,050 --> 00:10:02,940
+ال scalarsيبقى بقدر اقول هذا الكلام بيديه يساوي
+
+109
+00:10:02,940 --> 00:10:14,120
+AC1 في ال U1 زائد AC2 في ال U2 زائد ACK في ال UK
+
+110
+00:10:15,680 --> 00:10:21,140
+يبقى الـ AU كتبته على شكل مين؟ على شكل linear
+
+111
+00:10:21,140 --> 00:10:26,260
+combination لأن اللي بين جثين كله scholars هدول و
+
+112
+00:10:26,260 --> 00:10:31,340
+هذا ال vectors U1 و U2 و U3 و UK يبقى مدم كتبتم
+
+113
+00:10:31,340 --> 00:10:37,060
+هذا موجود في U ولا لأ صح؟عشان أشكل linear
+
+114
+00:10:37,060 --> 00:10:41,800
+combinations من U1 و U2 و U3 و UK خلصنا ال
+
+115
+00:10:41,800 --> 00:10:44,780
+condition التاني بيدروح أخد ال condition التالت
+
+116
+00:10:44,780 --> 00:10:53,200
+يبقى ال condition التالت بدا أقول له F U تساوي C1
+
+117
+00:10:53,200 --> 00:11:01,600
+U1 C1 U1 C1 زائد C2
+
+118
+00:11:02,830 --> 00:11:14,210
+U2 زائد زائد CK UK والتاني هذا أخدت ال V بده يساوي
+
+119
+00:11:14,210 --> 00:11:23,970
+A1 U1 زائد A2 U2 زائد AK UK موجود هذا في ال U ولا
+
+120
+00:11:23,970 --> 00:11:31,260
+لا؟ مظبوطموجات في ال U ليش؟ انه كل واحد فيهم كتبته
+
+121
+00:11:31,260 --> 00:11:37,780
+على شكل linear combination من مين؟ من ال U1 و U2 و
+
+122
+00:11:37,780 --> 00:11:45,320
+لغاية UKبدا اثبت له ان مجموعهم هدول موجود في ال U
+
+123
+00:11:45,320 --> 00:11:52,040
+يبقى بادروح اخد ال U زائد ال V ال U زائد ال V
+
+124
+00:11:52,040 --> 00:11:56,300
+وقتها الساوية اذا باداجي اجمع component wise
+
+125
+00:11:56,300 --> 00:12:05,960
+ياباناتي يبقى C1U1 زائد كل عنصر مع نظيره A1U1أخدت
+
+126
+00:12:05,960 --> 00:12:10,680
+هذا المع بعض الجزء الثاني مع الجزء الثاني يبقى
+
+127
+00:12:10,680 --> 00:12:19,440
+c2u2 زائد a2u2 شكل اللي عندنا هنا زائد وضلت ماشي
+
+128
+00:12:19,440 --> 00:12:28,100
+لغاية ما وصلت لآخر عنصر اللي هو ckuk زائد akuk
+
+129
+00:12:30,110 --> 00:12:34,430
+هذا الكلام بده يساوي ممكن اخد U1 عامل مشترك بيظل
+
+130
+00:12:34,430 --> 00:12:43,550
+C1 زائد A1 في ال U1 زائد C2 زائد A2 في ال U2 زائد
+
+131
+00:12:43,550 --> 00:12:53,350
+زائد الى ان نصل الى CK زائد AK كله في ال UKيبقى
+
+132
+00:12:53,350 --> 00:13:01,170
+بالنسبة لي اليوم ما له is a subspace of V سا اليوم
+
+133
+00:13:01,170 --> 00:13:13,770
+اللي هو ال Spain تبع U1 و U2 و UK is a subspace of
+
+134
+00:13:13,770 --> 00:13:21,180
+Vيعني يا بنات كأنه هذه النظرية مثال جديد على من
+
+135
+00:13:21,180 --> 00:13:25,580
+على ال subspaces مش احنا المحاضرة الصبح والتلات
+
+136
+00:13:25,580 --> 00:13:28,980
+المرة اللي بدأت بجينا بنجيب أمثلة على ال subspaces
+
+137
+00:13:28,980 --> 00:13:34,080
+يبقى كأنه احنا جيبنا مثال جديد على من على ال
+
+138
+00:13:34,080 --> 00:13:41,040
+subspacesطب في عندي ملاحظة هنا الملاحظة ما يأتي
+
+139
+00:13:41,040 --> 00:13:46,560
+لما اقول يا بنات ان ال elements هدول اللي هو U1 و
+
+140
+00:13:46,560 --> 00:13:53,280
+U2 هدول Spain V سؤالي هو هل بقدر اكتب اي واحد فيهم
+
+141
+00:13:53,280 --> 00:14:00,660
+بدلالة الباقي يعني هل بقدر اكتب U2 بدلالة U1 و U2
+
+142
+00:14:00,660 --> 00:14:04,740
+و U3 و UK و لا بقدر نقدر
+
+143
+00:14:06,260 --> 00:14:10,400
+يعني بقدر اكتب اي واحد فيهم as a linear
+
+144
+00:14:10,400 --> 00:14:16,020
+combination مع الآخرين؟ يعني بقدر اكتب اي واحد
+
+145
+00:14:16,020 --> 00:14:20,600
+فيهم كك .. افهمولي السؤال مرة تانية بقول انا عندي
+
+146
+00:14:20,600 --> 00:14:27,200
+من يواحد ليه كذا بولدولي كل ست يوم؟ طبعا؟ طب لما
+
+147
+00:14:27,200 --> 00:14:32,700
+بولدولي كل ست يوم هل اي واحد منهم يولد باقي
+
+148
+00:14:32,700 --> 00:14:38,490
+العناصر اللي في ال Spain هدول؟أه طبعا بوالده مثال
+
+149
+00:14:38,490 --> 00:14:44,230
+و ذلك لو جيت و قلت لك U واحد بقدر اكتب واحد فيه
+
+150
+00:14:44,230 --> 00:14:47,270
+واحد زائد Zero في U اتنين زائد Zero في U تلاتة
+
+151
+00:14:47,270 --> 00:14:51,370
+زائد Zero في U K يبقى صالين ال combination منهم
+
+152
+00:14:51,370 --> 00:14:56,550
+ولا لا اذا صار موجود بالمثل U اتنين و بالمثل U
+
+153
+00:14:56,550 --> 00:15:04,180
+تلاتة و بالمثل U Kبقدر اكتبها هي 0 في U1 0 في U2 0
+
+154
+00:15:04,180 --> 00:15:09,860
+في U3 زائد 1 في UK وبالتالي صار ماعندي مشكلة يبقى
+
+155
+00:15:09,860 --> 00:15:15,020
+اي element من العناصر اللي بولد ال U بقدر اكتبه
+
+156
+00:15:15,020 --> 00:15:18,900
+على صيغة linear combination من بقية العناصر
+
+157
+00:15:18,900 --> 00:15:23,260
+بالاستثناء خدي هذه الملاحظة بكتبها لك على شكل
+
+158
+00:15:23,260 --> 00:15:35,050
+الملاحظة التالية يبقى notملاحظة الـ UI موجودة في
+
+159
+00:15:35,050 --> 00:15:47,310
+الـ Spain تبع U1 و U2 و UK والـ I من الـ 1 لغاية 8
+
+160
+00:15:47,310 --> 00:15:57,380
+لغاية الـ K because شو السبب؟لو جيت لل U1 بقدر
+
+161
+00:15:57,380 --> 00:16:08,700
+اكتب 1 في ال U1 0U2 0U3 وضل ماشي لغاية 0UKلو جيت
+
+162
+00:16:08,700 --> 00:16:15,680
+لل U2 بقدر اكتب Zero U واحد زائد واحد U اتنين زائد
+
+163
+00:16:15,680 --> 00:16:22,880
+Zero U تلاتة زائد Zero U K لو بليت مستمر هوصل الى
+
+164
+00:16:22,880 --> 00:16:30,440
+U K Zero U واحد Zero U اتنين Zero U تلاتة زائد
+
+165
+00:16:30,440 --> 00:16:34,060
+واحد في U K بالشكل اللي عندنا
+
+166
+00:16:37,490 --> 00:16:42,990
+يبقى أي element في الـ span بقدر اكتب بدلالة بقية
+
+167
+00:16:42,990 --> 00:16:48,950
+العناصر نبدأ الأن بالأمثلة على هذا الكلام يبقى
+
+168
+00:16:48,950 --> 00:16:57,110
+example one example
+
+169
+00:16:57,110 --> 00:17:00,270
+one هو سؤال تلاتة من الكتاب
+
+170
+00:17:05,860 --> 00:17:18,360
+Show that the set of all elements
+
+171
+00:17:18,360 --> 00:17:36,260
+of R3 of the form على الشكلاللي هو a زائد b وناقص
+
+172
+00:17:36,260 --> 00:17:47,800
+a واتنين b where حيث ال a and ال b are any real
+
+173
+00:17:47,800 --> 00:17:48,500
+numbers
+
+174
+00:17:57,750 --> 00:18:14,430
+or any real numbers is a subspace of R3 show
+
+175
+00:18:14,430 --> 00:18:16,370
+that the geometric interpretation
+
+176
+00:18:39,210 --> 00:18:50,170
+interpretation of this subspace of
+
+177
+00:18:50,170 --> 00:19:01,330
+this subspace is a plane is a plane and find
+
+178
+00:19:03,090 --> 00:19:09,730
+its equation يبقى بدنا كمان جديش المعادلة تبعته
+
+179
+00:19:59,320 --> 00:20:03,840
+نرجع لسؤالنا مرة ثانية يبجي أول مثال على هذا
+
+180
+00:20:03,840 --> 00:20:09,220
+الموضوع بقول ما يأتي بيقول إن مجموعة كل العناصر
+
+181
+00:20:09,220 --> 00:20:13,840
+اللي في R3 اللي ماقدر أكتبه على الشكل التالي يبجي
+
+182
+00:20:13,840 --> 00:20:19,350
+أنا جيت على R3 في يوتيوب اللي أخدت كل العناصراللي
+
+183
+00:20:19,350 --> 00:20:23,970
+عند المركبة الأولى A زائد B المركبة الثانية الناقص
+
+184
+00:20:23,970 --> 00:20:30,230
+A المركبة التالتة اتنين B كل الأعداد التي تحقق هذا
+
+185
+00:20:30,230 --> 00:20:34,030
+الكلام قطة مع بعض حيث A وB are any real numbers
+
+186
+00:20:34,030 --> 00:20:36,610
+يبقى as a subspace of R
+
+187
+00:20:55,190 --> 00:21:02,390
+التفسير الهندسي of this subspace is a planar fine
+
+188
+00:21:02,390 --> 00:21:06,410
+sequenceيعني بيبيني أن التفسير الهندسي لهذا ال
+
+189
+00:21:06,410 --> 00:21:11,050
+subspace هو عبارة عن مستوى و بدنا إيش معادلة
+
+190
+00:21:11,050 --> 00:21:17,530
+المستوى أظن كلكم أخدتوا كالكلصي ولا واحدة
+
+191
+00:21:20,200 --> 00:21:24,020
+بنذكركم بمعادلة المستوى المعادلة المستوى constant
+
+192
+00:21:24,020 --> 00:21:27,460
+في x زائد constant في y زائد constant في z زائد
+
+193
+00:21:27,460 --> 00:21:32,200
+constant اكس زائد بي وي زائد سي زائد يساوي مقدار
+
+194
+00:21:32,200 --> 00:21:36,000
+ثابت وليكن كتير يبقى هذه معادلة مستوى يعني إذا
+
+195
+00:21:36,000 --> 00:21:40,580
+جدرنا نحط المعادلة تبعتنا على هذه الصيرة بصير هذه
+
+196
+00:21:40,580 --> 00:21:46,060
+معادلة مستوى وبنشوف المستوى بمر بمين كمان إذا
+
+197
+00:21:46,060 --> 00:21:52,910
+حبيلها ونشوف كيفطبعا المطلوب الأول هحله بأكثر من
+
+198
+00:21:52,910 --> 00:21:56,330
+طريقة الطريقة الأولى اللى هي الطريقة الروتينية
+
+199
+00:21:56,330 --> 00:22:00,390
+اللى متعودين عليها و بعدين هعلمك طريقة جديدة يمكن
+
+200
+00:22:00,390 --> 00:22:04,770
+تكون أسهل أو أكثر الله أعلم احنا مش عارفين لما نجي
+
+201
+00:22:04,770 --> 00:22:09,530
+نشوف خلينا مع الطريقة الأولى انا عندى كل الـU كل
+
+202
+00:22:09,530 --> 00:22:14,230
+العناصر اللى بالشكل اللى عندنا هذا تمام؟يبقى انا
+
+203
+00:22:14,230 --> 00:22:24,910
+عند ال U كل العناصر على الشكل A زائد ال B و سالب A
+
+204
+00:22:24,910 --> 00:22:30,250
+و اتنين B حيث ال A و ال B موجودة في ال set of real
+
+205
+00:22:30,250 --> 00:22:37,140
+numbersصح ؟ اذا قال له انا real number بدي اثبت ان
+
+206
+00:22:37,140 --> 00:22:43,160
+هذه الست هي ال sub space من مين من R3 R3 كلها
+
+207
+00:22:43,160 --> 00:22:47,360
+مركوة من تلت مركبات وهذه فعلا من تلت مركبات اذا
+
+208
+00:22:47,360 --> 00:22:52,700
+كنت روحت اثبتها تمام يبقى بدي اجلب نقطة الأولى
+
+209
+00:22:52,700 --> 00:22:57,500
+النقطة الأولى بدي اثبتله ان هذه ال none empty
+
+210
+00:22:57,500 --> 00:22:59,900
+بتقدر تجيبولي عنصر فيها
+
+211
+00:23:03,950 --> 00:23:11,290
+زيرو زائد زيرو لاقص زيرو هو زيرو يبقى
+
+212
+00:23:11,290 --> 00:23:21,140
+زيرو زيرو زيرو موجود يبقى هنا الis man empty since
+
+213
+00:23:21,140 --> 00:23:30,240
+اللي هو since ال zero و ال zero و ال zero موجودات
+
+214
+00:23:30,240 --> 00:23:38,220
+في اليوم that isيعني زيرو زائد زيرو ناقص زيرو ولا
+
+215
+00:23:38,220 --> 00:23:42,920
+زائد زيرو كل واحد واتنين في زيرو برضه اللي هو
+
+216
+00:23:42,920 --> 00:23:49,560
+بزيرو كله موجود في ال U النقطة الثانية بدأ أخد
+
+217
+00:23:49,560 --> 00:23:56,020
+element موجود في R يبقى باجي بقوله إذا كان مش عند
+
+218
+00:23:56,020 --> 00:24:03,820
+سيها كويس إذا كان ال C موجود في ال R andالـ U بده
+
+219
+00:24:03,820 --> 00:24:10,820
+يساوي A زائد B و ناقص A و اتنين B موجودات في الـ U
+
+220
+00:24:10,820 --> 00:24:17,300
+بده انا اخد الان C في الـ U يبقى هذي يا بنات بده
+
+221
+00:24:17,300 --> 00:24:23,560
+اضرب C ديوه دوري على طول الخط يبقى C في A زائد الـ
+
+222
+00:24:23,560 --> 00:24:33,680
+B C في ناقص A C في اتنين B بالشكل اللي عندناطيب
+
+223
+00:24:33,680 --> 00:24:46,500
+أليست هذه هي CA زائد CB وهذه ناقص CA وهذه اتنين CB
+
+224
+00:24:46,500 --> 00:24:53,480
+ولا لا طيب اتطلعلي هذا element وهذا element هنا
+
+225
+00:24:53,480 --> 00:24:59,440
+سالب ال element الأول هنا اتنين ال element الثاني
+
+226
+00:24:59,440 --> 00:25:05,030
+إذا موجودة في U ولا لايبقى هذه belongs to you
+
+227
+00:25:05,030 --> 00:25:07,490
+بالدرجة لل condition التالت
+
+228
+00:25:11,050 --> 00:25:19,450
+F U A B-A2B
+
+229
+00:25:19,450 --> 00:25:25,770
+V A1B1
+
+230
+00:25:25,770 --> 00:25:29,770
+-A1A2B1
+
+231
+00:25:29,770 --> 00:25:38,240
+كله موجود في U then بدا أخذ المجموعيبقى لما أجي
+
+232
+00:25:38,240 --> 00:25:44,180
+أخد المجموع تبعهم بدي ال U زائد ال V و يساوي بدي
+
+233
+00:25:44,180 --> 00:25:51,540
+أجمع component-wise يبقى A زائد ال B زائد ال A1
+
+234
+00:25:51,540 --> 00:25:58,510
+زائد ال B1وعندك هنا هاي جمعنا هذه وهذه هذي بدها
+
+235
+00:25:58,510 --> 00:26:05,990
+تصير سالب a سالب a one اللي بعدها اتنين b زائد
+
+236
+00:26:05,990 --> 00:26:13,890
+اتنين b one هذا الكلام بده يساوي بقدر اقول يا بنات
+
+237
+00:26:13,890 --> 00:26:21,370
+هذا اللي عبارة عن مين a زائد ال a one زائد ال b
+
+238
+00:26:21,370 --> 00:26:27,570
+زائد ال b oneكل هذا المُركّب الأولى يعني أخذت هذه
+
+239
+00:26:27,570 --> 00:26:32,750
+و هذه مع بعض و هذه و هذه ما لهم مع بعض تين تين
+
+240
+00:26:32,750 --> 00:26:39,070
+أخدتهم بجوز بهذا الشكل هذه ههه بقدر أخد سالب عامل
+
+241
+00:26:39,070 --> 00:26:46,630
+مشترك بظل a زائد a1 هذه بقدر أخد اتنين عامل مشترك
+
+242
+00:26:46,630 --> 00:26:54,940
+بظل b زائد b1 طلعوا لي هناهذه المركبة الأولى مجموع
+
+243
+00:26:54,940 --> 00:27:04,750
+two terms هنا سالب ال term الأولمظبوط؟ هنا اتنين
+
+244
+00:27:04,750 --> 00:27:08,650
+ال term التاني صحيح ولا لأ؟ إذا هذه موجودة فيه ولا
+
+245
+00:27:08,650 --> 00:27:15,850
+لأ؟ يبقى هذه موجودة موجودة في ال you belongs to
+
+246
+00:27:15,850 --> 00:27:21,590
+you معناته تحققت الخاصية التالتة يبقى بناء عليه
+
+247
+00:27:21,590 --> 00:27:28,430
+ذات وهكذا ال you is a subspace
+
+248
+00:27:32,660 --> 00:27:36,940
+يبقى أثبت له الآن بالطريقة الروتينية أو الطريقة
+
+249
+00:27:36,940 --> 00:27:44,560
+العادية أن ال U is a subspace of V ثم نيجي الآن
+
+250
+00:27:44,560 --> 00:27:49,380
+بدي أحل نفس المطلوب هذا بطريقة ثانية ما اتعودناش
+
+251
+00:27:49,380 --> 00:27:55,520
+نحل عليها قبل ذلك باجي بقوله كويس الان another
+
+252
+00:27:55,520 --> 00:27:56,520
+solution
+
+253
+00:28:03,200 --> 00:28:09,760
+حل آخر و من هنا بدأنا ايش بدأنا في نمرة A يبقى انا
+
+254
+00:28:09,760 --> 00:28:17,580
+بدي اجي لنمرة A مباشرة ال U كل العناصر A زائد ال B
+
+255
+00:28:17,580 --> 00:28:24,540
+سالب A و اتنين B بالشكل اللي عندنا هذا بحيث ال A و
+
+256
+00:28:24,540 --> 00:28:31,580
+ال B موجودة في ال set of real numbers كويس
+
+257
+00:28:33,000 --> 00:28:40,000
+طب ايش رأيكوا انا اخدت في الشبتر الماضي ان ل three
+
+258
+00:28:40,000 --> 00:28:45,420
+tuple بقدر اكتبها ك call vector و بقدر اكتبها ك
+
+259
+00:28:45,420 --> 00:28:50,840
+raw vector صح ولا لأ اذا انا لو جيت هنا قلت ما
+
+260
+00:28:50,840 --> 00:29:00,680
+يأتي اخد ال a زائد ال b و سلب a و اتنين bالشيء
+
+261
+00:29:00,680 --> 00:29:06,820
+المكافئ لها تماما اني اكتبها على شكل ال vector a
+
+262
+00:29:06,820 --> 00:29:18,280
+زائد b وناقص a و2b مظبوط؟ ساكت الشعب صح ولا لا؟ مش
+
+263
+00:29:18,280 --> 00:29:23,200
+خناها في ال chapter الماضي زي هيك؟ طيبأيش رايك؟
+
+264
+00:29:23,200 --> 00:29:28,360
+هذه يعني كتبتها على شكل مصوفة بثلاث صفوف وعمود
+
+265
+00:29:28,360 --> 00:29:34,340
+واحد احطها على شكل جمع مصوفين في مشكلة؟ لا تعالى
+
+266
+00:29:34,340 --> 00:29:41,020
+نشوف يبقى انا لو جيت حاطيتها بده اقول A و سالب A و
+
+267
+00:29:41,020 --> 00:29:49,960
+Zero زائد B و Zero و اتنين B بنفعلك؟
+
+268
+00:29:50,620 --> 00:29:56,180
+A زائد B هيها ناقص A و Zero بناقص A Zero و اتنين B
+
+269
+00:29:56,180 --> 00:30:00,620
+و اتنين B يعني كأنه مش عامل فاصلة ال A مع بعض و ال
+
+270
+00:30:00,620 --> 00:30:05,560
+B مع بعض طيب لما في عامل مشترك في جميع أنصار
+
+271
+00:30:05,560 --> 00:30:10,820
+المصممة مش بقدر اكتبه برا صح ولا لأ يعني بقدر اكتب
+
+272
+00:30:10,820 --> 00:30:19,290
+هذاA في ال vector واحد سالب واحد Zero زائد B في ال
+
+273
+00:30:19,290 --> 00:30:26,770
+vector واحد Zero اتنين يعني كأنه بكتب هذا A في ال
+
+274
+00:30:26,770 --> 00:30:34,630
+V1 زائد B في ال vector V2 صح ولا لأ يعني ايش عملت
+
+275
+00:30:34,900 --> 00:30:41,140
+كأنه كتبت هذا على صيغة linear combination من
+
+276
+00:30:41,140 --> 00:30:46,950
+الاتنينصح ولا لا يعني معنى هذا الكلام انه any
+
+277
+00:30:46,950 --> 00:30:52,390
+element موجود في ال vector space هذا بقدر اكتبه
+
+278
+00:30:52,390 --> 00:30:56,910
+على صيغة linear combination من ال two vectors هذول
+
+279
+00:30:56,910 --> 00:31:02,370
+صحيح ولا لا يعني معناته ال V واحد وال V اتنين سبين
+
+280
+00:31:02,370 --> 00:31:09,110
+ال U بيولدول ال U صحيح ولا لا مظبوط يبقى هنا سا
+
+281
+00:31:09,110 --> 00:31:12,190
+any vector
+
+282
+00:31:13,460 --> 00:31:24,700
+ن U is a linear combination of
+
+283
+00:31:24,700 --> 00:31:32,540
+V واحد اللي هو بده يساوي واحد سالب واحد زيرو and V
+
+284
+00:31:32,540 --> 00:31:38,120
+اتنين اللي هو بده يساوي and V اتنين
+
+285
+00:31:40,210 --> 00:31:47,510
+اللي هو بده يساوي واحد زيرو اتنين بالشكل اللي
+
+286
+00:31:47,510 --> 00:31:54,050
+عندنا طب مادام هيك يبقى two vectors هدول this
+
+287
+00:31:54,050 --> 00:32:05,010
+means that انه اليوم يساوي لسبين تبع اللي هو في
+
+288
+00:32:05,010 --> 00:32:10,470
+واحد وفي اتنين صحيح ولا لاطب ماذا مش فين؟ من
+
+289
+00:32:10,470 --> 00:32:14,910
+النظرية اللي قبل قليل هذي subspace ولا لا؟ بيبقى
+
+290
+00:32:14,910 --> 00:32:25,030
+هنا by the previous theorem بالنظرية السابقة قبل
+
+291
+00:32:25,030 --> 00:32:32,030
+قليل by the previous theorem اللي هو LU is a
+
+292
+00:32:32,030 --> 00:32:39,710
+subspace ofفين؟ مين اللي أسأل؟ هذا والله اللي
+
+293
+00:32:39,710 --> 00:32:45,590
+جابال يبقى حل هذه الطريقتين، حل باللي تعجبك إن جاك
+
+294
+00:32:45,590 --> 00:32:49,110
+أي سؤال زي هذا أحل بالطريقة ده، أسهل، خلاص بحل
+
+295
+00:32:49,110 --> 00:32:54,370
+بها، تمام؟ طبعا هذه هنتكرر الشغل بها كتير في باقها
+
+296
+00:32:54,370 --> 00:32:59,060
+الشبتر والشبتر القادم كمانأه يعني دي ربالك من
+
+297
+00:32:59,060 --> 00:33:03,440
+هالطريقة هذه إذا قدرت أكتب هذا على شكل هنا
+
+298
+00:33:03,440 --> 00:33:08,220
+transformation بالشكل ان هذا لسه احنا حلنا المطلوب
+
+299
+00:33:08,220 --> 00:33:13,200
+الأول بطريقة تانية بدنا نروح للمطلوب التاني نمربي
+
+300
+00:33:13,200 --> 00:33:19,820
+نمربي إيش بقولني؟يقول في السؤال show that the
+
+301
+00:33:19,820 --> 00:33:22,960
+geometric interpretation of this subspace is a
+
+302
+00:33:22,960 --> 00:33:28,080
+plane وبدنا معادلته بيقولوا أن المعنى الهندسي لهذا
+
+303
+00:33:28,080 --> 00:33:32,560
+ال subspace هو عبارة عن مستوى و بدي معادلة مين؟
+
+304
+00:33:32,560 --> 00:33:38,760
+بدي معادلة هذا المستوى بقوله بسيطة جدا احنا عندنا
+
+305
+00:33:38,760 --> 00:33:43,280
+لو يا بنات صارواين هي اليوم الشكل اللي عندنا كتبنا
+
+306
+00:33:43,280 --> 00:33:51,780
+هييبقى انا عند ال U تساوي اللي هو A زائد B و سالب
+
+307
+00:33:51,780 --> 00:34:00,920
+A و اتنين B بحيث ان هذا كله ال A و ال B موجودة في
+
+308
+00:34:00,920 --> 00:34:05,800
+ال set of real numbers يعني هذا مكون من كام مركبة
+
+309
+00:34:06,900 --> 00:34:12,380
+من ثلاث مركبات يبقى كأنه عندي mean اللي هو x واحد
+
+310
+00:34:12,380 --> 00:34:18,260
+بدي يسوى ال a زائد ال b وال x اتنين يسوى ناقص ال a
+
+311
+00:34:18,260 --> 00:34:25,900
+وال x تلاتة يسوى اتنين bمظبوط يعني هي لما اقول
+
+312
+00:34:25,900 --> 00:34:30,020
+مركب X واحد و X اتنين و X تلاتة الاولة A زياد B
+
+313
+00:34:30,020 --> 00:34:34,580
+والتانية سلب A والتالتة اتنين B اقول والله كلامي
+
+314
+00:34:34,580 --> 00:34:40,040
+كويس طب ايش رأيك اجمع هدول مع بعض التنتين لو
+
+315
+00:34:40,040 --> 00:34:45,940
+جمعتهم مش بصير هدول يبقى بصيري عندي X واحد زائد X
+
+316
+00:34:45,940 --> 00:34:50,920
+اتنين يساوي B طيب
+
+317
+00:34:51,370 --> 00:34:58,450
+الحين انا عندي and ال X تلاتة يساوي اتنين بي يبقى
+
+318
+00:34:58,450 --> 00:35:04,830
+you say هذا بده يعطيكي ان X تلاتة تساوي اتنين بي
+
+319
+00:35:04,830 --> 00:35:12,350
+هي mainly X واحد زائد X اتنينيعني ايش صار عندى؟
+
+320
+00:35:12,350 --> 00:35:19,530
+صار عندى x تلاتة نقص اتنين x واحد نقص اتنين x
+
+321
+00:35:19,530 --> 00:35:24,510
+اتنين يساوي zero مظبوط
+
+322
+00:35:24,510 --> 00:35:31,240
+طب هذا ال system أخدناه قبل هيك ولا لا؟Homogeneous
+
+323
+00:35:31,240 --> 00:35:37,000
+system ممتاز يبقى هذا system of linear equations
+
+324
+00:35:37,000 --> 00:35:42,980
+تمام طبعا ماعنديش ال equation واحدة بثلاثة مجاهيل
+
+325
+00:35:42,980 --> 00:35:48,100
+تمام يبقى هذا system of linear homogenous system
+
+326
+00:35:48,100 --> 00:35:53,320
+هذا ال homogenous system يا إما له حل وحيد هو الحل
+
+327
+00:35:53,320 --> 00:35:59,140
+الصفرييعملوا حل عدد لا نهائي من الحلول يجتمل على
+
+328
+00:35:59,140 --> 00:36:05,870
+الحل الصفري إذا هذه معادلة plane ولا لا يا بنات؟مش
+
+329
+00:36:05,870 --> 00:36:10,370
+قلتلكوا قبل قليل AX زي BY زي C زي Z يبقى constant
+
+330
+00:36:10,370 --> 00:36:18,750
+يبقى بدل XY وزي X1 X2 وX3 يعني بمعنى أخر كأنه هذه
+
+331
+00:36:18,750 --> 00:36:26,750
+المعادلة لو قعدت ترتيبها يبقى 2 X1 زي 2 X2 نقص X3
+
+332
+00:36:26,750 --> 00:36:35,720
+يبقى zero يبقى adequation of A planeطب ايش رايك ال
+
+333
+00:36:35,720 --> 00:36:42,900
+plain هذا يمر بنقطة الأصل لأن
+
+334
+00:36:42,900 --> 00:36:48,460
+هي أحد الحلول مظبوط ولا لا يبقى plain passes
+
+335
+00:36:48,460 --> 00:36:58,040
+through the origin because
+
+336
+00:37:01,940 --> 00:37:08,900
+اللي هو x واحد و x اتنين و x تلاتة تساوي زيرو و
+
+337
+00:37:08,900 --> 00:37:18,300
+زيرو زيرو is the او is its a trivial solution
+
+338
+00:37:19,970 --> 00:37:25,190
+يبقى قال لي وصفلي شوهد احنا وصفناله يا وقال لي
+
+339
+00:37:25,190 --> 00:37:28,950
+اثبت انه معادلة plane يبقى اثبتناله هي معادلة
+
+340
+00:37:28,950 --> 00:37:33,670
+plane يبقى ال subspace اللي عندنا صار معادلة plane
+
+341
+00:37:33,670 --> 00:37:38,510
+وبالتالي كنا بنترابطنا هذا ال chapter بموضوع ال
+
+342
+00:37:38,510 --> 00:37:43,390
+chapter الأول اللي هو system of linear equations
+
+343
+00:37:43,390 --> 00:37:48,060
+حد يلها اي تساول هنا؟يبقى ايه اثبت انه subspace
+
+344
+00:37:48,060 --> 00:37:55,140
+بطريقة تانية و اثبت ان هذا subspace يمثل من؟ يمثل
+
+345
+00:37:55,140 --> 00:37:58,420
+plane و الصبح و قلتلكم بدأنا في ال jet اليوم و ده
+
+346
+00:37:58,420 --> 00:38:02,140
+احنا بنشتغل ال jet على غير الشيء اللي كنا متعرفين
+
+347
+00:38:02,140 --> 00:38:04,200
+عليه قبل ذلك
+
+348
+00:38:21,850 --> 00:38:32,210
+مثال اتنين مثال اتنين مثال اتنين
+
+349
+00:38:32,210 --> 00:38:37,730
+مثال اتنين مثال اتنين مثال اتنين مثال اتنين مثال
+
+350
+00:38:37,730 --> 00:38:38,130
+اتنين مثال اتنين مثال اتنين مثال اتنين مثال اتنين
+
+351
+00:38:38,130 --> 00:38:38,210
+مثال اتنين مثال اتنين مثال اتنين مثال اتنين مثال
+
+352
+00:38:38,210 --> 00:38:42,050
+اتنين مثال اتنين مثال
+
+353
+00:38:42,050 --> 00:38:59,810
+اتn مثالof R3 that is spanned by
+
+354
+00:38:59,810 --> 00:39:03,710
+the
+
+355
+00:39:03,710 --> 00:39:11,990
+vectors اللي هو V1 يساوي
+
+356
+00:39:13,720 --> 00:39:26,000
+V1 يساوي سالب اتنين و واحد و واحد و V2 يساوي واحد
+
+357
+00:39:26,000 --> 00:39:29,840
+و ناقص تلاتة و خمسة
+
+358
+00:39:32,260 --> 00:39:51,200
+show that the geometric interpretation
+
+359
+00:39:51,200 --> 00:39:56,800
+of this subspace
+
+360
+00:40:09,920 --> 00:40:21,440
+و هاتينا كمان المعادلة تبعه
+
+361
+00:40:21,440 --> 00:40:25,500
+و
+
+362
+00:40:25,500 --> 00:40:26,960
+من هذه الخيارة انتهينا منها
+
+363
+00:40:45,840 --> 00:40:51,540
+نرجع لمثالنا هذا مرة ثانية ونشوف كيف بدنا نشتغل
+
+364
+00:40:51,540 --> 00:40:57,880
+هذا المثالالمثال اللي بقول ياخد ال U subspace من
+
+365
+00:40:57,880 --> 00:41:04,600
+R3 that is spanned by the vectors V1 وV2 يبقى U
+
+366
+00:41:04,600 --> 00:41:11,760
+هذا أخدته subset من من من ال vector space اللي هو
+
+367
+00:41:11,760 --> 00:41:17,540
+R3 بحيث هذا يولد ب two vectors مادام يولد بال two
+
+368
+00:41:17,540 --> 00:41:19,860
+vectors يبقى هذا subspace ولا لا
+
+369
+00:41:28,400 --> 00:41:38,800
+يبقى الأن كأن ال U عبارة عنالـ U هو عبارة عن ال
+
+370
+00:41:38,800 --> 00:41:47,780
+set of all real numbers C1V1 زي C2V2 such that C1
+
+371
+00:41:47,780 --> 00:41:53,160
+وC2 موجودة في ال set of real numbersليش؟ لأن هو
+
+372
+00:41:53,160 --> 00:41:58,700
+قال لي هذا يولد بهذه العنصرين يعني لو بدأ أكتبه
+
+373
+00:41:58,700 --> 00:42:04,920
+بصيغة أخرى بدأ أقول كل العناصر على الشكل التالي C1
+
+374
+00:42:04,920 --> 00:42:14,660
+في V1 سالب 2 و 1 و 1 زائد C2 في 8 في 1 و ناقص 3 و
+
+375
+00:42:14,660 --> 00:42:22,150
+5 بحيث C1 و C2 موجودة في set of real numbersيعني
+
+376
+00:42:22,150 --> 00:42:27,810
+هذا كأنه ال vector u ال vector space u هو عبارة
+
+377
+00:42:27,810 --> 00:42:34,330
+بده افك و اجمع يا بنات دوري يبقى سالب اتنين C واحد
+
+378
+00:42:34,330 --> 00:42:39,920
+زائد C اتنين هذه هي المركبة الأولىالمُركّبة
+
+379
+00:42:39,920 --> 00:42:47,840
+الثانية C1 ناقص ثلاثة C2 المُركّبة التالتة C1 زائد
+
+380
+00:42:47,840 --> 00:42:53,880
+خمسة C2 بها الـ C1 و C2 موجودة في الـ set of real
+
+381
+00:42:53,880 --> 00:43:01,980
+number طب استنوا شوية نوقف وقفة محاسبة مع النفس
+
+382
+00:43:01,980 --> 00:43:09,870
+كالتاليهنجيل ان V1 و V2 بيولدوا لمين؟ بيولدوا لـ U
+
+383
+00:43:09,870 --> 00:43:14,390
+إذا اليوم بقدر أكتب علاصية Linear Combination من
+
+384
+00:43:14,390 --> 00:43:21,270
+V1 و V2 فهي كتبنا C1 V1 C2 و C1 V2 Any Scalars
+
+385
+00:43:21,270 --> 00:43:26,850
+تمام؟ إلا أن شيلت ال V1 و V2 و حطيت قيمتها و ضال
+
+386
+00:43:26,850 --> 00:43:32,730
+بالزائد هدول مجموعة two vectors بتخليهم vector
+
+387
+00:43:32,730 --> 00:43:40,270
+واحديبقى أفك و أجمع C1 فى سالب 2 مع C2 فى 1 يبقى
+
+388
+00:43:40,270 --> 00:43:46,210
+سالب 2 C1 زائد C2 هى المركبة الأولى بدأجى المركبة
+
+389
+00:43:46,210 --> 00:43:51,690
+التانية C1 فى 1 بC1وC2 في السالب تلاتة بالسالب
+
+390
+00:43:51,690 --> 00:43:58,550
+تلاتة C2 اللي بعده C1 في واحد وC2 في خمسة بC1 زي
+
+391
+00:43:58,550 --> 00:44:05,090
+الخمسة C2 تمام يعني إيش اللي حصل عندي حصل عندي
+
+392
+00:44:05,090 --> 00:44:13,060
+الآن ما يأتيإن X1 المركبة الأولى نقص 2C1 زائد C2
+
+393
+00:44:13,060 --> 00:44:24,940
+X2 عبارة عن C1 نقص 3C2 X3 يساوي C1 زائد 5C2
+
+394
+00:44:25,940 --> 00:44:29,460
+طيب هو ايش بيقوللي هذا السؤال بيقوللي show that
+
+395
+00:44:29,460 --> 00:44:32,120
+the geometrical interpretation of this subspace is
+
+396
+00:44:32,120 --> 00:44:37,740
+a plane و بدنا معادلته يبقى بد أبين ان هذا معادلة
+
+397
+00:44:37,740 --> 00:44:42,990
+a plane و بد أشوف شو هي معادلةبقول بسيطة جدا إذا
+
+398
+00:44:42,990 --> 00:44:49,110
+أنا بدأ اتخلص من c1 و c2 و أخلّي المثلة بدلة x1 و
+
+399
+00:44:49,110 --> 00:44:54,170
+x2 و x3 اللي هي main اللي كانها x و y و z لإنه
+
+400
+00:44:54,170 --> 00:44:59,430
+قلتلك معادلة leap line دائما و أبدا على صيغة ax
+
+401
+00:44:59,430 --> 00:45:05,680
+زائد by زائد cz بده يسوي constant و ليكن bالـ A و
+
+402
+00:45:05,680 --> 00:45:10,200
+الـ B و الـ C و الـ D ثوابت والـ X و الـ Y و الـ Z
+
+403
+00:45:10,200 --> 00:45:14,380
+اللي هي المجاهيل D تكون Zero ما تكون Zero بهمنيش
+
+404
+00:45:14,380 --> 00:45:17,720
+جد ما تكون تكون والـ A و الـ B و الـ C كمان بيه
+
+405
+00:45:17,720 --> 00:45:21,920
+ثوابته و يمكن يكون بعضهم ب Zero قد يكون بعضهم ب
+
+406
+00:45:21,920 --> 00:45:27,570
+Zero ماعندي مشكلة في هذه الحالةبقول تمام، إذا احنا
+
+407
+00:45:27,570 --> 00:45:31,690
+بدنا إيه؟ يجي نحل المعذرتين هدول مع بعض و نطلع كده
+
+408
+00:45:31,690 --> 00:45:36,290
+X1 و X2 يعني نتخلص من السيهات اللي عندنا حد يا
+
+409
+00:45:36,290 --> 00:45:40,370
+بنات ما علمتش كمال اسم هايانة؟ تعالوا خدوا يالا
+
+410
+00:45:43,620 --> 00:45:47,960
+بدأجي للمعادلة الأولى اللي هو الثانية هدول اتنين
+
+411
+00:45:47,960 --> 00:45:52,660
+اظن لو ضربت التانية في اتنين و جمعت بتخلص من احد
+
+412
+00:45:52,660 --> 00:45:59,000
+المجاهيل اللي هو ال C واحد وبجيب جداش C اتنين يبقى
+
+413
+00:45:59,000 --> 00:46:03,800
+بناء عليه من المعادلتين هدول بقول ما يأتييبقى اي
+
+414
+00:46:03,800 --> 00:46:08,380
+اكس واحد يساوي سالب اتنين C واحد زاد C اتنين بدي
+
+415
+00:46:08,380 --> 00:46:13,580
+اضرب هذه في اتنين يبقى اتنين X اتنين سالب اتنين C
+
+416
+00:46:13,580 --> 00:46:21,700
+واحد او موجة باتنين C واحد ناقص ستة اللي هو C
+
+417
+00:46:21,700 --> 00:46:25,760
+اتنين ونجي نجمع ضربت المعادلة التانية في اتنين
+
+418
+00:46:25,760 --> 00:46:30,800
+هدول مع السلامةيبقى من هدول اتنين ايش بستنتج
+
+419
+00:46:30,800 --> 00:46:41,860
+بستنتج انه X1 زائد 2 X2 بدر ساوي ناقص خمسة C2 يبقى
+
+420
+00:46:41,860 --> 00:46:48,980
+زائد واحد وناقص ستة بضل جداش ناقص خمسة ومنها C2
+
+421
+00:46:48,980 --> 00:46:58,180
+بدر ساوي ناقص X1 زائد 2 X2 كله على خمسةيبقى هاي
+
+422
+00:46:58,180 --> 00:47:05,000
+جبت C2
+
+423
+00:47:05,000 --> 00:47:13,160
+بدلالة X1 و X2 بقدر أجيب C1 كمان بدلالة X1 و X2
+
+424
+00:47:13,160 --> 00:47:19,300
+برجع بعود في أي من المعادلتينإذا لو رجعنا و عوضنا
+
+425
+00:47:19,300 --> 00:47:24,300
+في أي من المعادلة بدي أمسك النتيجة التي توصل إليها
+
+426
+00:47:24,300 --> 00:47:28,680
+هذه و أجي أعوض مثلا في المعادلة رقم 2 عشان بدي
+
+427
+00:47:28,680 --> 00:47:39,490
+أجيب C1 فبجي بقول X2 يساوي C1نقص ثلاثة في C2 C2
+
+428
+00:47:39,490 --> 00:47:50,410
+التي هي ناقص لل X1 زائد 2 X2 كله رداش على خمسة
+
+429
+00:47:50,410 --> 00:47:55,950
+يبقى هذا الكلام يعطيني C1 ناقص مع ناقص في الصيرة
+
+430
+00:47:55,950 --> 00:48:03,610
+زائد ثلاثة في X1زي دي اتنين اكس اتنين كله علامين
+
+431
+00:48:03,610 --> 00:48:09,930
+على خمسة بالشكل اللي عندنا هذا معنى هذا الكلام انه
+
+432
+00:48:09,930 --> 00:48:17,490
+c واحد بده يساوي اكس اتنين ناقص تلت أخماس في اكس
+
+433
+00:48:17,490 --> 00:48:24,170
+واحد زي دي اتنين اكس اتنين يبقى جبت c واحد بدلالة
+
+434
+00:48:24,170 --> 00:48:29,730
+اكسبدلالة X1 و X2 اللي انا باجي على المعادلة
+
+435
+00:48:29,730 --> 00:48:34,650
+التالتة ما هي في C1 و C2 بشيلهم و بجيب قيمتهم يبقى
+
+436
+00:48:34,650 --> 00:48:45,640
+باجي بقول له X3 تساوي C1 زائد 5 C2 وتساويC1 هي
+
+437
+00:48:45,640 --> 00:48:55,920
+موجودة عند X2 ناقص تلت أخمس في X1 زائد 2 X2 هذا
+
+438
+00:48:55,920 --> 00:49:01,260
+كله في C1 زائد خمسة في C2
+
+439
+00:49:18,530 --> 00:49:23,150
+بناء على الـ X3 تساوي
+
+440
+00:49:24,750 --> 00:49:32,250
+أكس اتنين وهذا بنات كلها بقدر اقول ناقص اللي هو
+
+441
+00:49:32,250 --> 00:49:39,010
+مين تلاتة والله خليها ناقص زي ما هي هاي ناقص وهنا
+
+442
+00:49:39,010 --> 00:49:45,470
+تلاتة اكس واحد زائد ستة اكس اتنين كله على مين على
+
+443
+00:49:45,470 --> 00:49:54,050
+خمسة وهذه ناقصوالله خلّيها ناقص ماعش الحال و هنا
+
+444
+00:49:54,050 --> 00:50:01,350
+خمسة X واحد زائد عشرة X اتنين كله على مين على خمسة
+
+445
+00:50:01,350 --> 00:50:07,450
+ايش رأيك بدا واحد المقامات للكل كله على خمسةيبقى
+
+446
+00:50:07,450 --> 00:50:14,850
+بصير x3 يساوي خمسة x اتنين ناقص تلاتة x واحد ناقص
+
+447
+00:50:14,850 --> 00:50:22,810
+ستة x اتنين و هنا ناقص خمسة x واحد ناقص عشرة x
+
+448
+00:50:22,810 --> 00:50:29,610
+اتنينيبقى هذا الكلام بده يساوي هي عندي X2 وهي عندي
+
+449
+00:50:29,610 --> 00:50:38,890
+X2 وهي عندي X2 عندك هنا ناقص 16 X2 وزائد خمسة بيظل
+
+450
+00:50:38,890 --> 00:50:46,850
+ناقص 11 X2عندك سالب تلاتة اكس واحد و سالب خمسة
+
+451
+00:50:46,850 --> 00:50:53,130
+بسالب تمانية اكس واحد تمام كل هذا الكلام على جداش
+
+452
+00:50:53,130 --> 00:51:00,070
+على خمسة يساوي اكس تلاتة اضر بضرب تبادلي يبقى بصير
+
+453
+00:51:00,070 --> 00:51:09,540
+خمسة اكس تلاتةيساوي سالب 11 X 2 سالب 8 X 1 نعملها
+
+454
+00:51:09,540 --> 00:51:20,140
+معادلة صفرية يبقى بصير عندك 8 X 1 زي 11 X 2 زي 5 X
+
+455
+00:51:20,140 --> 00:51:25,180
+3 يساوي 0 يبقى هذه equation of
+
+456
+00:51:37,950 --> 00:51:47,070
+السؤال هو هل يمر هذا بنقطة الأصل؟ فهذا
+
+457
+00:51:47,070 --> 00:51:51,570
+باصد أثرى
+
+458
+00:51:53,510 --> 00:52:01,430
+فاصجت هو the origin لأيش؟
+
+459
+00:52:01,430 --> 00:52:04,530
+لأنه أخدت x واحد وx تانية وكل واحد بزير و بتلاقي
+
+460
+00:52:04,530 --> 00:52:11,590
+بحقق هذه المعادلة طيب السؤال هو هل يمر بالنقطة
+
+461
+00:52:11,590 --> 00:52:16,610
+سالب اتنين وواحد وواحد و النقطة واحد وناقص ثلاثة
+
+462
+00:52:16,610 --> 00:52:29,520
+وخمسة؟100% تمام يبقى هنا and passes through the
+
+463
+00:52:29,520 --> 00:52:33,500
+points ويمر
+
+464
+00:52:33,500 --> 00:52:39,040
+كذلك خلال النقطتين اللي هو سالب اتنين وواحد وواحد
+
+465
+00:52:39,040 --> 00:52:47,840
+and التانية واحد وناقص تلاتة وخمسة تحبوني اتركب؟
+
+466
+00:52:48,400 --> 00:52:53,000
+تعالوا نتأكد نتأكد من هنا بس نعود نشوف سهر ولا لا
+
+467
+00:52:53,000 --> 00:52:58,140
+القصة بسيطة جدا هاي ناقص اتنين في تمانية ناقص
+
+468
+00:52:58,140 --> 00:53:03,440
+ستاشر هاي ناقص ستاشر عندك واحد في احداشر زائد
+
+469
+00:53:03,440 --> 00:53:07,920
+احداشر عندك واحد في خمسة في خمسة خمسة و احداشر
+
+470
+00:53:07,920 --> 00:53:12,180
+بالمجموعة ستاشر و ستاشر إذا كلامي صحيح و بالمثل
+
+471
+00:53:12,180 --> 00:53:17,810
+بلاجين بمربى مين؟ بمربة النقطة الثانيةطيب لازلنا
+
+472
+00:53:17,810 --> 00:53:22,610
+في نفس الموضوع و المرة القادمة ان شاء الله نكمل
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOlfMJSH6b4_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOlfMJSH6b4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..314366a309dd0fddb060e39230fbd441bfef6408
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/DOlfMJSH6b4_raw.srt
@@ -0,0 +1,1904 @@
+1
+00:00:19,070 --> 00:00:24,270
+بسم الله الرحمن الرحيم بنرجع نكمل محاضرة الفترة
+
+2
+00:00:24,270 --> 00:00:28,470
+الصباحية و بدأنا في كلام جديد اللي هو linear
+
+3
+00:00:28,470 --> 00:00:32,430
+transformation بدي أذكر عفوا بال linear
+
+4
+00:00:32,430 --> 00:00:35,590
+combination بدي أذكر الان بال two definitions
+
+5
+00:00:35,590 --> 00:00:39,050
+تبعات الصبح في نهاية المحاضرةثم نبدأ في ال
+
+6
+00:00:39,050 --> 00:00:43,150
+definition الجديد و النظرية اللى بين إيدنا ال
+
+7
+00:00:43,150 --> 00:00:46,890
+definition تابعة الصبح ال definition ما قبل الأخير
+
+8
+00:00:46,890 --> 00:00:51,010
+قال لو كان ال V هو vector of space واخدت منه
+
+9
+00:00:51,010 --> 00:00:56,450
+مجموعة من ال vectors هدولولاقيت ان واحد من ال
+
+10
+00:00:56,450 --> 00:01:00,750
+vectors V من تعات ال vector space V قدرت اكتبه على
+
+11
+00:01:00,750 --> 00:01:05,710
+صورة Linear Combination من هدول كاف يعني يعني قدرت
+
+12
+00:01:05,710 --> 00:01:11,290
+اكتب ال V هو C1 في V1 زي تكون أسطن تاني في V2 زي
+
+13
+00:01:11,290 --> 00:01:16,990
+تكون أسطن تاني في V3 زي تكون أسطن CM في VM لقيت ال
+
+14
+00:01:16,990 --> 00:01:21,460
+vector هو مجموعهميبقى بقول إن الـ vector V هو
+
+15
+00:01:21,460 --> 00:01:28,200
+linear combination من الـ V1 و V2 و V3 و VM وهذا
+
+16
+00:01:28,200 --> 00:01:33,160
+ما ذكرناه في الفترة الصباحية نجلن التعريف الثاني
+
+17
+00:01:33,740 --> 00:01:39,720
+بقول إذا كان كل عنصر فيه V هو linear combination
+
+18
+00:01:39,720 --> 00:01:46,460
+من ال vectors هذا بقول إن ال V يولد بهذه العناصر
+
+19
+00:01:46,460 --> 00:01:50,980
+أو هذه العناصر بتجيب لمين؟ بتجيب لل vector space V
+
+20
+00:01:50,980 --> 00:01:57,600
+يعني بتجيب لكل عناصر V بلا ستة نايبقى إذا كان كل
+
+21
+00:01:57,600 --> 00:02:02,520
+عنصر في ال vector V بقدر أكتبه على صيغة linear
+
+22
+00:02:02,520 --> 00:02:07,180
+combination من ال vectors اللي عندنا هدول يبقى في
+
+23
+00:02:07,180 --> 00:02:11,000
+هذه الحالة بقول ال vector space V يولد بهذه
+
+24
+00:02:11,000 --> 00:02:15,800
+العناصر أو هذه العناصر Spain V بتولد لل vector
+
+25
+00:02:15,800 --> 00:02:20,040
+space V هذا ما تكلمنا عنه في الفترة الصباحية
+
+26
+00:02:20,040 --> 00:02:24,630
+الجديد هو التعريف اللي بين إيدينا هذابقول لو كان
+
+27
+00:02:24,630 --> 00:02:29,710
+الـU1 وU2 وUK are any k elements of a vector space
+
+28
+00:02:29,710 --> 00:02:34,730
+V يعني هدول vectors في ال vector space V وإذا كان
+
+29
+00:02:34,730 --> 00:02:38,810
+الـU the set of all linear combinations من الـU1
+
+30
+00:02:38,810 --> 00:02:44,970
+وU2 وUK then الـU is defined by يعني كيف؟ احنا
+
+31
+00:02:44,970 --> 00:02:49,550
+عندنا vector space V تمام؟أتخذت اي مجموعة من
+
+32
+00:02:49,550 --> 00:02:54,150
+العناصر تلاتة اربعة خمسة عشرة جد ما يكون و روحت
+
+33
+00:02:54,150 --> 00:02:58,730
+العناصر هدول جيبت كل ال linear combinations تبعتهم
+
+34
+00:02:58,730 --> 00:03:03,750
+ان اعبر عن هذا الكلام رياضيا بالشكل التالي بقول ال
+
+35
+00:03:03,750 --> 00:03:10,610
+Uهو الـ span تبع من U1 ل UK يعني مين يعني كل عنصر
+
+36
+00:03:10,610 --> 00:03:15,970
+اللي على شكل linear combination بهذا الشكل كل عنصر
+
+37
+00:03:15,970 --> 00:03:20,310
+فيه بقدر اكتبه على صيغة linear combination بهذا
+
+38
+00:03:20,310 --> 00:03:27,690
+الشكل C1U1 زي C2U2 زي زي CKUK بحيث الـ CI موجودة
+
+39
+00:03:27,690 --> 00:03:32,140
+في الارحيبجات كل الصيغات اللي عندها موجودةفي R
+
+40
+00:03:32,140 --> 00:03:38,090
+والـ I من واحد لغاية الـ Kتمام يبقى انا ايش اللي
+
+41
+00:03:38,090 --> 00:03:46,170
+حصل عندى يبقى كوانت ست جديدة الست جديدة هي التي
+
+42
+00:03:46,170 --> 00:03:52,390
+تولد بالعناصر U1 و U2 و UK هل هي كل ال vector
+
+43
+00:03:52,390 --> 00:03:58,270
+space فيه قد يكون و قد لا يكون ليش ان انا ماخدتش
+
+44
+00:03:58,270 --> 00:04:01,550
+ان هذا العنصر بولدولي ال vector space كله اخدت
+
+45
+00:04:01,550 --> 00:04:05,690
+حيال العناصر من مكان يكونوايبقى انا روحت جبت كل ال
+
+46
+00:04:05,690 --> 00:04:11,830
+linear combinations اللي هم سميتها 6U يبقى U هي ال
+
+47
+00:04:11,830 --> 00:04:17,050
+span تبع ال vectors اللي عندنا هدول تمام؟ طيب هذا
+
+48
+00:04:17,050 --> 00:04:20,930
+التعريف اللي أنا اش بتقول النظريةيقول اللي جيبتها
+
+49
+00:04:20,930 --> 00:04:26,050
+هذه هي subspace من ال vector space الأساسي V يعني
+
+50
+00:04:26,050 --> 00:04:31,890
+هذه ممكن يجيبلي V كله و ممكن يجيبلي جزء منه مش كله
+
+51
+00:04:31,890 --> 00:04:37,390
+على أي حال إن كانت كله فهي subspace لأن any set is
+
+52
+00:04:37,390 --> 00:04:41,850
+a subset of itself ويمكن ما تجيبش بتبقى subset
+
+53
+00:04:41,850 --> 00:04:46,580
+عادية من ال vector space اللي عندنايبقى أنا بدأ
+
+54
+00:04:46,580 --> 00:04:51,240
+أروح أثبت له أن الـ U اللي جيبناها بهذا الشكل هي
+
+55
+00:04:51,240 --> 00:04:56,640
+مين هي sub space من ال vector space الأصلي بدنا
+
+56
+00:04:56,640 --> 00:05:01,460
+نروح نبرهن صحة هذا الكلام مشان نبرهن صحة هذا
+
+57
+00:05:01,460 --> 00:05:06,560
+الكلام بدأ أروح أثبت مينتلات نقاط ان ال set U is
+
+58
+00:05:06,560 --> 00:05:10,520
+non-empty لو أخدت element اسكرال و element منها
+
+59
+00:05:10,520 --> 00:05:14,500
+ضربت اتنين في بعض بدلجيه في ال set هذه لو أخدت two
+
+60
+00:05:14,500 --> 00:05:19,820
+elements منها وجمعتهم بدلجيه في هذه ال set أول شيء
+
+61
+00:05:19,820 --> 00:05:24,620
+بدي أثبت له ان ال U هذه is non-empty يعني على
+
+62
+00:05:24,620 --> 00:05:32,260
+الأقل بدلجي فيها ولو عنصر واحدة تمام يبقى باجي
+
+63
+00:05:32,260 --> 00:05:41,850
+بقوله هناالـ U is not empty يعني
+
+64
+00:05:41,850 --> 00:05:47,610
+أنا أدعي أنها ليست فارغة أو ليست فاية بقى بدك
+
+65
+00:05:47,610 --> 00:05:52,730
+تجيبلي و لو عنصر و عادي لأن لو لجيت vector قدرت
+
+66
+00:05:52,730 --> 00:05:58,680
+أكتبه بدلالة هدوليبقى هذا ال element موجود فيه
+
+67
+00:05:58,680 --> 00:06:02,520
+صحيح ولا لأ؟ لأن هذه مكتوبة على صيغة linear
+
+68
+00:06:02,520 --> 00:06:06,860
+combination بالشكل هذا والصيغات هذه موجودة في R
+
+69
+00:06:06,860 --> 00:06:11,760
+ماعنديش قيود عليهم يبقى سالي بموجة بصفر ماعندي
+
+70
+00:06:11,760 --> 00:06:16,640
+مشكلة في هذه الحالة يبقى أنا بدعي أن هذه non-empty
+
+71
+00:06:16,640 --> 00:06:21,920
+بدي أروح أجيب و لو عنصر واحد فقط موجود في هذه ال
+
+72
+00:06:21,920 --> 00:06:27,870
+set بقول له اه becauseالـ zero موجود في ال U
+
+73
+00:06:27,870 --> 00:06:33,410
+معقول؟ معقول ال zero vector موجود في ال U؟ اه
+
+74
+00:06:33,410 --> 00:06:38,130
+معقول، معقول كيف؟ لو جدرها اكتب ال zero على صيغة
+
+75
+00:06:38,130 --> 00:06:42,890
+linear compilation من هدول بيكبر كلامي صح؟ مظبوط
+
+76
+00:06:42,890 --> 00:06:51,620
+يبقى باجي بقوله because sinceلأن الـ zero هه ..
+
+77
+00:06:51,620 --> 00:06:58,280
+بقدر اقول scalar zero في U1 scalar zero تاني في ال
+
+78
+00:06:58,280 --> 00:07:06,340
+U2 زائد scalar zero في ال UKصحيح ولا لا يبقى كتبت
+
+79
+00:07:06,340 --> 00:07:11,940
+الـ zero على صيغة linear combination من U1 و U2 و
+
+80
+00:07:11,940 --> 00:07:16,940
+لغاية UK و ال scholars كلهم أخدتهم بأصفر حتى دي
+
+81
+00:07:16,940 --> 00:07:20,760
+يبقى كلامي صحيح يبقى سعر ال U empty ولا ال non
+
+82
+00:07:20,760 --> 00:07:26,120
+-empty non-empty بهاي جبت في عنصر ولو العنصر
+
+83
+00:07:26,120 --> 00:07:31,740
+الصفرينتمام؟ يبقى هذا أول نقطة طب انت ليش بتختار
+
+84
+00:07:31,740 --> 00:07:35,540
+العنصر الصفري دايما؟ مش شاك سؤال؟ سؤال يطرح ليش
+
+85
+00:07:35,540 --> 00:07:38,940
+انت بتختار العنصر الصفري؟ بقولك اه ما هو ال
+
+86
+00:07:38,940 --> 00:07:43,840
+subspace أصلا vector space صحيح ولا لأ؟ ومن خواص
+
+87
+00:07:43,840 --> 00:07:48,150
+لل vector space أنه يحتوي على العنصر الصفرييبقى
+
+88
+00:07:48,150 --> 00:07:53,690
+أنا بختاره متعمد انه دائما اثبت ان العنصر الصفري
+
+89
+00:07:53,690 --> 00:07:57,530
+موجود في هذا ال vector space هذا ال condition
+
+90
+00:07:57,530 --> 00:08:04,570
+الأول ال condition التاني بدي اخد element من عرس
+
+91
+00:08:04,570 --> 00:08:09,610
+color و element menu و اشوف هل موجود ولا لا يبقى
+
+92
+00:08:09,610 --> 00:08:20,510
+باجي بقوله F ال A موجود في R andالـ U موجود في
+
+93
+00:08:20,510 --> 00:08:29,170
+كابتة U then الـ U يستوي الـ U يا بنات موجود في U
+
+94
+00:08:29,170 --> 00:08:34,010
+وهذا الـ Uبقدر اكتبه على صيغة linear combination
+
+95
+00:08:34,010 --> 00:08:39,990
+بهذا الشكل صحيح ولا لا يبقى بقدر اكتبه اللي هو c1
+
+96
+00:08:39,990 --> 00:08:50,610
+u1 زائد c2 u2 زائد زائد ck uk و ال ci موجودة في r
+
+97
+00:08:50,610 --> 00:08:56,350
+و ال I أكبر من أو تساوي واحد و أقل من أو تساوي k
+
+98
+00:08:57,770 --> 00:09:03,690
+طيب بدي أخد حاصل ضربهما يبقى بدي أخد ال a في ال u
+
+99
+00:09:03,690 --> 00:09:16,770
+يبقى بده يساوي يبقى a في c1u1 زائد a في c2u2
+
+100
+00:09:16,770 --> 00:09:21,730
+زائد
+
+101
+00:09:21,730 --> 00:09:25,490
+ونظل ماشيين لغاية a في ck
+
+102
+00:09:28,600 --> 00:09:35,510
+Okay بالشكل اللي عندناطيب هذا الكلام يساوي بدا
+
+103
+00:09:35,510 --> 00:09:40,750
+ارجع لخواص ال vector space من ضمن خواص ال vector
+
+104
+00:09:40,750 --> 00:09:45,430
+space لو كان ال a ليش ان ال u1 و ال u2 و ال un
+
+105
+00:09:45,430 --> 00:09:49,610
+هدول عناصر في v الأصلي صحيح ان هم موجودات في u لكن
+
+106
+00:09:49,610 --> 00:09:52,970
+هدول أصلا وين في ال vector space الأصلي اذا من
+
+107
+00:09:52,970 --> 00:09:58,050
+خواص ال vector space انه عملية ضرب associative على
+
+108
+00:09:58,050 --> 00:10:02,940
+ال scalarsيبقى بقدر اقول هذا الكلام بيديه يساوي
+
+109
+00:10:02,940 --> 00:10:14,120
+AC1 في ال U1 زائد AC2 في ال U2 زائد ACK في ال UK
+
+110
+00:10:15,680 --> 00:10:21,140
+يبقى الـ AU كتبته على شكل مين؟ على شكل linear
+
+111
+00:10:21,140 --> 00:10:26,260
+combination لأن اللي بين جثين كله scholars هدول و
+
+112
+00:10:26,260 --> 00:10:31,340
+هذا ال vectors U1 و U2 و U3 و UK يبقى مدم كتبتم
+
+113
+00:10:31,340 --> 00:10:37,060
+هذا موجود في U ولا لأ صح؟عشان أشكل linear
+
+114
+00:10:37,060 --> 00:10:41,800
+combinations من U1 و U2 و U3 و UK خلصنا ال
+
+115
+00:10:41,800 --> 00:10:44,780
+condition التاني بيدروح أخد ال condition التالت
+
+116
+00:10:44,780 --> 00:10:53,200
+يبقى ال condition التالت بدا أقول له F U تساوي C1
+
+117
+00:10:53,200 --> 00:11:01,600
+U1 C1 U1 C1 زائد C2
+
+118
+00:11:02,830 --> 00:11:14,210
+U2 زائد زائد CK UK والتاني هذا أخدت ال V بده يساوي
+
+119
+00:11:14,210 --> 00:11:23,970
+A1 U1 زائد A2 U2 زائد AK UK موجود هذا في ال U ولا
+
+120
+00:11:23,970 --> 00:11:31,260
+لا؟ مظبوطموجات في ال U ليش؟ انه كل واحد فيهم كتبته
+
+121
+00:11:31,260 --> 00:11:37,780
+على شكل linear combination من مين؟ من ال U1 و U2 و
+
+122
+00:11:37,780 --> 00:11:45,320
+لغاية UKبدا اثبت له ان مجموعهم هدول موجود في ال U
+
+123
+00:11:45,320 --> 00:11:52,040
+يبقى بادروح اخد ال U زائد ال V ال U زائد ال V
+
+124
+00:11:52,040 --> 00:11:56,300
+وقتها الساوية اذا باداجي اجمع component wise
+
+125
+00:11:56,300 --> 00:12:05,960
+ياباناتي يبقى C1U1 زائد كل عنصر مع نظيره A1U1أخدت
+
+126
+00:12:05,960 --> 00:12:10,680
+هذا المع بعض الجزء الثاني مع الجزء الثاني يبقى
+
+127
+00:12:10,680 --> 00:12:19,440
+c2u2 زائد a2u2 شكل اللي عندنا هنا زائد وضلت ماشي
+
+128
+00:12:19,440 --> 00:12:28,100
+لغاية ما وصلت لآخر عنصر اللي هو ckuk زائد akuk
+
+129
+00:12:30,110 --> 00:12:34,430
+هذا الكلام بده يساوي ممكن اخد U1 عامل مشترك بيظل
+
+130
+00:12:34,430 --> 00:12:43,550
+C1 زائد A1 في ال U1 زائد C2 زائد A2 في ال U2 زائد
+
+131
+00:12:43,550 --> 00:12:53,350
+زائد الى ان نصل الى CK زائد AK كله في ال UKيبقى
+
+132
+00:12:53,350 --> 00:13:01,170
+بالنسبة لي اليوم ما له is a subspace of V سا اليوم
+
+133
+00:13:01,170 --> 00:13:13,770
+اللي هو ال Spain تبع U1 و U2 و UK is a subspace of
+
+134
+00:13:13,770 --> 00:13:21,180
+Vيعني يا بنات كأنه هذه النظرية مثال جديد على من
+
+135
+00:13:21,180 --> 00:13:25,580
+على ال subspaces مش احنا المحاضرة الصبح والتلات
+
+136
+00:13:25,580 --> 00:13:28,980
+المرة اللي بدأت بجينا بنجيب أمثلة على ال subspaces
+
+137
+00:13:28,980 --> 00:13:34,080
+يبقى كأنه احنا جيبنا مثال جديد على من على ال
+
+138
+00:13:34,080 --> 00:13:41,040
+subspacesطب في عندي ملاحظة هنا الملاحظة ما يأتي
+
+139
+00:13:41,040 --> 00:13:46,560
+لما اقول يا بنات ان ال elements هدول اللي هو U1 و
+
+140
+00:13:46,560 --> 00:13:53,280
+U2 هدول Spain V سؤالي هو هل بقدر اكتب اي واحد فيهم
+
+141
+00:13:53,280 --> 00:14:00,660
+بدلالة الباقي يعني هل بقدر اكتب U2 بدلالة U1 و U2
+
+142
+00:14:00,660 --> 00:14:04,740
+و U3 و UK و لا بقدر نقدر
+
+143
+00:14:06,260 --> 00:14:10,400
+يعني بقدر اكتب اي واحد فيهم as a linear
+
+144
+00:14:10,400 --> 00:14:16,020
+combination مع الآخرين؟ يعني بقدر اكتب اي واحد
+
+145
+00:14:16,020 --> 00:14:20,600
+فيهم كك .. افهمولي السؤال مرة تانية بقول انا عندي
+
+146
+00:14:20,600 --> 00:14:27,200
+من يواحد ليه كذا بولدولي كل ست يوم؟ طبعا؟ طب لما
+
+147
+00:14:27,200 --> 00:14:32,700
+بولدولي كل ست يوم هل اي واحد منهم يولد باقي
+
+148
+00:14:32,700 --> 00:14:38,490
+العناصر اللي في ال Spain هدول؟أه طبعا بوالده مثال
+
+149
+00:14:38,490 --> 00:14:44,230
+و ذلك لو جيت و قلت لك U واحد بقدر اكتب واحد فيه
+
+150
+00:14:44,230 --> 00:14:47,270
+واحد زائد Zero في U اتنين زائد Zero في U تلاتة
+
+151
+00:14:47,270 --> 00:14:51,370
+زائد Zero في U K يبقى صالين ال combination منهم
+
+152
+00:14:51,370 --> 00:14:56,550
+ولا لا اذا صار موجود بالمثل U اتنين و بالمثل U
+
+153
+00:14:56,550 --> 00:15:04,180
+تلاتة و بالمثل U Kبقدر اكتبها هي 0 في U1 0 في U2 0
+
+154
+00:15:04,180 --> 00:15:09,860
+في U3 زائد 1 في UK وبالتالي صار ماعندي مشكلة يبقى
+
+155
+00:15:09,860 --> 00:15:15,020
+اي element من العناصر اللي بولد ال U بقدر اكتبه
+
+156
+00:15:15,020 --> 00:15:18,900
+على صيغة linear combination من بقية العناصر
+
+157
+00:15:18,900 --> 00:15:23,260
+بالاستثناء خدي هذه الملاحظة بكتبها لك على شكل
+
+158
+00:15:23,260 --> 00:15:35,050
+الملاحظة التالية يبقى notملاحظة الـ UI موجودة في
+
+159
+00:15:35,050 --> 00:15:47,310
+الـ Spain تبع U1 و U2 و UK والـ I من الـ 1 لغاية 8
+
+160
+00:15:47,310 --> 00:15:57,380
+لغاية الـ K because شو السبب؟لو جيت لل U1 بقدر
+
+161
+00:15:57,380 --> 00:16:08,700
+اكتب 1 في ال U1 0U2 0U3 وضل ماشي لغاية 0UKلو جيت
+
+162
+00:16:08,700 --> 00:16:15,680
+لل U2 بقدر اكتب Zero U واحد زائد واحد U اتنين زائد
+
+163
+00:16:15,680 --> 00:16:22,880
+Zero U تلاتة زائد Zero U K لو بليت مستمر هوصل الى
+
+164
+00:16:22,880 --> 00:16:30,440
+U K Zero U واحد Zero U اتنين Zero U تلاتة زائد
+
+165
+00:16:30,440 --> 00:16:34,060
+واحد في U K بالشكل اللي عندنا
+
+166
+00:16:37,490 --> 00:16:42,990
+يبقى أي element في الـ span بقدر اكتب بدلالة بقية
+
+167
+00:16:42,990 --> 00:16:48,950
+العناصر نبدأ الأن بالأمثلة على هذا الكلام يبقى
+
+168
+00:16:48,950 --> 00:16:57,110
+example one example
+
+169
+00:16:57,110 --> 00:17:00,270
+one هو سؤال تلاتة من الكتاب
+
+170
+00:17:05,860 --> 00:17:18,360
+Show that the set of all elements
+
+171
+00:17:18,360 --> 00:17:36,260
+of R3 of the form على الشكلاللي هو a زائد b وناقص
+
+172
+00:17:36,260 --> 00:17:47,800
+a واتنين b where حيث ال a and ال b are any real
+
+173
+00:17:47,800 --> 00:17:48,500
+numbers
+
+174
+00:17:57,750 --> 00:18:14,430
+or any real numbers is a subspace of R3 show
+
+175
+00:18:14,430 --> 00:18:16,370
+that the geometric interpretation
+
+176
+00:18:39,210 --> 00:18:50,170
+interpretation of this subspace of
+
+177
+00:18:50,170 --> 00:19:01,330
+this subspace is a plane is a plane and find
+
+178
+00:19:03,090 --> 00:19:09,730
+its equation يبقى بدنا كمان جديش المعادلة تبعته
+
+179
+00:19:59,320 --> 00:20:03,840
+نرجع لسؤالنا مرة ثانية يبجي أول مثال على هذا
+
+180
+00:20:03,840 --> 00:20:09,220
+الموضوع بقول ما يأتي بيقول إن مجموعة كل العناصر
+
+181
+00:20:09,220 --> 00:20:13,840
+اللي في R3 اللي ماقدر أكتبه على الشكل التالي يبجي
+
+182
+00:20:13,840 --> 00:20:19,350
+أنا جيت على R3 في يوتيوب اللي أخدت كل العناصراللي
+
+183
+00:20:19,350 --> 00:20:23,970
+عند المركبة الأولى A زائد B المركبة الثانية الناقص
+
+184
+00:20:23,970 --> 00:20:30,230
+A المركبة التالتة اتنين B كل الأعداد التي تحقق هذا
+
+185
+00:20:30,230 --> 00:20:34,030
+الكلام قطة مع بعض حيث A وB are any real numbers
+
+186
+00:20:34,030 --> 00:20:36,610
+يبقى as a subspace of R
+
+187
+00:20:55,190 --> 00:21:02,390
+التفسير الهندسي of this subspace is a planar fine
+
+188
+00:21:02,390 --> 00:21:06,410
+sequenceيعني بيبيني أن التفسير الهندسي لهذا ال
+
+189
+00:21:06,410 --> 00:21:11,050
+subspace هو عبارة عن مستوى و بدنا إيش معادلة
+
+190
+00:21:11,050 --> 00:21:17,530
+المستوى أظن كلكم أخدتوا كالكلصي ولا واحدة
+
+191
+00:21:20,200 --> 00:21:24,020
+بنذكركم بمعادلة المستوى المعادلة المستوى constant
+
+192
+00:21:24,020 --> 00:21:27,460
+في x زائد constant في y زائد constant في z زائد
+
+193
+00:21:27,460 --> 00:21:32,200
+constant اكس زائد بي وي زائد سي زائد يساوي مقدار
+
+194
+00:21:32,200 --> 00:21:36,000
+ثابت وليكن كتير يبقى هذه معادلة مستوى يعني إذا
+
+195
+00:21:36,000 --> 00:21:40,580
+جدرنا نحط المعادلة تبعتنا على هذه الصيرة بصير هذه
+
+196
+00:21:40,580 --> 00:21:46,060
+معادلة مستوى وبنشوف المستوى بمر بمين كمان إذا
+
+197
+00:21:46,060 --> 00:21:52,910
+حبيلها ونشوف كيفطبعا المطلوب الأول هحله بأكثر من
+
+198
+00:21:52,910 --> 00:21:56,330
+طريقة الطريقة الأولى اللى هي الطريقة الروتينية
+
+199
+00:21:56,330 --> 00:22:00,390
+اللى متعودين عليها و بعدين هعلمك طريقة جديدة يمكن
+
+200
+00:22:00,390 --> 00:22:04,770
+تكون أسهل أو أكثر الله أعلم احنا مش عارفين لما نجي
+
+201
+00:22:04,770 --> 00:22:09,530
+نشوف خلينا مع الطريقة الأولى انا عندى كل الـU كل
+
+202
+00:22:09,530 --> 00:22:14,230
+العناصر اللى بالشكل اللى عندنا هذا تمام؟يبقى انا
+
+203
+00:22:14,230 --> 00:22:24,910
+عند ال U كل العناصر على الشكل A زائد ال B و سالب A
+
+204
+00:22:24,910 --> 00:22:30,250
+و اتنين B حيث ال A و ال B موجودة في ال set of real
+
+205
+00:22:30,250 --> 00:22:37,140
+numbersصح ؟ اذا قال له انا real number بدي اثبت ان
+
+206
+00:22:37,140 --> 00:22:43,160
+هذه الست هي ال sub space من مين من R3 R3 كلها
+
+207
+00:22:43,160 --> 00:22:47,360
+مركوة من تلت مركبات وهذه فعلا من تلت مركبات اذا
+
+208
+00:22:47,360 --> 00:22:52,700
+كنت روحت اثبتها تمام يبقى بدي اجلب نقطة الأولى
+
+209
+00:22:52,700 --> 00:22:57,500
+النقطة الأولى بدي اثبتله ان هذه ال none empty
+
+210
+00:22:57,500 --> 00:22:59,900
+بتقدر تجيبولي عنصر فيها
+
+211
+00:23:03,950 --> 00:23:11,290
+زيرو زائد زيرو لاقص زيرو هو زيرو يبقى
+
+212
+00:23:11,290 --> 00:23:21,140
+زيرو زيرو زيرو موجود يبقى هنا الis man empty since
+
+213
+00:23:21,140 --> 00:23:30,240
+اللي هو since ال zero و ال zero و ال zero موجودات
+
+214
+00:23:30,240 --> 00:23:38,220
+في اليوم that isيعني زيرو زائد زيرو ناقص زيرو ولا
+
+215
+00:23:38,220 --> 00:23:42,920
+زائد زيرو كل واحد واتنين في زيرو برضه اللي هو
+
+216
+00:23:42,920 --> 00:23:49,560
+بزيرو كله موجود في ال U النقطة الثانية بدأ أخد
+
+217
+00:23:49,560 --> 00:23:56,020
+element موجود في R يبقى باجي بقوله إذا كان مش عند
+
+218
+00:23:56,020 --> 00:24:03,820
+سيها كويس إذا كان ال C موجود في ال R andالـ U بده
+
+219
+00:24:03,820 --> 00:24:10,820
+يساوي A زائد B و ناقص A و اتنين B موجودات في الـ U
+
+220
+00:24:10,820 --> 00:24:17,300
+بده انا اخد الان C في الـ U يبقى هذي يا بنات بده
+
+221
+00:24:17,300 --> 00:24:23,560
+اضرب C ديوه دوري على طول الخط يبقى C في A زائد الـ
+
+222
+00:24:23,560 --> 00:24:33,680
+B C في ناقص A C في اتنين B بالشكل اللي عندناطيب
+
+223
+00:24:33,680 --> 00:24:46,500
+أليست هذه هي CA زائد CB وهذه ناقص CA وهذه اتنين CB
+
+224
+00:24:46,500 --> 00:24:53,480
+ولا لا طيب اتطلعلي هذا element وهذا element هنا
+
+225
+00:24:53,480 --> 00:24:59,440
+سالب ال element الأول هنا اتنين ال element الثاني
+
+226
+00:24:59,440 --> 00:25:05,030
+إذا موجودة في U ولا لايبقى هذه belongs to you
+
+227
+00:25:05,030 --> 00:25:07,490
+بالدرجة لل condition التالت
+
+228
+00:25:11,050 --> 00:25:19,450
+F U A B-A2B
+
+229
+00:25:19,450 --> 00:25:25,770
+V A1B1
+
+230
+00:25:25,770 --> 00:25:29,770
+-A1A2B1
+
+231
+00:25:29,770 --> 00:25:38,240
+كله موجود في U then بدا أخذ المجموعيبقى لما أجي
+
+232
+00:25:38,240 --> 00:25:44,180
+أخد المجموع تبعهم بدي ال U زائد ال V و يساوي بدي
+
+233
+00:25:44,180 --> 00:25:51,540
+أجمع component-wise يبقى A زائد ال B زائد ال A1
+
+234
+00:25:51,540 --> 00:25:58,510
+زائد ال B1وعندك هنا هاي جمعنا هذه وهذه هذي بدها
+
+235
+00:25:58,510 --> 00:26:05,990
+تصير سالب a سالب a one اللي بعدها اتنين b زائد
+
+236
+00:26:05,990 --> 00:26:13,890
+اتنين b one هذا الكلام بده يساوي بقدر اقول يا بنات
+
+237
+00:26:13,890 --> 00:26:21,370
+هذا اللي عبارة عن مين a زائد ال a one زائد ال b
+
+238
+00:26:21,370 --> 00:26:27,570
+زائد ال b oneكل هذا المُركّب الأولى يعني أخذت هذه
+
+239
+00:26:27,570 --> 00:26:32,750
+و هذه مع بعض و هذه و هذه ما لهم مع بعض تين تين
+
+240
+00:26:32,750 --> 00:26:39,070
+أخدتهم بجوز بهذا الشكل هذه ههه بقدر أخد سالب عامل
+
+241
+00:26:39,070 --> 00:26:46,630
+مشترك بظل a زائد a1 هذه بقدر أخد اتنين عامل مشترك
+
+242
+00:26:46,630 --> 00:26:54,940
+بظل b زائد b1 طلعوا لي هناهذه المركبة الأولى مجموع
+
+243
+00:26:54,940 --> 00:27:04,750
+two terms هنا سالب ال term الأولمظبوط؟ هنا اتنين
+
+244
+00:27:04,750 --> 00:27:08,650
+ال term التاني صحيح ولا لأ؟ إذا هذه موجودة فيه ولا
+
+245
+00:27:08,650 --> 00:27:15,850
+لأ؟ يبقى هذه موجودة موجودة في ال you belongs to
+
+246
+00:27:15,850 --> 00:27:21,590
+you معناته تحققت الخاصية التالتة يبقى بناء عليه
+
+247
+00:27:21,590 --> 00:27:28,430
+ذات وهكذا ال you is a subspace
+
+248
+00:27:32,660 --> 00:27:36,940
+يبقى أثبت له الآن بالطريقة الروتينية أو الطريقة
+
+249
+00:27:36,940 --> 00:27:44,560
+العادية أن ال U is a subspace of V ثم نيجي الآن
+
+250
+00:27:44,560 --> 00:27:49,380
+بدي أحل نفس المطلوب هذا بطريقة ثانية ما اتعودناش
+
+251
+00:27:49,380 --> 00:27:55,520
+نحل عليها قبل ذلك باجي بقوله كويس الان another
+
+252
+00:27:55,520 --> 00:27:56,520
+solution
+
+253
+00:28:03,200 --> 00:28:09,760
+حل آخر و من هنا بدأنا ايش بدأنا في نمرة A يبقى انا
+
+254
+00:28:09,760 --> 00:28:17,580
+بدي اجي لنمرة A مباشرة ال U كل العناصر A زائد ال B
+
+255
+00:28:17,580 --> 00:28:24,540
+سالب A و اتنين B بالشكل اللي عندنا هذا بحيث ال A و
+
+256
+00:28:24,540 --> 00:28:31,580
+ال B موجودة في ال set of real numbers كويس
+
+257
+00:28:33,000 --> 00:28:40,000
+طب ايش رأيكوا انا اخدت في الشبتر الماضي ان ل three
+
+258
+00:28:40,000 --> 00:28:45,420
+tuple بقدر اكتبها ك call vector و بقدر اكتبها ك
+
+259
+00:28:45,420 --> 00:28:50,840
+raw vector صح ولا لأ اذا انا لو جيت هنا قلت ما
+
+260
+00:28:50,840 --> 00:29:00,680
+يأتي اخد ال a زائد ال b و سلب a و اتنين bالشيء
+
+261
+00:29:00,680 --> 00:29:06,820
+المكافئ لها تماما اني اكتبها على شكل ال vector a
+
+262
+00:29:06,820 --> 00:29:18,280
+زائد b وناقص a و2b مظبوط؟ ساكت الشعب صح ولا لا؟ مش
+
+263
+00:29:18,280 --> 00:29:23,200
+خناها في ال chapter الماضي زي هيك؟ طيبأيش رايك؟
+
+264
+00:29:23,200 --> 00:29:28,360
+هذه يعني كتبتها على شكل مصوفة بثلاث صفوف وعمود
+
+265
+00:29:28,360 --> 00:29:34,340
+واحد احطها على شكل جمع مصوفين في مشكلة؟ لا تعالى
+
+266
+00:29:34,340 --> 00:29:41,020
+نشوف يبقى انا لو جيت حاطيتها بده اقول A و سالب A و
+
+267
+00:29:41,020 --> 00:29:49,960
+Zero زائد B و Zero و اتنين B بنفعلك؟
+
+268
+00:29:50,620 --> 00:29:56,180
+A زائد B هيها ناقص A و Zero بناقص A Zero و اتنين B
+
+269
+00:29:56,180 --> 00:30:00,620
+و اتنين B يعني كأنه مش عامل فاصلة ال A مع بعض و ال
+
+270
+00:30:00,620 --> 00:30:05,560
+B مع بعض طيب لما في عامل مشترك في جميع أنصار
+
+271
+00:30:05,560 --> 00:30:10,820
+المصممة مش بقدر اكتبه برا صح ولا لأ يعني بقدر اكتب
+
+272
+00:30:10,820 --> 00:30:19,290
+هذاA في ال vector واحد سالب واحد Zero زائد B في ال
+
+273
+00:30:19,290 --> 00:30:26,770
+vector واحد Zero اتنين يعني كأنه بكتب هذا A في ال
+
+274
+00:30:26,770 --> 00:30:34,630
+V1 زائد B في ال vector V2 صح ولا لأ يعني ايش عملت
+
+275
+00:30:34,900 --> 00:30:41,140
+كأنه كتبت هذا على صيغة linear combination من
+
+276
+00:30:41,140 --> 00:30:46,950
+الاتنينصح ولا لا يعني معنى هذا الكلام انه any
+
+277
+00:30:46,950 --> 00:30:52,390
+element موجود في ال vector space هذا بقدر اكتبه
+
+278
+00:30:52,390 --> 00:30:56,910
+على صيغة linear combination من ال two vectors هذول
+
+279
+00:30:56,910 --> 00:31:02,370
+صحيح ولا لا يعني معناته ال V واحد وال V اتنين سبين
+
+280
+00:31:02,370 --> 00:31:09,110
+ال U بيولدول ال U صحيح ولا لا مظبوط يبقى هنا سا
+
+281
+00:31:09,110 --> 00:31:12,190
+any vector
+
+282
+00:31:13,460 --> 00:31:24,700
+ن U is a linear combination of
+
+283
+00:31:24,700 --> 00:31:32,540
+V واحد اللي هو بده يساوي واحد سالب واحد زيرو and V
+
+284
+00:31:32,540 --> 00:31:38,120
+اتنين اللي هو بده يساوي and V اتنين
+
+285
+00:31:40,210 --> 00:31:47,510
+اللي هو بده يساوي واحد زيرو اتنين بالشكل اللي
+
+286
+00:31:47,510 --> 00:31:54,050
+عندنا طب مادام هيك يبقى two vectors هدول this
+
+287
+00:31:54,050 --> 00:32:05,010
+means that انه اليوم يساوي لسبين تبع اللي هو في
+
+288
+00:32:05,010 --> 00:32:10,470
+واحد وفي اتنين صحيح ولا لاطب ماذا مش فين؟ من
+
+289
+00:32:10,470 --> 00:32:14,910
+النظرية اللي قبل قليل هذي subspace ولا لا؟ بيبقى
+
+290
+00:32:14,910 --> 00:32:25,030
+هنا by the previous theorem بالنظرية السابقة قبل
+
+291
+00:32:25,030 --> 00:32:32,030
+قليل by the previous theorem اللي هو LU is a
+
+292
+00:32:32,030 --> 00:32:39,710
+subspace ofفين؟ مين اللي أسأل؟ هذا والله اللي
+
+293
+00:32:39,710 --> 00:32:45,590
+جابال يبقى حل هذه الطريقتين، حل باللي تعجبك إن جاك
+
+294
+00:32:45,590 --> 00:32:49,110
+أي سؤال زي هذا أحل بالطريقة ده، أسهل، خلاص بحل
+
+295
+00:32:49,110 --> 00:32:54,370
+بها، تمام؟ طبعا هذه هنتكرر الشغل بها كتير في باقها
+
+296
+00:32:54,370 --> 00:32:59,060
+الشبتر والشبتر القادم كمانأه يعني دي ربالك من
+
+297
+00:32:59,060 --> 00:33:03,440
+هالطريقة هذه إذا قدرت أكتب هذا على شكل هنا
+
+298
+00:33:03,440 --> 00:33:08,220
+transformation بالشكل ان هذا لسه احنا حلنا المطلوب
+
+299
+00:33:08,220 --> 00:33:13,200
+الأول بطريقة تانية بدنا نروح للمطلوب التاني نمربي
+
+300
+00:33:13,200 --> 00:33:19,820
+نمربي إيش بقولني؟يقول في السؤال show that the
+
+301
+00:33:19,820 --> 00:33:22,960
+geometric interpretation of this subspace is a
+
+302
+00:33:22,960 --> 00:33:28,080
+plane وبدنا معادلته بيقولوا أن المعنى الهندسي لهذا
+
+303
+00:33:28,080 --> 00:33:32,560
+ال subspace هو عبارة عن مستوى و بدي معادلة مين؟
+
+304
+00:33:32,560 --> 00:33:38,760
+بدي معادلة هذا المستوى بقوله بسيطة جدا احنا عندنا
+
+305
+00:33:38,760 --> 00:33:43,280
+لو يا بنات صارواين هي اليوم الشكل اللي عندنا كتبنا
+
+306
+00:33:43,280 --> 00:33:51,780
+هييبقى انا عند ال U تساوي اللي هو A زائد B و سالب
+
+307
+00:33:51,780 --> 00:34:00,920
+A و اتنين B بحيث ان هذا كله ال A و ال B موجودة في
+
+308
+00:34:00,920 --> 00:34:05,800
+ال set of real numbers يعني هذا مكون من كام مركبة
+
+309
+00:34:06,900 --> 00:34:12,380
+من ثلاث مركبات يبقى كأنه عندي mean اللي هو x واحد
+
+310
+00:34:12,380 --> 00:34:18,260
+بدي يسوى ال a زائد ال b وال x اتنين يسوى ناقص ال a
+
+311
+00:34:18,260 --> 00:34:25,900
+وال x تلاتة يسوى اتنين bمظبوط يعني هي لما اقول
+
+312
+00:34:25,900 --> 00:34:30,020
+مركب X واحد و X اتنين و X تلاتة الاولة A زياد B
+
+313
+00:34:30,020 --> 00:34:34,580
+والتانية سلب A والتالتة اتنين B اقول والله كلامي
+
+314
+00:34:34,580 --> 00:34:40,040
+كويس طب ايش رأيك اجمع هدول مع بعض التنتين لو
+
+315
+00:34:40,040 --> 00:34:45,940
+جمعتهم مش بصير هدول يبقى بصيري عندي X واحد زائد X
+
+316
+00:34:45,940 --> 00:34:50,920
+اتنين يساوي B طيب
+
+317
+00:34:51,370 --> 00:34:58,450
+الحين انا عندي and ال X تلاتة يساوي اتنين بي يبقى
+
+318
+00:34:58,450 --> 00:35:04,830
+you say هذا بده يعطيكي ان X تلاتة تساوي اتنين بي
+
+319
+00:35:04,830 --> 00:35:12,350
+هي mainly X واحد زائد X اتنينيعني ايش صار عندى؟
+
+320
+00:35:12,350 --> 00:35:19,530
+صار عندى x تلاتة نقص اتنين x واحد نقص اتنين x
+
+321
+00:35:19,530 --> 00:35:24,510
+اتنين يساوي zero مظبوط
+
+322
+00:35:24,510 --> 00:35:31,240
+طب هذا ال system أخدناه قبل هيك ولا لا؟Homogeneous
+
+323
+00:35:31,240 --> 00:35:37,000
+system ممتاز يبقى هذا system of linear equations
+
+324
+00:35:37,000 --> 00:35:42,980
+تمام طبعا ماعنديش ال equation واحدة بثلاثة مجاهيل
+
+325
+00:35:42,980 --> 00:35:48,100
+تمام يبقى هذا system of linear homogenous system
+
+326
+00:35:48,100 --> 00:35:53,320
+هذا ال homogenous system يا إما له حل وحيد هو الحل
+
+327
+00:35:53,320 --> 00:35:59,140
+الصفرييعملوا حل عدد لا نهائي من الحلول يجتمل على
+
+328
+00:35:59,140 --> 00:36:05,870
+الحل الصفري إذا هذه معادلة plane ولا لا يا بنات؟مش
+
+329
+00:36:05,870 --> 00:36:10,370
+قلتلكوا قبل قليل AX زي BY زي C زي Z يبقى constant
+
+330
+00:36:10,370 --> 00:36:18,750
+يبقى بدل XY وزي X1 X2 وX3 يعني بمعنى أخر كأنه هذه
+
+331
+00:36:18,750 --> 00:36:26,750
+المعادلة لو قعدت ترتيبها يبقى 2 X1 زي 2 X2 نقص X3
+
+332
+00:36:26,750 --> 00:36:35,720
+يبقى zero يبقى adequation of A planeطب ايش رايك ال
+
+333
+00:36:35,720 --> 00:36:42,900
+plain هذا يمر بنقطة الأصل لأن
+
+334
+00:36:42,900 --> 00:36:48,460
+هي أحد الحلول مظبوط ولا لا يبقى plain passes
+
+335
+00:36:48,460 --> 00:36:58,040
+through the origin because
+
+336
+00:37:01,940 --> 00:37:08,900
+اللي هو x واحد و x اتنين و x تلاتة تساوي زيرو و
+
+337
+00:37:08,900 --> 00:37:18,300
+زيرو زيرو is the او is its a trivial solution
+
+338
+00:37:19,970 --> 00:37:25,190
+يبقى قال لي وصفلي شوهد احنا وصفناله يا وقال لي
+
+339
+00:37:25,190 --> 00:37:28,950
+اثبت انه معادلة plane يبقى اثبتناله هي معادلة
+
+340
+00:37:28,950 --> 00:37:33,670
+plane يبقى ال subspace اللي عندنا صار معادلة plane
+
+341
+00:37:33,670 --> 00:37:38,510
+وبالتالي كنا بنترابطنا هذا ال chapter بموضوع ال
+
+342
+00:37:38,510 --> 00:37:43,390
+chapter الأول اللي هو system of linear equations
+
+343
+00:37:43,390 --> 00:37:48,060
+حد يلها اي تساول هنا؟يبقى ايه اثبت انه subspace
+
+344
+00:37:48,060 --> 00:37:55,140
+بطريقة تانية و اثبت ان هذا subspace يمثل من؟ يمثل
+
+345
+00:37:55,140 --> 00:37:58,420
+plane و الصبح و قلتلكم بدأنا في ال jet اليوم و ده
+
+346
+00:37:58,420 --> 00:38:02,140
+احنا بنشتغل ال jet على غير الشيء اللي كنا متعرفين
+
+347
+00:38:02,140 --> 00:38:04,200
+عليه قبل ذلك
+
+348
+00:38:21,850 --> 00:38:32,210
+مثال اتنين مثال اتنين مثال اتنين
+
+349
+00:38:32,210 --> 00:38:37,730
+مثال اتنين مثال اتنين مثال اتنين مثال اتنين مثال
+
+350
+00:38:37,730 --> 00:38:38,130
+اتنين مثال اتنين مثال اتنين مثال اتنين مثال اتنين
+
+351
+00:38:38,130 --> 00:38:38,210
+مثال اتنين مثال اتنين مثال اتنين مثال اتنين مثال
+
+352
+00:38:38,210 --> 00:38:38,210
+اتنين مثال اتنين مثال اتنين مثال اتنين مثال اتنين
+
+353
+00:38:38,210 --> 00:38:38,210
+مثال اتنين مثال اتنين مثال اتنين مثال اتنين مثال
+
+354
+00:38:38,210 --> 00:38:38,210
+اتنين مثال اتنين مثال اتنين مثال اتنين مثال اتنين
+
+355
+00:38:38,210 --> 00:38:38,210
+مثال اتنين مثال اتنين مثال اتنين مثال اتنين مثال
+
+356
+00:38:38,210 --> 00:38:42,050
+اتنين مثال اتنين مثال
+
+357
+00:38:42,050 --> 00:38:59,810
+اتn مثالof R3 that is spanned by
+
+358
+00:38:59,810 --> 00:39:03,710
+the
+
+359
+00:39:03,710 --> 00:39:11,990
+vectors اللي هو V1 يساوي
+
+360
+00:39:13,720 --> 00:39:26,000
+V1 يساوي سالب اتنين و واحد و واحد و V2 يساوي واحد
+
+361
+00:39:26,000 --> 00:39:29,840
+و ناقص تلاتة و خمسة
+
+362
+00:39:32,260 --> 00:39:51,200
+show that the geometric interpretation
+
+363
+00:39:51,200 --> 00:39:56,800
+of this subspace
+
+364
+00:40:09,920 --> 00:40:21,440
+و هاتينا كمان المعادلة تبعه
+
+365
+00:40:21,440 --> 00:40:25,500
+و
+
+366
+00:40:25,500 --> 00:40:26,960
+من هذه الخيارة انتهينا منها
+
+367
+00:40:45,840 --> 00:40:51,540
+نرجع لمثالنا هذا مرة ثانية ونشوف كيف بدنا نشتغل
+
+368
+00:40:51,540 --> 00:40:57,880
+هذا المثالالمثال اللي بقول ياخد ال U subspace من
+
+369
+00:40:57,880 --> 00:41:04,600
+R3 that is spanned by the vectors V1 وV2 يبقى U
+
+370
+00:41:04,600 --> 00:41:11,760
+هذا أخدته subset من من من ال vector space اللي هو
+
+371
+00:41:11,760 --> 00:41:17,540
+R3 بحيث هذا يولد ب two vectors مادام يولد بال two
+
+372
+00:41:17,540 --> 00:41:19,860
+vectors يبقى هذا subspace ولا لا
+
+373
+00:41:28,400 --> 00:41:38,800
+يبقى الأن كأن ال U عبارة عنالـ U هو عبارة عن ال
+
+374
+00:41:38,800 --> 00:41:47,780
+set of all real numbers C1V1 زي C2V2 such that C1
+
+375
+00:41:47,780 --> 00:41:53,160
+وC2 موجودة في ال set of real numbersليش؟ لأن هو
+
+376
+00:41:53,160 --> 00:41:58,700
+قال لي هذا يولد بهذه العنصرين يعني لو بدأ أكتبه
+
+377
+00:41:58,700 --> 00:42:04,920
+بصيغة أخرى بدأ أقول كل العناصر على الشكل التالي C1
+
+378
+00:42:04,920 --> 00:42:14,660
+في V1 سالب 2 و 1 و 1 زائد C2 في 8 في 1 و ناقص 3 و
+
+379
+00:42:14,660 --> 00:42:22,150
+5 بحيث C1 و C2 موجودة في set of real numbersيعني
+
+380
+00:42:22,150 --> 00:42:27,810
+هذا كأنه ال vector u ال vector space u هو عبارة
+
+381
+00:42:27,810 --> 00:42:34,330
+بده افك و اجمع يا بنات دوري يبقى سالب اتنين C واحد
+
+382
+00:42:34,330 --> 00:42:39,920
+زائد C اتنين هذه هي المركبة الأولىالمُركّبة
+
+383
+00:42:39,920 --> 00:42:47,840
+الثانية C1 ناقص ثلاثة C2 المُركّبة التالتة C1 زائد
+
+384
+00:42:47,840 --> 00:42:53,880
+خمسة C2 بها الـ C1 و C2 موجودة في الـ set of real
+
+385
+00:42:53,880 --> 00:43:01,980
+number طب استنوا شوية نوقف وقفة محاسبة مع النفس
+
+386
+00:43:01,980 --> 00:43:09,870
+كالتاليهنجيل ان V1 و V2 بيولدوا لمين؟ بيولدوا لـ U
+
+387
+00:43:09,870 --> 00:43:14,390
+إذا اليوم بقدر أكتب علاصية Linear Combination من
+
+388
+00:43:14,390 --> 00:43:21,270
+V1 و V2 فهي كتبنا C1 V1 C2 و C1 V2 Any Scalars
+
+389
+00:43:21,270 --> 00:43:26,850
+تمام؟ إلا أن شيلت ال V1 و V2 و حطيت قيمتها و ضال
+
+390
+00:43:26,850 --> 00:43:32,730
+بالزائد هدول مجموعة two vectors بتخليهم vector
+
+391
+00:43:32,730 --> 00:43:40,270
+واحديبقى أفك و أجمع C1 فى سالب 2 مع C2 فى 1 يبقى
+
+392
+00:43:40,270 --> 00:43:46,210
+سالب 2 C1 زائد C2 هى المركبة الأولى بدأجى المركبة
+
+393
+00:43:46,210 --> 00:43:51,690
+التانية C1 فى 1 بC1وC2 في السالب تلاتة بالسالب
+
+394
+00:43:51,690 --> 00:43:58,550
+تلاتة C2 اللي بعده C1 في واحد وC2 في خمسة بC1 زي
+
+395
+00:43:58,550 --> 00:44:05,090
+الخمسة C2 تمام يعني إيش اللي حصل عندي حصل عندي
+
+396
+00:44:05,090 --> 00:44:13,060
+الآن ما يأتيإن X1 المركبة الأولى نقص 2C1 زائد C2
+
+397
+00:44:13,060 --> 00:44:24,940
+X2 عبارة عن C1 نقص 3C2 X3 يساوي C1 زائد 5C2
+
+398
+00:44:25,940 --> 00:44:29,460
+طيب هو ايش بيقوللي هذا السؤال بيقوللي show that
+
+399
+00:44:29,460 --> 00:44:32,120
+the geometrical interpretation of this subspace is
+
+400
+00:44:32,120 --> 00:44:37,740
+a plane و بدنا معادلته يبقى بد أبين ان هذا معادلة
+
+401
+00:44:37,740 --> 00:44:42,990
+a plane و بد أشوف شو هي معادلةبقول بسيطة جدا إذا
+
+402
+00:44:42,990 --> 00:44:49,110
+أنا بدأ اتخلص من c1 و c2 و أخلّي المثلة بدلة x1 و
+
+403
+00:44:49,110 --> 00:44:54,170
+x2 و x3 اللي هي main اللي كانها x و y و z لإنه
+
+404
+00:44:54,170 --> 00:44:59,430
+قلتلك معادلة leap line دائما و أبدا على صيغة ax
+
+405
+00:44:59,430 --> 00:45:05,680
+زائد by زائد cz بده يسوي constant و ليكن bالـ A و
+
+406
+00:45:05,680 --> 00:45:10,200
+الـ B و الـ C و الـ D ثوابت والـ X و الـ Y و الـ Z
+
+407
+00:45:10,200 --> 00:45:14,380
+اللي هي المجاهيل D تكون Zero ما تكون Zero بهمنيش
+
+408
+00:45:14,380 --> 00:45:17,720
+جد ما تكون تكون والـ A و الـ B و الـ C كمان بيه
+
+409
+00:45:17,720 --> 00:45:21,920
+ثوابته و يمكن يكون بعضهم ب Zero قد يكون بعضهم ب
+
+410
+00:45:21,920 --> 00:45:27,570
+Zero ماعندي مشكلة في هذه الحالةبقول تمام، إذا احنا
+
+411
+00:45:27,570 --> 00:45:31,690
+بدنا إيه؟ يجي نحل المعذرتين هدول مع بعض و نطلع كده
+
+412
+00:45:31,690 --> 00:45:36,290
+X1 و X2 يعني نتخلص من السيهات اللي عندنا حد يا
+
+413
+00:45:36,290 --> 00:45:40,370
+بنات ما علمتش كمال اسم هايانة؟ تعالوا خدوا يالا
+
+414
+00:45:43,620 --> 00:45:47,960
+بدأجي للمعادلة الأولى اللي هو الثانية هدول اتنين
+
+415
+00:45:47,960 --> 00:45:52,660
+اظن لو ضربت التانية في اتنين و جمعت بتخلص من احد
+
+416
+00:45:52,660 --> 00:45:59,000
+المجاهيل اللي هو ال C واحد وبجيب جداش C اتنين يبقى
+
+417
+00:45:59,000 --> 00:46:03,800
+بناء عليه من المعادلتين هدول بقول ما يأتييبقى اي
+
+418
+00:46:03,800 --> 00:46:08,380
+اكس واحد يساوي سالب اتنين C واحد زاد C اتنين بدي
+
+419
+00:46:08,380 --> 00:46:13,580
+اضرب هذه في اتنين يبقى اتنين X اتنين سالب اتنين C
+
+420
+00:46:13,580 --> 00:46:21,700
+واحد او موجة باتنين C واحد ناقص ستة اللي هو C
+
+421
+00:46:21,700 --> 00:46:25,760
+اتنين ونجي نجمع ضربت المعادلة التانية في اتنين
+
+422
+00:46:25,760 --> 00:46:30,800
+هدول مع السلامةيبقى من هدول اتنين ايش بستنتج
+
+423
+00:46:30,800 --> 00:46:41,860
+بستنتج انه X1 زائد 2 X2 بدر ساوي ناقص خمسة C2 يبقى
+
+424
+00:46:41,860 --> 00:46:48,980
+زائد واحد وناقص ستة بضل جداش ناقص خمسة ومنها C2
+
+425
+00:46:48,980 --> 00:46:58,180
+بدر ساوي ناقص X1 زائد 2 X2 كله على خمسةيبقى هاي
+
+426
+00:46:58,180 --> 00:47:05,000
+جبت C2
+
+427
+00:47:05,000 --> 00:47:13,160
+بدلالة X1 و X2 بقدر أجيب C1 كمان بدلالة X1 و X2
+
+428
+00:47:13,160 --> 00:47:19,300
+برجع بعود في أي من المعادلتينإذا لو رجعنا و عوضنا
+
+429
+00:47:19,300 --> 00:47:24,300
+في أي من المعادلة بدي أمسك النتيجة التي توصل إليها
+
+430
+00:47:24,300 --> 00:47:28,680
+هذه و أجي أعوض مثلا في المعادلة رقم 2 عشان بدي
+
+431
+00:47:28,680 --> 00:47:39,490
+أجيب C1 فبجي بقول X2 يساوي C1نقص ثلاثة في C2 C2
+
+432
+00:47:39,490 --> 00:47:50,410
+التي هي ناقص لل X1 زائد 2 X2 كله رداش على خمسة
+
+433
+00:47:50,410 --> 00:47:55,950
+يبقى هذا الكلام يعطيني C1 ناقص مع ناقص في الصيرة
+
+434
+00:47:55,950 --> 00:48:03,610
+زائد ثلاثة في X1زي دي اتنين اكس اتنين كله علامين
+
+435
+00:48:03,610 --> 00:48:09,930
+على خمسة بالشكل اللي عندنا هذا معنى هذا الكلام انه
+
+436
+00:48:09,930 --> 00:48:17,490
+c واحد بده يساوي اكس اتنين ناقص تلت أخماس في اكس
+
+437
+00:48:17,490 --> 00:48:24,170
+واحد زي دي اتنين اكس اتنين يبقى جبت c واحد بدلالة
+
+438
+00:48:24,170 --> 00:48:29,730
+اكسبدلالة X1 و X2 اللي انا باجي على المعادلة
+
+439
+00:48:29,730 --> 00:48:34,650
+التالتة ما هي في C1 و C2 بشيلهم و بجيب قيمتهم يبقى
+
+440
+00:48:34,650 --> 00:48:45,640
+باجي بقول له X3 تساوي C1 زائد 5 C2 وتساويC1 هي
+
+441
+00:48:45,640 --> 00:48:55,920
+موجودة عند X2 ناقص تلت أخمس في X1 زائد 2 X2 هذا
+
+442
+00:48:55,920 --> 00:49:01,260
+كله في C1 زائد خمسة في C2
+
+443
+00:49:18,530 --> 00:49:23,150
+بناء على الـ X3 تساوي
+
+444
+00:49:24,750 --> 00:49:32,250
+أكس اتنين وهذا بنات كلها بقدر اقول ناقص اللي هو
+
+445
+00:49:32,250 --> 00:49:39,010
+مين تلاتة والله خليها ناقص زي ما هي هاي ناقص وهنا
+
+446
+00:49:39,010 --> 00:49:45,470
+تلاتة اكس واحد زائد ستة اكس اتنين كله على مين على
+
+447
+00:49:45,470 --> 00:49:54,050
+خمسة وهذه ناقصوالله خلّيها ناقص ماعش الحال و هنا
+
+448
+00:49:54,050 --> 00:50:01,350
+خمسة X واحد زائد عشرة X اتنين كله على مين على خمسة
+
+449
+00:50:01,350 --> 00:50:07,450
+ايش رأيك بدا واحد المقامات للكل كله على خمسةيبقى
+
+450
+00:50:07,450 --> 00:50:14,850
+بصير x3 يساوي خمسة x اتنين ناقص تلاتة x واحد ناقص
+
+451
+00:50:14,850 --> 00:50:22,810
+ستة x اتنين و هنا ناقص خمسة x واحد ناقص عشرة x
+
+452
+00:50:22,810 --> 00:50:29,610
+اتنينيبقى هذا الكلام بده يساوي هي عندي X2 وهي عندي
+
+453
+00:50:29,610 --> 00:50:38,890
+X2 وهي عندي X2 عندك هنا ناقص 16 X2 وزائد خمسة بيظل
+
+454
+00:50:38,890 --> 00:50:46,850
+ناقص 11 X2عندك سالب تلاتة اكس واحد و سالب خمسة
+
+455
+00:50:46,850 --> 00:50:53,130
+بسالب تمانية اكس واحد تمام كل هذا الكلام على جداش
+
+456
+00:50:53,130 --> 00:51:00,070
+على خمسة يساوي اكس تلاتة اضر بضرب تبادلي يبقى بصير
+
+457
+00:51:00,070 --> 00:51:09,540
+خمسة اكس تلاتةيساوي سالب 11 X 2 سالب 8 X 1 نعملها
+
+458
+00:51:09,540 --> 00:51:20,140
+معادلة صفرية يبقى بصير عندك 8 X 1 زي 11 X 2 زي 5 X
+
+459
+00:51:20,140 --> 00:51:25,180
+3 يساوي 0 يبقى هذه equation of
+
+460
+00:51:37,950 --> 00:51:47,070
+السؤال هو هل يمر هذا بنقطة الأصل؟ فهذا
+
+461
+00:51:47,070 --> 00:51:51,570
+باصد أثرى
+
+462
+00:51:53,510 --> 00:52:01,430
+فاصجت هو the origin لأيش؟
+
+463
+00:52:01,430 --> 00:52:04,530
+لأنه أخدت x واحد وx تانية وكل واحد بزير و بتلاقي
+
+464
+00:52:04,530 --> 00:52:11,590
+بحقق هذه المعادلة طيب السؤال هو هل يمر بالنقطة
+
+465
+00:52:11,590 --> 00:52:16,610
+سالب اتنين وواحد وواحد و النقطة واحد وناقص ثلاثة
+
+466
+00:52:16,610 --> 00:52:29,520
+وخمسة؟100% تمام يبقى هنا and passes through the
+
+467
+00:52:29,520 --> 00:52:33,500
+points ويمر
+
+468
+00:52:33,500 --> 00:52:39,040
+كذلك خلال النقطتين اللي هو سالب اتنين وواحد وواحد
+
+469
+00:52:39,040 --> 00:52:47,840
+and التانية واحد وناقص تلاتة وخمسة تحبوني اتركب؟
+
+470
+00:52:48,400 --> 00:52:53,000
+تعالوا نتأكد نتأكد من هنا بس نعود نشوف سهر ولا لا
+
+471
+00:52:53,000 --> 00:52:58,140
+القصة بسيطة جدا هاي ناقص اتنين في تمانية ناقص
+
+472
+00:52:58,140 --> 00:53:03,440
+ستاشر هاي ناقص ستاشر عندك واحد في احداشر زائد
+
+473
+00:53:03,440 --> 00:53:07,920
+احداشر عندك واحد في خمسة في خمسة خمسة و احداشر
+
+474
+00:53:07,920 --> 00:53:12,180
+بالمجموعة ستاشر و ستاشر إذا كلامي صحيح و بالمثل
+
+475
+00:53:12,180 --> 00:53:17,810
+بلاجين بمربى مين؟ بمربة النقطة الثانيةطيب لازلنا
+
+476
+00:53:17,810 --> 00:53:22,610
+في نفس الموضوع و المرة القادمة ان شاء الله نكمل
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HH8I6sciKRM_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HH8I6sciKRM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..aa02b7e697c4c645939a0474dc00411ea6563594
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HH8I6sciKRM_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4275, "start": 20.69, "end": 42.75, "text": "بسم الله الرحمن الرحيم المرة اللي فاتت ابتدأنا ب section ال homogeneous systems وأخدنا على ذلك مثالين وهذا هو المثال رقم تلاتة يعني اللي قلنا المرة اللي فاتت ال homogeneous system يا إما إله ل trivial solution", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 48127, 2655, 3215, 10721, 8315, 4724, 3541, 2423, 42632, 3652, 36725, 9778, 3215, 8315, 15844, 29910, 23275, 50113, 6027, 9957, 37037, 15730, 31439, 9673, 12984, 6027, 12602, 4587, 2304, 6055, 1211, 9307, 3660, 37495, 22653, 13672, 1829, 12174, 1211, 8315, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 2423, 42632, 1185, 35186, 11933, 15042, 11933, 43761, 5296, 26703, 3827], "avg_logprob": -0.16406249364217124, "compression_ratio": 1.7287234042553192, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 20.69, "end": 20.89, "word": "بسم", "probability": 0.429443359375}, {"start": 20.89, "end": 21.09, "word": " الله", "probability": 0.95849609375}, {"start": 21.09, "end": 21.51, "word": " الرحمن", "probability": 0.96826171875}, {"start": 21.51, "end": 22.03, "word": " الرحيم", "probability": 0.9930013020833334}, {"start": 22.03, "end": 23.57, "word": " المرة", "probability": 0.849853515625}, {"start": 23.57, "end": 23.75, "word": " اللي", "probability": 0.71142578125}, {"start": 23.75, "end": 24.25, "word": " فاتت", "probability": 0.9912109375}, {"start": 24.25, "end": 25.11, "word": " ابتدأنا", "probability": 0.95009765625}, {"start": 25.11, "end": 25.47, "word": " ب", "probability": 0.87744140625}, {"start": 25.47, "end": 26.21, "word": " section", "probability": 0.87841796875}, {"start": 26.21, "end": 26.43, "word": " ال", "probability": 0.861328125}, {"start": 26.43, "end": 26.93, "word": " homogeneous", "probability": 0.58935546875}, {"start": 26.93, "end": 27.69, "word": " systems", "probability": 0.51220703125}, {"start": 27.69, "end": 29.51, "word": " 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{"start": 981.73, "end": 981.99, "word": " the", "probability": 0.93212890625}, {"start": 981.99, "end": 982.43, "word": " same", "probability": 0.91162109375}, {"start": 982.43, "end": 983.41, "word": " وبالتالي", "probability": 0.9111328125}, {"start": 983.41, "end": 983.81, "word": " بنضرب", "probability": 0.9117838541666666}, {"start": 983.81, "end": 984.05, "word": " هذا", "probability": 0.974609375}, {"start": 984.05, "end": 984.45, "word": " الرقم", "probability": 0.9405924479166666}, {"start": 984.45, "end": 984.63, "word": " في", "probability": 0.95068359375}, {"start": 984.63, "end": 984.87, "word": " كل", "probability": 0.984375}, {"start": 984.87, "end": 985.25, "word": " عنصر", "probability": 0.7659505208333334}, {"start": 985.25, "end": 985.41, "word": " من", "probability": 0.96044921875}, {"start": 985.41, "end": 985.97, "word": " عناصر", "probability": 0.9876302083333334}, {"start": 985.97, "end": 986.59, "word": " المصوفة", "probability": 0.99072265625}, {"start": 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991.73, "word": " تلاتة", "probability": 0.9779052734375}, {"start": 991.73, "end": 991.85, "word": " في", "probability": 0.9736328125}, {"start": 991.85, "end": 992.21, "word": " كل", "probability": 0.9765625}, {"start": 992.21, "end": 992.63, "word": " عنصر", "probability": 0.9820963541666666}, {"start": 992.63, "end": 992.75, "word": " من", "probability": 0.97705078125}, {"start": 992.75, "end": 993.09, "word": " عنصر", "probability": 0.9832356770833334}, {"start": 993.09, "end": 993.77, "word": " المصوفة", "probability": 0.9921875}], "temperature": 1.0}, {"id": 42, "seek": 102294, "start": 994.04, "end": 1022.94, "text": "اللي في الداخل فبصير 690-3-690315 وبالتالي هذا معنى ضرب اللي هو عنصر أو ضرب رقم في مصفوفة نجد الخاصية الثانية من هذه الخواص اللي بتقول لي ما يأتي if ال A and ال B are", "tokens": [6027, 20292, 8978, 32748, 47283, 1211, 6156, 3555, 9381, 13546, 1386, 7771, 12, 18, 12, 21, 7771, 18, 5211, 46599, 6027, 2655, 6027, 1829, 23758, 20449, 1863, 7578, 48812, 25513, 13672, 1829, 31439, 18871, 9381, 2288, 34051, 48812, 25513, 12602, 4587, 2304, 8978, 3714, 9381, 5172, 38688, 3660, 8717, 7435, 3215, 33962, 33546, 10632, 6024, 104, 7649, 10632, 9154, 29538, 33962, 14407, 9381, 13672, 1829, 39894, 39648, 32239, 19446, 7251, 10721, 31371, 498, 2423, 316, 293, 2423, 363, 366], "avg_logprob": -0.17636718936264514, "compression_ratio": 1.5248618784530388, "no_speech_prob": 0.0, "words": [{"start": 994.04, "end": 994.3, "word": "اللي", "probability": 0.6234130859375}, {"start": 994.3, "end": 994.38, "word": " في", "probability": 0.79296875}, {"start": 994.38, "end": 994.74, "word": " الداخل", "probability": 0.9920247395833334}, {"start": 994.74, "end": 995.24, "word": " فبصير", "probability": 0.8504638671875}, {"start": 995.24, "end": 996.3, "word": " 690", "probability": 0.546875}, {"start": 996.3, "end": 997.28, "word": "-3", "probability": 0.5880126953125}, {"start": 997.28, "end": 1000.56, "word": "-690315", "probability": 0.756201171875}, {"start": 1000.56, "end": 1001.58, "word": " وبالتالي", "probability": 0.94248046875}, {"start": 1001.58, "end": 1001.88, "word": " هذا", "probability": 0.88037109375}, {"start": 1001.88, "end": 1002.38, "word": " معنى", "probability": 0.8504231770833334}, {"start": 1002.38, "end": 1002.68, "word": " ضرب", "probability": 0.9677734375}, {"start": 1002.68, "end": 1003.26, "word": " اللي", "probability": 0.92138671875}, {"start": 1003.26, "end": 1003.48, "word": " هو", "probability": 0.98046875}, {"start": 1003.48, "end": 1004.16, "word": " عنصر", "probability": 0.95654296875}, {"start": 1004.16, "end": 1004.68, "word": " أو", "probability": 0.580078125}, {"start": 1004.68, "end": 1005.0, "word": " ضرب", "probability": 0.97998046875}, {"start": 1005.0, "end": 1005.74, "word": " رقم", "probability": 0.9964192708333334}, {"start": 1005.74, "end": 1006.4, "word": " في", "probability": 0.9521484375}, {"start": 1006.4, "end": 1007.46, "word": " مصفوفة", "probability": 0.956640625}, {"start": 1007.46, "end": 1008.16, "word": " نجد", "probability": 0.8938802083333334}, {"start": 1008.16, "end": 1009.0, "word": " الخاصية", "probability": 0.9596354166666666}, {"start": 1009.0, "end": 1010.2, "word": " الثانية", "probability": 0.888916015625}, {"start": 1010.2, "end": 1010.44, "word": " من", "probability": 0.98486328125}, {"start": 1010.44, "end": 1010.86, "word": " هذه", "probability": 0.982421875}, {"start": 1010.86, "end": 1012.02, "word": " الخواص", "probability": 0.5885416666666666}, {"start": 1012.02, "end": 1012.52, "word": " اللي", "probability": 0.959228515625}, {"start": 1012.52, "end": 1012.94, "word": " بتقول", "probability": 0.977294921875}, {"start": 1012.94, "end": 1013.1, "word": " لي", "probability": 0.3408203125}, {"start": 1013.1, "end": 1013.3, "word": " ما", "probability": 0.9208984375}, {"start": 1013.3, "end": 1014.16, "word": " يأتي", "probability": 0.8917643229166666}, {"start": 1014.16, "end": 1017.56, "word": " if", "probability": 0.62939453125}, {"start": 1017.56, "end": 1019.36, "word": " ال", "probability": 0.84228515625}, {"start": 1019.36, "end": 1019.78, "word": " A", "probability": 0.353515625}, {"start": 1019.78, "end": 1020.64, "word": " and", "probability": 0.91845703125}, {"start": 1020.64, "end": 1021.54, "word": " ال", "probability": 0.873046875}, {"start": 1021.54, "end": 1021.94, "word": " B", "probability": 0.8388671875}, {"start": 1021.94, "end": 1022.94, "word": " are", "probability": 0.9482421875}], "temperature": 1.0}, {"id": 43, "seek": 105415, "start": 1043.79, "end": 1054.15, "text": "مثلًا M في N ثم", "tokens": [2304, 12984, 1211, 14111, 995, 376, 8978, 426, 38637, 2304], "avg_logprob": -0.5756392262198708, "compression_ratio": 0.75, "no_speech_prob": 0.0, "words": [{"start": 1043.79, "end": 1045.19, "word": "مثلًا", "probability": 0.6307373046875}, {"start": 1045.19, "end": 1045.95, "word": " M", "probability": 0.43017578125}, {"start": 1045.95, "end": 1047.61, "word": " في", "probability": 0.73974609375}, {"start": 1047.61, "end": 1048.21, "word": " N", "probability": 0.97119140625}, {"start": 1048.21, "end": 1054.15, "word": " ثم", "probability": 0.5908203125}], "temperature": 1.0}, {"id": 44, "seek": 108561, "start": 1056.22, "end": 1085.62, "text": "الـ A زي دي ال B الـ A matrix is a matrix of the same size of the same size M في N ماديش صوت بالمرة", "tokens": [6027, 39184, 316, 30767, 1829, 11778, 1829, 2423, 363, 2423, 39184, 316, 8141, 307, 257, 8141, 295, 264, 912, 2744, 295, 264, 912, 2744, 376, 8978, 426, 19446, 16254, 8592, 20328, 35473, 20666, 2304, 25720], "avg_logprob": -0.3693576322661506, "compression_ratio": 1.2828282828282829, "no_speech_prob": 0.0, "words": [{"start": 1056.22, "end": 1056.7, "word": "الـ", "probability": 0.5953369140625}, {"start": 1056.7, "end": 1057.26, "word": " A", "probability": 0.5361328125}, {"start": 1057.26, "end": 1057.64, "word": " زي", "probability": 0.5096435546875}, {"start": 1057.64, "end": 1058.04, "word": " دي", "probability": 0.6397705078125}, {"start": 1058.04, "end": 1058.2, "word": " ال", "probability": 0.8076171875}, {"start": 1058.2, "end": 1058.52, "word": " B", "probability": 0.6943359375}, {"start": 1058.52, "end": 1060.3, "word": " الـ", "probability": 0.46630859375}, {"start": 1060.3, "end": 1060.5, "word": " A", "probability": 0.7255859375}, {"start": 1060.5, "end": 1061.28, "word": " matrix", "probability": 0.5205078125}, {"start": 1061.28, "end": 1062.48, "word": " is", "probability": 0.48486328125}, {"start": 1062.48, "end": 1063.68, "word": " a", "probability": 0.7041015625}, {"start": 1063.68, "end": 1065.16, "word": " matrix", "probability": 0.9541015625}, {"start": 1065.16, "end": 1067.1, "word": " of", "probability": 0.94091796875}, {"start": 1067.1, "end": 1067.34, "word": " the", "probability": 0.94091796875}, {"start": 1067.34, "end": 1067.68, "word": " same", "probability": 0.91552734375}, {"start": 1067.68, "end": 1068.74, "word": " size", "probability": 0.84033203125}, {"start": 1068.74, "end": 1069.84, "word": " of", "probability": 0.57470703125}, {"start": 1069.84, "end": 1074.78, "word": " the", "probability": 0.93896484375}, {"start": 1074.78, "end": 1075.18, "word": " same", "probability": 0.90576171875}, {"start": 1075.18, "end": 1075.92, "word": " size", "probability": 0.7939453125}, {"start": 1075.92, "end": 1077.34, "word": " M", "probability": 0.560546875}, {"start": 1077.34, "end": 1078.6, "word": " في", "probability": 0.58056640625}, {"start": 1078.6, "end": 1079.3, "word": " N", "probability": 0.982421875}, {"start": 1079.3, "end": 1085.0, "word": " ماديش", "probability": 0.737548828125}, {"start": 1085.0, "end": 1085.18, "word": " صوت", "probability": 0.8818359375}, {"start": 1085.18, "end": 1085.62, "word": " بالمرة", "probability": 0.6293538411458334}], "temperature": 1.0}, {"id": 45, "seek": 112725, "start": 1103.83, "end": 1127.25, "text": "يبقى هذا بتكلم على جمع مصففين بيقول لو كان عند A وB مصففين لهم نفس ال size اللي هو M في N مثلا يبقى المجموع تبعهم بيديهوله نفس ال size اللي هو M في M نعطي مثال تعوضيها for example F", "tokens": [1829, 3555, 4587, 7578, 23758, 39894, 4117, 19528, 15844, 10874, 2304, 3615, 3714, 9381, 5172, 5172, 9957, 4724, 1829, 39648, 45164, 25961, 43242, 316, 4032, 33, 3714, 9381, 5172, 5172, 9957, 5296, 16095, 8717, 36178, 2423, 2744, 13672, 1829, 31439, 376, 8978, 426, 50113, 15040, 7251, 3555, 4587, 7578, 9673, 7435, 2304, 45367, 6055, 3555, 3615, 16095, 4724, 1829, 16254, 3224, 12610, 3224, 8717, 36178, 2423, 2744, 13672, 1829, 31439, 376, 8978, 376, 8717, 3615, 9566, 1829, 50113, 6027, 37279, 2407, 11242, 1829, 11296, 337, 1365, 479], "avg_logprob": -0.21324574100700291, "compression_ratio": 1.6408839779005524, "no_speech_prob": 0.0, "words": [{"start": 1103.83, "end": 1104.29, "word": "يبقى", "probability": 0.8558349609375}, {"start": 1104.29, "end": 1104.49, "word": " هذا", "probability": 0.79248046875}, {"start": 1104.49, "end": 1104.99, "word": " بتكلم", "probability": 0.7027180989583334}, {"start": 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"end": 1111.65, "word": " ال", "probability": 0.765625}, {"start": 1111.65, "end": 1112.05, "word": " size", "probability": 0.54443359375}, {"start": 1112.05, "end": 1112.29, "word": " اللي", "probability": 0.812744140625}, {"start": 1112.29, "end": 1112.41, "word": " هو", "probability": 0.8857421875}, {"start": 1112.41, "end": 1112.61, "word": " M", "probability": 0.6953125}, {"start": 1112.61, "end": 1112.83, "word": " في", "probability": 0.6494140625}, {"start": 1112.83, "end": 1113.15, "word": " N", "probability": 0.94775390625}, {"start": 1113.15, "end": 1113.73, "word": " مثلا", "probability": 0.974609375}, {"start": 1113.73, "end": 1114.91, "word": " يبقى", "probability": 0.93115234375}, {"start": 1114.91, "end": 1115.61, "word": " المجموع", "probability": 0.962890625}, {"start": 1115.61, "end": 1116.11, "word": " تبعهم", "probability": 0.91357421875}, {"start": 1116.11, "end": 1116.73, "word": " بيديهوله", "probability": 0.6129964192708334}, {"start": 1116.73, "end": 1117.03, "word": " نفس", "probability": 0.996337890625}, {"start": 1117.03, "end": 1117.21, "word": " ال", "probability": 0.98388671875}, {"start": 1117.21, "end": 1117.57, "word": " size", "probability": 0.93408203125}, {"start": 1117.57, "end": 1117.97, "word": " اللي", "probability": 0.982666015625}, {"start": 1117.97, "end": 1118.25, "word": " هو", "probability": 0.97705078125}, {"start": 1118.25, "end": 1118.83, "word": " M", "probability": 0.962890625}, {"start": 1118.83, "end": 1119.35, "word": " في", "probability": 0.9716796875}, {"start": 1119.35, "end": 1119.71, "word": " M", "probability": 0.94287109375}, {"start": 1119.71, "end": 1120.69, "word": " نعطي", "probability": 0.973876953125}, {"start": 1120.69, "end": 1121.03, "word": " مثال", "probability": 0.937255859375}, {"start": 1121.03, "end": 1121.75, "word": " تعوضيها", "probability": 0.659423828125}, {"start": 1121.75, "end": 1122.03, "word": " for", "probability": 0.64697265625}, {"start": 1122.03, "end": 1122.89, "word": " 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"probability": 0.92236328125}, {"start": 1810.71, "end": 1811.13, "word": " الشكل", "probability": 0.990966796875}, {"start": 1811.13, "end": 1811.45, "word": " is", "probability": 0.890625}, {"start": 1811.45, "end": 1812.31, "word": " called", "probability": 0.9345703125}], "temperature": 1.0}, {"id": 75, "seek": 184606, "start": 1818.2, "end": 1846.06, "text": "and in dimensional convector ماحدش أحسن من حد ندى a matrix with", "tokens": [474, 294, 18795, 416, 303, 1672, 19446, 24401, 8592, 5551, 5016, 3794, 1863, 9154, 11331, 3215, 8717, 3215, 7578, 257, 8141, 365], "avg_logprob": -0.38722824791203375, "compression_ratio": 0.9518072289156626, "no_speech_prob": 0.0, "words": [{"start": 1818.2, "end": 1819.06, "word": "and", "probability": 0.572265625}, {"start": 1819.06, "end": 1820.84, "word": " in", "probability": 0.28466796875}, {"start": 1820.84, "end": 1824.52, "word": " dimensional", "probability": 0.7509765625}, {"start": 1824.52, "end": 1832.9, "word": " convector", "probability": 0.7098795572916666}, {"start": 1832.9, "end": 1836.12, "word": " ماحدش", "probability": 0.6464029947916666}, {"start": 1836.12, "end": 1836.58, "word": " أحسن", "probability": 0.8948974609375}, {"start": 1836.58, "end": 1836.76, "word": " من", "probability": 0.982421875}, {"start": 1836.76, "end": 1837.24, "word": " حد", "probability": 0.9365234375}, {"start": 1837.24, "end": 1839.28, "word": " ندى", "probability": 0.66552734375}, {"start": 1839.28, "end": 1839.7, "word": " a", "probability": 0.470947265625}, {"start": 1839.7, "end": 1840.56, "word": " matrix", "probability": 0.97216796875}, {"start": 1840.56, "end": 1846.06, "word": " with", "probability": 0.58544921875}], "temperature": 1.0}, {"id": 76, "seek": 187896, "start": 1853.74, "end": 1878.96, "text": "مع شكل Y1 و Y2", "tokens": [2304, 3615, 13412, 28820, 398, 16, 4032, 398, 17], "avg_logprob": -0.8343749821186066, "compression_ratio": 0.6896551724137931, "no_speech_prob": 0.0, "words": [{"start": 1853.7399999999998, "end": 1855.1399999999999, "word": "مع", "probability": 0.21392822265625}, {"start": 1855.1399999999999, "end": 1856.54, "word": " شكل", "probability": 0.4771728515625}, {"start": 1856.54, "end": 1877.26, "word": " Y1", "probability": 0.5762939453125}, {"start": 1877.26, "end": 1878.3, "word": " و", "probability": 0.5224609375}, {"start": 1878.3, "end": 1878.96, "word": " Y2", "probability": 0.6546630859375}], "temperature": 1.0}, {"id": 77, "seek": 190224, "start": 1879.6, "end": 1902.24, "text": "و لغاية yn is called بروح نسميه indimensional raw vector", "tokens": [2407, 5296, 17082, 995, 10632, 17861, 307, 1219, 4724, 32887, 5016, 8717, 38251, 1829, 3224, 1016, 332, 11075, 8936, 8062], "avg_logprob": -0.5621279988970075, "compression_ratio": 0.8658536585365854, "no_speech_prob": 0.0, "words": [{"start": 1879.6, "end": 1879.9, "word": "و", "probability": 0.525390625}, {"start": 1879.9, "end": 1880.7, "word": " لغاية", "probability": 0.87158203125}, {"start": 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تساوي", "probability": 0.8248291015625}, {"start": 1936.21, "end": 1938.59, "word": " A11", "probability": 0.584228515625}, {"start": 1938.59, "end": 1940.27, "word": " A12", "probability": 0.73388671875}], "temperature": 1.0}, {"id": 79, "seek": 196753, "start": 1941.15, "end": 1967.53, "text": "A1N A21 A22 A2N AM1 AM2 AMN شكل ان هذا اللي سميها هذه المصفوفة star with size", "tokens": [32, 16, 45, 316, 4436, 316, 7490, 316, 17, 45, 6475, 16, 6475, 17, 6475, 45, 13412, 28820, 16472, 23758, 13672, 1829, 8608, 2304, 1829, 11296, 29538, 9673, 9381, 5172, 38688, 3660, 3543, 365, 2744], "avg_logprob": -0.354383678899871, "compression_ratio": 1.0824742268041236, "no_speech_prob": 0.0, "words": [{"start": 1941.15, "end": 1942.93, "word": "A1N", "probability": 0.5783284505208334}, {"start": 1942.93, "end": 1945.65, "word": " A21", "probability": 0.75048828125}, {"start": 1945.65, "end": 1947.35, "word": " A22", "probability": 0.83740234375}, {"start": 1947.35, "end": 1949.41, "word": " A2N", 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"probability": 0.82275390625}, {"start": 2360.92, "end": 2361.24, "word": " زي", "probability": 0.803466796875}, {"start": 2361.24, "end": 2361.32, "word": " ما", "probability": 0.73388671875}, {"start": 2361.32, "end": 2361.62, "word": " ديته", "probability": 0.4522298177083333}, {"start": 2361.62, "end": 2362.64, "word": " الرمز", "probability": 0.8777669270833334}, {"start": 2362.64, "end": 2363.0, "word": " V", "probability": 0.9697265625}, {"start": 2363.0, "end": 2364.04, "word": " يبقى", "probability": 0.9608154296875}, {"start": 2364.04, "end": 2364.28, "word": " U", "probability": 0.97119140625}, {"start": 2364.28, "end": 2365.16, "word": " أطلقتها", "probability": 0.7805908203125}, {"start": 2365.16, "end": 2365.32, "word": " على", "probability": 0.939453125}, {"start": 2365.32, "end": 2365.84, "word": " الصفوف", "probability": 0.9493815104166666}, {"start": 2365.84, "end": 2366.12, "word": " و", "probability": 0.79443359375}, {"start": 2366.12, "end": 2366.48, "word": " V", 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4587, 7578, 624, 16, 4032, 624, 17, 4032, 5296, 17082, 3660, 624, 43, 23032, 3555, 3615, 995, 23758, 6225, 2304, 23328, 4032, 23758, 6225, 2304, 23328, 4032, 23758, 6225, 2304, 23328, 4032, 23758, 6225, 2304, 23328, 1975, 2407, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 11296, 15844, 25124, 28820, 16712, 6027, 1829, 4032, 28242, 36764, 24401, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 6225, 3555, 9640, 3660, 18871, 20328, 5172, 8608, 2407, 16606, 25961, 23758, 4032, 20193, 23758, 2423, 9307, 1863, 9957, 366, 264, 912, 8032, 1863, 5016, 995, 12610, 8717, 3615, 9566, 1829, 5551, 2304, 12984, 37977, 9673, 25720, 25724, 995, 10632, 15844, 2423, 732, 21988, 8032, 8848, 12610, 16472, 13412, 16606, 21984, 37279, 6027, 7578, 1975, 3615, 9566, 1829, 4117, 14407, 18863, 5172, 2407], "avg_logprob": -0.13420542635658914, "compression_ratio": 1.8326530612244898, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2378.04, "end": 2378.6, "word": "يبقى", "probability": 0.916015625}, {"start": 2378.6, "end": 2379.04, "word": " U1", "probability": 0.810302734375}, {"start": 2379.04, "end": 2379.22, "word": " و", "probability": 0.91357421875}, {"start": 2379.22, "end": 2379.7, "word": " U2", "probability": 0.779296875}, {"start": 2379.7, "end": 2379.84, "word": " و", "probability": 0.93212890625}, {"start": 2379.84, "end": 2380.14, "word": " لغة", "probability": 0.9542643229166666}, {"start": 2380.14, "end": 2380.46, "word": " UL", "probability": 0.5689697265625}, {"start": 2380.46, "end": 2380.82, "word": " طبعا", "probability": 0.9146728515625}, {"start": 2380.82, "end": 2381.06, "word": " هذا", "probability": 0.67724609375}, {"start": 2381.06, "end": 2381.7, "word": " عمود", "probability": 0.9451497395833334}, {"start": 2381.7, "end": 2382.0, "word": " و", "probability": 0.55712890625}, {"start": 2382.0, "end": 2382.2, "word": " هذا", "probability": 0.9111328125}, {"start": 2382.2, "end": 2382.76, "word": " عمود", "probability": 0.98291015625}, {"start": 2382.76, "end": 2382.94, "word": " و", "probability": 0.85107421875}, {"start": 2382.94, "end": 2383.16, "word": " هذا", "probability": 0.96826171875}, {"start": 2383.16, "end": 2383.64, "word": " عمود", "probability": 0.9817708333333334}, {"start": 2383.64, "end": 2384.08, "word": " و", "probability": 0.771484375}, {"start": 2384.08, "end": 2384.28, "word": " هذا", "probability": 0.9716796875}, {"start": 2384.28, "end": 2384.7, "word": " عمود", "probability": 0.98876953125}, {"start": 2384.7, "end": 2385.2, "word": " او", "probability": 0.788818359375}, {"start": 2385.2, "end": 2385.56, "word": " بقدر", "probability": 0.9454752604166666}, {"start": 2385.56, "end": 2386.1, "word": " اكتبها", "probability": 0.9685546875}, {"start": 2386.1, "end": 2386.36, "word": " على", "probability": 0.89501953125}, {"start": 2386.36, "end": 2387.0, "word": " الشكل", "probability": 0.973388671875}, {"start": 2387.0, "end": 2387.94, "word": " التالي", "probability": 0.9685872395833334}, {"start": 2387.94, "end": 2388.42, "word": " و", "probability": 0.97900390625}, {"start": 2388.42, "end": 2388.78, "word": " كل", "probability": 0.783203125}, {"start": 2388.78, "end": 2389.2, "word": " واحد", "probability": 0.99169921875}, {"start": 2389.2, "end": 2389.68, "word": " عبارة", "probability": 0.99169921875}, {"start": 2389.68, "end": 2389.9, "word": " عن", "probability": 0.984375}, {"start": 2389.9, "end": 2390.26, "word": " مين", "probability": 0.7127685546875}, {"start": 2390.26, "end": 2391.36, "word": " عبارة", "probability": 0.9444580078125}, {"start": 2391.36, "end": 2391.76, "word": " عن", "probability": 0.99755859375}, {"start": 2391.76, "end": 2392.12, "word": " صف", "probability": 0.975830078125}, {"start": 2392.12, "end": 2392.52, "word": " سواء", "probability": 0.8995768229166666}, {"start": 2392.52, "end": 2392.8, "word": " كان", "probability": 0.92578125}, {"start": 2392.8, "end": 2393.06, "word": " هذا", "probability": 0.91357421875}, {"start": 2393.06, "end": 2393.18, "word": " و", "probability": 0.611328125}, {"start": 2393.18, "end": 2393.3, "word": " لا", "probability": 0.548828125}, {"start": 2393.3, "end": 2393.66, "word": " هذا", "probability": 0.8740234375}, {"start": 2393.66, "end": 2394.88, "word": " الاتنين", "probability": 0.7972412109375}, {"start": 2394.88, "end": 2395.26, "word": " are", "probability": 0.90576171875}, {"start": 2395.26, "end": 2395.5, "word": " the", "probability": 0.931640625}, {"start": 2395.5, "end": 2395.94, "word": " same", "probability": 0.90869140625}, {"start": 2395.94, "end": 2397.18, "word": " هنحاول", "probability": 0.816552734375}, {"start": 2397.18, "end": 2397.58, "word": " نعطي", "probability": 0.9727783203125}, {"start": 2397.58, "end": 2398.18, "word": " أمثلة", "probability": 0.8856201171875}, {"start": 2398.18, "end": 2398.74, "word": " المرة", "probability": 0.933349609375}, {"start": 2398.74, "end": 2399.3, "word": " الجاية", "probability": 0.908203125}, {"start": 2399.3, "end": 2399.96, "word": " على", "probability": 0.85986328125}, {"start": 2399.96, "end": 2400.16, "word": " ال", "probability": 0.71484375}, {"start": 2400.16, "end": 2400.28, "word": " two", "probability": 0.771484375}, {"start": 2400.28, "end": 2400.92, "word": " definitions", "probability": 0.89892578125}, {"start": 2400.92, "end": 2401.56, "word": " هذول", "probability": 0.7930501302083334}, {"start": 2401.56, "end": 2402.0, "word": " ان", "probability": 0.796875}, {"start": 2402.0, "end": 2402.3, "word": " شاء", "probability": 0.969970703125}, {"start": 2402.3, "end": 2402.6, "word": " الله", "probability": 0.9326171875}, {"start": 2402.6, "end": 2403.08, "word": " تعالى", "probability": 0.9866536458333334}, {"start": 2403.08, "end": 2403.48, "word": " اعطيكوا", "probability": 0.8138834635416666}, {"start": 2403.48, "end": 2403.72, "word": " العفو", "probability": 0.87548828125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2404.9835, "duration_after_vad": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HSZXZRH7pd0.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HSZXZRH7pd0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1f84ec1d3f009bffca3b44bbeb2a18d85ea3f6ab
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/HSZXZRH7pd0.srt
@@ -0,0 +1,1438 @@
+1
+00:00:19,290 --> 00:00:23,430
+بسم الله الرحمن الرحيم في نهاية المحاضرة الماضية
+
+2
+00:00:23,430 --> 00:00:27,850
+ابتدأنا في section واحد خمسة وهو ال linear first 
+
+3
+00:00:27,850 --> 00:00:32,050
+order differential equation وعرفنا أن شكل ال first
+
+4
+00:00:32,050 --> 00:00:35,990
+order linear differential equation على الشكل a
+
+5
+00:00:35,990 --> 00:00:40,310
+node of x في ال y prime زائد a one of x في ال y
+
+6
+00:00:40,310 --> 00:00:44,610
+بدل سوى ال f of x وبعد ذلك رحنا لمعامل y prime
+
+7
+00:00:44,610 --> 00:00:51,550
+خلينا الواحد الصحيح واشترطنا عند تطبيق الحل لهذه
+
+8
+00:00:51,550 --> 00:00:56,570
+المعادلة لازم يكون المعامل هو واحد صحيح فأصبحت
+
+9
+00:00:56,570 --> 00:00:59,190
+الصورة الجديدة لل first order differential
+
+10
+00:00:59,190 --> 00:01:05,670
+equation على صيغة y prime زائد P of x في y بدو يساوي
+
+11
+00:01:05,670 --> 00:01:11,210
+مين ال Q of x حيث الـ P والـ X  الـ P والـ Q دالتان
+
+12
+00:01:11,210 --> 00:01:16,750
+متصلتان على فترة ما وقلنا إن حل هذه المعادلة على
+
+13
+00:01:16,750 --> 00:01:24,770
+صيغة الـ Mu of X في Y بتساوي تكامل Mu of X في Q of 
+
+14
+00:01:24,770 --> 00:01:30,310
+X في DX حيث الـ Mu of X اللي هو عامل التكامل هو
+
+15
+00:01:30,310 --> 00:01:37,150
+عبارة عن E أس تكامل P of X DX  واخدنا على ذلك
+
+16
+00:01:37,150 --> 00:01:43,460
+مثالين وهذا اللي بين أيدينا هو المثال رقم 3 يبقى 
+
+17
+00:01:43,460 --> 00:01:46,400
+المثال رقم ثلاثة بيقول solve the differential
+
+18
+00:01:46,400 --> 00:01:53,080
+equation xy prime زائد y بيساوي x sin x علما بأن x
+
+19
+00:01:53,080 --> 00:01:59,180
+دائما وأبدا أكبر من 0 يبقى مثلا مشان نحل 
+
+20
+00:01:59,180 --> 00:02:02,760
+المعادلة التفاضلية اللي قدامنا هذه بدي أكتبها على
+
+21
+00:02:02,760 --> 00:02:08,370
+ال standard form تبعها اللي بدي أخلّي معامل y' هو 
+
+22
+00:02:08,370 --> 00:02:14,270
+يساوي واحد، إذا بروح بنقسم الطرفين على x وهذا ممكن
+
+23
+00:02:14,270 --> 00:02:18,490
+لأن x greater than zero ولا تساوي zero إذا
+
+24
+00:02:18,490 --> 00:02:25,930
+المعادلة العادية هتأخذ الصيغة الجديدة هي y' زائد
+
+25
+00:02:25,930 --> 00:02:32,130
+واحد على x في y بيساوي بيساوي sin x يبقى هاي
+
+26
+00:02:32,130 --> 00:02:37,390
+حطيناها على صيغة y prime زائد P of x في y بيساوي ل
+
+27
+00:02:37,390 --> 00:02:42,990
+Q of x يبقى بناء عليه بقدر أجيب عامل التكامل
+
+28
+00:02:42,990 --> 00:02:49,430
+لهذه المعادلة فبروح بقول ل Mu of x بيساوي E أس
+
+29
+00:02:49,430 --> 00:02:57,830
+تكامل واحد على x dx يبقى E أس ln ال x يبقى ال x
+
+30
+00:02:57,830 --> 00:03:03,900
+بتصير يبقى عامل التكامل هو X إذا لو روحت سميت 
+
+31
+00:03:03,900 --> 00:03:12,620
+المعادلة الأصلية star بقول له solution of the
+
+32
+00:03:12,620 --> 00:03:23,080
+differential equation star is اللي هو الـ x في الـ
+
+33
+00:03:23,080 --> 00:03:30,120
+y بيساوي تكامل x في sin الـ x كله بالنسبة لهذه الـ 
+
+34
+00:03:30,120 --> 00:03:35,320
+x يبقى ضايل علينا تكامل هذه طب نكامل هذه الدالة
+
+35
+00:03:35,320 --> 00:03:40,380
+يا بنات تكامل integration by parts وهذه أخدناها
+
+36
+00:03:40,380 --> 00:03:49,180
+بصيغة محددة وقلنا بروح بناخد الدالة ومشتقتها يبقى
+
+37
+00:03:49,180 --> 00:03:58,490
+باجي بأخد اللي هو مين الـ .. الـ U وهذه الـ DV الـ U 
+
+38
+00:03:58,490 --> 00:04:04,410
+اللي هي عبارة عن X والـ DV اللي هي sin الـ X بروح 
+
+39
+00:04:04,410 --> 00:04:09,270
+بأفاضل هذه بقى تفاضلها بواحد وباجي أو بقول هذه
+
+40
+00:04:09,270 --> 00:04:13,090
+derivatives وهذه integrals in general يعني هذه 
+
+41
+00:04:13,090 --> 00:04:17,530
+بقول عليها derivatives وهذه بروح بقول عليها
+
+42
+00:04:17,530 --> 00:04:19,610
+integrals
+
+43
+00:04:25,340 --> 00:04:32,500
+بعد ذلك اشتغل كمان مرة يبقى مشتقة هذه بـ0 تكامل هذه 
+
+44
+00:04:32,500 --> 00:04:39,920
+بـ-Sin X بعدين بقول الدالة هذه في الدالة هذه والدالة
+
+45
+00:04:39,920 --> 00:04:44,400
+اللي عندنا هذه في الدالة هذه وبروح باستخدام قاعدة
+
+46
+00:04:44,400 --> 00:04:49,660
+الإشارات يبقى ببدأ بالموجب اللي بعده سالب موجب
+
+47
+00:04:49,660 --> 00:04:54,840
+سالب إلى ما شاء الله يبقى بناء عليها أصبح عندنا ال X
+
+48
+00:04:54,840 --> 00:05:02,580
+Y بيساوي ناقص X في cos X حصل ضرب الاتنين زائد
+
+49
+00:05:02,580 --> 00:05:09,780
+sin X زائد constant C أنا بدي y as a function of x
+
+50
+00:05:09,780 --> 00:05:15,280
+إذا بروح بقسم كله على مين؟ على x يبقى بيصير حل
+
+51
+00:05:15,280 --> 00:05:21,680
+المعادلة التفاضلية الى star هو y بتساوي سالب cos
+
+52
+00:05:21,680 --> 00:05:28,760
+ال x زائد sin ال x على x زائد c على x هذا ال
+
+53
+00:05:28,760 --> 00:05:33,740
+general solution لمين؟ للمعادلة التفاضلية اللي هي
+
+54
+00:05:33,740 --> 00:05:39,670
+ال star يبقى بناء عليه أخدنا على هذه المعادلة ثلاثة
+
+55
+00:05:39,670 --> 00:05:43,010
+أمثلة أو على ال first order linear differential
+
+56
+00:05:43,010 --> 00:05:47,610
+equation ثلاثة أمثلة مثالين المرة الماضية وهذا هو
+
+57
+00:05:47,610 --> 00:05:52,750
+المثال الثالث مش دائما المعادلة بمجرد ما أطلع لها
+
+58
+00:05:52,750 --> 00:05:58,390
+تكون linear أحيان بدي أضطر أحولها إلى linear first
+
+59
+00:05:58,390 --> 00:06:03,770
+order differential equation يعني المعادلة بمجرد
+
+60
+00:06:03,770 --> 00:06:08,410
+النظر لا تكون Linear لكن بقدر أحولها إلى Linear زي
+
+61
+00:06:08,410 --> 00:06:10,970
+ما في ال Homogeneous حولناها إلى Homogeneous وال
+
+62
+00:06:10,970 --> 00:06:14,630
+Exact كانت ماهياش Exact حولناها إلى Exact وال
+
+63
+00:06:14,630 --> 00:06:18,290
+Superb كانت ماهياش Superb وحولناها إلى Superb لا 
+
+64
+00:06:18,290 --> 00:06:22,850
+Superb يعني ما حدش أحسن من حد طيب بدنا نيجي نشوف 
+
+65
+00:06:22,990 --> 00:06:29,010
+النوع من المعادلات ليست Linear لكن يمكن تحويلها
+
+66
+00:06:29,010 --> 00:06:33,830
+إلى Linear وهذا ما يسمى معادلة Bernoulli يبقى
+
+67
+00:06:33,830 --> 00:06:38,270
+Bernoulli equation بدنا نعطيها Definition وبعدها 
+
+68
+00:06:38,270 --> 00:06:44,750
+نحل معادلة Bernoulli يبقى باجي بقول Definition 
+
+69
+00:06:44,750 --> 00:06:48,230
+differential equation
+
+70
+00:06:50,280 --> 00:06:56,980
+differential equation المعادلة التفاضلية y prime
+
+71
+00:06:56,980 --> 00:07:05,820
+زائد P of x في ال y بدو يساوي ل Q of x في Y أس N 
+و
+
+72
+00:07:05,820 --> 00:07:15,340
+الـ N لا تساوي zero and وكذلك 
+
+73
+00:07:15,340 --> 00:07:25,200
+الـ N لا تساوي واحد is called بنروح نسميها 
+
+74
+00:07:25,200 --> 00:07:31,380
+Bernoulli equation Bernoulli 
+
+75
+00:07:31,380 --> 00:07:35,540
+Bernoulli
+
+76
+00:07:35,540 --> 00:07:39,500
+equation يبقى معادلة Bernoulli
+
+77
+00:07:49,170 --> 00:07:55,790
+طيب الآن ظهرت عندنا معادلة جديدة هذه المعادلة ليست
+
+78
+00:07:55,790 --> 00:08:00,470
+linear first order differential equation السبب في
+
+79
+00:08:00,470 --> 00:08:04,870
+ذلك أنها ماهياش linear لو طلعت للطرف الشمال اللي 
+
+80
+00:08:04,870 --> 00:08:09,310
+عندنا يبقى هو ال linear first order differential 
+
+81
+00:08:09,310 --> 00:08:13,160
+equation اللي احنا عارفينه الـ Q of X هي يبقى
+
+82
+00:08:13,160 --> 00:08:19,560
+الجديد من Y أس N يبقى بسبب وجود الـ Y أس
+
+83
+00:08:19,560 --> 00:08:24,060
+N بطلت تصير هذه first order differential
+
+84
+00:08:24,060 --> 00:08:28,960
+equation طيب حط لي شرط هنا قال الـ N ممنوع تساوي
+
+85
+00:08:28,960 --> 00:08:34,640
+Zero وكذلك الـ N ممنوع تساوي واحد السؤال هو ليش 
+
+86
+00:08:34,640 --> 00:08:37,260
+الـ N ممنوع تساوي Zero يعني لو تساوي Zero إيش
+
+87
+00:08:37,260 --> 00:08:42,440
+بيصير؟ بيصير هادي واحد وبتالي بيصير linear طبيعي يعني
+
+88
+00:08:42,440 --> 00:08:48,460
+وبالتالي احنا ما سوينا شي طيب؟ لو كانت الـ N بواحد
+
+89
+00:08:48,460 --> 00:08:53,020
+بيصير هنا Y إذا بجيبها على الشجة التانية و
+
+90
+00:08:53,020 --> 00:08:57,680
+بأخد Y عامل مشترك وبيصير P of X زائد لـ Q of X و
+
+91
+00:08:57,680 --> 00:09:02,360
+بتساوي Zero وبالتالي صارت Linear كذلك إذا مشان
+
+92
+00:09:02,360 --> 00:09:06,740
+أضمن إنها ماهياش Linear لازم الـ N ممنوع تساوي 
+
+93
+00:09:06,740 --> 00:09:13,000
+Zero والـ N ممنوع تساوي واحد تمام السؤال هو كيف
+
+94
+00:09:13,000 --> 00:09:19,740
+يمكن حل هذه المعادلة بنقولك بنقدر نحلها كالتالي بدي 
+
+95
+00:09:19,740 --> 00:09:24,740
+أحولها إلى linear كيف بدي أحولها إلى linear هذا ما
+
+96
+00:09:24,740 --> 00:09:32,400
+سنشير إليه يبقى باجي بقوله هنا to solve Bernoulli 
+
+97
+00:09:32,400 --> 00:09:38,280
+equation Bernoulli
+
+98
+00:09:38,280 --> 00:09:41,320
+equation multiply
+
+99
+00:09:46,660 --> 00:09:54,180
+both sides كلا الطرفين هذا ما نسميه ال equation
+
+100
+00:09:54,180 --> 00:10:06,620
+star نضربها
+
+101
+00:10:06,620 --> 00:10:14,660
+بـ Y أس ناقص  في Y to gain بنحصل على بدأ اضغط في Y to
+
+102
+00:10:14,660 --> 00:10:22,380
+power سالب N يبقى بيصير سالب N في ال Y prime زائد
+
+103
+00:10:22,380 --> 00:10:33,080
+P of X في Y أس 1-N تمام بدأ أساوي من A Q of 
+
+104
+00:10:33,080 --> 00:10:33,480
+X
+
+105
+00:10:36,350 --> 00:10:41,670
+بعملية الضرب البسيطة اللي عملته هذه يبقى طارت Y أس
+
+106
+00:10:41,670 --> 00:10:47,310
+N من الطرف اليمين في المعادلة وأصبحت 
+
+107
+00:10:47,310 --> 00:10:51,470
+المعادلة على الشكل الجديد اللي عندنا هل هذه linear
+
+108
+00:10:51,470 --> 00:10:59,470
+لا يبقى مش أنا أحولها إلى linear بجي بقوله pot حط
+
+109
+00:10:59,470 --> 00:11:07,690
+لي الـ U بيساوي Y أس 1-N اشتقوا يا بنات بيصير
+
+110
+00:11:07,690 --> 00:11:17,390
+U' 1-N في Y أس -N في ال Y' مظبوط
+
+111
+00:11:17,390 --> 00:11:23,310
+هيك؟ طيب كويس لو قسمنا الطرفين على المقدار اللي
+
+112
+00:11:23,310 --> 00:11:27,970
+عندنا هذا بيصير 1 على 1-N
+
+113
+00:11:41,030 --> 00:11:46,350
+الترم اللي عندنا هذا في المعادلة إذا بقدر أحول
+
+114
+00:11:46,350 --> 00:11:51,170
+المعادلة تبعتي إلى الشكل التالي يبقى المعادلة
+
+115
+00:11:51,170 --> 00:11:57,970
+ستصبح على الشكل التالي يبقى باجي بقول المعادلة
+
+116
+00:11:57,970 --> 00:12:05,130
+بدها تصير 1 على 1-N في ال U prime زائد
+
+117
+00:12:05,130 --> 00:12:15,040
+P of X في ال U بدها تساوي Q of X هذا متغير ولا رقم؟ 
+
+118
+00:12:15,040 --> 00:12:22,880
+رقم لأن هو الـ 1-N إذا بدي أضرب في هذا الرقم
+
+119
+00:12:22,880 --> 00:12:29,980
+يبقى بيصير المعادلة U prime زائد 1-N في P
+
+120
+00:12:29,980 --> 00:12:38,400
+of X في U بيساوي 1-N في Q of X إذا هذا ثابت
+
+121
+00:12:38,400 --> 00:12:44,160
+رقم وهذا رقم لا يغير من شكل المعادلة السؤال هو 
+
+122
+00:12:44,160 --> 00:12:50,820
+المعادلة دي شو أصبح شكلها linear مظبوط هي y prime
+
+123
+00:12:50,820 --> 00:12:57,100
+function في x في y ال y أجابتها ل u بتساوي ل Q of
+
+124
+00:12:57,100 --> 00:13:06,720
+x فقط لغير يبقى هذه linear first order 
+
+125
+00:13:06,720 --> 00:13:08,860
+differential
+
+126
+00:13:09,820 --> 00:13:23,700
+equation that can be solved as before يبقى هذه
+
+127
+00:13:23,700 --> 00:13:28,820
+بروح بحلها زي ما كنت بحل ال linear اللي هو قبل
+
+128
+00:13:28,820 --> 00:13:35,360
+قليل واضحة أظن هذه طيب نبدأ نعطي أمثلة على ال
+
+129
+00:13:35,360 --> 00:13:38,920
+Bernoulli equation يبقى example one
+
+130
+00:13:51,100 --> 00:13:59,880
+Solve the differential equation المعادلة التفاضلية
+
+131
+00:13:59,880 --> 00:14:05,140
+Y'-2Sin 
+
+132
+00:14:05,140 --> 00:14:20,280
+X كل هذا في Y بيساوي -2Sin XY أس ثلاثة على 
+
+133
+00:14:20,280 --> 00:14:21,460
+اثنين
+
+134
+00:14:52,430 --> 00:14:56,350
+نعود إلى أسئلة قبل أن نعود إلى أسئلة سأعود إلى
+
+135
+00:14:56,350 --> 00:15:00,470
+التعريف قالي Bernoulli equation هي معادلة بالشكل هذا 
+
+136
+00:15:00,470 --> 00:15:05,290
+استبعدت أن ال N بتساوي زيرو واستبعدت أن ال N بتساوي
+
+137
+00:15:05,290 --> 00:15:10,770
+واحد لكن هل قلت أن ال N لازم يكون عدد صحيح؟ موجهة لم
+
+138
+00:15:10,770 --> 00:15:16,410
+أقول ذلك قد تكون ال N عدد موجب وقد يكون عدد سالب
+
+139
+00:15:16,410 --> 00:15:21,050
+وقد يكون كسر موجب وقد يكون كسر سالب كل
+
+140
+00:15:21,050 --> 00:15:25,450
+الاحتمالات واردة يعني ليس بالضرورة أن يكون عددا
+
+141
+00:15:25,450 --> 00:15:30,650
+صحيحا وهذا مثال بين أيدينا على أن الأس تبع ال Y 
+
+142
+00:15:30,650 --> 00:15:36,790
+هناك ليس عددا صحيحا طب الطرف الشمال جاهز على شكل ال 
+
+143
+00:15:36,790 --> 00:15:41,930
+linear الطرف اليمين لا لأن Y أس 3 على 2 هذه ايه
+
+144
+00:15:41,930 --> 00:15:45,530
+اللي جديدة في المثال اللي خلتني المثال ماهووش 
+
+145
+00:15:45,530 --> 00:15:51,230
+linear لذلك بروح بأحولها إلى linear ثم أحلها
+
+146
+00:15:51,230 --> 00:15:55,290
+بطريقة ال linear first order differential
+
+147
+00:15:55,290 --> 00:16:00,620
+equation يبقى شو نعمل يا بنات؟ بنذهب نضرب في Y
+
+148
+00:16:00,620 --> 00:16:07,380
+مرفوعة لهذا الأس بعلامة سالب يبقى اسميها لمعادلة
+
+149
+00:16:07,380 --> 00:16:12,360
+هذه ال main التي هي star يبقى باجي بقول هنا
+
+150
+00:16:12,360 --> 00:16:17,600
+multiply equation 
+
+151
+00:16:17,600 --> 00:16:28,030
+star by Y أس سالب ثلاثة على اثنين together نحصل 
+
+152
+00:16:28,030 --> 00:16:36,410
+على Y أس سالب ثلاثة على اثنين في الـ y' ناقص
+
+153
+00:16:36,410 --> 00:16:45,450
+اثنين sin x Y أس عندك Y أس واحد و Y أس سالب 
+
+154
+00:16:45,450 --> 00:17:01,910
+واحد ونص بيظل Y أس سالب نص بدي أعمل
+
+155
+00:17:01,910 --> 00:17:07,270
+تعويض في المثال هذه التعويض بتحولها إلى linear
+
+156
+00:17:07,270 --> 00:17:11,770
+first order differential equation شو هذه التعويض
+
+157
+00:17:11,770 --> 00:17:18,820
+بروح بقول له let عن طريق الوصول لـ U بيساوي Y أس سالب
+
+158
+00:17:18,820 --> 00:17:29,920
+نصف Y أس سالب نصف يبقى نشتق
+
+159
+00:17:29,920 --> 00:17:38,840
+يبقى الـ U' بتساوي سالب نصف Y أس سالب ثلاثة على اثنين
+
+160
+00:17:38,840 --> 00:17:44,960
+في من؟ في الـ Y' هنا ما عنديش نص يبقى بروح بضرب
+
+161
+00:17:44,960 --> 00:17:50,840
+كله في مين؟ في سالب اثنين لو ضربت في سالب اثنين
+
+162
+00:17:50,840 --> 00:17:57,580
+بيصير سالب اثنين U prime بتساوي Y أس سالب ثلاثة على 
+
+163
+00:17:57,580 --> 00:18:02,500
+اثنين في ال Y prime الآن الطرف اليمين في التعويض
+
+164
+00:18:02,500 --> 00:18:08,250
+هو هذا ال term مظبوط؟ إذا بقدر أشيل وقته بدل سالب
+
+165
+00:18:08,250 --> 00:18:15,550
+باتنين U' يبقى هذا بصيرة سالب اثنين U' سالب
+
+166
+00:18:15,550 --> 00:18:23,660
+اثنين في sin ال X هذه مين يا بنات؟ الـ U يبقى
+
+167
+00:18:23,660 --> 00:18:30,480
+بشيلها وبحط بدالها U بيساوي سالب اثنين في sin X
+
+168
+00:18:30,480 --> 00:18:36,000
+شو رأيك نقسم المعادلة كلها على سالب اثنين إذا لو 
+
+169
+00:18:36,000 --> 00:18:42,880
+قسمنا على سالب اثنين بتصبح المعادلة U Prime ناقص
+
+170
+00:18:42,880 --> 00:18:52,880
+زائد sin X في الـ U بدو يساوي له sin X وهذه عبارة
+
+171
+00:18:52,880 --> 00:19:02,060
+عن first order linear differential
+
+172
+00:19:02,060 --> 00:19:03,920
+equation
+
+173
+00:19:06,230 --> 00:19:11,110
+يبقى بالعملية اللي عملتها هذه استطاعت تحويل المعادلة
+
+174
+00:19:11,110 --> 00:19:14,990
+هذه اللي هي non-linear differential equation إلى
+
+175
+00:19:14,990 --> 00:19:20,170
+first order linear differential equation إذا بدنا 
+
+176
+00:19:20,170 --> 00:19:26,470
+نحلها زي ما كنا بنحل من قبل يبقى بدي أروح أجيب عامل 
+
+177
+00:19:26,470 --> 00:19:33,430
+التكامل لهذه المعادلة يبقى الـ Mu of X بيساوي E أس
+
+178
+00:19:33,430 --> 00:19:43,230
+
+201
+00:22:34,120 --> 00:22:37,320
+أريد أن أشهد أن يجب أن يكون الـ U لوحدها يبقى
+
+202
+00:22:37,320 --> 00:22:44,700
+بأضرب الطرفين في E أس كوساين X يبقى بناء على
+
+203
+00:22:44,700 --> 00:22:53,470
+الـ U ده يساوي 1 زائد C في E أس كوساين X برجع مرة
+
+204
+00:22:53,470 --> 00:23:01,350
+ثانية أنا الـ U حاططها كده؟ Y أس ناقص نصف يبقى بصير
+
+205
+00:23:01,350 --> 00:23:10,110
+عندنا هنا ميم Y أس ناقص نصف يساوي واحد زائد C في E
+
+206
+00:23:10,110 --> 00:23:15,310
+أس Cos X هنشكل
+
+207
+00:23:15,310 --> 00:23:24,840
+هذه يعني 1 على Y أُس نُص بيكون 1 زائد C في E أُس
+
+208
+00:23:24,840 --> 00:23:32,100
+Cos X مش هنجيب؟ يبقى لو هنجيب المثل بصير Y أُس
+
+209
+00:23:32,100 --> 00:23:43,120
+نُص يساوي 1 على 1 زائد C في E أُس Cos X خلص الحل؟
+
+210
+00:23:44,810 --> 00:23:50,750
+بقدر أجيب Y شو نعمل؟ بربع الطرفين يبقى لو ربعنا
+
+211
+00:23:50,750 --> 00:23:55,890
+الطرفين بنحصل على الحل اللي هو Y مربع الواحد بواحد
+
+212
+00:23:55,890 --> 00:24:05,210
+واحد زائد C في E أس Cos X لكل تربيع يبقى هذا هو حل
+
+213
+00:24:05,210 --> 00:24:10,730
+الـ differential equation الأصلية حدا فيكم بتحب
+
+214
+00:24:10,730 --> 00:24:16,770
+تسأل أي نقطة هنا؟ أي خطوة أو نقطة ما فهمتهاش تحب
+
+215
+00:24:16,770 --> 00:24:22,310
+تسأل أي سؤال في الموضوع عندما نيجي للمنواصة اه في
+
+216
+00:24:22,310 --> 00:24:34,010
+عرفت تسأل؟ differential equation Y' ناقص واحد على
+
+217
+00:24:34,010 --> 00:24:43,980
+X زائد واحد في الـ Y في Ln الـ Y بتساوي X زي الواحد
+
+218
+00:24:43,980 --> 00:24:57,460
+في Y والـ X greater than Zero باجي
+
+219
+00:24:57,460 --> 00:25:04,300
+بتطلع في مثلتي هذه ليست Linear لسببين السبب الأول
+
+220
+00:25:04,300 --> 00:25:09,000
+عندي Y في الناحية الثانية والسبب الثاني في عندي
+
+221
+00:25:09,000 --> 00:25:15,160
+هنا الـ Y إذا شغلتي أحاول أحول المعادلة هذه إلى
+
+222
+00:25:15,160 --> 00:25:20,480
+Linear مشان أقدر أحلها وأحصل على حل هذه المثلة
+
+223
+00:25:20,480 --> 00:25:26,040
+بيقولوا تمام هذه المعادلة بدي أسميها استعار يبقى
+
+224
+00:25:26,040 --> 00:25:34,970
+هذه بدي أسميها اللي عندنا استعار طيب مشان هيك بدي
+
+225
+00:25:34,970 --> 00:25:40,770
+أقول له هذه جاهزة صح والله ايش رأيكم أضرب كله في
+
+226
+00:25:40,770 --> 00:25:46,890
+Y أس سالب واحد عشان أتخلص من Y اللي على اليمين بدي
+
+227
+00:25:46,890 --> 00:25:52,870
+أقوله هنا multiply أو solution بالأول solution
+
+228
+00:25:52,870 --> 00:25:57,350
+multiply
+
+229
+00:25:57,350 --> 00:26:01,250
+both
+
+230
+00:26:01,250 --> 00:26:02,030
+sides
+
+231
+00:26:04,680 --> 00:26:16,720
+of equation star by Y أس سالب واحد we get بصير عند
+
+232
+00:26:16,720 --> 00:26:26,860
+هنا Y أس سالب واحد Y prime ناقص واحد على X زائد واحد
+
+233
+00:26:26,860 --> 00:26:32,520
+في Ln الـ Y يساوي X زائد واحد
+
+234
+00:26:35,780 --> 00:26:42,220
+يبقى كتبنا المعادلة بشكل جديد لكن هذه شكلها مش زي
+
+235
+00:26:42,220 --> 00:26:47,040
+مين مش زي السؤال اللي قبله ليش إنه عندي هنا Ln
+
+236
+00:26:47,040 --> 00:26:53,020
+و Y ما عنديش Y to the power n واي Ln مش Ln بدك
+
+237
+00:26:53,020 --> 00:26:59,660
+تحول هالي إلى مين؟ إلى بيرنولي يعني الشكل اللي قلناه
+
+238
+00:26:59,660 --> 00:27:05,820
+لبرنولي قبل قليل ليس قرآنا نزل من السماء لكن هو
+
+239
+00:27:05,820 --> 00:27:09,720
+الـ general form يعني ممكن ألاقي حالة والله تنتهي
+
+240
+00:27:09,720 --> 00:27:15,060
+الشكل لكن تبقى كذلك بيرنولي إذا أنا مشكلتي مع مين
+
+241
+00:27:15,060 --> 00:27:20,720
+هنا؟ مع Ln الواي يفضل أروح أقوله هنا بالهامش أقعد
+
+242
+00:27:25,640 --> 00:27:32,100
+يبقى الـ U' بواحد على Y في الـ Y' يعني Y أس سالب
+
+243
+00:27:32,100 --> 00:27:37,400
+واحد في الـ Y' هي هذه يعني يا بنات لما نشتق لازم
+
+244
+00:27:37,400 --> 00:27:42,300
+تطلع المقدار هذا أو مقدار مضروب فيه أرقام فيه عدد
+
+245
+00:27:42,300 --> 00:27:51,000
+تمام إذا هذه بأكتب بدالها U' ناقص واحد على X زائد
+
+246
+00:27:51,000 --> 00:27:57,740
+واحد في الـ U بدها تساوي X زائد واحد ايش رأيك وصلت
+
+247
+00:27:57,740 --> 00:28:02,540
+Linear؟ يبقى اللي كانت Non-linear ليه سببه اللي
+
+248
+00:28:02,540 --> 00:28:10,500
+قدرنا نحولها إلى Linear؟ يبقى هذه هنا Linear first
+
+249
+00:28:10,500 --> 00:28:12,480
+order
+
+250
+00:28:16,380 --> 00:28:22,800
+مشان هيك بدها تروح تجيب عامل التكامل لميو as a
+
+251
+00:28:22,800 --> 00:28:29,140
+function of X يبقى E أس ناقص تكامل واحد على X زائد
+
+252
+00:28:29,140 --> 00:28:39,020
+واحد DX أو إن شئتم فقولوا E أس ناقص Ln X زائد واحد
+
+253
+00:28:39,530 --> 00:28:47,910
+يعني هذه E أس Ln X ناقص واحد أس ناقص واحد يعني X
+
+254
+00:28:47,910 --> 00:28:53,770
+ناقص واحد أس ناقص واحد أو واحد على X ناقص واحد
+
+255
+00:28:53,770 --> 00:28:59,950
+يبقى هذا الآن عامل التكامل يبقى بناء عليه حل
+
+256
+00:28:59,950 --> 00:29:05,270
+المعادلة هذه اللي هي Double Star سموها ليا بنات حل
+
+257
+00:29:05,270 --> 00:29:10,550
+المعادلة Double Star سيكون على الشكل التالي يبقى
+
+258
+00:29:10,550 --> 00:29:28,050
+هنا solution of
+
+259
+00:29:28,050 --> 00:29:39,990
+the differential Equation W star S A
+
+260
+00:29:39,990 --> 00:29:48,490
+لـ Mu هو واحد على X زائد واحد في الـ U بدها تساوي
+
+261
+00:29:48,490 --> 00:29:56,090
+تكامل واحد على X زائد واحد في الـ Q قداش الـ Q هو
+
+262
+00:29:56,090 --> 00:30:05,540
+X زائد واحد كله بالنسبة الى DX طيب هذا بدها تساوي
+
+263
+00:30:05,540 --> 00:30:13,640
+تكامل لـ DX واللي بدها تساوي X زائد كونستان C إذن الـ
+
+264
+00:30:13,640 --> 00:30:23,080
+U يا بناتي تساوي X زائد واحد X زائد كونستان C برجع
+
+265
+00:30:23,080 --> 00:30:29,120
+لمين؟ للـ U الـ U اللي عندي كده؟ لإن الـ Y إذا بدي
+
+266
+00:30:29,120 --> 00:30:35,780
+أشيل الـ U هذه وأكتب بدلها من؟ لإن الـ Y يبقى باجي
+
+267
+00:30:35,780 --> 00:30:43,720
+هنا Ln الـ Y بدها تساوي X زائد واحد في X زائد كونص
+
+268
+00:30:43,720 --> 00:30:49,760
+تن C هذا لا يزال حل ضمني أنا ما جبتش الـ Y جبت له
+
+269
+00:30:49,760 --> 00:30:56,430
+لغارتما الـ Y بقدر أجيب له الـ Y يبقى برفع اثنين كأس
+
+270
+00:30:56,430 --> 00:31:03,450
+للعدد E يبقى بناء عليه هذا بدي يعطيني إنه solution
+
+271
+00:31:03,450 --> 00:31:13,210
+أو بقدر أقول له هنا دوري the solution of the
+
+272
+00:31:13,850 --> 00:31:23,150
+Differential equation أسطار الأصلية is Y تساوي E
+
+273
+00:31:23,150 --> 00:31:31,490
+أس X زائد واحد في X زائد Constant C يعني رفعت
+
+274
+00:31:31,490 --> 00:31:38,870
+الطرفين كأس للعدد D وبالتالي حصلنا على هذا الحل الحد
+
+275
+00:31:38,870 --> 00:31:47,310
+هنا stop في عندنا مجموعة من المسائل Exercises واحد
+
+276
+00:31:47,310 --> 00:31:57,770
+خمسة المسائل التالية واحد اثنين ثلاثة خمسة ستة
+
+277
+00:31:57,770 --> 00:32:12,610
+سبعة عشرة أحد عشر خمسة عشر ستة عشر ثمانية عشر تسعة عشر واحد
+
+278
+00:32:12,610 --> 00:32:18,150
+وعشرين اثنين وعشرين ثلاثة وعشرين
+
+279
+00:32:37,860 --> 00:32:44,940
+طيب، حد بتحب تسأل أي سؤال هنا يا بنات؟ خلاص؟ أيوة
+
+280
+00:32:44,940 --> 00:32:52,420
+لو ايش؟
+
+281
+00:32:52,420 --> 00:32:58,620
+ممنوع تساوي صفر، ممنوع تساوي واحد هذا لمن تبقى جيش
+
+282
+00:32:58,620 --> 00:33:06,180
+لمن تبقى هادى هنا واحد لحالها صح فإن ما صرتش يصير Y
+
+283
+00:33:06,180 --> 00:33:11,560
+في الـ n Y إذا اختلف الشكل العام اللي عندنا مظبوط
+
+284
+00:33:11,560 --> 00:33:16,080
+يبقى من هنا صرتك لو ساوي واحد والله غيره ما عنديش
+
+285
+00:33:16,080 --> 00:33:20,320
+مشكلة في هذه العالم كويس إنه فكرت وقالت أنت قلت
+
+286
+00:33:20,320 --> 00:33:25,340
+كلامه هذا خلفه السؤال هذا خلف المسألة كلها ليش؟
+
+287
+00:33:25,340 --> 00:33:29,060
+إنه صرت المخالف على اليمين وصرت المخالف على الشمال
+
+288
+00:33:29,060 --> 00:33:34,740
+لكن باقية المعادلة هي معادلة Bernoulli طيب حدا فيكم
+
+289
+00:33:34,740 --> 00:33:38,700
+بتسأل أي سؤال بالنسبة لهذا الـ Section اللي هو
+
+290
+00:33:38,700 --> 00:33:43,560
+Linear first order differential equation طيب حدا
+
+291
+00:33:43,560 --> 00:33:48,740
+فيكم بتسأل أي سؤال بالنسبة للخمسة Sections اللي
+
+292
+00:33:48,740 --> 00:33:58,260
+درسناهم أول خمسة Sections من هذا الشبطر اقرأ
+
+293
+00:33:58,260 --> 00:34:05,770
+الامتحان وصل أقل من شهر باقي للامتحان Zero point اه
+
+294
+00:34:05,770 --> 00:34:12,990
+اه هاليومين هينزلولكم موعد لامتحان اه اه هينزل في
+
+295
+00:34:12,990 --> 00:34:18,050
+الجدول رسميا لأن هاي شبه عند الطلاب وشبه عند
+
+296
+00:34:18,050 --> 00:34:22,170
+الطلبات إذا العدد كبير لازم ينزلولكم يهدف الجدول
+
+297
+00:34:22,170 --> 00:34:26,870
+فأنت ما تناميش على روحك مش discussion يبغي إنك تروحي
+
+298
+00:34:26,870 --> 00:34:31,050
+تحلي وتجي تسألي حتى الآن ولا واحدة اجت فيكم
+
+299
+00:34:31,050 --> 00:34:38,010
+تسألي سؤال هذا إما إنكم كلكم علماء وفاهمين تماما
+
+300
+00:34:38,010 --> 00:34:47,150
+لكنني لا أظن ذلك أو إنكم كلكم سهلان وبتبقي بالكم هذا
+
+301
+00:34:47,150 --> 00:34:50,910
+بينعكس سلبا عليك بعد هيك وأنا قلتلك من أول يوم
+
+302
+00:34:50,910 --> 00:34:56,190
+دخلت المحاضرة بتروح تجري المحاضرة تاخديها مباشرة و
+
+303
+00:34:56,190 --> 00:35:00,050
+تحلي الأسئلة اللي عليها واللي بيصبح إنه موجودين و
+
+304
+00:35:00,050 --> 00:35:07,670
+أعطيتك ساعات مكتبية يبقى بعد ذنبك على جنبك لذنب
+
+305
+00:35:07,670 --> 00:35:13,970
+لخير لازلنا في نفس الـ Chapter لكن في مسائل اللي
+
+306
+00:35:13,970 --> 00:35:19,950
+عندي Second order differential equation بدي أنزلها
+
+307
+00:35:19,950 --> 00:35:24,290
+إلى First order differential equation ويمكن تطلع
+
+308
+00:35:24,290 --> 00:35:29,610
+Separable ويمكن تطلع Homogeneous ويمكن تطلع Exact
+
+309
+00:35:29,610 --> 00:35:34,270
+ويمكن تطلع Linear ويمكن تطلع Bernoulli ونحولها إلى
+
+310
+00:35:34,270 --> 00:35:39,750
+Linear يبقى كل الاحتمالات واردة هذا الكلام اللي هو
+
+311
+00:35:39,750 --> 00:35:45,110
+Section واحد أحد عشر يبقى من واحد خمسة بدنا نقفز لمين
+
+312
+00:35:45,110 --> 00:35:50,410
+إلى واحد أحد عشر يبقى نتوجه الآن إلى Section واحد
+
+313
+00:35:50,410 --> 00:36:00,110
+أحد عشر مباشرة إذا Section واحد أحد عشر بيقول two
+
+314
+00:36:00,110 --> 00:36:06,390
+special two special types
+
+315
+00:36:09,820 --> 00:36:15,680
+of Second order
+
+316
+00:36:15,680 --> 00:36:19,000
+differential
+
+317
+00:36:19,000 --> 00:36:22,560
+equations
+
+318
+00:36:22,560 --> 00:36:25,620
+شكلنا
+
+319
+00:36:25,620 --> 00:36:31,980
+نعطيها Definition a
+
+320
+00:36:31,980 --> 00:36:35,920
+Second order
+
+321
+00:36:39,130 --> 00:36:51,250
+Differential equation is an equation in فورا في
+
+322
+00:36:51,250 --> 00:37:05,570
+الشكل التالي F of F T و X و DX على DT و D² X على
+
+323
+00:37:05,570 --> 00:37:16,620
+DT² بدها تساوي من؟ بدها تساوي صفر نرجع مرة ثانية أنا
+
+324
+00:37:16,620 --> 00:37:20,560
+عندي معادلة من الرتبة الثانية وبتنزل رتبتها إلى
+
+325
+00:37:20,560 --> 00:37:26,360
+الرتبة الأولى ومن ثم أروح أحل هذه المعادلة فجال لي
+
+326
+00:37:26,360 --> 00:37:31,260
+two special types نوعين من الأنواع الخاصة لـ Second
+
+327
+00:37:31,260 --> 00:37:34,420
+order differential equation يعني Second order
+
+328
+00:37:34,420 --> 00:37:41,140
+كثيرة جدا أنا بدي آخد بس نوعين والباقي بنخليه فيما
+
+329
+00:37:41,140 --> 00:37:44,950
+بعد بقول الـ Second order differential equation هي
+
+330
+00:37:44,950 --> 00:37:50,250
+عبارة عن معادلة في الشكل التالي هي Function تحتوي
+
+331
+00:37:50,250 --> 00:37:55,450
+على المتغير T والمتغير X ومشتقة X بالنسبة إلى T
+
+332
+00:37:55,450 --> 00:38:01,890
+والمشتقة الثانية X بالنسبة إلى T وكل هذا بدها تساوي
+
+333
+00:38:01,890 --> 00:38:06,860
+مين؟ بدها تساوي صفر يعني أنا عندي دالة هذه الدالة
+
+334
+00:38:06,860 --> 00:38:12,100
+تحتوي على المتغير المستقل X الـ independent
+
+335
+00:38:12,100 --> 00:38:16,260
+variable والمتغير التابع اللي هو dependent
+
+336
+00:38:16,260 --> 00:38:22,020
+variable X ومشتقة الـ X بالنسبة إلى T والمشتقة
+
+337
+00:38:22,020 --> 00:38:26,080
+الثانية بالنسبة إلى X بالنسبة إلى T كون المشتقة
+
+338
+00:38:26,080 --> 00:38:31,540
+الثانية موجودة يبقى من هنا سميناها Second order
+
+339
+00:38:31,540 --> 00:38:35,660
+differential equation لسه ما اتكلمناش في الـ two
+
+340
+00:38:35,660 --> 00:38:41,480
+types لسه احنا أعطينا صورة عامة لـ Second order
+
+341
+00:38:41,480 --> 00:38:45,820
+differential equation بدها تيجي لأول نوع من هذه
+
+342
+00:38:45,820 --> 00:38:52,090
+الأنواع اللي بنسميها equations with X missing يعني
+
+343
+00:38:52,090 --> 00:38:57,490
+معادلة المتغيرة التي تبقى الـ Y مش موجود مفقود من
+
+344
+00:38:57,490 --> 00:39:02,790
+المعادلة كيف بدنا نحل هذا النوع من المعادلات you
+
+345
+00:39:02,790 --> 00:39:07,810
+can بالدرجة لأول نوع من هذه المعادلات اللي هو
+
+346
+00:39:07,810 --> 00:39:15,210
+differential equations المعادلات التفاضلية with
+
+347
+00:39:15,210 --> 00:39:19,330
+the dependent
+
+348
+00:39:22,130 --> 00:39:28,090
+with a dependent variable X
+
+349
+00:39:28,090 --> 00:39:36,950
+missing يبقى الـ X مفقودة It is an equation in
+
+350
+00:39:36,950 --> 00:39:45,630
+the form يبقى It is an equation in the form هي
+
+351
+00:39:45,630 --> 00:39:54,790
+عبارة عن معادلة على الشكل التالي G و T و DX على DT
+
+352
+00:39:54,790 --> 00:40:02,910
+و D² X على DT² كله بدها تساوي صفر وبدها تسمي هذه
+
+353
+00:40:02,910 --> 00:40:05,090
+المعادلة رقم واحد
+
+354
+00:40:07,670 --> 00:40:12,010
+يبقى المعادلة اللي فوق يا بنات هي نفس المعادلة
+
+355
+00:40:12,010 --> 00:40:17,450
+التحت بس الـ X هذا ماله؟ لا يظهر في المعادلة بتظهر
+
+356
+00:40:17,450 --> 00:40:23,410
+مين؟ بس مشتقته الأولى والثانية لكن هو بسلامته بظهر
+
+357
+00:40:23,410 --> 00:40:26,750
+ليش يعني؟ مش موجود حد ما يشوف المعادلة بيقول ما فيش
+
+358
+00:40:26,750 --> 00:40:32,940
+فيها X كيف بدي أحل هذه المعادلة؟ يبقى باجي بقوله to
+
+359
+00:40:32,940 --> 00:40:41,620
+solve the differential equation one شو بدي أعمل
+
+360
+00:40:41,620 --> 00:40:53,330
+put حط لي V تساوي DX على DT تمام يبقى هذا يعطينا إنه
+
+361
+00:40:53,330 --> 00:41:05,710
+الـ DV على DT هو D² X على DT² يبقى هنا سة equation
+
+362
+00:41:05,710 --> 00:41:17,510
+one becomes تصبح على الشكل التالي G of T موجودة و V
+
+363
+00:41:17,510 --> 00:41:25,230
+موجودة و DV على DT يبدو يساوي 0 ايش رأيك في هذه
+
+364
+00:41:25,230 --> 00:41:34,210
+Second ولا First First order يبقى هذه First order
+
+365
+00:41:34,210 --> 00:41:47,670
+differential equation that can be solved as before
+
+366
+00:41:47,670 --> 00:41:53,730
+يبقى بروح أحلها زي ما كنا نحل من قبل اللي هو الـ
+
+367
+00:41:53,730 --> 00:41:56,570
+First order ده الحلقة اللي يمكن تطلع Exactly يمكن
+
+368
+00:41:56,570 --> 00:42:00,950
+Linear يمكن Homogeneous يمكن Separable كل الأمور
+
+369
+00:42:00,950 --> 00:42:05,490
+اللي مرت علينا بصير واردة عندنا يبقى هذه اللي هي
+
+370
+00:42:05,490 --> 00:42:12,450
+النقطة الأولى بنجي للنقطة الثانية يبقى نمر اثنين
+
+371
+00:42:12,870 --> 00:42:18,710
+بدنا نيجي إلى differential equations with the
+
+372
+00:42:18,710 --> 00:42:26,370
+independent variable with the independent
+
+373
+00:42:26,370 --> 00:42:29,830
+variable
+
+374
+00:42:29,830 --> 00:42:37,310
+T
+
+375
+00:42:37,310 --> 00:42:37,830
+missing
+
+376
+00:42:41,050 --> 00:42:48,990
+يبقى الـ T قد تكون مفقودة يبقى في هذه الحالة تصبح
+
+377
+00:42:48,990 --> 00:
+
+401
+00:46:15,010 --> 00:46:19,170
+تول exact أو تول separable يبقى أي واحدة فيهم 
+
+402
+00:46:19,170 --> 00:46:23,010
+بيكون اتعلمنا الحل في الخمسة sections الماضية
+
+403
+00:46:23,010 --> 00:46:27,330
+بنروح نحلها كما كنا بنحل في الخمسة sections 
+
+404
+00:46:27,330 --> 00:46:34,180
+الماضية. بقيت الآن مجموعة من الأمثلة على هذا 
+
+405
+00:46:34,180 --> 00:46:38,880
+section للمرة القادمة إن شاء الله تبارك وتعالى 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/JYkoCgwSRmw_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/JYkoCgwSRmw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a60f6bcb36f55dd5422492573cccb66b512e17ef
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/JYkoCgwSRmw_postprocess.srt
@@ -0,0 +1,1672 @@
+1
+00:00:19,510 --> 00:00:24,150
+بسم الله الرحمن الرحيم بنتابع الحديث في الموضوع
+
+2
+00:00:24,150 --> 00:00:27,510
+اللي ابتدينا ابوه وهو إيجاد معكوس المصفوفة
+
+3
+00:00:27,510 --> 00:00:31,310
+بطريقتين شرحنا الطريقة الأولى والآن بدنا نروح
+
+4
+00:00:31,310 --> 00:00:35,730
+لطريقة الثانية الطريقة الثانية قولنا تتكون من ثلاث
+
+5
+00:00:35,730 --> 00:00:40,370
+نقاط النقطة الأولى بده اشيل كل عنصر في المصفوفة A
+
+6
+00:00:40,370 --> 00:00:45,530
+I J وحط بدل ال cofactor المناظر له
+
+7
+00:00:49,180 --> 00:00:55,200
+الخطوة الثانية بده يجيب مدور هذه المصفوفة الناتجة
+
+8
+00:00:55,200 --> 00:01:02,080
+الخطوة التالتة بده يجيب محدد المصفوفة الأصلية
+
+9
+00:01:02,080 --> 00:01:07,060
+ويقول معكوس المصفوفة يساوي واحد على محدد المصفوفة
+
+10
+00:01:07,060 --> 00:01:11,940
+في ال Transpose اللي جيبناه في الخطوة الثانيةبيها
+
+11
+00:01:11,940 --> 00:01:17,160
+هذا بيكون جيبنا ميه؟ جيبنا معكوس المصفوفة، واضح
+
+12
+00:01:17,160 --> 00:01:19,920
+كلامي؟ يبقى هاي الخطوات التلاتة اللي كتبتيها في
+
+13
+00:01:19,920 --> 00:01:24,500
+المحاضرة السابقة قبل ساعة وشوية، تمام؟ لما بدنا
+
+14
+00:01:24,500 --> 00:01:27,500
+نطبقها عمليا، المصفوفة اللي قدامنا هادي يا بنات
+
+15
+00:01:27,500 --> 00:01:32,970
+أوجدنا المعكوس سبعها بالطريقة الأولىاللي هي طريقة
+
+16
+00:01:32,970 --> 00:01:37,610
+انه المصوفة الموسعة و احولها الى مصوفة واحدة الطرف
+
+17
+00:01:37,610 --> 00:01:40,450
+اليمين والطرف الشمال والطرف اليمين بيكون هي
+
+18
+00:01:40,450 --> 00:01:45,190
+المعكوزة الان هحل نفس السؤال لكن بمهم بالطريقة
+
+19
+00:01:45,190 --> 00:01:48,830
+الجديدة و نثبت ان إيجابتين الإتنين ما لهم نفس
+
+20
+00:01:48,830 --> 00:01:54,500
+الشيءإذا أنا بداجي للحل بداجي للمصفوفة اللي عندى
+
+21
+00:01:54,500 --> 00:02:01,380
+يبقى في هذه المصفوفة بدى أروح أشيل كل عنصر من
+
+22
+00:02:01,380 --> 00:02:06,340
+عناصر المصفوفة و أكتب بداله مين و أكتب بداله ال
+
+23
+00:02:06,340 --> 00:02:11,060
+cofactor تبعه أو العامل المرافق لهم يبقى لو جيت
+
+24
+00:02:11,060 --> 00:02:16,300
+للمصفوفة الأولى بداجي أقول هذه المصفوفة الأولى بدى
+
+25
+00:02:16,300 --> 00:02:20,770
+أشيل الواحد يا منامحسب قاعدة الإشارات شرطه بالموجة
+
+26
+00:02:20,770 --> 00:02:25,370
+يبقى اشطب صفه و عموده يبقى تمانية ناقص اتنين يبقى
+
+27
+00:02:25,370 --> 00:02:31,770
+كم؟ تمانية يبقى عنصر تلاتة حسب قاعدة الإشارات
+
+28
+00:02:31,770 --> 00:02:37,530
+الشرط هي سالبة يبقى هذه السالبة يبقى اشطب صفه و
+
+29
+00:02:37,530 --> 00:02:44,130
+عموده صفه و عموده يبقى Zero زائد اتنين يبقى ناقص
+
+30
+00:02:44,130 --> 00:02:49,710
+اتنينبالدالي للعنصر التالت سالب واحد قشط بصفه و
+
+31
+00:02:49,710 --> 00:02:56,450
+عموده بيظل zero زائد واحد يبقى بواحد حسب قاعدة
+
+32
+00:02:56,450 --> 00:02:57,570
+الإشارات
+
+33
+00:03:00,950 --> 00:03:05,930
+بتجي للصف الثاني الصف الثاني بتجي لزيرو حسب قاعدة
+
+34
+00:03:05,930 --> 00:03:10,910
+الإشارات شرط مالها سالبة يبقى بدنا نشطب صفه و
+
+35
+00:03:10,910 --> 00:03:16,450
+عموده تلاتة في تمانية باربع و عشرين ناقص زيرو يبقى
+
+36
+00:03:16,450 --> 00:03:22,090
+باربع و عشرينالعنصر اللي بعده حسب قاعة الإشارات
+
+37
+00:03:22,090 --> 00:03:27,870
+شرطه موجبه يبقى بالنشط بصفه عمودي يبقى تمانية ناقص
+
+38
+00:03:27,870 --> 00:03:32,710
+واحد اللي هو بيطلع بقداش بسبعة حسب قاعة الإشارات
+
+39
+00:03:32,710 --> 00:03:36,990
+اللي بعده اللي شرطه السالب يبقى بالروح نشط بصفه
+
+40
+00:03:36,990 --> 00:03:43,750
+وعموده يبقى zero زائد تلاتة يبقى بصير ناقص تلاتة
+
+41
+00:03:44,270 --> 00:03:48,630
+بالدالي للصف التالت حسب قاعد الإشارات شرطه بالموجة
+
+42
+00:03:48,630 --> 00:03:54,950
+يبقى بالداشطه بصفه عموده ستة زائد واحد واللي هي
+
+43
+00:03:54,950 --> 00:03:59,890
+جداش سبعة بالدالي للعنصر بعده حسب قاعد الإشارات
+
+44
+00:03:59,890 --> 00:04:06,490
+شرطه السالبنشطه بصفه وعموده يبقى اتنين واللي بعده
+
+45
+00:04:06,490 --> 00:04:10,890
+zero يبقى ماعنديش الا اتنين نيجي العنصر التالت حسب
+
+46
+00:04:10,890 --> 00:04:14,950
+قرص الشرط شرطه موجهه من نشطه بصفه وعموده يبقى واحد
+
+47
+00:04:14,950 --> 00:04:19,110
+ناقص تلاتة اللي يبقى داشت بواحد بالشكل اللي عندنا
+
+48
+00:04:19,110 --> 00:04:26,170
+هذا يبقى هذه الخطوة الأولى الخطوة الثانية بدي أجيب
+
+49
+00:04:26,170 --> 00:04:28,030
+له المصوف بيه
+
+50
+00:04:40,960 --> 00:04:45,680
+بببببببببببببببيبقى بدي أجيب لـ Transpose بالنسبة
+
+51
+00:04:45,680 --> 00:04:50,300
+إليها يبقى هذا الكلام بدي يساوي المصوفة على الشكل
+
+52
+00:04:50,300 --> 00:04:55,340
+التالي الصف الأول بدي يصير العمود الأول الصف
+
+53
+00:04:55,340 --> 00:05:02,040
+الثاني بدي يصير العمود الثاني الصف التالت بدي يصير
+
+54
+00:05:02,040 --> 00:05:07,220
+العمود التالت نقص اتنين واحد بالشكل اللي عندنا هنا
+
+55
+00:05:07,880 --> 00:05:12,380
+يبقى هذه المصوفة بيحصلنا عليها من خطواتين الخطوة
+
+56
+00:05:12,380 --> 00:05:16,920
+الأولى استبدلنا كل عنصر بالـ cofactor تبعه خطوة
+
+57
+00:05:16,920 --> 00:05:21,220
+ثانية جيبنا ل Transpose ل المصوفة الناتجة بقيت
+
+58
+00:05:21,220 --> 00:05:26,640
+علينا الخطوةمش هجيب الخطوة الأخيرة بلزمني محدد
+
+59
+00:05:26,640 --> 00:05:31,920
+المصوفة إيه، إذا بروح بقوله بدي أجيبله determinant
+
+60
+00:05:31,920 --> 00:05:36,740
+للمصوفة إيه، يبقى هذه الخطوة الأولى و هذه الخطوة
+
+61
+00:05:36,740 --> 00:05:40,740
+التانية يا بناتبتجي للخطوة التالتة determinant
+
+62
+00:05:40,740 --> 00:05:49,560
+لإيه؟ بتسوي المحدد بتجي لإيه الأصلية؟ 1 3-1 0 1 2
+
+63
+00:05:49,560 --> 00:05:58,260
+-1 0 8 بالشكل اللي عندنابدا فك المصوفة باستخدام
+
+64
+00:05:58,260 --> 00:06:04,320
+عناصر العمود الأول مثلا يبقى هذا الكلام واحد فيه
+
+65
+00:06:04,320 --> 00:06:10,140
+نشطب صفه عموده يبقى تمانية ناقص Zero اللي بعده
+
+66
+00:06:10,140 --> 00:06:16,520
+ناقص Zero زائد ناقص واحد فيهأشط بيصفوا عمود بيصير
+
+67
+00:06:16,520 --> 00:06:24,800
+ستة زائد واحد يبقى ستة زائد واحد الشكل عن هنا يبقى
+
+68
+00:06:24,800 --> 00:06:30,760
+هنا تمانية و هنا نقص سبعة يبقى الجواب كدهش؟واحد
+
+69
+00:06:30,760 --> 00:06:37,140
+صحيح يبقى الـ A inverse يبقى واحد على ال
+
+70
+00:06:37,140 --> 00:06:43,760
+determinant للـ A في المصوفة B يبقى واحد على واحد
+
+71
+00:06:43,760 --> 00:06:48,840
+في المصوفة B اللي طلعت اللي هي تمانية سالب اربعة
+
+72
+00:06:48,840 --> 00:06:57,020
+وعشرين سبعة ناقص اتنين سبعة ناقص اتنين واحد ناقص
+
+73
+00:06:57,020 --> 00:07:04,230
+تلاتة واحد بالشكل اللي عندناطبعا هذه هي نفسها
+
+74
+00:07:04,230 --> 00:07:12,210
+الهمين تمانية سالب اربعة وعشرين سابعة سالب اتنين
+
+75
+00:07:12,210 --> 00:07:19,210
+سابعة سالب اتنين واحد لبتلاتة واحدةالطلاعيل في
+
+76
+00:07:19,210 --> 00:07:22,170
+النتيجة هذه والنتيجة اللى أوجدناها في المحاضرة
+
+77
+00:07:22,170 --> 00:07:26,210
+السابقة الاتنين are the same يبقى نفس النتيجة
+
+78
+00:07:26,210 --> 00:07:30,970
+بالحرف الوعيد إذا سواء استخدمت الطريقة الأولى في
+
+79
+00:07:30,970 --> 00:07:34,870
+إيجاد معكوس المصوفة أو استخدمت الطريقة الثانية في
+
+80
+00:07:34,870 --> 00:07:41,840
+إيجاد معكوس المصوفة الاتنين are the same تمام؟طيب
+
+81
+00:07:41,840 --> 00:07:47,940
+بدنا نيجي الآن بعد ما انتهينا من ذلك نعطيكي كمان
+
+82
+00:07:47,940 --> 00:07:56,920
+مثال المثال بيقول ما يأتي example find
+
+83
+00:07:56,920 --> 00:08:09,550
+the inverse ofالـ A تساوي اللي هو مين الـ A تساوي
+
+84
+00:08:09,550 --> 00:08:14,810
+اتنين تلاتة واحد اربعة بالشكل اللي عندنا هذا
+
+85
+00:08:14,810 --> 00:08:18,210
+solution
+
+86
+00:08:18,210 --> 00:08:31,970
+طلبتي
+
+87
+00:08:31,970 --> 00:08:42,480
+ايش؟هادي واحد على ال determinant في ال B واحدة
+
+88
+00:08:42,480 --> 00:08:45,860
+واحدة بس ناس ماعيش بتقول تاني عيدي تاني هيقولنا
+
+89
+00:08:45,860 --> 00:08:49,920
+واحد على ال determinant في بي بي اللي هي هادي لإن
+
+90
+00:08:49,920 --> 00:08:54,580
+كاتب عليها Transpose لسه بدي أحولي فبكتب هادي
+
+91
+00:08:54,580 --> 00:09:02,110
+تمام؟طيب نجي يالا كل واحد يتعلمك بالاسمة وإياك
+
+92
+00:09:02,110 --> 00:09:05,650
+واحدة تعلم قدام اسمة واحدة تانية دي يا ربالكم، فضل
+
+93
+00:09:05,650 --> 00:09:08,290
+يالا، تعلم اسمك باسم المحاضرة هادي
+
+94
+00:09:12,560 --> 00:09:16,100
+طيب، بدنا نيجي للمصوفة اللي قدامنا يا بنات، هذه
+
+95
+00:09:16,100 --> 00:09:22,160
+المصوفة 2×2 وليست 3×3 كما كانت المصوفة قبل قليل،
+
+96
+00:09:22,160 --> 00:09:26,580
+تمام؟ لكن أنا بدي أحاول أحل بنفس الطريقة اللي
+
+97
+00:09:26,580 --> 00:09:31,700
+اتبعت هنا قبل قليل، فباجي أول خطة، بدي أجيب الـ
+
+98
+00:09:31,700 --> 00:09:33,020
+Determinant
+
+99
+00:09:34,840 --> 00:09:40,620
+يبقى المحدد اتنين تلاتة واحد اربعة تمانية ناقص
+
+100
+00:09:40,620 --> 00:09:46,980
+تلاتة ويساوي كم؟ خمسة يبقى هذا قيمة المحدد يساوي
+
+101
+00:09:46,980 --> 00:09:53,520
+خمسة بعد هيك بدي اجي لالمصوف اللي عندي واستبدل كل
+
+102
+00:09:53,520 --> 00:10:01,000
+عنصر بال cofactor المناظر لهيبقى باجي بقوله الان
+
+103
+00:10:01,000 --> 00:10:04,420
+بدي اجيل المصعوفة اللي عندنا هذه و بدي اجيب ال
+
+104
+00:10:04,420 --> 00:10:10,460
+cofactor يبقى بدي اشيل اتنين و اشطب صف و عمود و
+
+105
+00:10:10,460 --> 00:10:15,580
+بضل قداش عندنا اربعة بس يبقى جاهز بحط اربعة زي مين
+
+106
+00:10:15,580 --> 00:10:20,000
+و حسب قاعدة الإشارات العنصر هذا إشارته بالمين
+
+107
+00:10:20,000 --> 00:10:24,560
+بالموجةالان بدى اروح للعنصر بعده اللى هو التلاتة
+
+108
+00:10:24,560 --> 00:10:29,440
+يبقى بدي اشطب صفه و عموده بضال قداش واحد بس حسب
+
+109
+00:10:29,440 --> 00:10:38,060
+قاعدة الإشارات الإشارة مالها بالثاني بدي اشطب صفه
+
+110
+00:10:38,060 --> 00:10:42,900
+و عموده بضال قداش تلاتة بس حسب قاعدة الإشارات
+
+111
+00:10:42,900 --> 00:10:50,060
+الإشارةبالسالب تمام بالداجل العنصر أربعة رشد بصفه
+
+112
+00:10:50,060 --> 00:10:57,320
+و عموده بضاله كده اتنين و حسب قاعدة الإشاراتموجة
+
+113
+00:10:57,320 --> 00:11:03,560
+تمام طيب انا بدي اشهد بدي لترانسبوز تبعها يبقى
+
+114
+00:11:03,560 --> 00:11:10,220
+بكتب عليها ترانسبوز و بروح بسميها المصوفة بي تمام
+
+115
+00:11:10,220 --> 00:11:18,020
+مين لترانسبوز تبعها يساوي اللي هو الصف الأول بده
+
+116
+00:11:18,020 --> 00:11:23,020
+يصير العمود الأول الصف الثاني بده يصير العمود
+
+117
+00:11:23,020 --> 00:11:28,220
+الثاني بالشكل اللي عندنا هذابعد ذلك بدي أروح أجيب
+
+118
+00:11:28,220 --> 00:11:35,360
+معكوس المصفوفة A من الصيغة 1 على محدد ال A في
+
+119
+00:11:35,360 --> 00:11:50,140
+المصفوفة B يبقى 1 على 5 في المصفوفة B 4-3-1 2 يا
+
+120
+00:11:50,140 --> 00:11:55,400
+بتخليها زي ما هييا إما بتدخليها عليها وتقوليلي هذه
+
+121
+00:11:55,400 --> 00:12:02,400
+أربع أخماس ناقص ثلاث أخماس وهنا ناقص خمس وهنا
+
+122
+00:12:02,400 --> 00:12:08,820
+خمسين بالشكل اللي عندنا هذا طيب
+
+123
+00:12:10,080 --> 00:12:14,680
+بصوا صبر شوية لسه مخلصتش يعني احنا هيك جيبنا
+
+124
+00:12:14,680 --> 00:12:19,800
+المعكوس تماما مائة بالمائة بدون اي مشاكل السؤال
+
+125
+00:12:19,800 --> 00:12:25,900
+اللي بده اطرحه طب خليني ندقيق النظر في المصفوفة B
+
+126
+00:12:25,900 --> 00:12:31,960
+هذه و نشوف نقارنها بالمصفوفة الأصلية لو جيتلى
+
+127
+00:12:31,960 --> 00:12:37,590
+المصفوفة الأصلية بلاحظبدلت عناصر القطر الرئيسي
+
+128
+00:12:37,590 --> 00:12:43,550
+مكان بعض وغيرت إشارات عناصر القطري الثانوي، مظبوط
+
+129
+00:12:43,550 --> 00:12:48,730
+ولا لأ؟ إذا من الآن فساعدا يا بنات، إذا بدي أجيب
+
+130
+00:12:48,730 --> 00:12:53,910
+المصفوف بيهاديلا داعي أن أذهب و أبدأ أحسب من أول و
+
+131
+00:12:53,910 --> 00:12:58,050
+جديد يبقى بس بدلي عناصر القطر الرئيسي مكان بعض
+
+132
+00:12:58,050 --> 00:13:01,990
+مليون متشين عناصر القطر الثانوي خليهم زي ما هم
+
+133
+00:13:01,990 --> 00:13:05,790
+بسحطنهم شهر السالم بكون جيبتي المصوفة بياش ضايل
+
+134
+00:13:05,790 --> 00:13:10,490
+عليه ضايل عليه أجيب جدش محدد المصوفة ايه و أضرب
+
+135
+00:13:10,490 --> 00:13:13,630
+واحد على قيمة المحدد في هذه المصوفة بكون جيبتي
+
+136
+00:13:13,630 --> 00:13:19,870
+المعكوس بس هذه للمصوفة اللي نضامها اتنين في اتنين
+
+137
+00:13:20,110 --> 00:13:26,330
+واللي ال inverse تبعها exist مش لاي مصبوفة يبقى
+
+138
+00:13:26,330 --> 00:13:32,270
+شرطين المعكوس هذا ماله موجود اتنين ويكون نظامها
+
+139
+00:13:32,270 --> 00:13:38,990
+اتنين في اتنين ماشي في اي تساؤل؟ خلاصنا عظمنا
+
+140
+00:13:38,990 --> 00:13:47,050
+جابنا تساؤلك؟كما أنت سؤالة اتفضلي اذا
+
+141
+00:13:47,050 --> 00:13:50,910
+ال determinant سالب و الله موجب و الله كسر ايش ما
+
+142
+00:13:50,910 --> 00:13:54,750
+يكون يكون لا دخلة له في الموضوع واحد على المحدد
+
+143
+00:13:54,750 --> 00:14:00,330
+ماجي و اللي جوا جوا المصوفة زي ما هي لحد هيك يكون
+
+144
+00:14:00,330 --> 00:14:06,230
+انتهى هذا ال section و لا يكون ارقام المسائلاللي
+
+145
+00:14:06,230 --> 00:14:13,810
+هي exercises اللي هو اتنين اتناشر المسائل التالية
+
+146
+00:14:13,810 --> 00:14:22,110
+اللي هي واحد و تلاتة و خمسة و سبعة و من عشرة لغاية
+
+147
+00:14:22,110 --> 00:14:29,650
+خمستاشر و بنروح ال additional exercises additional
+
+148
+00:14:29,650 --> 00:14:37,490
+exercises و بدنا المسائل من واحد لغاية تمانىلكن في
+
+149
+00:14:37,490 --> 00:14:41,870
+المقابل في بعض الأسئلة النظرية في الـ Additional
+
+150
+00:14:41,870 --> 00:14:49,670
+Exercises بدي أروح أحل هذه الأسئلة حالها كالتالي
+
+151
+00:15:05,220 --> 00:15:11,500
+مين اللي بتسأل السؤال؟ كيف؟ وين مابدك؟ لو كان ال
+
+152
+00:15:11,500 --> 00:15:14,120
+system معين، عدد ال unknowns فيه بيساوي عدد
+
+153
+00:15:14,120 --> 00:15:18,040
+المعادلات، بقدر أقول مية بالمية إنه خلّاها؟ لأ
+
+154
+00:15:18,040 --> 00:15:21,180
+طيب،
+
+155
+00:15:21,180 --> 00:15:23,840
+على أي حال، بدنا نيجي ل exercises
+
+156
+00:15:30,340 --> 00:15:41,080
+اتنين اتناشر page صفحة مية وخمسة واربعين لغاية مية
+
+157
+00:15:41,080 --> 00:15:49,940
+وستة واربعين السؤال اتناشر بيقول ما يأتي if ال a
+
+158
+00:15:49,940 --> 00:15:54,500
+is non singular
+
+159
+00:15:56,270 --> 00:16:08,370
+non-singular matrix show that بيّن إن الـ A
+
+160
+00:16:08,370 --> 00:16:09,470
+transpose
+
+161
+00:16:15,830 --> 00:16:25,890
+الكل inverse يساوي a inverse transpose بالشكل
+
+162
+00:16:25,890 --> 00:16:30,670
+اللي عندنا هنا solution
+
+163
+00:16:39,690 --> 00:16:45,290
+الان بدي أحلك مجموعة من الأسئلة عن نظرية على هذا
+
+164
+00:16:45,290 --> 00:16:49,510
+ال section الأسئلة
+
+165
+00:16:49,510 --> 00:17:03,870
+هذه موجودة كلها في الكتابهو نفسه
+
+166
+00:17:03,870 --> 00:17:09,850
+بالضبط تماما كما لو جبت المعكوس أولا ثم جبت المدور
+
+167
+00:17:09,850 --> 00:17:15,730
+من المصوفة الناتجة يبقى A inverse transpose هو A
+
+168
+00:17:15,730 --> 00:17:21,170
+transpose inverse تمام؟ بنقوله بسيطة احنا عندنا ال
+
+169
+00:17:21,170 --> 00:17:29,310
+Ais non-singular يبقى هذا أيش معناه يا بنات؟ ان ال
+
+170
+00:17:29,310 --> 00:17:35,390
+a inverse existأو الـ determinant للـ A اللي لا
+
+171
+00:17:35,390 --> 00:17:40,790
+يساوي 0 يقبل A inverse exist مدام A inverse exist
+
+172
+00:17:40,790 --> 00:17:48,330
+هذا معناه ايش ان ال A في ال A inverse بده يساوي ال
+
+173
+00:17:48,330 --> 00:17:54,770
+identity matrix and ال A inverse في ال A كمان بده
+
+174
+00:17:54,770 --> 00:18:00,210
+يساوي ال identity matrix مظبوط؟طب احنا موضوعنا
+
+175
+00:18:00,210 --> 00:18:05,790
+موضوعش اللي مطلوب الـ Transpose إذا بدي أروح أدخل
+
+176
+00:18:05,790 --> 00:18:08,230
+ال Transpose في الموضوع معناه أنني بدي أخد ال
+
+177
+00:18:08,230 --> 00:18:13,970
+Transpose للطرفين يقول لو أخدت ال Transpose عندنا
+
+178
+00:18:13,970 --> 00:18:19,190
+هنا إيش بصير؟هذا بدّي يعطيكي أن الـ A في الـ A
+
+179
+00:18:19,190 --> 00:18:25,330
+inverse transpose بده يساوي الآية transpose and
+
+180
+00:18:25,330 --> 00:18:31,110
+الـ A inverse A transpose بده يساوي الآية
+
+181
+00:18:31,110 --> 00:18:38,350
+transposeطيب هذا معناهم أظن أخدنا لو كان عندي حاصل
+
+182
+00:18:38,350 --> 00:18:43,190
+ضرب A في B Transpose بيصير B Transpose A Transpose
+
+183
+00:18:43,190 --> 00:18:47,910
+نجلبها يبقى بناء عليه بدهاجي هادي و أجلبهاش بيصير
+
+184
+00:18:47,910 --> 00:18:55,070
+عندنا A Inverse Transpose في ال A Transpose بده
+
+185
+00:18:55,070 --> 00:18:58,450
+يساوي مصفوفتي اللي واحدة اللي همجيبها ال Transpose
+
+186
+00:18:58,450 --> 00:19:05,130
+ده بقىنفسها تمام يبقى هذا بده يعطينا مصوفة الوحدة
+
+187
+00:19:05,130 --> 00:19:12,930
+and اللي هو ال a transpose a inverse a transpose
+
+188
+00:19:12,930 --> 00:19:22,020
+كله بده يساوي مصوفة الوحدة طيب هذا معناه ايه؟هذه
+
+189
+00:19:22,020 --> 00:19:25,280
+مصفوفة الوحدة وهذه مصفوفة الوحدة المعناهة وحصل ضرب
+
+190
+00:19:25,280 --> 00:19:31,320
+الاتنين هدول are equal يبقى هذا معناه ان ال A
+
+191
+00:19:31,320 --> 00:19:36,780
+inverse transpose في ال A transpose بده يسوى A
+
+192
+00:19:36,780 --> 00:19:41,880
+transpose في ال A inverse transpose بده يسوى مين؟
+
+193
+00:19:41,880 --> 00:19:47,940
+بده يسوى مصفوفة الوحدةما هو معنى هذا الكلام؟ إن
+
+194
+00:19:47,940 --> 00:19:53,740
+هؤلاء المصففين هو معكوسات لبعضهم، صح ولا لأ؟ يبقى
+
+195
+00:19:53,740 --> 00:20:00,960
+هذا معناه إن الـ A inverse A transpose is the
+
+196
+00:20:00,960 --> 00:20:06,060
+inverse of A transpose
+
+197
+00:20:13,080 --> 00:20:19,680
+معكوس المصفوفة ثانية يعني كأن هذه هي a transpose
+
+198
+00:20:19,680 --> 00:20:20,680
+inverse
+
+199
+00:20:22,710 --> 00:20:31,270
+يبقى هذا معناه ان ال a inverse transpose بالضبط ال
+
+200
+00:20:31,270 --> 00:20:36,530
+inverse تبع a transpose يبقى هي a transpose
+
+201
+00:20:36,530 --> 00:20:40,490
+inverse أظن
+
+202
+00:20:40,490 --> 00:20:46,870
+هو المطلوب مش هي اللي بدنا نتبته؟ خلصنا أيضا، صعب؟
+
+203
+00:20:47,520 --> 00:20:52,020
+والهجر أخذنا تاريف non-singular يبقى المعكوس موجود
+
+204
+00:20:52,020 --> 00:20:58,160
+عرفنا المعكوس أخذنا ال Transpose وعملنا المساوية
+
+205
+00:20:58,160 --> 00:21:02,980
+ليس إلا لو طلعت معانا على طول القاطع ماعنداش مشكلة
+
+206
+00:21:02,980 --> 00:21:09,700
+يبقى هذا كان سؤال 12 عندك من الكتاب نجلس سؤال 13
+
+207
+00:21:09,700 --> 00:21:18,770
+اللي ورا مباشرة هذا سؤال 13ثلاثاش بيقول افترض ان
+
+208
+00:21:18,770 --> 00:21:25,550
+ال A and ال B بيكون بيكون بيكون بيكون بيكون بيكون
+
+209
+00:21:25,550 --> 00:21:26,290
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+210
+00:21:26,290 --> 00:21:27,250
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+211
+00:21:27,250 --> 00:21:28,650
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+212
+00:21:28,650 --> 00:21:28,890
+بيكون بيكون بيكون بيكون بيكون بيكون بيكون بيكون
+
+213
+00:21:28,890 --> 00:21:37,850
+بيكون بيكون بيكون بيكون بيكون بيكون بي
+
+214
+00:21:37,990 --> 00:21:44,850
+the same order اتن تان من نفس الرثبه او نفس النظام
+
+215
+00:21:44,850 --> 00:21:54,370
+بيقول ل F إذا كان ال C إذا كان المصوفة C بدها
+
+216
+00:21:54,370 --> 00:22:04,540
+السوى حصل الضرب F بي show thatShow that بيّلي ان
+
+217
+00:22:04,540 --> 00:22:11,920
+الـ C inverse بده يساوي B inverse في ال A inverse
+
+218
+00:22:11,920 --> 00:22:24,480
+نرجع
+
+219
+00:22:24,480 --> 00:22:30,110
+لسؤالنا مرة تانيةالسؤال بيقول لو كان كل من a و b
+
+220
+00:22:30,110 --> 00:22:34,490
+non singular matrices يبقى محدد كل واحدة فيهم ماله
+
+221
+00:22:34,490 --> 00:22:40,950
+لا يساوي zero وتنتهي من نفس الورقة قال لو كان ال c
+
+222
+00:22:40,950 --> 00:22:48,030
+حصل لضرب a في b بدي أثبت أن المعكوس تبع المصوفة c
+
+223
+00:22:48,030 --> 00:22:53,730
+هو ال b inverse في ال a inverse طب هو قال هل ال a
+
+224
+00:22:53,730 --> 00:23:01,550
+b لها معكوسماجاليش انا بدي اثبت ان الها معكوس
+
+225
+00:23:01,550 --> 00:23:05,670
+وبعدين اروح اثبت ان المعكوس هذا بيساوي بعضه صح ولا
+
+226
+00:23:05,670 --> 00:23:12,650
+لا بقوله بسيطة جدا اذا انا بدي اجي لل solution بدي
+
+227
+00:23:12,650 --> 00:23:22,710
+اجي للمعطيات ال a and ال b are non singular هذا
+
+228
+00:23:22,710 --> 00:23:28,580
+ايش معناه يا بناتnon singular هذا معناته أن ال
+
+229
+00:23:28,580 --> 00:23:34,780
+determinant لل A لا يساوي zero and ال determinant
+
+230
+00:23:34,780 --> 00:23:40,640
+لل B لا يساوي zero صح؟
+
+231
+00:23:41,180 --> 00:23:47,260
+طب لو ضربت اتنين في بعض يبقى هذا بده يعطينا ان ال
+
+232
+00:23:47,260 --> 00:23:53,400
+determinant لل A في ال determinant لل B ماله لا
+
+233
+00:23:53,400 --> 00:24:01,170
+يساوي Zero هذا معناه انه حصل الضربهذا الـ
+
+234
+00:24:01,170 --> 00:24:05,170
+determinant للـ A فالـ determinant للـ B اللي بده
+
+235
+00:24:05,170 --> 00:24:10,550
+يساوي الـ determinant للـ A في B لا يساوي Zero
+
+236
+00:24:10,550 --> 00:24:18,090
+تمام؟ هذا معناته إيش؟ معناته إن الـ A في B is non
+
+237
+00:24:18,090 --> 00:24:28,870
+singularهذا معناته أن الـ A B إنفرس exist
+
+238
+00:24:31,040 --> 00:24:37,780
+يبقى المعكوس هذا ماله موجود طيب هو بيقول لو كان ال
+
+239
+00:24:37,780 --> 00:24:43,040
+C يساوي ال A في ال B بدك تثبت لي أن هذا المعكوس
+
+240
+00:24:43,040 --> 00:24:47,820
+يساوي B inverse A inverse يعني كأنه أنا بدأ أثبت
+
+241
+00:24:47,820 --> 00:24:52,640
+أن ال A بي الكل inverse يساوي B inverse يعني كأنه
+
+242
+00:24:52,640 --> 00:24:57,620
+بنغلب و أضعهم زي ال transpose بالظبطمش حصل ضرب a
+
+243
+00:24:57,620 --> 00:25:00,880
+بي لكل transpose بجينا نقول بي transpose في ال a
+
+244
+00:25:00,880 --> 00:25:05,080
+transpose يبقى هنا نفس الجثة كل واحد علمت على اسم
+
+245
+00:25:05,080 --> 00:25:13,600
+هنا بنادر كله تمام طيبنرجع الان نجي نشوف صحة هذا
+
+246
+00:25:13,600 --> 00:25:23,840
+الكلام لو انا جيت اخدت ال a,b في ال a,b او a في ده
+
+247
+00:25:23,840 --> 00:25:30,800
+في اخده في مين في ال b inverse a inverse اللي قايل
+
+248
+00:25:30,800 --> 00:25:38,250
+عليه هذا طيب هذا الكلام بده يساويبدي اجي لخاصية ال
+
+249
+00:25:38,250 --> 00:25:43,110
+associativity على المصففات خاصية الدمج اذا هذه
+
+250
+00:25:43,110 --> 00:25:50,450
+تساوي A في الـ B بي انفرس A انفرس، مظبوط؟ هذه اللي
+
+251
+00:25:50,450 --> 00:25:56,050
+بين قوسين مين هي ال identity matrix يبقى ال A في
+
+252
+00:25:56,050 --> 00:26:00,830
+ال identity matrix في ال A انفرس ال identity
+
+253
+00:26:00,830 --> 00:26:04,990
+matrix لما تضربيها في اي مصففة شو بيطلع؟نفس
+
+254
+00:26:04,990 --> 00:26:08,870
+المصوفة the same matrix يبقى الـA في الـA inverse
+
+255
+00:26:08,870 --> 00:26:16,150
+اللي هي الـmain المصوفة A طيب and لو أخدت الـB
+
+256
+00:26:16,150 --> 00:26:21,770
+inverse A inverse ضربت في الـAB يا مانا شو بدي
+
+257
+00:26:21,770 --> 00:26:26,750
+يعطيني؟ بدي أستخدم خاصية ال associativity يبقى B
+
+258
+00:26:26,750 --> 00:26:36,240
+inverse A inverse ABمعكوس المصوفة في المصوفة الـ
+
+259
+00:26:36,240 --> 00:26:43,480
+Identity Matrix يبقى B inverse IB يعني B inverse B
+
+260
+00:26:43,480 --> 00:26:49,180
+يعني الـ Identity Matrixإذا من الاتنين هدول، إيش
+
+261
+00:26:49,180 --> 00:26:56,520
+بنستنتج يا بنات؟ بنستنتج إن الـAB في الـB inverse
+
+262
+00:26:56,520 --> 00:27:03,020
+A inverse بدو يساوي الـB inverse A inverse في
+
+263
+00:27:03,020 --> 00:27:10,890
+الـAB في الـAB بدو يساوي 100يبقى معناته كل واحدة
+
+264
+00:27:10,890 --> 00:27:17,950
+فيهم معكس للتانية هذا معناه ان ال b inverse a
+
+265
+00:27:17,950 --> 00:27:31,150
+inverse is the inverse of a في b صح ولا لأ but the
+
+266
+00:27:31,150 --> 00:27:35,010
+inverse of
+
+267
+00:27:37,100 --> 00:27:48,620
+A B is denoted by A B الكل انفر
+
+268
+00:27:51,920 --> 00:27:55,860
+و قبل شوية في المحاضرة الصحيفة أثبتنا نظرية أن ال
+
+269
+00:27:55,860 --> 00:28:02,500
+inverse يكون واحدا إذا هذا هو التاني يبقى but the
+
+270
+00:28:02,500 --> 00:28:09,360
+inverse of a b is denoted by كذا and the inverse
+
+271
+00:28:09,360 --> 00:28:12,740
+of
+
+272
+00:28:12,740 --> 00:28:17,180
+a matrix is
+
+273
+00:28:18,080 --> 00:28:23,940
+يكون هناك يكون وحيداً هذا بدي يعطينا ان ال a b
+
+274
+00:28:23,940 --> 00:28:29,720
+الكل inverse بدي يسوى b inverse a inverse
+
+275
+00:28:33,320 --> 00:28:38,080
+هتحين لما تكون هذه الـC بده يساوي الـAB قال لي
+
+276
+00:28:38,080 --> 00:28:42,660
+اثبتلي ان الـC inverse يساوي كذا، مظبوط؟ الحين
+
+277
+00:28:42,660 --> 00:28:47,440
+الـC inverse بده يساوي مين؟ AB inverse يبقى هذا
+
+278
+00:28:47,440 --> 00:28:53,960
+بده يعطينا ان الـC inverse بده يساوي B inverse A
+
+279
+00:28:53,960 --> 00:28:59,350
+inverse عظم ما هو المطلوبإذا من الآن فصاعدا هذا
+
+280
+00:28:59,350 --> 00:29:03,650
+السؤال ليش بيقول ليه؟ بيقول لو عندي حاصل ضرب
+
+281
+00:29:03,650 --> 00:29:09,370
+مفصوفين A وB واختلهم الكل inverse تساوي inverse
+
+282
+00:29:09,370 --> 00:29:13,490
+التانية في inverse الأميرة الأولى بدنا نجلبها زي
+
+283
+00:29:13,490 --> 00:29:16,330
+ال transpose بالضبط تماما
+
+284
+00:29:31,740 --> 00:29:37,780
+هذا كان سؤال 13 من الكتاب نجي لسؤال 14 برضه نظري
+
+285
+00:29:37,780 --> 00:29:50,280
+سؤال 14 بيقول مياتي let ال a be a non singular
+
+286
+00:29:50,280 --> 00:30:00,470
+matrix non singular matrix show thatShow that أن
+
+287
+00:30:00,470 --> 00:30:07,910
+الـ A Inverse Inverse بدي يعطيني الـ A
+
+288
+00:30:19,610 --> 00:30:23,630
+نفس التكتيك اللي اتبع في السؤالين السابقين بمسك
+
+289
+00:30:23,630 --> 00:30:27,590
+المعلومة بحاول أستفيد منها مش بيعطينا المعلومة
+
+290
+00:30:27,590 --> 00:30:31,270
+بلاش بس نتفرج عليها لأ لأ لأ بحاول نستفيد منها إذا
+
+291
+00:30:31,270 --> 00:30:39,890
+احنا بدنا نيجي هنا الان let ال a be a non singular
+
+292
+00:30:39,890 --> 00:30:47,000
+matrix يبقى هذا معناه يا جماعةأن الـ determinant
+
+293
+00:30:47,000 --> 00:30:54,740
+للـ A لا يسوي 0 هذا معناه أن الـ A inverse exists
+
+294
+00:30:54,740 --> 00:31:01,120
+يعني هذا معناه أن الـ A في الـ A inverse سيكون مهم
+
+295
+00:31:01,120 --> 00:31:08,420
+مصفوفة الوحدة تمام؟ حتى لأن كلام اللي بقوله كأنه
+
+296
+00:31:08,420 --> 00:31:12,720
+ليس له علاقة بالمطلوب المطلوب دي أثبت أن معكوس
+
+297
+00:31:12,720 --> 00:31:18,910
+المعكوس يعطينا الأصلصح؟ يعني لو جيبت معكوس مصوفة و
+
+298
+00:31:18,910 --> 00:31:23,030
+روحت جيبت لها كمان معكوس للمعكوس بديه يطلع المصوفة
+
+299
+00:31:23,030 --> 00:31:27,570
+الأصلي، مظبوط؟هو اللي بيقول لي اثبت ان a inverse
+
+300
+00:31:27,570 --> 00:31:32,610
+inverse بدي ساوي من ال a اذا انا مشان اجيب له ال
+
+301
+00:31:32,610 --> 00:31:36,110
+inverse بدي اروح اخد inverse لمين للنتيجة اللي انا
+
+302
+00:31:36,110 --> 00:31:44,390
+توصلت لها تمام فبجي بقول له هذا معناه ان ال a في
+
+303
+00:31:44,390 --> 00:31:50,510
+ال a inverse الكل inverse بدي ساوي ال I inverse
+
+304
+00:31:53,570 --> 00:32:00,070
+سؤال كمان مرة، معكوس مصفوفة الوحدة مين هي؟ نفس
+
+305
+00:32:00,070 --> 00:32:05,870
+الوحدة itself، مظبوط؟ يبقى باجي بقول هنا هذا بده
+
+306
+00:32:05,870 --> 00:32:11,330
+يعطيك بدرجة على الخواص تبعت من؟ تبعت ال inverse
+
+307
+00:32:11,330 --> 00:32:14,970
+اللي أثبتناها هنا، يبقى هذا ال inverse ليش بدنا
+
+308
+00:32:14,970 --> 00:32:19,850
+نسويه؟ بدنا نجلب وضعهايبقى هذا بيعطيك a inverse
+
+309
+00:32:19,850 --> 00:32:25,050
+inverse في ال a inverse بده يسوى ال identity
+
+310
+00:32:25,050 --> 00:32:30,190
+matrix هذا جيبته من وين؟ من السؤال وين؟ من السؤال
+
+311
+00:32:30,190 --> 00:32:40,390
+13 يبقى هذا from exercises 13 طيب كويس ايش رأيك؟
+
+312
+00:32:40,390 --> 00:32:48,290
+انا بدي هذه صح؟طب خليني اضرب من جهة اليمين في
+
+313
+00:32:48,290 --> 00:32:53,850
+المصفوفة A مش انا اخليها دي لوحدها اذا لو جهة ضربت
+
+314
+00:32:53,850 --> 00:33:00,070
+من جهة اليمين في المصفوفة A بصير A inverse inverse
+
+315
+00:33:00,070 --> 00:33:06,290
+A inverse في مين في المصفوفة A بدو سوى ال identity
+
+316
+00:33:06,290 --> 00:33:12,740
+matrix في المصفوفة Aهذا معناه ان ال a inverse
+
+317
+00:33:12,740 --> 00:33:19,740
+inverse هدف هدف من بال identity matrix بده يساوي
+
+318
+00:33:19,740 --> 00:33:25,220
+المصوفة a طيب المصوفة الوحدة لما نضربها في أي
+
+319
+00:33:25,220 --> 00:33:30,800
+مصوفة بتعطيني مين نفس المصوفة يبقى ال a inverse
+
+320
+00:33:30,800 --> 00:33:38,940
+inverse بده يساوي المصوفة a itselfمظبوط هكذا؟ يبقى
+
+321
+00:33:38,940 --> 00:33:44,420
+ماسوّناش اشي خلاصنا يبقى أثبتنا أن معكوس لمعكوس
+
+322
+00:33:44,420 --> 00:33:50,620
+المصفوفة بيعطينا المصفوفة itsel ناخد كمان سؤال
+
+323
+00:33:50,620 --> 00:33:59,640
+السؤال الخامس عشر بيقول لي the matrix the matrix
+
+324
+00:33:59,640 --> 00:34:03,160
+IN
+
+325
+00:34:03,160 --> 00:34:14,280
+لل identity matrix isits is its own inverse يعني
+
+326
+00:34:14,280 --> 00:34:23,060
+هي معكوس لنفسها since ليش؟ لأن ال identity matrix
+
+327
+00:34:23,060 --> 00:34:28,520
+لما نضربها في ال identity matrix بيطلع من عندنا ال
+
+328
+00:34:28,520 --> 00:34:33,660
+identity matrix المطلوب الأول من السؤال find
+
+329
+00:34:35,470 --> 00:34:45,290
+at least على الأقل to second
+
+330
+00:34:45,290 --> 00:34:48,830
+order
+
+331
+00:34:48,830 --> 00:34:57,030
+to second order matrices matrices
+
+332
+00:34:57,030 --> 00:35:04,050
+other than I N
+
+333
+00:35:07,740 --> 00:35:18,800
+that have this property إلا
+
+334
+00:35:18,800 --> 00:35:27,080
+دي الخاصية نمر بيه if ال a بده يساوي ال a inverse
+
+335
+00:35:27,080 --> 00:35:28,800
+show that
+
+336
+00:35:32,000 --> 00:35:39,460
+show that بيّلي أن الـ determinant للإيه بده يساوي
+
+337
+00:35:39,460 --> 00:35:41,860
+زائد أو ناقص واحد
+
+338
+00:36:10,490 --> 00:36:16,950
+نرجع لسؤالنا مرة ثانية السؤال ذو شقين نقرأ السؤال
+
+339
+00:36:16,950 --> 00:36:21,370
+كويس و بعد هي كده تعالي يا بنت، يا بنت تعالي تعالي
+
+340
+00:36:21,370 --> 00:36:27,510
+تعالي بقول طلعت
+
+341
+00:36:27,510 --> 00:36:30,990
+كلمة جوال، مش هيك؟ بتاخدي كتبك وصلي تعودي على
+
+342
+00:36:30,990 --> 00:36:35,750
+المحاضرة أبدا، يا بتقعدي وانسي حكاية الجوال أنا من
+
+343
+00:36:35,750 --> 00:36:37,630
+أول محاضرة قلتك يا جوال يا محاضرة
+
+344
+00:36:48,030 --> 00:36:52,030
+قلتك المحاضرة مثل صلاة الجمعة فاش الإيمان بالمخطب
+
+345
+00:36:52,030 --> 00:36:55,410
+واحد يطلع يرد على الجوال ويعود لخطبة مسخرة هذه مش
+
+346
+00:36:55,410 --> 00:37:00,510
+صلاة واحنا هنا مكان المحاضرة مكان عبادة تماما مثل
+
+347
+00:37:00,510 --> 00:37:07,150
+الصلاة عندي يبقى يا دي دراسة يا إما جوال نرجع
+
+348
+00:37:07,150 --> 00:37:08,190
+لسؤالنا مرة تانية
+
+349
+00:37:13,170 --> 00:37:18,390
+مثوفة الوحدة هي مصوفة معكوس لنفسها
+
+350
+00:37:29,590 --> 00:37:37,050
+هاتلي at least على الأقل مصفوفتين من ال second
+
+351
+00:37:37,050 --> 00:37:42,530
+order يعني النظام هتنين في اتنين من غير ال I انت
+
+352
+00:37:42,530 --> 00:37:45,910
+مش هتروح تقولي المصفوف I too صفين و عاملين تقولي
+
+353
+00:37:45,910 --> 00:37:51,650
+أي واحد لأ ده هتجيب مصفوفتين غيرهمبحيث لهم هذه
+
+354
+00:37:51,650 --> 00:37:55,770
+الخاصية يعني لو ضرب المصوفة في نفسها بدي أطيني
+
+355
+00:37:55,770 --> 00:38:01,290
+مصوفة الوحدة بس بشرط ما تكونش مصوفة الوحدة تمام؟
+
+356
+00:38:01,290 --> 00:38:05,490
+ايوة هذا المطلوب الأول مطلوب التاني بقول لو كان ال
+
+357
+00:38:05,490 --> 00:38:09,030
+a بدو يساوي ال inverse show that أن ال determinant
+
+358
+00:38:09,030 --> 00:38:14,670
+لل a بدو يساوي زائد أو ناقص واحد بسيطة جدا خلينا
+
+359
+00:38:14,670 --> 00:38:20,460
+مع المطلوب الأول بدي أحاول أدور على مصوفةلو ضربت
+
+360
+00:38:20,460 --> 00:38:25,940
+في نفسي يطلع مين عندي مصفوفة الوحدة حد فيكم بتقدر
+
+361
+00:38:25,940 --> 00:38:28,480
+تجيبلي مصفوفة نظامها اتنين في اتنين مابتداش كتير
+
+362
+00:38:28,480 --> 00:38:36,140
+يعني اغششك اكتر القطر الرئيسي أسفارا يلا ضل عليكي
+
+363
+00:38:36,140 --> 00:38:41,020
+عددين بس مصفوفة نظامها اتنين في اتنين و القطر
+
+364
+00:38:41,020 --> 00:38:46,620
+الرئيسي أسفارا بدي لو ضربت تطلع مصفوفة الوحدة
+
+365
+00:39:14,950 --> 00:39:16,550
+تلاتة و تلت تلاتة و تلت تلت تلت تلت تلت تلت تلت
+
+366
+00:39:18,130 --> 00:39:23,410
+بنفع أربعة و رابعة بنفع خمسة و خمس يبجى هاي مش
+
+367
+00:39:23,410 --> 00:39:28,410
+مصفف تينهاد صار ملاي .. إيجاداش ملايين عدد لانهاء
+
+368
+00:39:28,410 --> 00:39:32,270
+من المصففات و ليس .. بس من ده اتكد ان كلامنا هذا
+
+369
+00:39:32,270 --> 00:39:37,450
+صح ولا لأ يبجى انا الاول اقتراح كان عند الطلبات
+
+370
+00:39:37,450 --> 00:39:45,750
+اللي هم يأتي بيداخد المصففة Zero اتنين نص Zeroمش
+
+371
+00:39:45,750 --> 00:39:47,970
+شايف لما اعطاك القدرة ياسي واحد يقعد تلات اتنين و
+
+372
+00:39:47,970 --> 00:39:54,050
+نص الان بدي اضربها في نفسها يبقى zero اتنين نص
+
+373
+00:39:54,050 --> 00:40:01,270
+zero النتج يساوي الصف الأول في العمود الأول بواحد
+
+374
+00:40:01,270 --> 00:40:07,350
+الصف الأول في العمود التاني بزيرو الصف التاني في
+
+375
+00:40:07,350 --> 00:40:11,910
+العمود الأول بزيرو الصف التاني في العمود الثاني
+
+376
+00:40:11,910 --> 00:40:19,250
+بواحداللي هي الـ identity matrix اللي عندنا يبقى
+
+377
+00:40:19,250 --> 00:40:23,950
+هيجيبنا لهياش مصفوفة اتنين هذا بنفعله التلاتة اه
+
+378
+00:40:23,950 --> 00:40:29,930
+بنفعله الأربعة الخمسة اذا بقوله in general يبقى
+
+379
+00:40:29,930 --> 00:40:40,050
+باجي بقوله in general for any real number
+
+380
+00:40:41,660 --> 00:40:46,500
+مثلًا K for
+
+381
+00:40:46,500 --> 00:40:54,920
+any real number K we have يبقى لو جيت قلت Zero K
+
+382
+00:40:54,920 --> 00:41:05,300
+واحد على K Zero في Zero K واحد على K Zero يبقى
+
+383
+00:41:05,300 --> 00:41:11,010
+الناتج واحد زيرو زيرو واحديبقى جبتله مش مصففتين،
+
+384
+00:41:11,010 --> 00:41:16,050
+جبتله مليارات المصففات، شيل كده و حط أي رقم عدى
+
+385
+00:41:16,050 --> 00:41:19,870
+الـ0، يبقى ايش قولت ان انا ساوي الـ0 for any real
+
+386
+00:41:19,870 --> 00:41:24,890
+number كده، لا يساوي الـ0، ضروري مايساويش ان انا
+
+387
+00:41:24,890 --> 00:41:29,360
+ساوي الـ0، بصي كلامنا مش صحيحيبقى بالناشي يساوي
+
+388
+00:41:29,360 --> 00:41:34,060
+zero يبقى بصير كلامنا يعني استبعد السفر وحطي موجة
+
+389
+00:41:34,060 --> 00:41:37,360
+بسالب اللي بدك إياه يبقى بصير كلامنا هذا ما قاله
+
+390
+00:41:37,360 --> 00:41:41,540
+صح على طول اللي هو المطلوب الأول من المسألة
+
+391
+00:41:41,540 --> 00:41:46,220
+المطلوب الثاني بيقول لو كان ال A في ال A بده يساوي
+
+392
+00:41:46,220 --> 00:41:51,300
+ال A inverse بيبين لي أن ال determinant لل A بده
+
+393
+00:41:51,300 --> 00:41:57,390
+يساوي واحد وكأنه بيقولاستبعدني اللي هو من ال
+
+394
+00:41:57,390 --> 00:42:03,070
+determinant لل A inverse صحيح ولا لأ بقوله بسيطة
+
+395
+00:42:03,070 --> 00:42:07,670
+احنا عندنا نمر بيه انا عند ال A بده يساوي ال A
+
+396
+00:42:07,670 --> 00:42:11,670
+inverse مش
+
+397
+00:42:11,670 --> 00:42:18,990
+رأيك تخلص من المعكوس هذامظرف في ايش؟ في ايه؟ يبقى
+
+398
+00:42:18,990 --> 00:42:27,370
+هدف يعطيني ان ايه في ايه يبقى ايه في ايه يبقى درفة
+
+399
+00:42:27,370 --> 00:42:33,430
+من جهة الشمال في ايه يبقى معناته ايه في ايه يبقى
+
+400
+00:42:33,430 --> 00:42:39,870
+ايهالـ Identity Matrix يبقى
+
+401
+00:42:39,870 --> 00:42:45,310
+بيصير عندي الـ determinant للـ A في الـ A بده
+
+402
+00:42:45,310 --> 00:42:51,390
+يساوي ال determinant لمصفوفة الوحدة I حسب خواص ال
+
+403
+00:42:51,390 --> 00:42:56,490
+determinant يبقى هذا determinant للـ Aفي الـ
+
+404
+00:42:56,490 --> 00:43:01,990
+determinant للـ a بده يساوي ال determinant لمصوفة
+
+405
+00:43:01,990 --> 00:43:08,590
+الواحدة هذا معناه ان ال determinant لل a لكل تربيع
+
+406
+00:43:08,590 --> 00:43:13,010
+بده يساوي قداش ال determinant لمصوفة الواحدة واحدة
+
+407
+00:43:13,010 --> 00:43:17,030
+لو أخدنا الجدر التربيع إلى الطرفين يبقى بيصير ال
+
+408
+00:43:17,030 --> 00:43:22,510
+determinant لل a يساوي ازايد او ناقص واحدة اظن وهو
+
+409
+00:43:22,510 --> 00:43:28,560
+المطلوبيبقى هذول أربع أسئلة متوالية و كلهم أسئلة
+
+410
+00:43:28,560 --> 00:43:33,740
+نظرية موجودة عندك في الكتاب 12 و 13 و 14 و 15 وهي
+
+411
+00:43:33,740 --> 00:43:40,380
+حللنا لك الأربع أسئلة النظرية ولا عذر لك بعد ذلك
+
+412
+00:43:40,380 --> 00:43:45,200
+طبعا احنا قولنا ال exercises اتنين اتناشطة ناكل
+
+413
+00:43:45,200 --> 00:43:49,140
+مسائل عليهم اللي هو واحد تلاتة خمسة سبعة و من عشر
+
+414
+00:43:49,140 --> 00:43:54,300
+لخمستاشروالـ exercise من واحد لتمانية مش هيك تمام
+
+415
+00:43:54,300 --> 00:44:00,940
+تمام يبقى على هيك يكون انتهى هذا ال section اللي
+
+416
+00:44:00,940 --> 00:44:08,700
+هو section اتنين اتناش وبنتهيه ينتهي chapter اتنين
+
+417
+00:44:08,700 --> 00:44:14,520
+والمرة الجاية بدنا نتيجي مفتحين ومخكوا صاحي ونظيف
+
+418
+00:44:14,520 --> 00:44:20,680
+مشان نبدأ chapter تلاتةاللي بتكلم عن vector spaces
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d1f63f7f4b85d66b777d83a426acf42a7da0dc67
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw.srt
@@ -0,0 +1,1553 @@
+1
+00:00:19,980 --> 00:00:23,680
+بسم الله الرحمن الرحيم آخر حاجة أخذناها في
+
+2
+00:00:23,680 --> 00:00:29,300
+المحاضرة الماضية وهو Laplace transform لمين 
+
+3
+00:00:29,300 --> 00:00:34,540
+للمشتقة فقولنا أخدنا Laplace transform للمشتقة 
+
+4
+00:00:34,540 --> 00:00:39,220
+الأولى عبارة عن S  الدالة في اشتقاق ناقص ال
+
+5
+00:00:39,220 --> 00:00:43,820
+function at zero وبعد ذلك رحنا أخذنا 
+
+6
+00:00:43,820 --> 00:00:49,180
+لبلاس للمشتقة الثانية قولنا هو عبارة عن S2 في
+
+7
+00:00:49,180 --> 00:00:55,620
+لبلاس لل F of T بدون اشتقاق ناقص S في F of Zero
+
+8
+00:00:55,620 --> 00:01:02,440
+ناقص F prime of Zero بعد ذلك عمّمناها لو كانت
+
+9
+00:01:02,440 --> 00:01:07,810
+مشتقة نونية، ناخد بعض الأمثلة على ذلك بيقول 
+
+10
+00:01:07,810 --> 00:01:11,090
+استخدم Laplace transform عشان نحل المعادلات 
+
+11
+00:01:11,090 --> 00:01:16,370
+التفاضلية الآتية، واخدنا المعادلة الأولى من الرتبة 
+
+12
+00:01:16,370 --> 00:01:22,200
+الأولى والمعادلة الثانية من الرتبة الثانية، يبقى 
+
+13
+00:01:22,200 --> 00:01:27,180
+بالنسبة للحل المعادلة الأولى نأخد لبلاس ترانسفورم 
+
+14
+00:01:27,180 --> 00:01:35,060
+للطرفين، يبقى لبلاس ترانسفورم لل X' of T زائد تلاتة 
+
+15
+00:01:35,060 --> 00:01:42,900
+X of T كله بده يسوى لبلاس ترانسفورم لل E أس اتنين 
+
+16
+00:01:42,900 --> 00:01:47,680
+T بالشكل اللي عنها، يبقى Laplace للطرف الشمال من 
+
+17
+00:01:47,680 --> 00:01:52,980
+المعادلة هو، Laplace الطرف اليمين من المعادلة المرة
+
+18
+00:01:52,980 --> 00:01:57,560
+الماضية أخذنا Laplace، هذا مؤثر خاطئ، إذا بروح 
+
+19
+00:01:57,560 --> 00:02:01,720
+أستخدم هذه الخاصية، إذا بصير Laplace الأول زائد
+
+20
+00:02:01,720 --> 00:02:07,800
+تلاتة Laplace للثاني، يبقى لبلاس ترانسفورم لمن؟ لل
+
+21
+00:02:07,800 --> 00:02:16,600
+X' of T زائد تلاتة لبلاس ترانسفورم لل X of T 
+
+22
+00:02:16,600 --> 00:02:22,040
+بالشكل ان هذا بدي يسوي لبلاس ترانسفورم لل E أس 
+
+23
+00:02:22,040 --> 00:02:28,360
+اتنين T، الان بدي اجي لبلاس ترانسفورم لل X' بدي بقول
+
+24
+00:02:28,360 --> 00:02:36,900
+هذا عبارة عن مين؟ عبارة عن S في X of S، X of S هو 
+
+25
+00:02:36,900 --> 00:02:41,620
+لبلاس ترانسفورم لدى X of T
+
+26
+00:02:50,710 --> 00:02:55,630
+خلصنا الترم الأول والترم الثاني زي التلاتة ل plus
+
+27
+00:02:55,630 --> 00:03:02,910
+لل X of T بدي أسميه X of S، يساوي هذه حسبناها المرة 
+
+28
+00:03:02,910 --> 00:03:10,270
+الماضية وقلنا هذه عبارة عن ايش؟ عبارة عن واحد على اس 
+
+29
+00:03:10,270 --> 00:03:16,230
+ناقص اتنين، يبقى واحد على اس ناقص اتنين، يبقى واحد
+
+30
+00:03:16,230 --> 00:03:18,410
+على اس ناقص اتنين، يبقى واحد على اس ناقص اتنين، يبقى
+
+31
+00:03:18,410 --> 00:03:18,470
+واحد على اس ناقص اتنين، يبقى واحد على اس ناقص اتنين
+
+32
+00:03:18,470 --> 00:03:20,430
+يبقى واحد على اس ناقص اتنين، يبقى واحد على اس ناقص
+
+33
+00:03:20,430 --> 00:03:21,630
+اتنين، يبقى واحد على اس ناقص اتنين، يبقى واحد على اس
+
+34
+00:03:21,630 --> 00:03:23,730
+ناقص اتنين، يبقى واحد على اس ناقص اتنين، يبقى واحد
+
+35
+00:03:23,730 --> 00:03:27,250
+على اس ناقص اتنين، يبقى واحد على اس ناقص اتنين، يبقى
+
+36
+00:03:27,250 --> 00:03:34,840
+واحد على اس ناقص اتنين، يبقى، وازائد تلاتة في ال X
+
+37
+00:03:34,840 --> 00:03:41,040
+of S ناقص ال X Zero بواحد، يبقى ناقص ناقص
+
+38
+00:03:41,040 --> 00:03:48,060
+بصير زائد واحد، بدي يسوي واحد على S ناقص اتنين
+
+39
+00:03:48,060 --> 00:03:53,090
+بالشكل اللي أنا أنا، طيب الآن بدي أجيب الواحد على
+
+40
+00:03:53,090 --> 00:03:59,470
+الجهة الثانية يبقاش بصير عندي بصير ال S زائد تلاتة
+
+41
+00:03:59,470 --> 00:04:06,870
+في ال X of S بدي أساوي واحد على S ناقص اتنين ناقص
+
+42
+00:04:06,870 --> 00:04:13,630
+الواحد، ان وحد المقامات للطرفين بيظل S ناقص اتنين
+
+43
+00:04:13,630 --> 00:04:22,070
+لمين؟ لا واحد، لا ناقص S، زائد اتنين، يبقى تلاتة ناقص S
+
+44
+00:04:22,070 --> 00:04:28,890
+على S ناقص اتنين، يبقى بناء انا عليه بقدر اجيبله ال
+
+45
+00:04:28,890 --> 00:04:37,410
+X of S يبقى ال X of S يساوي اللي هو من تلاتة ناقص
+
+46
+00:04:37,410 --> 00:04:46,270
+S على من؟ على S ناقص اتنين مقسومة على S زائد تلاتة
+
+47
+00:04:48,450 --> 00:04:55,330
+أنا جبت له لبلاسي ترانسفورم الألميم للحل تبعت ده 
+
+48
+00:04:55,330 --> 00:04:59,510
+اللي هو بدوش لبلاسي ترانسفورم للحل، بده الحل itself
+
+49
+00:04:59,510 --> 00:05:03,030
+لأنه يشرح جالي يستخدم لبلاسي ترانسفورم لتحل 
+
+50
+00:05:03,030 --> 00:05:06,810
+المعادلة
+
+51
+00:05:06,810 --> 00:05:13,110
+التفاضلية، بقول له كويس إذا انا بروح ادور على الدالة
+
+52
+00:05:13,110 --> 00:05:17,010
+اللي Laplace transform اللي هي يساوي مين؟ يساوي 
+
+53
+00:05:17,010 --> 00:05:20,090
+الجزء اللي قدامنا هذا، باجي بقول يا ورادي هو ايش
+
+54
+00:05:20,090 --> 00:05:22,830
+بدي .. ايش بدي أجيب لي Laplace لمين؟ هي الدالة 
+
+55
+00:05:22,830 --> 00:05:26,150
+Laplace اللي هي يساوي اللي هو الجزء اللي عندنا
+
+56
+00:05:26,650 --> 00:05:30,910
+بالشكل هذا، صعب مش عارفها، لكن ربنا سبحانه وتعالى 
+
+57
+00:05:30,910 --> 00:05:37,250
+أعطانا عقل نفكر به ونستنبط ونستنتج الأشياء أو
+
+58
+00:05:37,250 --> 00:05:41,770
+نخرج من المشكلة اللي احنا فيها إلى مشكلة بسيطة جدا
+
+59
+00:05:41,770 --> 00:05:49,270
+وسهل الحل تبعها، إذا البسط عندي معادلة من الدرجة
+
+60
+00:05:51,450 --> 00:05:57,730
+البسط معادلة من الدرجة، والمقام من الدرجة، ومحللة 
+
+61
+00:05:57,730 --> 00:06:03,750
+إلى two factors، وال two factors are different
+
+62
+00:06:03,750 --> 00:06:08,410
+أخذنا partial fractions صحيح ولا لأ؟ إذا بندروح 
+
+63
+00:06:08,410 --> 00:06:13,900
+أعمل لهذه partial fractions، يبقى لما أقعد أعمل لهدي
+
+64
+00:06:13,900 --> 00:06:20,140
+partial fractions بقدر أقول هدي a على s ناقص اتنين 
+
+65
+00:06:20,140 --> 00:06:26,980
+زائد b على s زائد تلاتة بالشكل اللي عندنا، طيب بدا
+
+66
+00:06:26,980 --> 00:06:30,800
+أجي على ال term هذا كله واستخدم خاصية ال partial 
+
+67
+00:06:30,800 --> 00:06:35,120
+fraction نبدأ نروح نضرب في مين؟ في المقام اللي
+
+68
+00:06:35,120 --> 00:06:40,580
+عندنا هذا نضرب الطرفين بنحصل على ما يأتي تلاتة
+
+69
+00:06:40,580 --> 00:06:48,900
+ناقص S يساوي A في S زائد تلاتة زائد B في S ناقص 
+
+70
+00:06:48,900 --> 00:06:54,020
+اتنين، الان بدي اجيب له قيمة a وb فبجيب اقول لو
+
+71
+00:06:54,020 --> 00:07:02,040
+حطينا ال s تساوي 2 then بصير هنا تلاتة نقص اتنين
+
+72
+00:07:02,040 --> 00:07:07,500
+هنا بدي نحطها اتنين بدي يساوي a في اتنين زائد
+
+73
+00:07:07,500 --> 00:07:15,480
+تلاتة زائد zero، ومنها الـ A تساوي خمسة، تلاتة نقص،
+
+74
+00:07:15,480 --> 00:07:18,880
+اتنين قطع الواحد، اتنين و تلاتة خمسة، يبقى الـ A
+
+75
+00:07:18,880 --> 00:07:24,820
+تساوي خمسة، الان لو جمنا حاطينا ال S تساوي سالب 
+
+76
+00:07:24,820 --> 00:07:33,500
+تلاتة then هذا بيروح بيظل ان تلاتة زائد تلاتة يساوي 
+
+77
+00:07:33,500 --> 00:07:39,420
+Zero زائد اللي هو B، تلاتة نقص اتنين اللي هو واحد 
+
+78
+00:07:39,420 --> 00:07:49,890
+وبالتالي فال B أنها تساوي قداش؟ تساوي ستة، يبقى مرة
+
+79
+00:07:49,890 --> 00:07:54,610
+ثانية بقول لو حطينا S بسالب تلاتة في المعادلة اللي
+
+80
+00:07:54,610 --> 00:07:59,530
+فوق بصير تلاتة زي التلاتة حطيها هنا سالب تلاتة 
+
+81
+00:07:59,530 --> 00:08:06,310
+بالطير هنا سالب تلاتة سالب تلاتة بصير 
+
+82
+00:08:13,290 --> 00:08:18,590
+إذا لو حطينا هذه بسلب تلاتة بصير هذه zero وهذه
+
+83
+00:08:18,590 --> 00:08:25,590
+زائد بي في سلب تلاتة سلب اتنين وبالتالي بي تساوي
+
+84
+00:08:25,590 --> 00:08:32,660
+سالب اللي هو ستة على خمسة، سالب ستة أخماس، يبقى بناء
+
+85
+00:08:32,660 --> 00:08:39,460
+عليه أصبح ال X as a function of S هو عبارة عن ال A 
+
+86
+00:08:39,460 --> 00:08:45,320
+بدهش لو حط مكانها خمسة يبقى صارت خمسة في واحد على S 
+
+87
+00:08:45,320 --> 00:08:53,260
+ناقص اتنين، وال B هذي بسالب ستة أخماس في واحد على S 
+
+88
+00:08:53,260 --> 00:09:00,160
+زائد تلاتة، إذا انجزت اللي هو Laplace transform للدالة 
+
+89
+00:09:00,160 --> 00:09:06,120
+اللي فوق هذه إلى جزئين، الجزئين كل واحد فيهم بعرف
+
+90
+00:09:06,120 --> 00:09:10,220
+Laplace transform الأصلي اللي هو وبالتالي قضيتنا
+
+91
+00:09:10,220 --> 00:09:17,680
+بصير سهلة، فبروح بقوله solution of
+
+92
+00:09:17,680 --> 00:09:26,270
+the Differential equation one is، سميها للمعادلة هذه 
+
+93
+00:09:26,270 --> 00:09:32,190
+اللي هي المعادلة رقم واحد is x of t، يبقى أنا
+
+94
+00:09:32,190 --> 00:09:36,490
+مابديش لابلاس ترانسفورم، بدي ارجعها للاصل، ابتباعها
+
+95
+00:09:36,490 --> 00:09:42,890
+يبقى ال x of t يساوي خمسة، مين هي الدالة اللي لابلاس 
+
+96
+00:09:42,890 --> 00:09:45,050
+يساوي واحدة وليس ناقص اتنين
+
+97
+00:10:03,220 --> 00:10:06,900
+طيب لو جربت أحلها بأي طريقة من الطرق السابقة، يعني 
+
+98
+00:10:06,900 --> 00:10:11,390
+الطرق اللي بدي أطلع هذا الجواب ولا غيره؟ نفس الجواب
+
+99
+00:10:11,390 --> 00:10:16,750
+وهذه بلغتنا لزمان initial value problem، ما علينا 
+
+100
+00:10:16,750 --> 00:10:23,330
+نجي لنمر بيه، نمنع بيه برضه بنفس الطريقة، بدي أخد
+
+101
+00:10:23,330 --> 00:10:27,110
+لبلاس ترانسفورم للطرفين، و بدي أدخل حسب ال
+
+102
+00:10:27,110 --> 00:10:31,010
+linearity تبع لبلاس على كل term من ال termات اللي 
+
+103
+00:10:31,010 --> 00:10:37,330
+عنها، اذا بدي أجي أقول لبلاس ترانسفورم لل x double prime
+
+104
+00:10:37,330 --> 00:10:48,240
+of t زائد اتنين لبلاس لل x prime of t زائد لبلاس لل 
+
+105
+00:10:48,240 --> 00:10:53,480
+X of T بالشكل اللي عندنا هذا كله بده يساوي لبلاس
+
+106
+00:10:53,480 --> 00:11:27,150
+لمين؟ ل T، إذا بدنا نجيب لبلاس لهذه الدلاله همين 
+
+107
+00:11:29,150 --> 00:11:36,550
+أتنين فيهم لبلاس ال X prime اللي هو S في X of S 
+
+108
+00:11:36,550 --> 00:11:44,590
+ناقص ال X عند ال zero فقط، لغير، ووصلنا للي بعدها 
+
+109
+00:11:44,590 --> 00:11:51,430
+زائد X as a function of S، بدنا لبلاس transform لل 
+
+110
+00:11:51,430 --> 00:11:56,420
+T، وتلك المرة اللي فات كل واحد أجيب كتابتها معاها 
+
+111
+00:11:56,420 --> 00:12:05,120
+مظبوط يابجي افتح لي على الجدول اللي هو في section 
+
+112
+00:12:05,120 --> 00:12:09,760
+تسعة تلاتة، ال section اللي بعد هيك يلا افتح لي
+
+113
+00:12:09,760 --> 00:12:18,120
+بسرعة في section تسعة تلاتة، بعدي اللي هو عنوانه 
+
+114
+00:12:18,120 --> 00:12:23,100
+properties of Laplace transform، Properties of
+
+115
+00:12:23,100 --> 00:12:28,740
+Laplace Transform، كاتب شوية Properties وتحتها مات
+
+116
+00:12:28,740 --> 00:12:33,840
+بعض Laplace Transform لبعض الدول وبدأ بأول دليل T
+
+117
+00:12:33,840 --> 00:12:41,080
+to the power N، Laplace ل T to the power N مكتوب 
+
+118
+00:12:41,080 --> 00:12:47,860
+عندك جنبها F of S ل N factorial على S أس N زائد 
+
+119
+00:12:47,860 --> 00:12:55,060
+واحد، يبقى N factorial يعني ال plus ل T أوس N هو N
+
+120
+00:12:55,060 --> 00:13:00,180
+factorial على S أوس N زي الواحد، يبقى بناء عليه ال
+
+121
+00:13:00,180 --> 00:13:05,140
+plus transform ل T عبارة عن ايه؟ واحد factorial 
+
+122
+00:13:05,140 --> 00:13:12,820
+على S أوس واحد زي الواحد يعني واحد على S، مظبوط؟ 
+
+123
+00:13:12,820 --> 00:13:20,040
+واحد على S، إذا بشيل هذه كلها وبكتب
+
+124
+00:13:20,040 --> 00:13:23,100
+بدلها واحد على S
+
+125
+00:13:26,700 --> 00:13:32,640
+هذه المناطق بالصير، وهذه فيها x of s وهذه لو جيت
+
+126
+00:13:32,640 --> 00:13:39,260
+فكتها ب x of s وهذه ب x of s يبقى هذه لو جيت أخدت ال
+
+127
+00:13:39,260 --> 00:13:45,500
+x of s عامل مشترك، مضل عندي s تربيع زائدي اتنين s
+
+128
+00:13:45,500 --> 00:13:57,110
+زائد واحد كله في ال x of s، بعد ذلك ناقص S X of 0، X
+
+129
+00:13:57,110 --> 00:14:05,330
+of 0 بقد إيش بواحد يبقى في واحد اللي بعدها ناقص X 
+
+130
+00:14:05,330 --> 00:14:14,210
+prime of 0 ناقص اتنين، خلصنا هذه دلنا ناقص اتنين في
+
+131
+00:14:14,210 --> 00:14:19,710
+ال X of Zero اللي هو قد إيش بواحد كله بده يساوي 
+
+132
+00:14:19,710 --> 00:14:24,930
+واحد على اس تربيع، إذا شيلنا X of Zero وحطينا بدلها
+
+133
+00:14:24,930 --> 00:14:28,930
+واحد، شيلنا X prime of Zero وحطينا مكانها اتنين 
+
+134
+00:14:28,930 --> 00:14:35,530
+واخدنا من اللي تحتهم خط هدول X of S عامل مشترك
+
+135
+00:14:35,530 --> 00:14:40,990
+تمام؟ يبقاش اللي حصل عندنا، حصل عندما يأتي اللي هو 
+
+136
+00:14:40,990 --> 00:14:52,470
+الـ S² زائد 2S زائد 1 في ال X of S بده يساوي 1 على
+
+137
+00:14:52,470 --> 00:14:57,210
+S تربيع، هذه يا بنات ناقص S لما نوديها على الشجة
+
+138
+00:14:57,210 --> 00:15:01,810
+التانية إيش بيصير؟ زائد S، هذه ناقص 4 لما نوديها
+
+139
+00:15:01,810 --> 00:15:08,530
+على الشجة التانية بيصير كده إيش؟ زائد 4، بمعنى أخر
+
+140
+00:15:08,530 --> 00:15:15,250
+لو جيت وحدة المقامات للكل هدول كله على استربيع بصير
+
+141
+00:15:15,250 --> 00:15:24,490
+واحد زائد استكيب زائد أربعة استربيع، الشكل اللي 
+
+142
+00:15:24,490 --> 00:15:30,010
+عندنا هنا، يبقى بناء عليه بدي يصبح عند ال X of S 
+
+143
+00:15:30,010 --> 00:15:38,010
+يساوي اللي هو S تكيب زائد أربعة S تربيع زائد واحد
+
+144
+00:15:38,010 --> 00:15:44,210
+كله مقسوما على S تربيع، هذا S تربيع زائد اتنين S
+
+145
+00:15:44,210 --> 00:15:49,470
+زائد واحد اللي هو S زائد واحد لكل تربيع
+
+146
+00:16:03,410 --> 00:16:09,950
+إذا توصلت إلى Laplace transform للحل تبع المعادلة
+
+147
+00:16:09,950 --> 00:16:15,130
+شو Laplace transform؟ معادلة من الدرجة الثالثة على
+
+148
+00:16:15,130 --> 00:16:20,230
+معادلة من الدرجة الرابعة، يبقى بقدر أقوم بعمل 
+
+149
+00:16:20,230 --> 00:16:25,050
+partial fractions لأن درجة البسط أقل من درجة 
+
+150
+00:16:25,050 --> 00:16:30,370
+المقام، يبقى جاهزين اتنين، محللة إلى أبسط العوامل
+
+151
+00:16:30,370 --> 00:16:35,770
+الأولية، يبقى بدي أرجع لل partial fractions و أعمل 
+
+152
+00:16:35,770 --> 00:16:41,270
+partial fractions لهذا المقدار، ال S تكيب زائد 
+
+153
+00:16:41,270 --> 00:16:48,330
+أربعة S تربيع زائد أربعة S تربيع زائد واحد كله 
+
+154
+00:16:48,330 --> 00:16:56,090
+مقسوما على مين؟ على S تربيع في مين؟ في S زائد واحد 
+
+155
+00:16:56,090 --> 00:17:03,580
+لكل تربيع، بدنا نيجي للـ Gauss الأول، المقدار الأول
+
+156
+00:17:03,580 --> 00:17:08,580
+هو معادلة من الدرجة الثانية لما تحط ال bus بمعادلة 
+
+157
+00:17:08,580 --> 00:17:16,940
+من الدرجة الأولى، يبقى هذا الكلام بده يساوي AS زائد 
+
+158
+00:17:16,940 --> 00:17:28,230
+B على S تربيع، هذا قسم مكرر مرتين، يبقى زائد C على S
+
+159
+00:17:28,230 --> 00:17:35,310
+زائد واحد زائد D على S زائد واحد لكل ترمية، يبقى 
+
+160
+00:17:35,310 --> 00:17:38,430
+عملنا ال partial fraction، أنا بده احاول اجيب قيمة
+
+161
+00:17:38,430 --> 00:17:44,070
+ثوابت الـA والـB والـC والـD، لذلك هروح أضرب في 
+
+162
+00:17:44,070 --> 00:17:48,730
+المقام اللي عندنا هذا، فبتصبح المعادلة على الشكل
+
+163
+00:17:48,730 --> 00:17:55,810
+التالي استكيب زياد أربع استربيع زياد واحد يساوي AS
+
+164
+00:17:55,810 --> 00:18:07,010
+زياد B في S زياد واحد لكل تربيع، زائد C S تربيع في S
+
+165
+00:18:07,010 --> 00:18:17,670
+زائد 1 زائد D في S تربيع، مرة تانية نضرب هنابطير
+
+166
+00:18:17,670 --> 00:18:22,250
+المقام بظل ال bus زي ما هو نضرب هنا بطير ال S
+
+167
+00:18:22,250 --> 00:18:27,970
+تر
+
+201
+00:22:15,070 --> 00:22:23,610
+سالب أربعة وزائد أربعة بروحه بصفر يبقى D تساوي
+
+202
+00:22:23,610 --> 00:22:30,230
+أربعة الشكل اللي عندنا يبقى بناء عليه أصبح عندنا ال
+
+203
+00:22:30,230 --> 00:22:36,230
+X of S كله بدرساه
+
+204
+00:22:38,840 --> 00:22:44,340
+أصبح الـ X of S يعني لل Laplace Transform لده لا بد
+
+205
+00:22:44,340 --> 00:22:51,960
+يساوي بدي أشيل الـ A و أحط مكانها ناقص 2S و أشيل
+
+206
+00:22:51,960 --> 00:22:58,840
+الـ B و أحط مكانها واحد و كل هذا على S تربيع زائد
+
+207
+00:22:58,840 --> 00:23:08,900
+الـ C عندي بتلاتة على S زائد واحد و بعد ذلك أضيف 4
+
+208
+00:23:08,900 --> 00:23:15,920
+على S زائد 2 لكل تربيع لو على الترتيب يا بناتي
+
+209
+00:23:15,920 --> 00:23:26,340
+بيصير ناقص 2 في 1 على S زائد 1 على S تربيع زائد
+
+210
+00:23:26,340 --> 00:23:38,380
+1 على S تربيع زائد 3 في 1 على S زائد 1 زائد 4 في
+
+211
+00:23:38,380 --> 00:23:47,180
+1 على S زائد 2 لكل تربيع اه
+
+212
+00:23:47,180 --> 00:23:57,260
+S زائد 1 S زائد 1 لكل تربيع طيب هذا Laplace
+
+213
+00:23:57,260 --> 00:24:02,900
+Transform للدالة إذا أنا ما بديش Laplace Transform
+
+214
+00:24:02,900 --> 00:24:06,620
+للدالة يعني للحل تبع ال differential equation
+
+215
+00:24:06,620 --> 00:24:12,580
+وإنما بدي الحل نفسه يبقى بروح بقول هنا the
+
+216
+00:24:12,580 --> 00:24:28,330
+solution of the given differential equation is
+
+217
+00:24:28,330 --> 00:24:39,940
+ال X of T بدرساه ناقص اثنين واحد على S هذه لمين؟ لـ 
+
+218
+00:24:39,940 --> 00:24:43,980
+Laplace Transform لمن؟ للواحد الصحيح أخذناه المرة
+
+219
+00:24:43,980 --> 00:24:50,660
+الماضية يبقى هذا ناقص اثنين في واحد الآن زائد واحد
+
+220
+00:24:50,660 --> 00:25:01,190
+على S تربيع لمين؟ T بس كويس يبقى هذه T زائد
+
+221
+00:25:01,190 --> 00:25:09,210
+ثلاثة واحد عليه زائد واحد لمين؟ E أس ناقص T مظبوط
+
+222
+00:25:09,210 --> 00:25:15,830
+ايه؟ بس هكذا  E ناقص 1 على S ناقص الـ A لو 
+
+223
+00:25:15,830 --> 00:25:22,710
+حطينا ناقص في الـ T لـ زائد يبقى ثلاثة E أس ناقص T زائد 
+
+224
+00:25:22,710 --> 00:25:29,390
+أربعة نيجي لهذه واحد على S زائد 1 لكل تربيع 
+
+225
+00:25:29,390 --> 00:25:33,930
+يلا شوفوا هذي من الجدول اللي قلت لكم عليه برضه
+
+226
+00:25:40,530 --> 00:25:46,390
+يا ضنيات منهم؟ كيف؟
+
+227
+00:25:46,390 --> 00:25:49,430
+اه طبعاً، هجيب لك ال ... الجدول، هي اللي بتاعك،
+
+228
+00:25:49,430 --> 00:25:53,230
+صورته، ما ناقص اللي راح هتصور كل امتحان بيجيك
+
+229
+00:25:53,230 --> 00:25:57,850
+الجدول، مش هذا، كله أكثر منه كمان، مصور من أوله
+
+230
+00:25:57,850 --> 00:26:05,110
+إلى آخره طبعاً .. طبعاً مشان تكون في الصورة رقم تسعة 
+
+231
+00:26:05,110 --> 00:26:10,330
+في هذا الجدول عندك في الكتاب في Section تسعة ثلاثة
+
+232
+00:26:10,330 --> 00:26:15,930
+رقم تسعة بيقول لك لو كانت الدالة أو Laplace
+
+233
+00:26:15,930 --> 00:26:19,550
+Transform ل T to the power N
+
+234
+00:26:35,780 --> 00:26:42,570
+هذا الموضوع لأنه هذا ما أقدر أقوله يا شي واحد يبقى لو
+
+235
+00:26:42,570 --> 00:26:48,150
+كانت واحد بيصير هنا يا شي واحد Factorial اللي هو
+
+236
+00:26:48,150 --> 00:26:54,890
+بواحد و هنا S ناقص 1 أس 1 زائد 1 بيصير S 
+
+237
+00:26:54,890 --> 00:27:02,470
+ناقص 1 لكل تربيع احنا عندنا يا شي عندنا من عندنا S
+
+238
+00:27:02,470 --> 00:27:06,750
+زائد 1 يبقى E أس
+
+239
+00:27:23,570 --> 00:27:31,080
+لحد هنا انتهى هذا السؤال يبقى حلينا المعادلة
+
+240
+00:27:31,080 --> 00:27:36,280
+التفاضلية من الرتبة الثانية زي ما حلينا المعادلة
+
+241
+00:27:36,280 --> 00:27:40,800
+التفاضلية من الرتبة الأولى بطريقة Laplace
+
+242
+00:27:40,800 --> 00:27:56,620
+Transform بقى هناك مثال آخر المثال
+
+243
+00:27:56,620 --> 00:27:57,940
+بيقول ما يأتي
+
+244
+00:28:01,390 --> 00:28:11,970
+مثال Find Laplace Transform Find Laplace Transform 
+
+245
+00:28:20,140 --> 00:28:28,540
+لذلك F of T تساوي أحد أمرين، يا إما واحد لما T
+
+246
+00:28:28,540 --> 00:28:34,540
+محصورة بين Zero و واحد، يا إما Zero لما T greater
+
+247
+00:28:34,540 --> 00:28:41,360
+than one خلّي 
+
+248
+00:28:41,360 --> 00:28:46,060
+بالك بالك جليهات Laplace Transform للدالة اللي عندنا
+
+249
+00:28:46,060 --> 00:28:50,220
+طبعاً من يوم ما بدأنا نشتغل في Laplace Transform أول
+
+250
+00:28:50,220 --> 00:28:54,340
+مرة بنشوف Function من هذا القبيل لكن هذه ال
+
+251
+00:28:54,340 --> 00:29:00,080
+Function هتمر معانا كتير جداً في خلال دراستنا لـ ميل 
+
+252
+00:29:00,080 --> 00:29:04,340
+Laplace Transform في ال Sections القادمة و سنمر
+
+253
+00:29:04,340 --> 00:29:09,560
+عليها بعد قليل إن شاء الله لكن باجي بقول أنا
+
+254
+00:29:09,560 --> 00:29:14,340
+ما أخذتش إلا التعريف يبقى لما نقول Laplace Transform
+
+255
+00:29:14,340 --> 00:29:22,580
+بقول له Solution احنا بدنا ال Laplace Transform لمين؟
+
+256
+00:29:22,610 --> 00:29:29,510
+لـ F of T برجع للتعريف المرة اللي فاتت قلنا
+
+257
+00:29:29,510 --> 00:29:37,730
+من Zero إلى Infinity للـ E أس ناقص ST في F of T في
+
+258
+00:29:37,730 --> 00:29:41,050
+الـ DT مش هي التعريف اللي قلناه المرة اللي فاتت
+
+259
+00:29:41,050 --> 00:29:47,510
+الآن بدنا نطبق هذا التعريف لكن هذه كونها دالة مجزأة
+
+260
+00:29:47,510 --> 00:29:53,950
+إلى جزئين يبقى بدي أجزء هذا التكامل إلى تكاملين كل
+
+261
+00:29:53,950 --> 00:29:59,630
+بما يناسبه من Zero لـ واحد قيمة الدالة واحد إذا
+
+262
+00:29:59,630 --> 00:30:07,290
+بدّي أقول له تكامل من Zero لـ واحد للـ E أس ناقص ST ضرب 
+
+263
+00:30:07,290 --> 00:30:15,550
+واحد DT زائد تكامل من واحد إلى Infinity للـ E أس
+
+264
+00:30:15,550 --> 00:30:24,520
+ناقص ST الـ F of T هي Zero في DT يبقى آلة المثال 
+
+265
+00:30:24,520 --> 00:30:29,940
+طبعاً Zero في أي Term هو Zero يبقى بدرجين مين؟
+
+266
+00:30:29,940 --> 00:30:38,440
+بدرجين تكامل فقط من Zero إلى T للـ E أس ناقص S T DT
+
+267
+00:30:38,440 --> 00:30:45,600
+فقط لغيره يبقى هذا الكلام يساوي E أس ناقص S T على
+
+268
+00:30:45,600 --> 00:30:52,440
+تفاضل الأس اللي هو ناقص S و الحكي هذا من Zero لواحد
+
+269
+00:30:56,760 --> 00:31:02,920
+بنعوّض بالقيمة اللي فوق ناقص اللي تحت يبقى E أس
+
+270
+00:31:02,920 --> 00:31:16,890
+ناقص S على ناقص S ناقص E أس ناقص S على ناقص S يبقى
+
+271
+00:31:16,890 --> 00:31:25,190
+هذا الكلام بده يساوي 1 على S ناقص E أس ناقص S 
+
+272
+00:31:25,190 --> 00:31:33,090
+على S هذا Laplace Transform لدالة
+
+273
+00:31:33,090 --> 00:31:43,630
+المعطاة حد بتسأل أي سؤال هنا بنات؟ كيف؟
+
+274
+00:31:47,820 --> 00:31:52,840
+ما لها؟ ناقص 
+
+275
+00:31:52,840 --> 00:31:58,120
+لا لا زائد 1 على S 1 على S فقط ناقص ناقص
+
+276
+00:31:58,120 --> 00:32:03,000
+زائد 1 على S و هذه ناقص يعني بتقدر تقول كل
+
+277
+00:32:03,000 --> 00:32:09,700
+واحد على S عامل مشترك 1 ناقص E أس ناقص S 
+
+278
+00:32:09,700 --> 00:32:15,840
+بالشكل هذا طيب ننتقل الآن إلى ال Section اللي يليه 
+
+279
+00:32:15,840 --> 00:32:23,740
+بعد أن نعطيه الـ exercises اللي هي تسعة واحد تسعة
+
+280
+00:32:23,740 --> 00:32:32,260
+واحد المسائل التالية السؤال الأول بدنا منه A و C و F 
+
+281
+00:32:32,260 --> 00:32:45,500
+و G و I و السؤال الثاني بدنا منه A و D و E و F و السؤال
+
+282
+00:32:45,500 --> 00:32:54,300
+الثالث بدنا منه A و D و E و بعد هيك بدنا السؤال
+
+283
+00:32:54,300 --> 00:32:59,180
+الثامن بدنا 
+
+284
+00:32:59,180 --> 00:33:04,820
+نروح الآن لـ Section تسعة ثلاثة تسعة اثنين نشطب
+
+285
+00:33:04,820 --> 00:33:12,340
+ونروح لتسعة ثلاثة اللي هي ال Properties of Laplace
+
+286
+00:33:12,340 --> 00:33:19,260
+Transforms Laplace Transforms
+
+287
+00:33:19,260 --> 00:33:27,220
+يبقى خصائص تحويلات Laplace بقول
+
+288
+00:33:27,220 --> 00:33:30,720
+If Laplace
+
+289
+00:33:36,950 --> 00:33:43,730
+Transform exist for
+
+290
+00:33:43,730 --> 00:33:46,950
+a
+
+291
+00:33:46,950 --> 00:34:01,110
+given Function لدالة ماطعة Then نقطة
+
+292
+00:34:01,110 --> 00:34:10,300
+الأولى بدنا Laplace Transform لـ C1 في F of T زائد
+
+293
+00:34:10,300 --> 00:34:19,320
+C2 في G of T اللي هي بدها تساوي C1 Laplace
+
+294
+00:34:19,320 --> 00:34:28,960
+Transform للـ F of T زائد C2 Laplace Transform للـ G
+
+295
+00:34:28,960 --> 00:34:30,140
+of T
+
+296
+00:34:35,100 --> 00:34:47,980
+اللي هي بقدر أقول C1 F of S زائد C2 G of S هذه
+
+297
+00:34:47,980 --> 00:34:52,020
+خاصية Linearity خاصية طبيعية أخذناها المرة اللي
+
+298
+00:34:52,020 --> 00:35:04,440
+فاتت الجديد هو ما يأتي F H of T بدي يساوي E أس CT
+
+299
+00:35:05,020 --> 00:35:16,880
+في الـ F of T في الـ F of T Then H of S لـ Laplace
+
+300
+00:35:16,880 --> 00:35:25,700
+Transform لها بدها تساوي F في S ناقص الـ C
+
+301
+00:35:25,700 --> 00:35:38,480
+نمرة ثلاثة F الـ K of T بدي يساوي تكامل من Zero
+
+302
+00:35:38,480 --> 00:35:49,920
+تكامل من Zero إلى T للـ F of U دي U Then K
+
+303
+00:35:49,920 --> 00:35:59,800
+of S بدي يساوي 1 على S في مين؟ في F of 
+
+304
+00:35:59,800 --> 00:36:00,420
+S
+
+305
+00:36:02,830 --> 00:36:14,210
+نمرة أربعة If الـ P N as a Function of T هو عبارة عن
+
+306
+00:36:14,210 --> 00:36:22,290
+T to the power N فاهمين؟ في الـ F of T في الـ F of T 
+
+307
+00:36:22,290 --> 00:36:31,270
+Then الـ P N of S الـ P N of S 
+
+308
+00:36:49,230 --> 00:37:00,240
+نمرة خمسة بيقول F الـ Q of T بدها تساوي أحد أمرين 
+
+309
+00:37:00,240 --> 00:37:08,440
+يا إما Zero لما T أكبر من الـ Zero و أقل من C يا
+
+310
+00:37:08,440 --> 00:37:16,100
+إما الـ F of T ناقص الـ C لما T أكبر من الـ C
+
+311
+00:37:19,130 --> 00:37:35,140
+الـ Q of S بدها تساوي E أس ناقص CS في F of S آخر
+
+312
+00:37:35,140 --> 00:37:39,640
+حاجة كتبناها قبل هيك المرة في نهاية المحاضرة 
+
+313
+00:37:39,640 --> 00:37:47,620
+الماضية بدي لـ Laplace Transform لتفاضل رقم N عند T
+
+314
+00:37:47,620 --> 00:37:56,080
+بدها تساوي S to the power N F of S ناقص
+
+315
+00:37:56,080 --> 00:38:02,880
+افتح قوس اللي هو الـ S أس N ولا بلّغ القوس خلّيها
+
+316
+00:38:02,880 --> 00:38:13,500
+دغري يبقى ناقص SN-1F0
+
+317
+00:38:13,500 --> 00:38:20,460
+-SN-2F'0
+
+318
+00:38:23,450 --> 00:38:31,770
+نظلّ ناقص لغاية ما نوصل في التفضل رقم N ناقص واحد
+
+319
+00:38:31,770 --> 00:38:34,510
+عند مين؟ عند الـ Zero
+
+320
+00:38:55,110 --> 00:38:58,650
+الآن بدنا نجمّل بعض الشغلات اللي أخذناها في Laplace
+
+321
+00:38:58,650 --> 00:39:03,670
+Transform و اللي موجودة في الكتاب سواء أخذناها أو
+
+322
+00:39:03,670 --> 00:39:08,710
+ما أخذناها قبل ذلك هنعطيك جميل مثلها وهي Some
+
+323
+00:39:08,710 --> 00:39:15,190
+Basic Laplace
+
+324
+00:39:15,190 --> 00:39:18,210
+Transforms
+
+325
+00:39:23,680 --> 00:39:34,200
+النقطة الأولى If الـ F of T تساوي T to the power N 
+
+326
+00:39:34,200 --> 00:39:43,660
+Then اللي هو F of S بدها تساوي N Factorial
+
+327
+00:39:43,660 --> 00:39:52,060
+على S أس N زائد 1 نمرة اثنين If 
+
+328
+00:39:53,410 --> 00:40:07,810
+الـ F of T يبدو يساوي E أس AT ثم F of S يبدو
+
+329
+00:40:07,810 --> 00:40:12,570
+يساوي 1 على S ناقص الـ A
+
+330
+00:40:16,480 --> 00:40:26,080
+الـ F of T بدها تساوي Cosine AT Then F of S
+
+331
+00:40:26,080 --> 00:40:35,260
+بدها تساوي الـ S على S تربيع زائد A تربيع نمرة أربعة 
+
+332
+00:40:35,260 --> 00:40:46,050
+F الـ F of T بدها تساوي الـ Sine AT Then اللي هو 
+
+333
+00:40:46,050 --> 00:40:53,410
+F of S بدها تساوي من؟ بدها تساوي الـ A على S 
+
+334
+00:40:53,410 --> 00:41:02,070
+تربيع زائد A تربيع خمسة F الـ F of T بدها تساوي
+
+335
+00:41:02,070 --> 00:41:14,820
+Sinh AT Then F of S بدها تساوي A على S
+
+336
+00:41:14,820 --> 00:41:24,340
+تربيع ناقص A تربيع نمرة ستة لو كان الـ F of T والله 
+
+337
+00:41:24,340 --> 00:41:29,840
+F الـ F of T بدها تساوي Cosh
+
+338
+00:41:32,360 --> 00:41:44,520
+F of S بيساوي S على S تربيع ناقص A تربيع نمرة سبعة
+
+339
+00:41:44,520 --> 00:41:57,980
+F F of T بيساوي E أس AT في Sine BT 
+
+340
+00:42:02,120 --> 00:42:19,040
+بعد ذلك F of S بيساوي B على S ناقص A كل تربيع زائد 
+
+341
+00:42:19,040 --> 00:42:30,700
+B تربيع ثمانية F الـ F of T بدها تساوي E أس AT فيه
+
+342
+00:42:30,700 --> 00:42:38,760
+Cosine BT Then F of S بدها تساوي اللي هو الـ
+
+343
+00:42:38,760 --> 00:42:50,030
+S ناقص الـ A على S ناقص الـ A لكل تربيع زائد B 
+
+344
+00:42:50,030 --> 00:43:01,370
+تربيع آخر حاجة نمرة تسعة بيقول F الـ F of T بدها
+
+345
+00:43:01,370 --> 00:43:14,020
+تساوي T أس N E أس AT  Then the
+
+346
+00:43:14,020 --> 00:43:25,420
+F of S بدها تساوي N Factorial مقسومة على S
+
+347
+00:43:25,420 --> 00:43:35,480
+ناقص الـ A to the power N زائد 1 و الـ N is a
+
+348
+00:43:35,480 --> 00:43:38,940
+Positive Integer
+
+349
+00:43:54,030 --> 00:43:58,770
+ألا من أن أتعرض لكل نقطة بالتفصيل، شو مفهوم هذه
+
+350
+00:43:58,770 --> 00:44:03,830
+بنات، بيجيكوا مش 9 ولا 15 واحدة في الامتحان،
+
+351
+00:44:03,830 --> 00:44:09,290
+بيجيبونكوا في جدول مشان تستخدميها متى ما كان ذلك،
+
+352
+00:44:09,290 --> 00:44:12,330
+مش مشكلة موجودة عندك في الكتاب نفسها، ضايقش وقت
+
+353
+00:44:12,330 --> 00:44:16,450
+فيها، خلينا نفهم بس، لأن فهمنا هدول، بيصير
+
+354
+00:44:16,450 --> 00:44:22,320
+قضيتنا بعد ذلك قضية سهلة يبقى بنات الآن في خمسة 
+
+355
+00:44:22,320 --> 00:44:27,180
+نماذج امتحانات موجودة في مكتبة الطالب كل واحدة
+
+356
+00:44:27,180 --> 00:44:31,280
+بدها نسخة بتروح تاخد نسخة طبعاً امتحانات سابقة
+
+357
+00:44:31,280 --> 00:44:37,300
+و غالباً امتحانات حديثة الـ class Transform
+
+358
+00:44:37,870 --> 00:44:42,870
+بيقول لو كان Laplace Transform لدالة ما Exist يبقى
+
+359
+00:44:42,870 --> 00:44:48,790
+عندنا ست خواص أو ست خصائص نتعرض لهذه الخصائص الست 
+
+360
+00:44:48,790 --> 00:44:54,530
+خاصية الأولى خاصية الـ Linearity يعني اللي لما تدخل
+
+361
+00:44:54,530 --> 00:44:59,950
+على مجموعة من الدوال مضروبة في ثوابت بقول الثابت
+
+362
+00:44:59,950 --> 00:45:03,730
+في Laplace Transform للدالة الثابت الثاني في
+
+363
+00:45:03,730 --> 00:45:08,630
+Laplace Transform للدالة الثانية أو لـ Laplace Transform
+
+364
+00:45:08,630 --> 00:45:14,910
+الدالة بتعطي الرمز F of S و هذا قلناه
+
+365
+00:45:14,910 --> 00:45:17,710
+المرة اللي فاتت أول ما عرفنا Laplace Transform
+
+366
+00:45:17,710 --> 00:45:22,150
+للدالة F of T قلنا يا ابنتي تب Laplace للـ F of T هم 
+
+367
+00:45:22,150 --> 00:45:25,770
+يقولوا F of S و ليش F of S؟ لأن
+
+368
+00:45:25,770 --> 00:45:30,310
+الدالة بتطلع بتطلع بدلالة S يعني بتطلع As a
+
+369
+00:45:30,310 --> 00:45:39,550
+Function of S يبقى هنا بقول C1 F of S زي C2 G of S 
+
+370
+00:45:39,550 --> 00:45:45,190
+هذا الخاصية الأولى خاصية ثانية لو كان شكل الدالة 
+
+371
+00:45:45,190 --> 00:45:50,810
+اللي بدي أوجد لها Laplace على شكل E أس CT في F of T
+
+372
+00:45:50,810 --> 00:45:56,590
+و بدي Laplace Transform لها إذا Laplace Transform 
+
+373
+00:45:56,590 --> 00:46:02,110
+لهذه الدالة بتدي له H of S يساوي F of S
+
+374
+
+401
+00:48:26,960 --> 00:48:32,900
+بأنسى أن في عندك T والسن بأخذ Mيم F of T وبأروح
+
+402
+00:48:32,900 --> 00:48:37,660
+بجيبلها لابلاس الترانسفورم لما حصلت على ميم على F of
+
+403
+00:48:37,660 --> 00:48:45,120
+S بأروح بأفاضلها N من المرات، يعني لو كان أن ها ت تربيع
+
+404
+00:48:45,120 --> 00:48:50,800
+بأفاضل هنا مرتين، لو كان ت أس واحد بأفاضل مرة واحدة،
+
+405
+00:48:50,800 --> 00:48:55,300
+لو كان ت تكعيب بأفاضل ثلاث مرات، وفي كل مرة بدي 
+
+406
+00:48:55,300 --> 00:48:59,440
+أضرب نتيجة التفاضل في سالب واحد أو سالب واحد تربيع
+
+407
+00:48:59,440 --> 00:49:04,700
+أو سالب واحد تكعيب، حسب طبيعة المثلّة، لا تنسى مرة
+
+408
+00:49:04,700 --> 00:49:09,930
+ثانية T أو N في F of T بجيب لابلاس لـ F of T وبأروح
+
+409
+00:49:09,930 --> 00:49:14,830
+بأشتقها T من المرات وبأضرب فيه سالب واحد أو N بيكون 
+
+410
+00:49:14,830 --> 00:49:19,770
+حصلت على لابلاس ترانسفورم لهذه الدالة، قبل قليل كان
+
+411
+00:49:19,770 --> 00:49:24,710
+عندنا دالة مكونة من جزأين من هذا القبيل بدي أبحث
+
+412
+00:49:24,710 --> 00:49:29,690
+على لابلاس ترانسفورم لدالة من هذا القبيل، الدالة هذه
+
+413
+00:49:29,690 --> 00:49:34,430
+تساوي Zero من Zero إلى C لما الـ T تتغير من Zero إلى
+
+414
+00:49:34,430 --> 00:49:41,540
+C أو F of T ناقص C لما T أكبر من C يعني كانوا
+
+415
+00:49:41,540 --> 00:49:47,920
+الدالة معمولة لها shift إزاحة جهة اليمين بمقدار C
+
+416
+00:49:47,920 --> 00:49:52,940
+بدي لها لابلاس ترانسفورم لها، لابلاس ترانسفورم لـ Q of
+
+417
+00:49:52,940 --> 00:49:58,420
+T، بدي أقول كابيتال لـ Q of S، إيش بدي أسوي؟ بدي أجي
+
+418
+00:49:58,420 --> 00:50:04,430
+على الدالة هذه وأشيل الـ C بيظل مين عندي؟ F of D
+
+419
+00:50:04,430 --> 00:50:10,030
+بيظل، وأجيب لابلاس ترانسفورم للـ F of D مين بيطلع؟ F
+
+420
+00:50:10,030 --> 00:50:17,870
+of S بأضربه في E أس ناقص C S اللي عندنا، يعني لو كانت
+
+421
+00:50:17,870 --> 00:50:23,590
+هدى زائد بيصير هدى زائد هدى ناقص هدى ناقص مرة 
+
+422
+00:50:23,590 --> 00:50:28,710
+ثانية، الخاصية دي جي كويس، very important، أنا بدي
+
+423
+00:50:28,710 --> 00:50:33,670
+لابلاس لهذه الدالة، بأقول لابلاس لـ بأجي على الـ F of 
+
+424
+00:50:33,670 --> 00:50:40,590
+T وبأجيب لابلاس لـ بعدين هذه اللي جبتها بأضربها في
+
+425
+00:50:40,590 --> 00:50:45,730
+الـ E أس ناقص الـ shift اللي عندنا هذا مضروب في مين
+
+426
+00:50:45,730 --> 00:50:50,570
+في S، هذه ما هي جديدة، كتبناها معاك المرة اللي فاتت
+
+427
+00:50:50,570 --> 00:50:55,080
+هذه الـ A يوجد فيها أي حرف جديد، اللي هو الـ in 
+
+428
+00:50:55,080 --> 00:50:59,900
+general، عاممنا نظرية أخذناها المرة الماضية، هذا 
+
+429
+00:50:59,900 --> 00:51:03,920
+الجدول، لو كانت الدالة شكلها إيش، بيقولها لابلاس،
+
+430
+00:51:03,920 --> 00:51:07,100
+إيه هي ترانسفورم؟ هذه وهذه حسبناها المرة اللي
+
+431
+00:51:07,100 --> 00:51:11,920
+فاتت، مظبوط؟ الـ exponential كمان حسبناها المرة 
+
+432
+00:51:11,920 --> 00:51:16,740
+اللي فاتت، هذه ما حسبناش صحيح، هي قيمتها، هذه الباقية
+
+433
+00:51:16,740 --> 00:51:21,500
+جوش و سنش حسبنا ضربنا في نص وجبنا في حالة الـ 
+
+434
+00:51:21,500 --> 00:51:25,300
+linearity وجبنا ما بعرف هذه أو هذه واحدة منهم و
+
+435
+00:51:25,300 --> 00:51:29,740
+التانية زيها، هذول ما جبناهمش صحيح لكن هي لابلاس
+
+436
+00:51:29,740 --> 00:51:35,440
+ترانسفورم اللهم هذول وهذه وبعض الشغلات هذه كلها 
+
+437
+00:51:35,440 --> 00:51:40,130
+هتلاقيها موجودة وين في الجدول اللي بيجيك في نهاية
+
+438
+00:51:40,130 --> 00:51:45,390
+ورقة الامتحان، نكتفي بهذا القدر إن شاء الله ولأن
+
+439
+00:51:45,390 --> 00:51:52,010
+إليه عوضة في المحاضرة القادمة وسنبدأ بحل أمثلة على 
+
+440
+00:51:52,010 --> 00:51:57,190
+كيفية استخدام هذه الخواص وهو very important لذلك
+
+441
+00:51:57,190 --> 00:52:00,930
+المرة الجاية كل واحدة بتجيب كتابتها معاها بأكد على
+
+442
+00:52:00,930 --> 00:52:05,210
+وجود الكتاب بلاش تخلوني أطردكوا برا، كل واحدة بتجيب
+
+443
+00:52:05,210 --> 00:52:09,680
+كتابتها معاها وتيجي مطالعة عاليه على الخواص لإنها تطبيق
+
+444
+00:52:09,680 --> 00:52:13,680
+عامة اللي بيقولك افتح الكتاب وأي سؤال ونية خاصية
+
+445
+00:52:13,680 --> 00:52:18,340
+بتناسب ونروح نستخدم الخاصية لإن في الامتحان
+
+446
+00:52:18,340 --> 00:52:21,940
+بيجيكوا سؤال زي إيه دائماً هو بيجيب زي إيه بيبقى 
+
+447
+00:52:21,940 --> 00:52:25,300
+challenge وبتعرف أنت تستخدم الجدول اللي عندك و
+
+448
+00:52:25,300 --> 00:52:28,360
+تكتشف يلزم أم لا، بارك الله فيك 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..81b3e4f527b5f022009bd488a11a39632cfab622
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/O9lJH0x9RBw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4168, "start": 19.98, "end": 41.68, "text": "بسم الله الرحمن الرحيم آخر حاجة أخدناها في المحاضرة الماضية وهو Laplace transform لمين للمشتقة فقولنا أخدنا Laplace transform للمشتقة الأورا عبارة عن S الدلة بين اشتقاق ناقص ال function and when and zero", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 19753, 34740, 11331, 26108, 3660, 5551, 9778, 3215, 8315, 11296, 8978, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 37037, 2407, 2369, 6742, 4088, 32767, 9957, 5296, 19528, 8592, 2655, 28671, 6156, 39648, 8315, 5551, 9778, 3215, 8315, 2369, 6742, 4088, 5296, 19528, 8592, 2655, 28671, 16247, 13063, 995, 6225, 3555, 9640, 3660, 18871, 318, 32748, 37977, 49374, 1975, 8592, 2655, 4587, 995, 4587, 8717, 995, 4587, 9381, 2423, 2445, 293, 562, 293, 4018], "avg_logprob": -0.21103162399257522, "compression_ratio": 1.614213197969543, "no_speech_prob": 0.0, "words": [{"start": 19.98, "end": 20.32, "word": "بسم", "probability": 0.685546875}, {"start": 20.32, "end": 20.56, "word": " الله", "probability": 0.96728515625}, {"start": 20.56, "end": 20.94, "word": " الرحمن", "probability": 0.9488932291666666}, {"start": 20.94, "end": 21.52, "word": " الرحيم", "probability": 0.9928385416666666}, {"start": 21.52, "end": 22.76, "word": " آخر", "probability": 0.690673828125}, {"start": 22.76, "end": 23.06, "word": " حاجة", "probability": 0.97021484375}, {"start": 23.06, "end": 23.56, "word": " أخدناها", "probability": 0.901953125}, {"start": 23.56, "end": 23.68, "word": " في", "probability": 0.970703125}, {"start": 23.68, "end": 24.42, "word": " المحاضرة", "probability": 0.982666015625}, {"start": 24.42, "end": 25.38, "word": " الماضية", "probability": 0.9930013020833334}, {"start": 25.38, "end": 26.5, "word": " وهو", "probability": 0.6466064453125}, {"start": 26.5, "end": 27.16, "word": " Laplace", "probability": 0.53662109375}, {"start": 27.16, "end": 28.3, "word": " transform", "probability": 0.62744140625}, {"start": 28.3, "end": 29.3, "word": " لمين", "probability": 0.7196044921875}, {"start": 29.3, "end": 30.92, "word": " للمشتقة", "probability": 0.77431640625}, {"start": 30.92, "end": 31.94, "word": " فقولنا", "probability": 0.713623046875}, {"start": 31.94, "end": 32.28, "word": " أخدنا", "probability": 0.9696044921875}, {"start": 32.28, "end": 32.68, "word": " Laplace", "probability": 0.893798828125}, {"start": 32.68, "end": 33.5, "word": " transform", "probability": 0.96484375}, {"start": 33.5, "end": 34.54, "word": " للمشتقة", "probability": 0.938671875}, {"start": 34.54, "end": 35.06, "word": " الأورا", "probability": 0.6378580729166666}, {"start": 35.06, "end": 35.58, "word": " عبارة", "probability": 0.984130859375}, {"start": 35.58, "end": 35.88, "word": " عن", "probability": 0.99462890625}, {"start": 35.88, "end": 36.2, "word": " S", "probability": 0.67919921875}, {"start": 36.2, "end": 37.14, "word": " الدلة", "probability": 0.329833984375}, {"start": 37.14, "end": 37.42, "word": " بين", "probability": 0.9560546875}, {"start": 37.42, "end": 38.26, "word": " اشتقاق", "probability": 0.9432779947916666}, {"start": 38.26, "end": 38.98, "word": " ناقص", "probability": 0.9862060546875}, {"start": 38.98, "end": 39.22, "word": " ال", "probability": 0.93359375}, {"start": 39.22, "end": 39.8, "word": " function", "probability": 0.89794921875}, {"start": 39.8, "end": 40.2, "word": " and", "probability": 0.87060546875}, {"start": 40.2, "end": 40.6, "word": " when", "probability": 0.57763671875}, {"start": 40.6, "end": 41.22, "word": " and", "probability": 0.51806640625}, {"start": 41.22, "end": 41.68, "word": " zero", "probability": 0.274658203125}], "temperature": 1.0}, {"id": 2, "seek": 6400, "start": 42.02, "end": 64.0, "text": "و بعد ذلك رحنا اخدنا لبلاس للمشتقة الثانية قولنا هو عبارة عن S2 في لبلاس لل F of T بدون اشتقاق ناقص S في F of Zero ناقص F prime of Zero بعد ذلك عمّمناها لو كانت مشتقة نونية", "tokens": [2407, 39182, 29910, 23275, 12602, 5016, 8315, 1975, 9778, 3215, 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7435, 1829, 4117, 1829, 8978, 8717, 11296, 10632, 4032, 2288, 4587, 10632, 2423, 10943, 2655, 5016, 7649, 8717, 4117, 2655, 41185, 39627, 15730, 25062, 3215, 2288, 16472, 13412, 16606, 21984, 4032, 1211, 7649, 11933, 20292, 3224, 6225, 2407, 11242, 3660, 8978, 9673, 5016, 46958, 25720, 25062, 18513, 46007, 46952, 1863, 44510, 10721, 4724, 5016, 1211, 5551, 2304, 12984, 37977, 15844, 9122, 33911, 10632, 44713, 9778, 3215, 10943, 29538, 33962, 2407, 33546, 37037, 2407, 588, 1021, 5296, 8848, 23275, 9673, 25720, 25724, 995, 10632, 28242, 36764, 24401, 3660, 39894, 7435, 1829, 3555, 9122, 2655, 16758, 3660, 20449, 995, 11296, 4724, 10721, 4117, 3215, 15844, 49610, 23328, 33251, 2655, 16758, 4724, 1211, 33599, 6055, 9778, 1211, 11536, 1829, 5551, 9566, 2288, 3215, 4117, 14407, 4724, 23557, 28242, 36764, 24401, 3660, 39894, 7435, 1829, 3555, 9122, 2655, 16758, 3660, 20449, 995, 11296], "avg_logprob": -0.1295705723519228, "compression_ratio": 1.89010989010989, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 3097.03, "end": 3097.29, "word": "في", "probability": 0.755859375}, {"start": 3097.29, "end": 3097.85, "word": " الجدول", "probability": 0.95458984375}, {"start": 3097.85, "end": 3097.99, "word": " اللي", "probability": 0.7294921875}, {"start": 3097.99, "end": 3098.61, "word": " بجيكي", "probability": 0.837841796875}, {"start": 3098.61, "end": 3098.95, "word": " في", "probability": 0.92236328125}, {"start": 3098.95, "end": 3100.13, "word": " نهاية", "probability": 0.93017578125}, {"start": 3100.13, "end": 3100.81, "word": " ورقية", "probability": 0.67462158203125}, {"start": 3100.81, "end": 3101.47, "word": " الامتحان", "probability": 0.96484375}, {"start": 3101.47, "end": 3102.55, "word": " نكتفي", "probability": 0.9490966796875}, {"start": 3102.55, "end": 3102.97, "word": " بهذا", "probability": 0.821533203125}, {"start": 3102.97, "end": 3103.83, "word": " القدر", "probability": 0.9928385416666666}, {"start": 3103.83, "end": 3104.03, "word": " ان", "probability": 0.6484375}, {"start": 3104.03, "end": 3104.33, "word": " شاء", "probability": 0.986083984375}, {"start": 3104.33, "end": 3104.59, "word": " الله", "probability": 0.955078125}, {"start": 3104.59, "end": 3105.39, "word": " ولان", "probability": 0.6077473958333334}, {"start": 3105.39, "end": 3107.27, "word": " إليه", "probability": 0.6793619791666666}, {"start": 3107.27, "end": 3107.71, "word": " عوضة", "probability": 0.832763671875}, {"start": 3107.71, "end": 3107.85, "word": " في", "probability": 0.943359375}, {"start": 3107.85, "end": 3108.33, "word": " المحاضرة", "probability": 0.988037109375}, {"start": 3108.33, "end": 3108.69, "word": " القادمة", "probability": 0.9915364583333334}, {"start": 3108.69, "end": 3109.65, "word": " وسنبدأ", "probability": 0.87939453125}, {"start": 3109.65, "end": 3110.69, "word": " بحل", "probability": 0.9855143229166666}, {"start": 3110.69, "end": 3111.45, "word": " أمثلة", "probability": 0.916259765625}, {"start": 3111.45, "end": 3112.01, "word": " على", "probability": 0.70263671875}, {"start": 3112.01, "end": 3112.57, "word": " كيفية", "probability": 0.9881184895833334}, {"start": 3112.57, "end": 3113.25, "word": " استخدام", "probability": 0.96533203125}, {"start": 3113.25, "end": 3113.59, "word": " هذه", "probability": 0.97412109375}, {"start": 3113.59, "end": 3114.17, "word": " الخواص", "probability": 0.7119954427083334}, {"start": 3114.17, "end": 3114.85, "word": " وهو", "probability": 0.863525390625}, {"start": 3114.85, "end": 3115.21, "word": " very", "probability": 0.8525390625}, {"start": 3115.21, "end": 3116.49, "word": " important", "probability": 0.95263671875}, {"start": 3116.49, "end": 3117.19, "word": " لذلك", "probability": 0.9801432291666666}, {"start": 3117.19, "end": 3117.59, "word": " المرة", "probability": 0.9287109375}, {"start": 3117.59, "end": 3117.93, "word": " الجاية", "probability": 0.8282877604166666}, {"start": 3117.93, "end": 3118.15, "word": " كل", "probability": 0.93310546875}, {"start": 3118.15, "end": 3118.49, "word": " واحدة", "probability": 0.9920247395833334}, {"start": 3118.49, "end": 3118.95, "word": " بتجيب", "probability": 0.8731689453125}, {"start": 3118.95, "end": 3119.41, "word": " كتابة", "probability": 0.97509765625}, {"start": 3119.41, "end": 3119.71, "word": " معاها", "probability": 0.9226888020833334}, {"start": 3119.71, "end": 3120.35, "word": " بأكد", "probability": 0.8646240234375}, {"start": 3120.35, "end": 3120.93, "word": " على", "probability": 0.93896484375}, {"start": 3120.93, "end": 3121.35, "word": " وجود", "probability": 0.982666015625}, {"start": 3121.35, "end": 3122.05, "word": " الكتاب", "probability": 0.9903971354166666}, {"start": 3122.05, "end": 3122.67, "word": " بلاش", "probability": 0.7771809895833334}, {"start": 3122.67, "end": 3123.15, "word": " تخلوني", "probability": 0.8265625}, {"start": 3123.15, "end": 3123.63, "word": " أطردكوا", "probability": 0.9015299479166666}, {"start": 3123.63, "end": 3123.97, "word": " برا", "probability": 0.978759765625}, {"start": 3123.97, "end": 3124.63, "word": " كل", "probability": 0.8623046875}, {"start": 3124.63, "end": 3124.93, "word": " واحدة", "probability": 0.9938151041666666}, {"start": 3124.93, "end": 3125.21, "word": " بتجيب", "probability": 0.896728515625}, {"start": 3125.21, "end": 3125.59, "word": " كتابة", "probability": 0.990966796875}, {"start": 3125.59, "end": 3126.03, "word": " معاها", "probability": 0.96875}], "temperature": 1.0}, {"id": 135, "seek": 314836, "start": 3126.34, "end": 3148.36, "text": "و تيجي مطالع عالي على الخواص لإنه تضطيق عامة اللي بيقولك افتح الكتاب و اي سؤال و نية خاصية بتناسب و نروح نستخدم الخاصية لإن في الامتحان بيجيكوا سؤال زي ايه دايما هو بيجيب زي ايه بيبقى challenge و بتعرف انت تستخدمه الجدل اللي عندك و اكتشف يلزم ام لا برك الله فيك", "tokens": [2407, 6055, 1829, 7435, 1829, 3714, 9566, 6027, 3615, 6225, 6027, 1829, 15844, 33962, 2407, 33546, 5296, 28814, 1863, 3224, 6055, 11242, 9566, 1829, 4587, 6225, 10943, 3660, 13672, 1829, 4724, 1829, 39648, 4117, 1975, 5172, 2655, 5016, 2423, 4117, 2655, 16758, 4032, 1975, 1829, 8608, 33604, 6027, 4032, 8717, 10632, 16490, 33546, 10632, 39894, 8315, 35457, 4032, 8717, 32887, 5016, 8717, 14851, 9778, 40448, 33962, 33546, 10632, 5296, 28814, 1863, 8978, 2423, 10943, 2655, 5016, 7649, 4724, 1829, 7435, 1829, 4117, 14407, 8608, 33604, 6027, 30767, 1829, 1975, 1829, 3224, 11778, 47302, 15042, 31439, 4724, 1829, 7435, 1829, 3555, 30767, 1829, 1975, 1829, 3224, 4724, 1829, 3555, 4587, 7578, 3430, 4032, 39894, 3615, 28480, 16472, 2655, 6055, 14851, 9778, 40448, 3224, 25724, 3215, 1211, 13672, 1829, 43242, 4117, 4032, 1975, 4117, 2655, 8592, 5172, 7251, 1211, 11622, 2304, 1975, 2304, 20193, 4724, 31747, 21984, 8978, 4117], "avg_logprob": -0.22846283743510376, "compression_ratio": 1.8816326530612244, "no_speech_prob": 2.2649765014648438e-06, "words": [{"start": 3126.34, "end": 3126.62, "word": "و", "probability": 0.468017578125}, {"start": 3126.62, "end": 3126.96, "word": " تيجي", "probability": 0.8568115234375}, {"start": 3126.96, "end": 3127.66, "word": " مطالع", "probability": 0.7232666015625}, {"start": 3127.66, "end": 3127.94, "word": " عالي", "probability": 0.6464436848958334}, {"start": 3127.94, "end": 3128.06, "word": " على", "probability": 0.72119140625}, {"start": 3128.06, "end": 3128.66, "word": " الخواص", "probability": 0.8790690104166666}, {"start": 3128.66, "end": 3129.2, "word": " لإنه", "probability": 0.8309326171875}, {"start": 3129.2, "end": 3129.68, "word": " تضطيق", "probability": 0.88798828125}, {"start": 3129.68, "end": 3130.0, "word": " عامة", "probability": 0.6947428385416666}, {"start": 3130.0, "end": 3130.1, "word": " اللي", "probability": 0.71484375}, {"start": 3130.1, "end": 3130.5, "word": " بيقولك", "probability": 0.78662109375}, {"start": 3130.5, "end": 3130.78, "word": " افتح", "probability": 0.9371337890625}, {"start": 3130.78, "end": 3131.34, "word": " الكتاب", "probability": 0.81524658203125}, {"start": 3131.34, "end": 3131.8, "word": " و", "probability": 0.64794921875}, {"start": 3131.8, "end": 3132.02, "word": " اي", "probability": 0.6763916015625}, {"start": 3132.02, "end": 3132.6, "word": " سؤال", "probability": 0.9156901041666666}, {"start": 3132.6, "end": 3132.96, "word": " و", "probability": 0.9697265625}, {"start": 3132.96, "end": 3133.18, "word": " نية", "probability": 0.562744140625}, {"start": 3133.18, "end": 3133.68, "word": " خاصية", "probability": 0.9881184895833334}, {"start": 3133.68, "end": 3134.28, "word": " بتناسب", "probability": 0.8074544270833334}, {"start": 3134.28, "end": 3134.7, "word": " و", "probability": 0.8779296875}, {"start": 3134.7, "end": 3134.98, "word": " نروح", "probability": 0.90185546875}, {"start": 3134.98, "end": 3135.66, "word": " نستخدم", "probability": 0.9886474609375}, {"start": 3135.66, "end": 3137.22, "word": " الخاصية", "probability": 0.9757486979166666}, {"start": 3137.22, "end": 3137.7, "word": " لإن", "probability": 0.9612630208333334}, {"start": 3137.7, "end": 3137.8, "word": " في", "probability": 0.7265625}, {"start": 3137.8, "end": 3138.34, "word": " الامتحان", "probability": 0.94716796875}, {"start": 3138.34, "end": 3138.82, "word": " بيجيكوا", "probability": 0.9597981770833334}, {"start": 3138.82, "end": 3139.08, "word": " سؤال", "probability": 0.98876953125}, {"start": 3139.08, "end": 3139.34, "word": " زي", "probability": 0.9794921875}, {"start": 3139.34, "end": 3139.76, "word": " ايه", "probability": 0.787353515625}, {"start": 3139.76, "end": 3140.4, "word": " دايما", "probability": 0.8030598958333334}, {"start": 3140.4, "end": 3140.58, "word": " هو", "probability": 0.8662109375}, {"start": 3140.58, "end": 3140.98, "word": " بيجيب", "probability": 0.85029296875}, {"start": 3140.98, "end": 3141.24, "word": " زي", "probability": 0.90478515625}, {"start": 3141.24, "end": 3141.5, "word": " ايه", "probability": 0.83984375}, {"start": 3141.5, "end": 3141.94, "word": " بيبقى", "probability": 0.6536865234375}, {"start": 3141.94, "end": 3142.38, "word": " challenge", "probability": 0.5166015625}, {"start": 3142.38, "end": 3142.58, "word": " و", "probability": 0.56103515625}, {"start": 3142.58, "end": 3143.0, "word": " بتعرف", "probability": 0.9475911458333334}, {"start": 3143.0, "end": 3143.28, "word": " انت", "probability": 0.3785400390625}, {"start": 3143.28, "end": 3143.92, "word": " تستخدمه", "probability": 0.670654296875}, {"start": 3143.92, "end": 3144.6, "word": " الجدل", "probability": 0.7364095052083334}, {"start": 3144.6, "end": 3144.74, "word": " اللي", "probability": 0.940185546875}, {"start": 3144.74, "end": 3145.18, "word": " عندك", "probability": 0.986328125}, {"start": 3145.18, "end": 3145.3, "word": " و", "probability": 0.9443359375}, {"start": 3145.3, "end": 3145.72, "word": " اكتشف", "probability": 0.76142578125}, {"start": 3145.72, "end": 3146.2, "word": " يلزم", "probability": 0.976806640625}, {"start": 3146.2, "end": 3146.8, "word": " ام", "probability": 0.855712890625}, {"start": 3146.8, "end": 3147.1, "word": " لا", "probability": 0.92333984375}, {"start": 3147.1, "end": 3147.84, "word": " برك", "probability": 0.748291015625}, {"start": 3147.84, "end": 3148.04, "word": " الله", "probability": 0.97412109375}, {"start": 3148.04, "end": 3148.36, "word": " فيك", "probability": 0.912353515625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3148.99725, "duration_after_vad": 2994.0662499999926}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ONz55Bmglq8.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ONz55Bmglq8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..33b4b4f4a4ff187daa0bbccb74333d3d4a7eacf0
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ONz55Bmglq8.srt
@@ -0,0 +1,1302 @@
+1
+00:00:20,700 --> 00:00:25,220
+بسم الله الرحمن الرحيم نعود الآن إلى section 2.4
+
+2
+00:00:25,220 --> 00:00:31,220
+الذي ابتدأنا به المرة الماضية وذكرنا بما قلناه في نهاية
+
+3
+00:00:31,220 --> 00:00:36,060
+الـ section المرة الماضية تكلمنا عن نقطتين الـ raw
+
+4
+00:00:36,060 --> 00:00:40,180
+vector و الـ column vector فبجي بقول لو جيت على
+
+5
+00:00:40,180 --> 00:00:45,640
+المصفوفة و أخدت أعمدة المصفوفة كل عمود على حدة فهذا
+
+6
+00:00:45,640 --> 00:00:51,520
+العمود بسميه column vector يبقى متجه عمودي أو متجه 
+
+7
+00:00:51,520 --> 00:00:57,630
+العمود و لو أخدت كل صف من صفوف هذه المصفوفة بسمي كل 
+
+8
+00:00:57,630 --> 00:01:02,390
+صف هو الـ raw vector اللي هو متجه vector والعكس لو
+
+9
+00:01:02,390 --> 00:01:07,570
+عندي raw vectors أو column vectors بالنسبة لمصفوفة
+
+10
+00:01:07,570 --> 00:01:12,810
+بقدر أرجعهم إلى أصل المصفوفة الآن بدأ نعطي مثال
+
+11
+00:01:12,810 --> 00:01:18,770
+توضيحي بقول لو كان عندك U1 هي raw vector ولا 
+
+12
+00:01:18,770 --> 00:01:26,440
+column vector هذا column vector U3
+
+13
+00:01:26,440 --> 00:01:31,220
+يبقى من هذه الأعمدة بقدر أكتب المصفوفة تبعتهم على
+
+14
+00:01:31,220 --> 00:01:36,940
+الشكل التالي يبقى U1 و U2 و U3 كل من U1 و U2 و U3
+
+15
+00:01:36,940 --> 00:01:40,850
+عبارة عن عمود إذا بكتبهم داخل مصفوفة هي العمود
+
+16
+00:01:40,850 --> 00:01:45,750
+الأول هي العمود الثاني هي العمود الثالث يبقى من
+
+17
+00:01:45,750 --> 00:01:50,470
+خلال هذه الأعمدة كتبنا المصفوفة أو العكس لو بدأ
+
+18
+00:01:50,470 --> 00:01:54,930
+نكتبهم بدلالة الصفوف يبقى بدل الشكل اللي عندنا هذا
+
+19
+00:01:54,930 --> 00:02:00,710
+هكتب من الشكل اللي عندنا هذا V1 عبارة عن صف V2
+
+20
+00:02:00,710 --> 00:02:04,510
+عبارة عن من؟ عن صف لأن زي ما تشوفي المصفوفة دي
+
+21
+00:02:04,510 --> 00:02:09,370
+الصفين وثلاثة أعمدة إذا لو بدي أكتبها بواسط الصف
+
+22
+00:02:09,370 --> 00:02:13,890
+بدي أجي على أول واحد وسالب واحد واثنين وأروح
+
+23
+00:02:13,890 --> 00:02:16,690
+أقول واحد وسالب واحد واثنين وهذا هو عبارة عن
+
+24
+00:02:16,690 --> 00:02:23,080
+مين؟ عن V1 V2 هو عبارة عن اثنين وواحد وثلاثة يبقى 
+
+25
+00:02:23,080 --> 00:02:28,740
+اثنين وواحد وثلاثة إذا يمكن كتابة المصفوفة as a row
+
+26
+00:02:28,740 --> 00:02:34,360
+of vectors أو as a column of vectors والعكس صحيح لو
+
+27
+00:02:34,360 --> 00:02:38,120
+عندي row of vectors أو column of vectors ممكن أكتبهم
+
+28
+00:02:38,120 --> 00:02:44,500
+على شكل مصفوفة زي ما هو قدامنا هناك بنجي لتعريف جديد
+
+29
+00:02:44,500 --> 00:02:50,620
+الـ set RN مش المقصود فيها R أُس N يعني set of
+
+30
+00:02:50,620 --> 00:02:53,340
+real numbers مضروبة في بعضها N من المرات لأ مش هذا
+
+31
+00:02:53,340 --> 00:03:00,100
+المقصود يبقى RN رمز يدل على المجموعة الآتية هي
+
+32
+00:03:00,100 --> 00:03:06,340
+مجموعة كل عنصر من عناصرها يوجد فيه N من الـ
+
+33
+00:03:06,340 --> 00:03:11,980
+components زي ما أقول لك إحداثي نقطة واحدة في
+
+34
+00:03:11,980 --> 00:03:14,760
+الغرْب تقول إيه؟ الإحداثي السيني كذا والإحداثي الصادي
+
+35
+00:03:14,760 --> 00:03:18,920
+كذا اثنين أو ثلاثة مثلا يبقى اثنين أو ثلاثة هذا كل
+
+36
+00:03:18,920 --> 00:03:24,060
+element في مستوى الإحداثيات الإحداثيين نقطة موجودة
+
+37
+00:03:24,060 --> 00:03:30,010
+في مستوى الإحداثيات X و Y إذا لما أقول X1 و X2 و X3
+
+38
+00:03:30,010 --> 00:03:35,850
+و XN كلها دا عبارة عن عنصر واحد في الـ set RN في 
+
+39
+00:03:35,850 --> 00:03:40,810
+الـ set RN بس هذا العنصر مُركّب من N من الـ
+
+40
+00:03:40,810 --> 00:03:47,050
+components N من الإحداثيات أو المُركّبات حيث X1 و
+
+41
+00:03:47,050 --> 00:03:52,250
+X2 و XN موجودة في الـ set of real numbers يبقى R دي
+
+42
+00:03:52,250 --> 00:03:58,430
+هي مجموعة الأعداد الحقيقية يبقى لما أكتب R وفوقها
+
+43
+00:03:58,430 --> 00:04:04,670
+N معناته مجموعة الأعداد الحقيقية منها بدي أكون هذه
+
+44
+00:04:04,670 --> 00:04:10,510
+الـ set اللي كل عنصر في هذه الـ set يتكون من مجموعة
+
+45
+00:04:10,510 --> 00:04:15,690
+من المركبات يعني مجموعة من الـ components زي ما أنتَ
+
+46
+00:04:15,690 --> 00:04:21,370
+شايفه The set of
+
+47
+00:04:21,370 --> 00:04:28,530
+all n-dimensional vectors يبقى هي المجموعة المكونة
+
+48
+00:04:28,530 --> 00:04:34,570
+من المتجهات وكل متجهة له N من المُركّبات أو كما
+
+49
+00:04:34,570 --> 00:04:41,270
+سمّيناها في بداية هذا الفيديو قلنا ordered n-tuples
+
+50
+00:04:41,270 --> 00:04:46,910
+يبقى عبارة عن ابعاد كل واحدة فيها N من المراكبات
+
+51
+00:04:46,910 --> 00:04:50,710
+of real numbers يا التسمية هذه يا التسمية دي اللي
+
+52
+00:04:50,710 --> 00:04:55,950
+عاجبك ما عندها مشكلة على سبيل المثال لو قلت بدل الـ
+
+53
+00:04:55,950 --> 00:05:02,050
+N اثنين يبقى R2 يبقى بجي بقول هي the set of all
+
+54
+00:05:02,050 --> 00:05:07,530
+ordered pairs A وB بحيث A وB موجودة ضمنها
+
+55
+00:05:07,530 --> 00:05:14,240
+وكأن هذه النقاط إحداثيات في مستوى مستوى السينات
+
+56
+00:05:14,240 --> 00:05:18,460
+ومستوى الصادات محور السينات ومحور الصادات بيكونوا
+
+57
+00:05:18,460 --> 00:05:23,740
+لمستوى كل نقطة في هذا المستوى لها إحداثين فهي إلا
+
+58
+00:05:23,740 --> 00:05:29,720
+إحداثين فقط لو قلت لك R ثلاثة يبقى هذه إحداثيات
+
+59
+00:05:29,720 --> 00:05:34,390
+نقطة مكونة من ثلاثة مركبات يبقى هذه النقطة موجودة في
+
+60
+00:05:34,390 --> 00:05:39,650
+الفراغ يعني مثلا لو جيت نقول الغرفة اللي أنتَ فيها دي
+
+61
+00:05:39,650 --> 00:05:43,890
+النقطة اللي أنا بدي اعتبرها عبارة عن نقطة يبقى لها
+
+62
+00:05:43,890 --> 00:05:51,360
+إحداثي سيني وإحداثي صادي وإحداثي رأسي X Y و Z يبقى
+
+63
+00:05:51,360 --> 00:05:55,940
+ثلاثة إحداثيات يبقى هنا the set of all three
+
+64
+00:05:55,940 --> 00:06:00,840
+tuples اللي A وB وC بحيث الـ A,B وC موجودة في الـ
+
+65
+00:06:00,840 --> 00:06:06,760
+set of real numbers إذا يا بنات لما أقول RN الـ N
+
+66
+00:06:06,760 --> 00:06:14,230
+هذا هو عدد صحيح موجب تمام؟ لكن المُركّبات اللي في
+
+67
+00:06:14,230 --> 00:06:18,990
+الداخل يمكن كسور ويمكن أعداد سالبة ويمكن أصفار
+
+68
+00:06:18,990 --> 00:06:24,090
+ما عندي مشكلة يبقى الرقم اللي فوق هذا إنه عدد صحيح
+
+69
+00:06:24,090 --> 00:06:29,410
+موجب لكن الأرقام الداخلية هذه كسور كميات سالبة
+
+70
+00:06:29,410 --> 00:06:36,180
+موجبة ما عندي مشكلة طيب هنا ملاحظة تقول إننا نكتب
+
+71
+00:06:36,180 --> 00:06:39,840
+الـ n-dimensional vector by its components أي
+
+72
+00:06:39,840 --> 00:06:44,820
+vector هنا بكتبه بدلالة مركباته فمثلا
+
+73
+00:06:44,820 --> 00:06:49,240
+هذا الـ element لو قلت في هذه الـ set في عندي
+
+74
+00:06:49,240 --> 00:06:55,440
+vector اسمه x يبقى x يتكون من مجموعة مركبات x1 وx2
+
+75
+00:06:55,440 --> 00:07:01,620
+لغاية xn لو قلت في element تاني يكون y يبقى y1 وy2
+
+76
+00:07:01,620 --> 00:07:07,350
+لغاية yn لو قلت في element Z يجب أن أقول Z1, Z2, Z3
+
+77
+00:07:07,350 --> 00:07:13,750
+لغاية ZN وهكذا يعني كل عنصر في الـ RN يتركب أو
+
+78
+00:07:13,750 --> 00:07:20,320
+يتكون من N من المُركّبات هذه اللي بنقوله هنا الآن
+
+79
+00:07:20,320 --> 00:07:25,440
+بدي أجي للعمليات الرياضية على هذه الـ vectors يعني
+
+80
+00:07:25,440 --> 00:07:29,640
+كيف بدي أجمع الـ vectors كيف بدي أضرب vector في رقم
+
+81
+00:07:29,640 --> 00:07:33,240
+ما هو الـ zero vector هذا اللي بنقصده بالـ
+
+82
+00:07:33,240 --> 00:07:39,340
+operations on vectors بالعمليات على المتجه فبعدين
+
+83
+00:07:39,340 --> 00:07:44,780
+بقول لو كتبت الـ vector x بمركباته والـ y بمركباته
+
+84
+00:07:45,290 --> 00:07:49,110
+وكان عندنا c any real number موجب أو سالب صفر ما
+
+85
+00:07:49,110 --> 00:07:53,950
+بتفرقش عنها ضربت هذا c في الـ vector يبقى بروح
+
+86
+00:07:53,950 --> 00:07:59,790
+بضربه في كل مركبة من مركبات هذا الـ vector فمثلا
+
+87
+00:07:59,790 --> 00:08:05,350
+لما أقول c x يبقى الـ c بدي أضربها في كل مركبة من
+
+88
+00:08:05,350 --> 00:08:10,370
+هذه المركبات زي ما تشوفي يبقى بيصير المركبات
+
+89
+00:08:10,370 --> 00:08:17,270
+الجديدة للـ vector CX هي cX1, cX2, cX3 لغاية ما
+
+90
+00:08:17,270 --> 00:08:23,380
+أوصل إلى cXN طب العملية العكسية ايش العملية 
+
+91
+00:08:23,380 --> 00:08:27,580
+العكسية؟ لو كان عندي vector معطى مركباته
+
+92
+00:08:27,580 --> 00:08:32,120
+وطلعته بعيني اللي جيت فيه عمل مشترك ممكن أخده
+
+93
+00:08:32,120 --> 00:08:37,000
+برا إذا بقدر آخده برا الـ vector يبقى هذا يعتبر
+
+94
+00:08:37,000 --> 00:08:40,740
+constant مضروب في من؟ في الـ vector برضه هذا
+
+95
+00:08:40,740 --> 00:08:46,890
+الكلام صحيح الأمر الثاني لو بدي أجمع two vectors مع
+
+96
+00:08:46,890 --> 00:08:52,350
+بعض x زائد y الجمع component wise ايش المقصود بالـ
+
+97
+00:08:52,350 --> 00:08:57,730
+component wise يعني كل مركبة جاها مع نظيرتها
+
+98
+00:08:57,730 --> 00:09:02,860
+وما ليها دخل بالتانية يعني لما يكون عندي two vectors
+
+99
+00:09:02,860 --> 00:09:07,880
+هاي عندنا X وهذا Y وبدي أجمعهم يبقى المركبة الأولى
+
+100
+00:09:07,880 --> 00:09:13,260
+مع المركبة الأولى وتمثل المركبة الأولى في الـ
+
+101
+00:09:13,260 --> 00:09:18,420
+vector الناتج من عملية الجمع إذا لما أقول X زائد
+
+102
+00:09:18,420 --> 00:09:24,700
+Y يبقى X1 زائد Y1 المركبة الثانية X2 زائد Y2
+
+103
+00:09:24,700 --> 00:09:28,020
+المركبة الثانية من المتجه الأول زائد المركبة
+
+104
+00:09:28,020 --> 00:09:31,680
+الثانية من المتجه الثاني بتكون المركبة الثانية في
+
+105
+00:09:31,680 --> 00:09:37,610
+المتجه الجديد يبقى X2 زائد Y2 وهكذا نستمر لغاية ما نوصل
+
+106
+00:09:37,610 --> 00:09:44,010
+لآخر مركبة XN زائد YN يبقى يا بنات إذا عندي 
+
+107
+00:09:44,010 --> 00:09:48,490
+constant بضربه في جميع المركبات إذا عندي مجموعة 
+
+108
+00:09:48,490 --> 00:09:55,950
+vectors بجمع component wise طيب يعني لو جيت تخيل قولنا
+
+109
+00:09:55,950 --> 00:09:59,170
+لبنت هاد يقوم من أكانك بيصير هذا بدي أعتبره 
+
+110
+00:09:59,170 --> 00:10:04,070
+vector مركب من تلت عناصر vector من ثلاث عناصر بدي
+
+111
+00:10:04,070 --> 00:10:07,210
+أجمع .. بجمع الأول هنا مع الأول هناك اللي في النص
+
+112
+00:10:07,210 --> 00:10:11,330
+هنا مع النص اللي في الطرف مع الطرف وهكذا تمام
+
+113
+00:10:11,330 --> 00:10:15,710
+يبقى الجمع في هذه الـ vectors هو component wise طب
+
+114
+00:10:15,710 --> 00:10:21,560
+لو عندي zero vector يبقى zero vector بديله الرمز
+
+115
+00:10:21,560 --> 00:10:26,380
+اللي على الشكل اللي مطول شوية هذا وهذا عبارة عن
+
+116
+00:10:26,380 --> 00:10:35,040
+مجموعة من المركبات عدد هذه المركبات يساوي قداش؟ يساوي
+
+117
+00:10:35,040 --> 00:10:39,570
+N اللي عندنا هذه والراحة اللي هي N يبقى N 
+
+118
+00:10:39,570 --> 00:10:44,750
+dimensional zero vector يبقى zero vector هو عبارة
+
+119
+00:10:44,750 --> 00:10:49,690
+عن vector مكوّن من N من المراكبات وكل مركبة من
+
+120
+00:10:49,690 --> 00:10:56,370
+هذه المراكبات هي zero كل المركبات صفر تمام بحيث
+
+121
+00:10:56,370 --> 00:11:00,350
+الـ zero vector لو أضفته إلى الـ vector X من جهة
+
+122
+00:11:00,350 --> 00:11:06,230
+اليمين أو من جهة الشمال لا يؤثر على وضع الـ vector
+
+123
+00:11:06,230 --> 00:11:11,490
+أصل ليش؟ لأنه لما أجي وأقول هذا X وهذا Zero X
+
+124
+00:11:11,490 --> 00:11:15,170
+واحد زائد Zero ب X واحد لأن X واحد و Zero real
+
+125
+00:11:15,170 --> 00:11:19,910
+numbers وأجي وأقول X اثنين زائد Zero ب X اثنين X
+
+126
+00:11:19,910 --> 00:11:23,610
+ثلاثة زائد Zero ب X ثلاثة وأكده يبقوا ضلمين عندي 
+
+127
+00:11:23,610 --> 00:11:30,690
+X Zero زائد X هو X X زائد Zero هو X كذلك
+
+128
+00:11:30,690 --> 00:11:34,130
+نجمع يمين أو شمال اللي بتفرقش عندنا ليش؟ إن هدول 
+
+129
+00:11:34,130 --> 00:11:37,790
+عبارة عن real numbers الـ zero هذا بسميه
+
+130
+00:11:37,790 --> 00:11:46,250
+n-dimensional zero vector لحد هنا أيوة تفضلي لازم
+
+131
+00:11:46,250 --> 00:11:50,250
+يكون عدد الـ elements متساوي؟ بالضبط تماما وإلا
+
+132
+00:11:50,250 --> 00:11:55,490
+بقدرش يا بنات أجمع element من R2 مع element من R3
+
+133
+00:11:55,490 --> 00:12:00,690
+لأنه ما عنديش component wise ما عنديش اللي هو
+
+134
+00:12:00,690 --> 00:12:06,170
+المركبات المثنفة مثلا لما نيجي نقول هاي اثنين بقدر 
+
+135
+00:12:06,170 --> 00:12:10,910
+أجمع واحد من هنا مع واحد من هنا بمعنى آخر أنا عندي
+
+136
+00:12:10,910 --> 00:12:15,610
+نقطة في مستوى وعندي نقطة في الفراغ بقدر أجمع
+
+137
+00:12:15,610 --> 00:12:19,270
+الاثنتين؟ هذه لها مركبتين وهذه لها ثلاث مركبات
+
+138
+00:12:19,270 --> 00:12:23,670
+بقدرش أجمعهم بقدر أجمع هذه مع هذه وهذه مع هذه و
+
+139
+00:12:23,670 --> 00:12:27,980
+هذه مع مين؟ ما فيش مكان يبقى للمعنى هنا في هاتفها
+
+140
+00:12:27,980 --> 00:12:33,040
+does not exist يبقى أنا بقدر أجمع two vectors اللي
+
+141
+00:12:33,040 --> 00:12:39,980
+هما نفس العدد من الـ components غير هيك بقدرش تمام
+
+142
+00:12:39,980 --> 00:12:46,480
+طيب نيجي الآن للـ remark اللي عندنا هذه قبل ما نفوت للـ
+
+143
+00:12:46,480 --> 00:12:50,500
+remark حد بتسأل أي سؤال في الكلام اللي تحدثنا به 
+
+144
+00:12:50,500 --> 00:12:59,390
+قبل قليل؟ اه مين بتحب تسأل؟ مفهوم يعني واضح؟ ننتقل
+
+145
+00:12:59,390 --> 00:13:04,670
+إلى الـ Remark بقول الـ N dimensional raw vector أو
+
+146
+00:13:04,670 --> 00:13:10,310
+الـ column vector يبقى أنا عندي متجه صفي أو متجه عمودي
+
+147
+00:13:10,310 --> 00:13:16,530
+عدد العناصر في كل واحد منهم يساوي M هذا بقدر أكتبه
+
+148
+00:13:16,530 --> 00:13:21,890
+على شكل components ماله can be represented as N
+
+149
+00:13:21,890 --> 00:13:26,930
+tuple يعني بقدر أكتبه على شكل tuple اللي هو vector
+
+150
+00:13:26,930 --> 00:13:32,820
+بمركبات and vice versa والعكس بالعكس يعني لو عندي
+
+151
+00:13:32,820 --> 00:13:37,520
+vector مكتوب على شكل الـ components بقدر أكتبه متجه
+
+152
+00:13:37,520 --> 00:13:42,440
+عمودي وبقدر أكتبه متجه صفي سواء كان هذا ولا هذا
+
+153
+00:13:42,440 --> 00:13:47,500
+الاثنين بقدر أعمله فمثلا لو جاتي قولتلي في عندي الـ X
+
+154
+00:13:47,500 --> 00:13:52,200
+واحد X اثنين X اثنين ايش اسم هذا يا بنات؟ متجه 
+
+155
+00:13:52,200 --> 00:13:58,740
+عمودي كل vector تمام بقدر أكتبه بصيغة مكافئة له
+
+156
+00:13:58,740 --> 00:14:00,640
+وهي 
+
+157
+00:14:21,700 --> 00:14:27,500
+الـ raw vector بقدر أكتب كمان على شكل الـ
+
+158
+00:14:27,500 --> 00:14:31,240
+components بالشكل اللي عندنا هذا يبقى هي المقصود 
+
+159
+00:14:31,240 --> 00:14:35,200
+بالـ remark اللي عندنا لو عندنا vector بقدر أكتب 
+
+160
+00:14:35,200 --> 00:14:39,260
+سواء كان raw vector أو col vector بقدر أكتبه على
+
+161
+00:14:39,260 --> 00:14:48,540
+شكل الـ n-tuple الموجود في الـ set RN واضح هذا؟ طيب نبدأ
+
+162
+00:14:48,540 --> 00:14:53,960
+ناخد الأمثلة على كل ما قيل سابقا في هذه المحاضرة 
+
+163
+00:14:53,960 --> 00:14:59,450
+وفي المحاضرة الماضية بقول افترض إنه عندك مصفوفتين
+
+164
+00:14:59,450 --> 00:15:05,110
+بالشكل اللي عندك هذا المطلوب الأول بدي أجمع a زائد
+
+165
+00:15:05,110 --> 00:15:09,650
+b بعد هيك بدي 2a ناقص 3b المرة اللي
+
+166
+00:15:09,650 --> 00:15:15,610
+فاتت قلنا مشان أجمع two matrices لازم يكونوا اثنين 
+
+167
+00:15:15,610 --> 00:15:22,030
+من نفس الـ size تمام هذه واحدة الثانية بدأ تطلع
+
+168
+00:15:22,030 --> 00:15:25,530
+مصفوفة من نفس الـ size تبقى المصفوفتين اثنين 
+
+169
+00:15:25,530 --> 00:15:31,710
+السابقتين تمام إذا بدنا نروح نطبق هذا الكلام على
+
+170
+00:15:31,710 --> 00:15:33,470
+أرض الواقع
+
+171
+00:15:47,190 --> 00:15:52,570
+بدنا نجي لمصفوفتين اللي هو solution وبدنا نبدأ
+
+172
+00:15:52,570 --> 00:15:57,570
+بالنقطة الأولى اللي هي نمرة a بدي آخد الـ a زائد الـ
+
+173
+00:15:57,570 --> 00:16:03,490
+b ويساوي الجمع قلنا كمان component wise يبقى
+
+174
+00:16:03,490 --> 00:16:08,510
+
+201
+00:18:57,340 --> 00:19:04,440
+طبعا عندي A وB وكمان الناتج بده يطلع مصفوفة من نفس
+
+202
+00:19:04,440 --> 00:19:05,040
+النظام
+
+203
+00:19:09,790 --> 00:19:18,790
+النتيجة هي 2×3 يبقى هذه 2x لازم تكون 2×3 يبقى باجي
+
+204
+00:19:18,790 --> 00:19:28,830
+بقوله هنا 2x + a بدها تساوي مين؟ بدها تساوي V مش
+
+205
+00:19:28,830 --> 00:19:33,470
+هيك ما قال لي؟ بقول له تمام يبقى الآن مش هنقدر
+
+206
+00:19:33,470 --> 00:19:38,210
+نجمعهم بده يقول لي اثنين يبقى الـ X بقدر أكتبها
+
+207
+00:19:38,210 --> 00:19:46,390
+بمكونات و أروح أدور عن هذه المكونات إذا لو جيت قلت
+
+208
+00:19:46,390 --> 00:20:00,530
+A11 A12 A13 الصف اللي بعده إيه؟ اثنين اثنين اثنين
+
+209
+00:20:00,530 --> 00:20:01,430
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+210
+00:20:01,430 --> 00:20:05,490
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين 
+
+211
+00:20:06,900 --> 00:20:13,400
+عشان أقدر أجمعها مع مين؟ مع B تمام يبقى هذه زائد
+
+212
+00:20:13,400 --> 00:20:19,100
+اللي هو المصفوفة B زائد إيه؟ اللي هو المصفوفة A؟
+
+213
+00:20:19,100 --> 00:20:25,920
+واحد زيرو اثنين وهنا سالب ثلاثة واحد أربعة بالشكل
+
+214
+00:20:25,920 --> 00:20:31,000
+اللي عندنا هذا كله هذا الكلام بده يساوي V اللي
+
+215
+00:20:31,000 --> 00:20:36,640
+هي عبارة عن سالب اثنين اثنين أربعة و واحد واحد
+
+216
+00:20:36,640 --> 00:20:44,610
+ثلاثة بالشكل اللي عندنا هذا الآن قال لك الخيار يا 
+
+217
+00:20:44,610 --> 00:20:48,230
+بتضرب هذه في السالب وتوديها الناحية التالية بيخلي
+
+218
+00:20:48,230 --> 00:20:52,530
+كل شيء زي ما هو كيف أخلي كل شيء زي ما هو يبقى هدول
+
+219
+00:20:52,530 --> 00:20:56,870
+بدي أضربها جوا و أجمعها مع هذه يبقى المصفوفة
+
+220
+00:20:56,870 --> 00:21:05,830
+الجديدة بيصير اثنين a one one ناقص زائد واحد زائد
+
+221
+00:21:05,830 --> 00:21:16,010
+واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد
+
+222
+00:21:16,010 --> 00:21:18,830
+واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد
+
+223
+00:21:18,830 --> 00:21:26,020
+واحد زائد واحد زائد واحد زائد واحد زائد واحد العنصر
+
+224
+00:21:26,020 --> 00:21:33,240
+اللي بعده اثنين اثنين واحد زائد واحد واللي بعده
+
+225
+00:21:33,240 --> 00:21:41,420
+اثنين اثنين اثنين ناقص ثلاثة هذه ناقص ثلاثة ناقص
+
+226
+00:21:41,420 --> 00:21:48,560
+ثلاثة وهذه زائد واحد مظبوط تمام وهذه اثنين اثنين
+
+227
+00:21:48,560 --> 00:21:55,260
+ثلاثة زائد أربعة كل هذا الكلام سيكون ناقص اثنين
+
+228
+00:21:55,260 --> 00:22:01,300
+اثنين أربعة واحد واحد ثلاثة الآن صار عندي مصفوفتين
+
+229
+00:22:01,300 --> 00:22:07,700
+بيساوي بعض إذا كل عنصر بيساوي من نظيره يبقى اثنين
+
+230
+00:22:07,700 --> 00:22:15,740
+a one one زائد one يساوي سالب اثنين ومنها 2a
+
+231
+00:22:15,740 --> 00:22:24,080
+one one يساوي سالب ثلاثة نجمع على اثنين يبقى الـ a
+
+232
+00:22:24,080 --> 00:22:31,970
+one one يساوي سالب ثلاثة على اثنين اللي بعده اثنين
+
+233
+00:22:31,970 --> 00:22:41,570
+a one two بده يساوي قداش؟ بده يساوي اثنين مباشرة يبقى
+
+234
+00:22:41,570 --> 00:22:48,030
+a one two بده يساوي قداش؟ بده يساوي واحد يبقى هذا بده
+
+235
+00:22:48,030 --> 00:22:52,170
+يساوي واحد و هذا بده يساوي سالب ثلاثة على اثنين
+
+236
+00:22:52,170 --> 00:22:59,350
+نمسك اللي بعده اثنين a one ثلاثة زائد اثنين بده
+
+237
+00:22:59,350 --> 00:23:06,390
+يساوي قداش؟ أربعة يبقى 2a one three بده يساوي
+
+238
+00:23:06,390 --> 00:23:15,160
+اثنين يبقى a one three بده يساوي واحد كذلك يبقى
+
+239
+00:23:15,160 --> 00:23:23,800
+اثنين اثنين واحد ناقص ثلاثة يبقى اثنين اثنين واحد
+
+240
+00:23:23,800 --> 00:23:25,560
+ناقص ثلاثة يبقى اثنين اثنين واحد ناقص ثلاثة يبقى
+
+241
+00:23:25,560 --> 00:23:26,080
+اثنين اثنين واحد ناقص ثلاثة يبقى 
+
+242
+00:23:26,080 --> 00:23:26,380
+ناقص ثلاثة يبقى اثنين اثنين واحد ناقص ثلاثة يبقى
+
+243
+00:23:26,380 --> 00:23:29,260
+اثنين اثنين واحد ناقص ثلاثة يبقى اثنين اثنين واحد
+
+244
+00:23:29,260 --> 00:23:32,560
+ناقص ثلاثة يبقى اثنين اثنين واحد ناقص ثلاثة يبقى
+
+245
+00:23:32,560 --> 00:23:35,820
+اثنين اثنين واحد ناقص ثلاثة يبقى العنصر اللي بعده
+
+246
+00:23:35,820 --> 00:23:44,780
+اثنين اثنين اثنين زائد واحد بده يساوي واحد يبقى
+
+247
+00:23:44,780 --> 00:23:51,240
+اثنين اثنين اثنين بده يساوي صفر يبقى اثنين اثنين
+
+248
+00:23:51,240 --> 00:24:00,030
+بده يساوي صفر الآن اللي بعده اثنين اثنين ثلاثة
+
+249
+00:24:00,030 --> 00:24:06,650
+زائد أربعة بده يساوي قداش؟ ثلاثة يبقى بناء عليه
+
+250
+00:24:06,650 --> 00:24:14,710
+اثنين اثنين ثلاثة بده يساوي سالب واحد يبقى اثنين
+
+251
+00:24:14,710 --> 00:24:22,000
+ثلاثة بده يساوي سالب نصف يبقى بناء عليه أصبحت
+
+252
+00:24:22,000 --> 00:24:27,980
+المصفوفة هذه بدي أعطيك أن المصفوفة X المطلوبة
+
+253
+00:24:27,980 --> 00:24:35,180
+عناصرها كالتالي ناقص ثلاثة على اثنين a واحد اثنين
+
+254
+00:24:35,180 --> 00:24:40,280
+بواحد a واحد ثلاثة كمان بقداش؟ بواحد
+
+255
+00:24:46,550 --> 00:24:53,390
+A21 B2 A22 B0 A23 -1.5 يبقى هذه المصفوفة X اللي عندنا
+
+256
+00:24:53,390 --> 00:24:56,530
+قاعدين نبحث عليها
+
+257
+00:25:19,140 --> 00:25:27,040
+هذا مثال رقم واحد مثال رقم اثنين مثال
+
+258
+00:25:27,040 --> 00:25:28,640
+اثنين
+
+259
+00:25:50,000 --> 00:26:02,740
+Vectors روحنا نقول vectors of the matrix of the
+
+260
+00:26:02,740 --> 00:26:13,300
+matrix اللي هي مين؟ اثنين واحد ناقص ثلاثة Zero خمسة
+
+261
+00:26:13,300 --> 00:26:21,700
+Zero Zero اثنين زيرو واحد أربعة زيرو بالشكل اللي
+
+262
+00:26:21,700 --> 00:26:35,260
+عندنا هنا سؤال
+
+263
+00:26:35,260 --> 00:26:41,570
+مرة ثانية بقول لي هات لي الـ column vectors المتجهات
+
+264
+00:26:41,570 --> 00:26:45,990
+العمودية و الـ raw vectors المتجهات الصفّية لما هم
+
+265
+00:26:45,990 --> 00:26:51,310
+للمصفوفة اللي عندنا هذه بدأ أبدا بالمتجهات العمودية
+
+266
+00:26:51,310 --> 00:26:57,630
+فباجي بقول له the column vectors
+
+267
+00:26:57,630 --> 00:27:12,720
+are بدي آجي للـ V1 U1 يساوي
+
+268
+00:27:12,720 --> 00:27:25,930
+2 5 0 و U2 يساوي 1 0 1 و الـ U3 بده يساوي سالب ثلاثة
+
+269
+00:27:25,930 --> 00:27:38,340
+Zero أربعة and U4 بده يساوي Zero اثنين Zero يبقى
+
+270
+00:27:38,340 --> 00:27:42,940
+هذه الـ main الـ column vectors يبقى كإن المصفوفة
+
+271
+00:27:42,940 --> 00:27:48,240
+اللي عندنا هذه بقدر أكتبها بدلالة الـ U1 و U2 و U3
+
+272
+00:27:48,240 --> 00:27:52,240
+و U4 هذا الـ column vectors بتروح أجيب له الـ raw
+
+273
+00:27:52,240 --> 00:27:58,660
+vectors فباجي بقول له they are raw vectors
+
+274
+00:28:01,170 --> 00:28:08,770
+بدي آجي للـ V1 يبقى V1 بده يساوي صف الأول اثنين
+
+275
+00:28:08,770 --> 00:28:16,290
+واحد سالب ثلاثة زيرو والـ V2 اللي هو صف الثاني خمسة
+
+276
+00:28:16,290 --> 00:28:25,850
+زيرو زيرو اثنين and الـ V3 بده يساوي زيرو واحد
+
+277
+00:28:25,850 --> 00:28:31,750
+أربعة زيرو والعكس لو أنا الـ core vectors أو الـ raw
+
+278
+00:28:31,750 --> 00:28:39,450
+vectors بقدر أجيب من المصفوفة الأصلية لهم السؤال
+
+279
+00:28:39,450 --> 00:28:45,450
+الثالث display
+
+280
+00:28:45,450 --> 00:28:48,550
+the
+
+281
+00:28:48,550 --> 00:28:54,870
+elements display
+
+282
+00:28:54,870 --> 00:28:55,830
+the elements
+
+283
+00:28:59,020 --> 00:29:10,840
+the matrix who's convictors who's convictors
+
+284
+00:29:10,840 --> 00:29:21,340
+who convictors are الـ U1 بدي يساوي واحد Zero
+
+285
+00:29:21,340 --> 00:29:35,540
+واحد أربعة و U2 بتساوي اثنين واحد خمسة سالب واحد و
+
+286
+00:29:35,540 --> 00:29:43,600
+U3 و U3 بتساوي واحد اثنين ثلاثة أربعة
+
+287
+00:30:15,920 --> 00:30:23,960
+نرجع لسؤالنا مرة ثانية السؤال
+
+288
+00:30:23,960 --> 00:30:28,900
+بيقول لي display the elements of the matrix whose
+
+289
+00:30:28,900 --> 00:30:35,040
+cone vectors are U1 و U2 و U3 كلمة display ..
+
+290
+00:30:35,040 --> 00:30:41,250
+display إيش يعني يا بنات بالعربي؟ عرض، واضح، بيّن،
+
+291
+00:30:41,250 --> 00:30:47,350
+شغلات زي ذلك يبقى عرض أو بيّن يبقى عرض العناصر
+
+292
+00:30:47,350 --> 00:30:51,070
+تبعات المصفوفة اللي الـ column vectors على الشكل
+
+293
+00:30:51,070 --> 00:30:55,550
+اللي عندنا هنا بقول لك كويس المصفوفة هذه يا بنات لو
+
+294
+00:30:55,550 --> 00:31:01,930
+جيت رمزت لها الرمز A يبقى الـ A هدول كل vectors
+
+295
+00:31:01,930 --> 00:31:05,890
+يبقى كل من U واحد و U اثنين و U ثلاثة مكتوب على
+
+296
+00:31:05,890 --> 00:31:10,950
+شكل عمود بس العمود هذا جاب لي شوية كتاب إني بقدر
+
+297
+00:31:10,950 --> 00:31:15,150
+أكتبه على شكل in tuple يبقى هاي مكتوب على شكل for
+
+298
+00:31:15,150 --> 00:31:21,290
+tuple يبقى كل واحد من هدول عبارة عن عمود وليس صف
+
+299
+00:31:21,970 --> 00:31:27,690
+واضح؟ قال إنه يجيب لي كل vector يبقى مادام هيك هذه
+
+300
+00:31:27,690 --> 00:31:37,030
+عبارة عن الـ U1 و U2 و U3 وتساوي بالدرجة العمود
+
+301
+00:31:37,030 --> 00:31:40,570
+الأول 1014
+
+302
+00:31:41,710 --> 00:31:48,810
+العمودي الثاني اثنين واحد خمسة سالب واحد العمودي
+
+303
+00:31:48,810 --> 00:31:54,810
+الثالث واحد اثنين ثلاثة أربعة يبقى هاي الـ column
+
+304
+00:31:54,810 --> 00:31:58,910
+vectors كتبتهم على شكل main مصفوفة زي ما أنتم 
+
+305
+00:31:58,910 --> 00:32:07,790
+شايفينه فبالمثال الرابع برضه
+
+306
+00:32:07,790 --> 00:32:08,330
+display
+
+307
+00:32:11,880 --> 00:32:21,220
+display the elements of the matrix the elements of
+
+308
+00:32:21,220 --> 00:32:28,520
+the matrix whose raw vectors are
+
+309
+00:32:39,810 --> 00:33:06,230
+عندك V1 يساوي 1 2 3 و V2 يساوي 0 4 سالب 1 سؤال
+
+310
+00:33:06,230 --> 00:33:11,860
+مرة ثانية بقول عرض العناصر تبعات المصفوفة أو بيّن
+
+311
+00:33:11,860 --> 00:33:17,580
+العناصر تبعات المصفوفة whose raw vectors اللي هي
+
+312
+00:33:17,580 --> 00:33:23,020
+المتجهات الصفّية لها بالشكل اللي عندنا هذا إذا أنا
+
+313
+00:33:23,020 --> 00:33:30,620
+بدأ أروح أكتب المصفوفة إيه على شكل صفوف بقول V1 و
+
+314
+00:33:30,620 --> 00:33:35,570
+V2 هي الصفوف اللي عندي ما عنديش غيرهم شايفة كيف
+
+315
+00:33:35,570 --> 00:33:40,130
+كتبنا هناك وكيف كتبنا هناك كتبنا على شكل عمود هنا
+
+316
+00:33:40,130 --> 00:33:46,290
+كتبناها على شكل صفوف يبقى بداجي أكتب كل صف من هذه
+
+317
+00:33:46,290 --> 00:33:52,770
+الصفوف يبقى صف واحد اثنين ثلاثة الصف الثاني Zero
+
+318
+00:33:52,770 --> 00:33:59,890
+أربعة سالب واحد بهذا الشكل المثال
+
+319
+00:33:59,890 --> 00:34:00,650
+الخامس
+
+320
+00:34:07,680 --> 00:34:18,200
+بقول لي F الـ X بده يساوي واحد ثلاثة زيرو سالب اثنين
+
+321
+00:34:18,200 --> 00:34:28,840
+and Y تساوي أو capital Y بده يساوي اللي هو Zero
+
+322
+00:34:28,840 --> 00:34:33,640
+سالب واحد ثلاثة سالب أربعة
+
+323
+00:34:36,930 --> 00:34:51,730
+Vectors in R أربعة Find the vector بدنا
+
+324
+00:34:51,730 --> 00:34:59,870
+المتجه إيه اللي همين؟ 2X ناقص 3 capital Y
+
+325
+00:35:15,500 --> 00:35:21,400
+بنرجع لسؤالنا مرة ثانية ما تينا capital X موجود في
+
+326
+00:35:21,400 --> 00:35:28,120
+الـ set R4 وما تينا capital Y vector موجود كذلك في
+
+327
+00:35:28,120 --> 00:35:34,080
+R4 يبقى كتبنا كل vector بالمكونات تبعه طلب
+
+328
+00:35:34,080 --> 00:35:40,560
+مني Find the vector 2x-3 هو كأنه طلب العمليتين في
+
+329
+00:35:40,560 --> 00:35:45,360
+آن واحد بدك تضرب رقم في vector ورقم ثاني في
+
+330
+00:35:45,360 --> 00:35:51,300
+vector ثم تقوم بعملية مين؟ عملية الجمع إذا أنا لما
+
+331
+00:35:51,300 --> 00:35:57,880
+بداجي أقول له 2 capital X ناقص 3 capital Y
+
+332
+00:35:57,880 --> 00:36:05,760
+يساوي معناته بداجي أقول له اثنين في واحد ثلاثة زيرو
+
+333
+00:36:05,760 --> 00:36:12,520
+سالب اثنين ناقص ثلاثة أو زائد
+
+334
+00:36:14,640 --> 00:36:20,360
+لنقص ثلاثة في الـ vector الثاني الـ Zero سالب واحد
+
+335
+00:36:20,360 --> 00:36:25,260
+ثلاثة سالب أربعة بالشكل اللي عندنا هذا يبقى هذا
+
+336
+00:36:25,260 --> 00:36:30,660
+الكلام يساوي أخذنا أول خاصية أنه إذا ضربنا
+
+337
+00:36:30,660 --> 00:36:35,120
+Constant فيه vector وبنضربه في جميع مركبات هذا الـ
+
+338
+00:36:35,120 --> 00:36:41,880
+vector إذا إن الـ vector هذا 2 6 0 سالب 4 الـ vector
+
+339
+00:36:41,880 --> 00:36:51,780
+الثاني برضه 0 3 سالب 9 وهنا 12 بعد ذلك أخذنا خاصية
+
+340
+00:36:51,780 --> 00:36:55,920
+جمع two vectors يبقى بنجمع component wise كل
+
+341
+00:36:55,920 --> 00:37:02,060
+مركبة مع نظيرتها يبقى باجي بقول له اثنين زائد زيرو
+
+342
+00:37:02,060 --> 00:37:08,340
+باثنين ستة وثلاثة تسعة زيرو ناقص تسعة بناقص تسعة
+
+343
+00:37:08,340 --> 00:37:14,540
+ناقص أربعة واثنا عشر بظل قداش؟ ثمانية إذا أصبح الـ
+
+344
+00:37:14,540 --> 00:37:20,100
+vector 2x ناقص 3 capital Y هو اللي
+
+345
+00:37:20,100 --> 00:37:25,440
+بيساوي اثنين تسعة ناقص تسعة ثمانية وهكذا لحد هنا
+
+346
+00:37:25,440 --> 00:37:29,680
+stop انتهى هذا الـ section ولا يكون الـ exercise
+
+347
+00:37:29,680 --> 00:37:36,130
+اثنين أربعة يبقى exercises اثنين أربعة المسائل
+
+348
+00:37:36,130 --> 00:37:43,890
+التالية واحد واثنين وثلاثة وستة وسبعة وثمانية و
+
+349
+00:37:43,890 --> 00:37:47,910
+تسعة وعشرة وإحدى عشر
+
+350
+00:37:50,310 --> 00:37:53,770
+لحد هنا انتهى Section 2.4 والآن بدنا نيجي
+
+351
+00:37:53,770 --> 00:38:00,530
+لسيكشن 2.5 اللي سنبدأ به بعد ظهر اليوم إن
+
+352
+00:38:00,530 --> 00:38:01,930
+شاء الله تعالى
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ONz55Bmglq8_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ONz55Bmglq8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7ec063e94afc07410368f90d6da41f271af60ac4
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ONz55Bmglq8_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3802, "start": 20.7, "end": 38.02, "text": "بسم الله الرحمن الرحيم نعود الان الى section 2.4 الذي ابتدناه المرة الماضية وذكر بما قلناه في نهاية ال section المرة الماضية تكلمنا عن نقطتين ال raw vector و ال column vector", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 3615, 23328, 2423, 7649, 2423, 7578, 3541, 568, 13, 19, 43527, 48127, 2655, 3215, 8315, 3224, 9673, 25720, 9673, 46958, 10632, 4032, 8848, 37983, 4724, 15042, 12174, 1211, 8315, 3224, 8978, 8717, 11296, 10632, 2423, 3541, 9673, 25720, 9673, 46958, 10632, 6055, 4117, 19528, 8315, 18871, 8717, 47432, 2655, 9957, 2423, 8936, 8062, 4032, 2423, 7738, 8062], "avg_logprob": -0.16233915200128274, "compression_ratio": 1.680722891566265, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 20.7, "end": 21.02, "word": "بسم", "probability": 0.820068359375}, {"start": 21.02, "end": 21.24, "word": " الله", "probability": 0.9658203125}, {"start": 21.24, "end": 21.64, "word": " الرحمن", "probability": 0.9430338541666666}, {"start": 21.64, "end": 22.16, "word": " الرحيم", "probability": 0.9903971354166666}, {"start": 22.16, "end": 23.24, "word": " نعود", "probability": 0.8492838541666666}, {"start": 23.24, "end": 23.72, "word": " الان", "probability": 0.6798095703125}, {"start": 23.72, "end": 24.12, "word": " الى", "probability": 0.799072265625}, {"start": 24.12, "end": 24.48, "word": " section", "probability": 0.74365234375}, {"start": 24.48, "end": 24.84, "word": " 2", "probability": 0.71142578125}, {"start": 24.84, "end": 25.22, "word": ".4", "probability": 0.6873779296875}, {"start": 25.22, "end": 25.52, "word": " الذي", "probability": 0.5498046875}, {"start": 25.52, "end": 26.22, "word": " ابتدناه", "probability": 0.804736328125}, {"start": 26.22, "end": 26.6, "word": " المرة", "probability": 0.9697265625}, {"start": 26.6, "end": 27.16, "word": " الماضية", "probability": 0.9930013020833334}, {"start": 27.16, "end": 28.44, "word": " وذكر", "probability": 0.8429361979166666}, {"start": 28.44, "end": 29.94, "word": " بما", "probability": 0.955810546875}, {"start": 29.94, "end": 30.62, "word": " قلناه", "probability": 0.959228515625}, {"start": 30.62, "end": 30.74, "word": " في", "probability": 0.583984375}, {"start": 30.74, "end": 31.22, "word": " نهاية", "probability": 0.9879557291666666}, {"start": 31.22, "end": 31.78, "word": " ال", "probability": 0.5322265625}, {"start": 31.78, "end": 31.78, "word": " section", "probability": 0.65966796875}, {"start": 31.78, "end": 32.54, "word": " المرة", "probability": 0.988525390625}, {"start": 32.54, "end": 33.28, "word": " الماضية", "probability": 0.99609375}, {"start": 33.28, "end": 34.52, "word": " تكلمنا", "probability": 0.9566650390625}, {"start": 34.52, "end": 34.74, "word": " عن", "probability": 0.9833984375}, {"start": 34.74, "end": 35.42, "word": " نقطتين", "probability": 0.9764404296875}, {"start": 35.42, "end": 35.82, "word": " ال", "probability": 0.9638671875}, {"start": 35.82, "end": 36.06, "word": " raw", "probability": 0.4189453125}, {"start": 36.06, "end": 36.64, "word": " vector", "probability": 0.97412109375}, {"start": 36.64, "end": 36.86, "word": " و", "probability": 0.83056640625}, {"start": 36.86, "end": 37.08, "word": " ال", "probability": 0.87890625}, {"start": 37.08, "end": 37.52, "word": " column", "probability": 0.454345703125}, {"start": 37.52, "end": 38.02, "word": " vector", "probability": 0.98193359375}], "temperature": 1.0}, {"id": 2, "seek": 5624, "start": 38.62, "end": 56.24, "text": "فبجي بقول لو جيت على المصوفة و أخدت أعمدة المصوفة كل عمود على حدة فهذا العمود بسميه calm vector يبقى متجه عمودي أو متجه العمود و لو أخدت كل صف من صفوف هذه المصوفة", "tokens": [5172, 3555, 7435, 1829, 4724, 39648, 45164, 10874, 36081, 15844, 9673, 9381, 38688, 3660, 4032, 5551, 9778, 3215, 2655, 5551, 25957, 41891, 9673, 9381, 38688, 3660, 28242, 6225, 2304, 23328, 15844, 11331, 41891, 6156, 3224, 15730, 18863, 2304, 23328, 4724, 38251, 1829, 3224, 7151, 8062, 7251, 3555, 4587, 7578, 44650, 7435, 3224, 6225, 2304, 2407, 16254, 34051, 44650, 7435, 3224, 18863, 2304, 23328, 4032, 45164, 5551, 9778, 3215, 2655, 28242, 20328, 5172, 9154, 20328, 5172, 38688, 29538, 9673, 9381, 38688, 3660], "avg_logprob": -0.10927972579147757, "compression_ratio": 1.7898089171974523, "no_speech_prob": 0.0, "words": [{"start": 38.62, "end": 39.1, "word": "فبجي", "probability": 0.55865478515625}, {"start": 39.1, "end": 39.42, "word": " بقول", "probability": 0.974609375}, {"start": 39.42, "end": 39.62, "word": " لو", "probability": 0.935546875}, {"start": 39.62, "end": 39.92, "word": " جيت", "probability": 0.966796875}, {"start": 39.92, "end": 40.18, "word": " على", "probability": 0.8359375}, {"start": 40.18, "end": 40.96, "word": " المصوفة", "probability": 0.85736083984375}, {"start": 40.96, "end": 41.16, "word": " و", "probability": 0.859375}, {"start": 41.16, "end": 41.96, "word": " أخدت", "probability": 0.9119873046875}, {"start": 41.96, "end": 42.6, "word": " أعمدة", "probability": 0.9539388020833334}, {"start": 42.6, "end": 43.24, "word": " المصوفة", "probability": 0.965087890625}, {"start": 43.24, "end": 43.56, "word": " كل", "probability": 0.91455078125}, {"start": 43.56, "end": 44.04, "word": " عمود", "probability": 0.9415690104166666}, {"start": 44.04, "end": 44.34, "word": " على", "probability": 0.8037109375}, {"start": 44.34, "end": 44.78, "word": " حدة", "probability": 0.6912841796875}, {"start": 44.78, "end": 45.64, "word": " فهذا", "probability": 0.9680989583333334}, {"start": 45.64, "end": 46.04, "word": " العمود", "probability": 0.9775390625}, {"start": 46.04, "end": 46.88, "word": " بسميه", "probability": 0.9599609375}, {"start": 46.88, "end": 47.52, "word": " calm", "probability": 0.487060546875}, {"start": 47.52, "end": 48.26, "word": " vector", "probability": 0.96240234375}, {"start": 48.26, "end": 49.1, "word": " يبقى", "probability": 0.94287109375}, {"start": 49.1, "end": 49.84, "word": " متجه", 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56.24, "word": " المصوفة", "probability": 0.9913330078125}], "temperature": 1.0}, {"id": 3, "seek": 7979, "start": 56.53, "end": 79.79, "text": "بسمي كل صف هو ال raw vector اللي هو متجه vector و العكس لو عندي raw vectors أو column vectors بالنسبة لمصحوف بقدر أرجعهم إلى أصل المصحوفة الان بدأ نعطي مثال توضيحي بقول لو كان عندك U1 هي raw vector ولا column vector هذا", "tokens": [3555, 38251, 1829, 28242, 20328, 5172, 31439, 2423, 8936, 8062, 13672, 1829, 31439, 44650, 7435, 3224, 8062, 4032, 18863, 4117, 3794, 45164, 18871, 16254, 8936, 18875, 34051, 7738, 18875, 20666, 1863, 35457, 3660, 32767, 9381, 5016, 38688, 4724, 28543, 2288, 5551, 47341, 3615, 16095, 30731, 5551, 36520, 9673, 9381, 5016, 38688, 3660, 2423, 7649, 47525, 10721, 8717, 3615, 9566, 1829, 50113, 6027, 33427, 11242, 1829, 5016, 1829, 4724, 39648, 45164, 25961, 43242, 4117, 624, 16, 39896, 8936, 8062, 49429, 7738, 8062, 23758], "avg_logprob": -0.23249247634267234, "compression_ratio": 1.6534653465346534, "no_speech_prob": 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العكس", "probability": 0.87255859375}, {"start": 61.73, "end": 62.39, "word": " لو", "probability": 0.83642578125}, {"start": 62.39, "end": 62.79, "word": " عندي", "probability": 0.77490234375}, {"start": 62.79, "end": 63.05, "word": " raw", "probability": 0.791015625}, {"start": 63.05, "end": 63.85, "word": " vectors", "probability": 0.93701171875}, {"start": 63.85, "end": 64.53, "word": " أو", "probability": 0.48486328125}, {"start": 64.53, "end": 65.31, "word": " column", "probability": 0.291748046875}, {"start": 65.31, "end": 66.19, "word": " vectors", "probability": 0.96728515625}, {"start": 66.19, "end": 67.17, "word": " بالنسبة", "probability": 0.957275390625}, {"start": 67.17, "end": 67.57, "word": " لمصحوف", "probability": 0.6998291015625}, {"start": 67.57, "end": 68.05, "word": " بقدر", "probability": 0.9197591145833334}, {"start": 68.05, "end": 68.87, "word": " أرجعهم", "probability": 0.78240966796875}, {"start": 68.87, "end": 69.25, "word": " إلى", "probability": 0.85498046875}, {"start": 69.25, "end": 69.83, "word": " أصل", "probability": 0.90966796875}, {"start": 69.83, "end": 70.97, "word": " المصحوفة", "probability": 0.94501953125}, {"start": 70.97, "end": 71.63, "word": " الان", "probability": 0.5174560546875}, {"start": 71.63, "end": 71.87, "word": " بدأ", "probability": 0.5118408203125}, {"start": 71.87, "end": 72.23, "word": " نعطي", "probability": 0.964599609375}, {"start": 72.23, "end": 72.81, "word": " مثال", "probability": 0.987548828125}, {"start": 72.81, "end": 73.93, "word": " توضيحي", "probability": 0.95654296875}, {"start": 73.93, "end": 74.67, "word": " بقول", "probability": 0.940185546875}, {"start": 74.67, "end": 74.93, "word": " لو", "probability": 0.93896484375}, {"start": 74.93, "end": 75.23, "word": " كان", "probability": 0.9873046875}, {"start": 75.23, "end": 75.73, "word": " عندك", "probability": 0.811279296875}, {"start": 75.73, "end": 76.43, "word": " U1", "probability": 0.5836181640625}, {"start": 76.43, "end": 77.03, "word": " هي", "probability": 0.79736328125}, {"start": 77.03, "end": 78.01, "word": " raw", "probability": 0.6513671875}, {"start": 78.01, "end": 78.47, "word": " vector", "probability": 0.9794921875}, {"start": 78.47, "end": 78.77, "word": " ولا", "probability": 0.74267578125}, {"start": 78.77, "end": 79.15, "word": " column", "probability": 0.9111328125}, {"start": 79.15, "end": 79.49, "word": " vector", "probability": 0.97705078125}, {"start": 79.49, "end": 79.79, "word": " هذا", "probability": 0.58837890625}], "temperature": 1.0}, {"id": 4, "seek": 9808, "start": 80.48, "end": 98.08, "text": "Convector U3 يبقى من هذه الأعمدة بقدر اكتب المصفوفة تبعتهم على الشكل التالي يبقى U1 و U2 و U3 كل من U1 و U2 و U3 عبارة عن عمود", "tokens": [9838, 303, 1672, 624, 18, 7251, 3555, 4587, 7578, 9154, 29538, 16247, 25957, 41891, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 9673, 9381, 5172, 38688, 3660, 6055, 3555, 34268, 16095, 15844, 25124, 28820, 16712, 6027, 1829, 7251, 3555, 4587, 7578, 624, 16, 4032, 624, 17, 4032, 624, 18, 28242, 9154, 624, 16, 4032, 624, 17, 4032, 624, 18, 6225, 3555, 9640, 3660, 18871, 6225, 2304, 23328], "avg_logprob": -0.25722948917702065, "compression_ratio": 1.4154929577464788, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 80.48, "end": 81.48, "word": "Convector", "probability": 0.625762939453125}, {"start": 81.48, "end": 86.44, "word": " U3", "probability": 0.281982421875}, {"start": 86.44, "end": 87.5, "word": " يبقى", "probability": 0.72027587890625}, {"start": 87.5, "end": 87.62, "word": " من", "probability": 0.81689453125}, {"start": 87.62, "end": 88.08, "word": " هذه", "probability": 0.80859375}, {"start": 88.08, "end": 88.76, "word": " الأعمدة", "probability": 0.8387044270833334}, {"start": 88.76, "end": 89.32, "word": " بقدر", "probability": 0.758544921875}, {"start": 89.32, "end": 89.78, "word": " اكتب", "probability": 0.90576171875}, {"start": 89.78, "end": 90.44, "word": " المصفوفة", "probability": 0.70673828125}, {"start": 90.44, "end": 90.98, "word": " تبعتهم", "probability": 0.68939208984375}, {"start": 90.98, "end": 91.22, "word": " على", "probability": 0.85888671875}, {"start": 91.22, "end": 91.94, "word": " الشكل", "probability": 0.915771484375}, {"start": 91.94, "end": 92.66, "word": " التالي", "probability": 0.9676106770833334}, {"start": 92.66, "end": 93.34, "word": " يبقى", "probability": 0.8812255859375}, {"start": 93.34, "end": 93.74, "word": " U1", "probability": 0.84814453125}, {"start": 93.74, "end": 93.94, "word": " و", "probability": 0.84130859375}, {"start": 93.94, "end": 94.3, "word": " U2", "probability": 0.771240234375}, {"start": 94.3, "end": 94.42, "word": " و", "probability": 0.98974609375}, {"start": 94.42, "end": 94.82, "word": " U3", "probability": 0.970947265625}, {"start": 94.82, "end": 95.18, "word": " كل", "probability": 0.55126953125}, {"start": 95.18, "end": 95.38, "word": " من", "probability": 0.955078125}, {"start": 95.38, "end": 95.8, "word": " U1", "probability": 0.818115234375}, {"start": 95.8, "end": 96.0, "word": " و", "probability": 0.93701171875}, {"start": 96.0, "end": 96.38, "word": " U2", "probability": 0.9443359375}, {"start": 96.38, "end": 96.5, "word": " و", "probability": 0.9951171875}, {"start": 96.5, "end": 96.94, "word": " U3", "probability": 0.97998046875}, {"start": 96.94, "end": 97.44, "word": " عبارة", "probability": 0.986083984375}, {"start": 97.44, "end": 97.62, "word": " عن", "probability": 0.9931640625}, {"start": 97.62, "end": 98.08, "word": " عمود", "probability": 0.95556640625}], "temperature": 1.0}, {"id": 5, "seek": 12693, "start": 98.31, "end": 126.93, "text": "إذا بكتبهم داخل مصفوفة هي العمود الأول هي العمود الثاني هي العمود الثالث يبقى من خلال هذه الأعمدة كتبنا المصفوفة أو العكس لو بدأ اكتبهم بدلالة الصفوف يبقى بدل الشكل اللي عندنا هذا هكتب من الشكل اللي عندنا هذا V1 عبارة عن صف V2 عبارة عن من؟ عن صف لأن زي ما تشايفي المصفوفة دي الصفين وثلاثة أعمدة", "tokens": [28814, 15730, 4724, 4117, 2655, 3555, 16095, 11778, 47283, 1211, 3714, 9381, 5172, 38688, 3660, 39896, 18863, 2304, 23328, 16247, 12610, 39896, 18863, 2304, 23328, 6024, 104, 7649, 1829, 39896, 18863, 2304, 23328, 6024, 104, 6027, 12984, 7251, 3555, 4587, 7578, 9154, 16490, 1211, 6027, 29538, 16247, 25957, 41891, 9122, 2655, 3555, 8315, 9673, 9381, 5172, 38688, 3660, 34051, 18863, 4117, 3794, 45164, 47525, 10721, 1975, 4117, 2655, 3555, 16095, 47525, 1211, 6027, 3660, 31767, 5172, 38688, 7251, 3555, 4587, 7578, 47525, 1211, 25124, 28820, 13672, 1829, 43242, 8315, 23758, 8032, 4117, 2655, 3555, 9154, 25124, 28820, 13672, 1829, 43242, 8315, 23758, 691, 16, 6225, 3555, 9640, 3660, 18871, 20328, 5172, 691, 17, 6225, 3555, 9640, 3660, 18871, 9154, 22807, 18871, 20328, 5172, 5296, 33456, 30767, 1829, 19446, 6055, 8592, 995, 33911, 1829, 9673, 9381, 5172, 38688, 3660, 11778, 1829, 31767, 5172, 9957, 4032, 12984, 1211, 5718, 104, 3660, 5551, 25957, 41891], "avg_logprob": -0.14246323217753493, "compression_ratio": 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عبارة", "probability": 0.9498291015625}, {"start": 342.35, "end": 342.51, "word": " عن", "probability": 0.9912109375}, {"start": 342.51, "end": 343.13, "word": " نقطة", "probability": 0.9679361979166666}, {"start": 343.13, "end": 343.69, "word": " يبقى", "probability": 0.9576416015625}, {"start": 343.69, "end": 343.89, "word": " الا", "probability": 0.36669921875}, {"start": 343.89, "end": 344.39, "word": " إحداث", "probability": 0.81866455078125}, {"start": 344.39, "end": 344.85, "word": " سيني", "probability": 0.9230143229166666}, {"start": 344.85, "end": 344.99, "word": " و", "probability": 0.796875}, {"start": 344.99, "end": 345.33, "word": " إحداث", "probability": 0.88134765625}, {"start": 345.33, "end": 346.21, "word": " صادي", "probability": 0.6358235677083334}, {"start": 346.21, "end": 346.59, "word": " و", "probability": 0.96337890625}, {"start": 346.59, "end": 347.21, "word": " إحداث", "probability": 0.951904296875}, {"start": 347.21, "end": 348.67, "word": " رأسي", "probability": 0.9854736328125}, {"start": 348.67, "end": 349.13, "word": " X", "probability": 0.53759765625}, {"start": 349.13, "end": 349.91, "word": " Y", "probability": 0.50244140625}, {"start": 349.91, "end": 350.15, "word": " و", "probability": 0.8388671875}, {"start": 350.15, "end": 350.57, "word": " Z", "probability": 0.87158203125}], "temperature": 1.0}, {"id": 16, "seek": 37104, "start": 350.9, "end": 371.04, "text": "يبقى ثلاثة إحداثيات يبقى هنا the set of all three tuples اللي A وB وC بحيث الـA,B وC موجودة في ال set of real number إذا يا بنات لما أقول RN الـN هذا هو عدد صحيح مجبأ", "tokens": [1829, 3555, 4587, 7578, 38637, 1211, 5718, 104, 3660, 11933, 24401, 5718, 104, 1829, 9307, 7251, 3555, 4587, 7578, 34105, 264, 992, 295, 439, 1045, 2604, 2622, 13672, 1829, 316, 4032, 33, 4032, 34, 4724, 5016, 1829, 12984, 2423, 39184, 32, 11, 33, 4032, 34, 3714, 29245, 23328, 3660, 8978, 2423, 992, 295, 957, 1230, 11933, 15730, 35186, 4724, 8315, 2655, 5296, 15042, 5551, 39648, 45702, 2423, 39184, 45, 23758, 31439, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 7435, 3555, 10721], "avg_logprob": -0.19314759754272828, "compression_ratio": 1.3756906077348066, "no_speech_prob": 0.0, "words": [{"start": 350.9, "end": 351.36, "word": "يبقى", "probability": 0.9007568359375}, {"start": 351.36, "end": 352.18, "word": " ثلاثة", "probability": 0.93876953125}, {"start": 352.18, "end": 353.18, "word": " إحداثيات", "probability": 0.9457194010416666}, {"start": 353.18, "end": 353.94, "word": " يبقى", "probability": 0.943359375}, {"start": 353.94, "end": 354.24, "word": " هنا", "probability": 0.87255859375}, {"start": 354.24, "end": 354.48, "word": " the", "probability": 0.2237548828125}, {"start": 354.48, "end": 354.76, "word": " set", "probability": 0.9638671875}, {"start": 354.76, "end": 355.0, "word": " of", "probability": 0.9755859375}, {"start": 355.0, "end": 355.38, "word": " all", "probability": 0.92333984375}, {"start": 355.38, "end": 355.94, "word": " three", "probability": 0.8388671875}, {"start": 355.94, "end": 356.98, "word": " tuples", "probability": 0.843994140625}, {"start": 356.98, "end": 357.34, "word": " اللي", "probability": 0.786865234375}, {"start": 357.34, "end": 357.64, "word": " A", "probability": 0.406982421875}, {"start": 357.64, "end": 357.92, "word": " وB", "probability": 0.7900390625}, {"start": 357.92, "end": 358.38, "word": " وC", "probability": 0.974365234375}, {"start": 358.38, "end": 359.14, "word": " بحيث", "probability": 0.90478515625}, {"start": 359.14, "end": 359.42, "word": " الـA", "probability": 0.6143391927083334}, {"start": 359.42, "end": 359.52, "word": ",B", "probability": 0.6072998046875}, {"start": 359.52, "end": 359.82, "word": " وC", "probability": 0.63916015625}, {"start": 359.82, "end": 360.6, "word": " موجودة", "probability": 0.962646484375}, {"start": 360.6, "end": 360.7, "word": " في", "probability": 0.96337890625}, {"start": 360.7, "end": 360.84, "word": " ال", "probability": 0.66845703125}, {"start": 360.84, "end": 361.08, "word": " set", "probability": 0.6025390625}, {"start": 361.08, "end": 361.7, "word": " of", "probability": 0.96826171875}, {"start": 361.7, "end": 362.54, "word": " real", "probability": 0.8359375}, {"start": 362.54, "end": 363.2, "word": " number", "probability": 0.44873046875}, {"start": 363.2, "end": 363.9, "word": " إذا", "probability": 0.611328125}, {"start": 363.9, "end": 364.1, "word": " يا", "probability": 0.9638671875}, {"start": 364.1, "end": 364.5, "word": " بنات", "probability": 0.9420572916666666}, {"start": 364.5, "end": 364.74, "word": " لما", "probability": 0.92578125}, {"start": 364.74, "end": 365.06, "word": " أقول", "probability": 0.867431640625}, {"start": 365.06, "end": 365.84, "word": " RN", "probability": 0.41455078125}, {"start": 365.84, "end": 366.76, "word": " الـN", "probability": 0.7376302083333334}, {"start": 366.76, "end": 367.22, "word": " هذا", "probability": 0.73974609375}, {"start": 367.22, "end": 367.58, "word": " هو", "probability": 0.955078125}, {"start": 367.58, "end": 368.36, "word": " عدد", "probability": 0.9840494791666666}, {"start": 368.36, "end": 369.9, "word": " صحيح", "probability": 0.9935302734375}, {"start": 369.9, "end": 371.04, "word": " مجبأ", "probability": 0.8682861328125}], "temperature": 1.0}, {"id": 17, "seek": 39215, "start": 371.33, "end": 392.15, "text": "تمام؟ لكن المُركّبات اللي في الداخل يمكن كسور ويمكن أعداد سالبة ويمكن أصفر ماعندي مشكلة يبقى الرقم اللي فوق هذا إنه عدد صحيح موجب لكن الأرقام الداخلية هذه كسور كمية سالبة موجبة ماعندي مشكلة طيب", "tokens": [39237, 10943, 22807, 44381, 9673, 10859, 31747, 11703, 3555, 9307, 13672, 1829, 8978, 32748, 47283, 1211, 7251, 43020, 9122, 3794, 13063, 4032, 1829, 43020, 5551, 22488, 18513, 8608, 6027, 49401, 4032, 32640, 19452, 5551, 9381, 5172, 2288, 19446, 3615, 1863, 16254, 37893, 28820, 3660, 7251, 3555, 4587, 7578, 34892, 4587, 2304, 13672, 1829, 6156, 30543, 23758, 36145, 3224, 6225, 3215, 3215, 20328, 5016, 1829, 5016, 3714, 29245, 3555, 44381, 16247, 2288, 4587, 10943, 32748, 47283, 1211, 10632, 29538, 9122, 3794, 13063, 9122, 2304, 10632, 8608, 6027, 49401, 3714, 29245, 49401, 19446, 3615, 1863, 16254, 37893, 28820, 3660, 23032, 1829, 3555], "avg_logprob": -0.13652536833640372, "compression_ratio": 1.9664804469273742, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 371.33, "end": 372.43, "word": "تمام؟", "probability": 0.5138956705729166}, {"start": 372.43, "end": 372.93, "word": " لكن", "probability": 0.82958984375}, {"start": 372.93, "end": 373.97, "word": " المُركّبات", "probability": 0.8223470052083334}, {"start": 373.97, "end": 374.11, "word": " اللي", "probability": 0.852783203125}, {"start": 374.11, "end": 374.23, "word": " في", "probability": 0.93505859375}, {"start": 374.23, "end": 374.61, "word": " الداخل", "probability": 0.96044921875}, {"start": 374.61, "end": 375.01, "word": " يمكن", "probability": 0.939208984375}, {"start": 375.01, "end": 375.79, "word": " كسور", "probability": 0.8517252604166666}, {"start": 375.79, "end": 376.21, "word": " ويمكن", "probability": 0.7548828125}, {"start": 376.21, "end": 376.69, "word": " أعداد", "probability": 0.9611002604166666}, {"start": 376.69, "end": 377.33, "word": " سالبة", "probability": 0.9423828125}, {"start": 377.33, "end": 378.33, "word": " ويمكن", "probability": 0.900390625}, {"start": 378.33, "end": 378.99, "word": " أصفر", "probability": 0.82415771484375}, {"start": 378.99, "end": 379.47, "word": " ماعندي", "probability": 0.88623046875}, {"start": 379.47, "end": 380.09, "word": " مشكلة", "probability": 0.9876302083333334}, {"start": 380.09, "end": 380.81, "word": " يبقى", "probability": 0.9644775390625}, {"start": 380.81, "end": 381.31, "word": " الرقم", "probability": 0.9873046875}, {"start": 381.31, "end": 381.59, "word": " اللي", "probability": 0.95703125}, {"start": 381.59, "end": 381.99, "word": " فوق", "probability": 0.98876953125}, {"start": 381.99, "end": 382.45, "word": " هذا", "probability": 0.94287109375}, {"start": 382.45, "end": 382.93, "word": " إنه", "probability": 0.765869140625}, {"start": 382.93, "end": 383.43, "word": " عدد", "probability": 0.9847005208333334}, {"start": 383.43, "end": 384.09, "word": " صحيح", "probability": 0.9986572265625}, {"start": 384.09, "end": 384.59, "word": " موجب", "probability": 0.9207356770833334}, {"start": 384.59, "end": 385.59, "word": " لكن", "probability": 0.84423828125}, {"start": 385.59, "end": 386.41, "word": " الأرقام", "probability": 0.993896484375}, {"start": 386.41, "end": 387.17, "word": " الداخلية", "probability": 0.990234375}, {"start": 387.17, "end": 387.53, "word": " هذه", "probability": 0.4453125}, {"start": 387.53, "end": 388.29, "word": " كسور", "probability": 0.9822591145833334}, {"start": 388.29, "end": 388.87, "word": " كمية", "probability": 0.9773763020833334}, {"start": 388.87, "end": 389.41, "word": " سالبة", "probability": 0.9664713541666666}, {"start": 389.41, "end": 389.89, "word": " موجبة", "probability": 0.81005859375}, {"start": 389.89, "end": 390.31, "word": " ماعندي", "probability": 0.8514404296875}, {"start": 390.31, "end": 391.05, "word": " مشكلة", "probability": 0.9899088541666666}, {"start": 391.05, "end": 392.15, "word": " طيب", "probability": 0.9500325520833334}], "temperature": 1.0}, {"id": 18, "seek": 42282, "start": 393.54, "end": 422.82, "text": "هنا ملاحظة تقول اننا نكتب الـ n-dimensional vector by its component اي vector هنا بكتبه بدلالة من المركبات تبعته فمثلا هذا ال element لو قلت في هذه الستة فيها اندي vector اسمه x يبقى x يتكون من مجموعة مقربات x1 وx2 لغاية xn لو قلت في element تاني يكون y يبقى y1 وy2 لغاية yn", "tokens": [3224, 8315, 3714, 15040, 5016, 19913, 3660, 6055, 39648, 16472, 8315, 8717, 4117, 2655, 3555, 2423, 39184, 297, 12, 18759, 8062, 538, 1080, 6542, 1975, 1829, 8062, 34105, 4724, 4117, 2655, 3555, 3224, 47525, 1211, 6027, 3660, 9154, 9673, 31747, 3555, 9307, 6055, 3555, 34268, 3224, 6156, 2304, 12984, 15040, 23758, 2423, 4478, 45164, 12174, 1211, 2655, 8978, 29538, 2423, 14851, 3660, 8978, 11296, 16472, 16254, 8062, 24525, 2304, 3224, 2031, 7251, 3555, 4587, 7578, 2031, 7251, 2655, 30544, 9154, 3714, 7435, 2304, 2407, 27884, 3714, 4587, 25513, 9307, 2031, 16, 4032, 87, 17, 5296, 17082, 995, 10632, 2031, 77, 45164, 12174, 1211, 2655, 8978, 4478, 6055, 7649, 1829, 7251, 30544, 288, 7251, 3555, 4587, 7578, 288, 16, 4032, 88, 17, 5296, 17082, 995, 10632, 17861], "avg_logprob": -0.28887794477733103, "compression_ratio": 1.6867469879518073, "no_speech_prob": 0.0, "words": [{"start": 393.54, "end": 393.92, "word": "هنا", "probability": 0.41656494140625}, {"start": 393.92, "end": 394.66, "word": " ملاحظة", "probability": 0.82177734375}, {"start": 394.66, "end": 395.54, "word": " تقول", "probability": 0.4814453125}, {"start": 395.54, "end": 395.8, "word": " اننا", "probability": 0.34088134765625}, {"start": 395.8, "end": 396.18, "word": " نكتب", "probability": 0.9227294921875}, {"start": 396.18, "end": 396.4, "word": " الـ", "probability": 0.241943359375}, {"start": 396.4, "end": 396.66, "word": " n", "probability": 0.2025146484375}, {"start": 396.66, "end": 397.26, "word": "-dimensional", "probability": 0.746337890625}, {"start": 397.26, "end": 397.86, "word": " vector", "probability": 0.84912109375}, {"start": 397.86, "end": 398.1, "word": " by", "probability": 0.374755859375}, {"start": 398.1, "end": 398.42, "word": " its", "probability": 0.83837890625}, {"start": 398.42, "end": 399.28, "word": " component", "probability": 0.8515625}, {"start": 399.28, "end": 399.84, "word": " اي", "probability": 0.5638427734375}, {"start": 399.84, "end": 400.48, "word": " vector", "probability": 0.857421875}, {"start": 400.48, "end": 400.92, "word": " هنا", "probability": 0.81640625}, {"start": 400.92, "end": 402.08, "word": " بكتبه", "probability": 0.7517578125}, {"start": 402.08, "end": 402.72, "word": " بدلالة", "probability": 0.8265380859375}, {"start": 402.72, "end": 402.9, "word": " من", "probability": 0.9296875}, {"start": 402.9, "end": 403.76, "word": " المركبات", "probability": 0.83673095703125}, {"start": 403.76, "end": 404.22, "word": " تبعته", "probability": 0.75567626953125}, {"start": 404.22, "end": 404.82, "word": " فمثلا", "probability": 0.831298828125}, {"start": 404.82, "end": 405.84, "word": " هذا", "probability": 0.78662109375}, {"start": 405.84, "end": 406.04, "word": " ال", "probability": 0.9482421875}, {"start": 406.04, "end": 406.48, "word": " element", "probability": 0.7431640625}, {"start": 406.48, "end": 406.84, "word": " لو", "probability": 0.89599609375}, {"start": 406.84, "end": 407.44, "word": " قلت", "probability": 0.9425455729166666}, {"start": 407.44, "end": 407.68, "word": " في", "probability": 0.91015625}, {"start": 407.68, "end": 408.14, "word": " هذه", "probability": 0.8173828125}, {"start": 408.14, "end": 408.74, "word": " الستة", "probability": 0.6910807291666666}, {"start": 408.74, "end": 408.98, "word": " فيها", "probability": 0.5943603515625}, {"start": 408.98, "end": 409.24, "word": " اندي", "probability": 0.66748046875}, {"start": 409.24, "end": 409.64, "word": " vector", "probability": 0.92236328125}, {"start": 409.64, "end": 410.36, "word": " اسمه", "probability": 0.94384765625}, {"start": 410.36, "end": 410.7, "word": " x", "probability": 0.6201171875}, {"start": 410.7, "end": 411.62, "word": " يبقى", "probability": 0.9478759765625}, {"start": 411.62, "end": 411.94, "word": " x", "probability": 0.896484375}, {"start": 411.94, "end": 412.66, "word": " يتكون", "probability": 0.8870442708333334}, {"start": 412.66, "end": 412.96, "word": " من", "probability": 0.9912109375}, {"start": 412.96, "end": 413.4, "word": " مجموعة", "probability": 0.90283203125}, {"start": 413.4, "end": 414.08, "word": " مقربات", "probability": 0.6209564208984375}, {"start": 414.08, "end": 414.56, "word": " x1", "probability": 0.712890625}, {"start": 414.56, "end": 415.44, "word": " وx2", "probability": 0.8250325520833334}, {"start": 415.44, "end": 416.08, "word": " لغاية", "probability": 0.9681396484375}, {"start": 416.08, "end": 416.76, "word": " xn", "probability": 0.94287109375}, {"start": 416.76, "end": 417.36, "word": " لو", "probability": 0.8720703125}, {"start": 417.36, "end": 417.64, "word": " قلت", "probability": 0.9729817708333334}, {"start": 417.64, "end": 417.82, "word": " في", "probability": 0.9501953125}, {"start": 417.82, "end": 418.2, "word": " element", "probability": 0.90380859375}, {"start": 418.2, "end": 418.8, "word": " تاني", "probability": 0.9444986979166666}, {"start": 418.8, "end": 419.46, "word": " يكون", "probability": 0.597412109375}, {"start": 419.46, "end": 419.92, "word": " y", "probability": 0.7265625}, {"start": 419.92, "end": 420.4, "word": " يبقى", "probability": 0.97900390625}, {"start": 420.4, "end": 420.92, "word": " y1", "probability": 0.92529296875}, {"start": 420.92, "end": 421.62, "word": " وy2", "probability": 0.9104817708333334}, {"start": 421.62, "end": 422.2, "word": " لغاية", "probability": 0.926025390625}, {"start": 422.2, "end": 422.82, "word": " yn", "probability": 0.91943359375}], "temperature": 1.0}, {"id": 19, "seek": 43913, "start": 423.09, "end": 439.13, "text": "لو قلت في element Z يجب أن أقول Z1, Z2, Z3 لغاية ZN و هكذا يعني كل عنصر في الـ RN يتركب أو يتكون من N من المُركّبات هذه اللي بنقوله هنا", "tokens": [1211, 2407, 12174, 1211, 2655, 8978, 4478, 1176, 7251, 7435, 3555, 14739, 5551, 39648, 1176, 16, 11, 1176, 17, 11, 1176, 18, 5296, 17082, 995, 10632, 1176, 45, 4032, 8032, 4117, 15730, 37495, 22653, 28242, 18871, 9381, 2288, 8978, 2423, 39184, 45702, 7251, 2655, 31747, 3555, 34051, 7251, 2655, 30544, 9154, 426, 9154, 9673, 10859, 31747, 11703, 3555, 9307, 29538, 13672, 1829, 44945, 39648, 3224, 34105], "avg_logprob": -0.29384329692641303, "compression_ratio": 1.371069182389937, "no_speech_prob": 0.0, "words": [{"start": 423.09, "end": 423.43, "word": "لو", "probability": 0.57513427734375}, {"start": 423.43, "end": 423.71, "word": " قلت", "probability": 0.8308919270833334}, {"start": 423.71, "end": 423.85, "word": " في", "probability": 0.60205078125}, {"start": 423.85, "end": 424.31, "word": " element", "probability": 0.65576171875}, {"start": 424.31, "end": 424.79, "word": " Z", "probability": 0.27783203125}, {"start": 424.79, "end": 425.07, "word": " يجب", "probability": 0.7918294270833334}, {"start": 425.07, "end": 425.17, "word": " أن", "probability": 0.54248046875}, {"start": 425.17, "end": 425.41, "word": " أقول", "probability": 0.6593017578125}, {"start": 425.41, "end": 425.95, "word": " Z1,", "probability": 0.53271484375}, {"start": 426.13, "end": 426.67, "word": " Z2,", "probability": 0.908203125}, {"start": 426.83, "end": 427.35, "word": " Z3", "probability": 0.970947265625}, {"start": 427.35, "end": 427.71, "word": " لغاية", "probability": 0.859619140625}, {"start": 427.71, "end": 428.25, "word": " ZN", "probability": 0.7763671875}, {"start": 428.25, "end": 428.39, "word": " و", "probability": 0.72998046875}, {"start": 428.39, "end": 428.95, "word": " هكذا", "probability": 0.7854817708333334}, {"start": 428.95, "end": 429.79, "word": " يعني", "probability": 0.8798828125}, {"start": 429.79, "end": 430.41, "word": " كل", "probability": 0.91064453125}, {"start": 430.41, "end": 431.13, "word": " عنصر", "probability": 0.9786783854166666}, {"start": 431.13, "end": 431.29, "word": " في", "probability": 0.9033203125}, {"start": 431.29, "end": 431.69, "word": " الـ", "probability": 0.580810546875}, {"start": 431.69, "end": 432.13, "word": " RN", "probability": 0.5234375}, {"start": 432.13, "end": 433.55, "word": " يتركب", "probability": 0.9146728515625}, {"start": 433.55, "end": 433.75, "word": " أو", "probability": 0.82470703125}, {"start": 433.75, "end": 434.57, "word": " يتكون", "probability": 0.93798828125}, {"start": 434.57, "end": 434.93, "word": " من", "probability": 0.99169921875}, {"start": 434.93, "end": 435.35, "word": " N", "probability": 0.53125}, {"start": 435.35, "end": 435.89, "word": " من", "probability": 0.97802734375}, {"start": 435.89, "end": 437.73, "word": " المُركّبات", "probability": 0.848876953125}, {"start": 437.73, "end": 438.29, "word": " هذه", "probability": 0.18017578125}, {"start": 438.29, "end": 438.47, "word": " اللي", "probability": 0.859130859375}, {"start": 438.47, "end": 438.93, "word": " بنقوله", "probability": 0.8629557291666666}, {"start": 438.93, "end": 439.13, "word": " هنا", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 20, "seek": 46478, "start": 439.66, "end": 464.78, "text": "الان بدي اجي للعمليات الرياضية على هذه ال vectors يعني كيف بدي اجمع ال vectors كيف بدي اضرب vector في رقم ما هو ال zero vector هذا اللي بنقصده بال operations on vectors بالعمليات على المتجهة فبعدين بقول لو كاتبت ال vector x بمركباته و ال y بمركباته", "tokens": [6027, 7649, 4724, 16254, 1975, 7435, 1829, 24976, 25957, 20292, 9307, 2423, 16572, 46958, 10632, 15844, 29538, 2423, 18875, 37495, 22653, 9122, 33911, 4724, 16254, 1975, 7435, 2304, 3615, 2423, 18875, 9122, 33911, 4724, 16254, 1975, 11242, 25513, 8062, 8978, 12602, 4587, 2304, 19446, 31439, 2423, 4018, 8062, 23758, 13672, 1829, 44945, 4587, 9381, 3215, 3224, 20666, 7705, 322, 18875, 20666, 25957, 20292, 9307, 15844, 9673, 2655, 7435, 3224, 3660, 6156, 3555, 22488, 9957, 4724, 39648, 45164, 9122, 9307, 3555, 2655, 2423, 8062, 2031, 4724, 29973, 4117, 3555, 9307, 3224, 4032, 2423, 288, 4724, 29973, 4117, 3555, 9307, 3224], "avg_logprob": -0.16546875447034837, "compression_ratio": 1.893719806763285, "no_speech_prob": 0.0, "words": [{"start": 439.66, "end": 440.32, "word": "الان", "probability": 0.699462890625}, {"start": 440.32, "end": 440.62, "word": " بدي", "probability": 0.35302734375}, {"start": 440.62, "end": 440.9, "word": " اجي", "probability": 0.5897623697916666}, {"start": 440.9, "end": 441.88, "word": " للعمليات", "probability": 0.8118896484375}, {"start": 441.88, "end": 442.84, "word": " الرياضية", "probability": 0.9161376953125}, {"start": 442.84, "end": 443.36, "word": " على", "probability": 0.7294921875}, {"start": 443.36, "end": 443.96, "word": " هذه", "probability": 0.7080078125}, {"start": 443.96, "end": 444.18, "word": " ال", "probability": 0.9306640625}, {"start": 444.18, "end": 444.54, "word": " vectors", "probability": 0.5478515625}, {"start": 444.54, "end": 445.44, "word": " يعني", "probability": 0.8798828125}, {"start": 445.44, "end": 445.72, "word": " كيف", "probability": 0.9736328125}, {"start": 445.72, "end": 446.0, "word": " بدي", "probability": 0.9140625}, {"start": 446.0, "end": 446.36, "word": " اجمع", "probability": 0.879638671875}, {"start": 446.36, "end": 446.5, "word": " ال", "probability": 0.9560546875}, {"start": 446.5, "end": 446.88, "word": " vectors", "probability": 0.9345703125}, {"start": 446.88, "end": 447.2, "word": " كيف", "probability": 0.68359375}, {"start": 447.2, "end": 447.42, "word": " بدي", "probability": 0.97412109375}, {"start": 447.42, "end": 447.78, "word": " اضرب", "probability": 0.9371744791666666}, {"start": 447.78, "end": 448.44, "word": " vector", "probability": 0.91162109375}, {"start": 448.44, "end": 448.94, "word": " في", "probability": 0.9091796875}, {"start": 448.94, "end": 449.64, "word": " رقم", "probability": 0.9952799479166666}, {"start": 449.64, "end": 449.88, "word": " ما", "probability": 0.88525390625}, {"start": 449.88, "end": 450.24, "word": " هو", "probability": 0.791015625}, {"start": 450.24, "end": 450.5, "word": " ال", "probability": 0.9326171875}, {"start": 450.5, "end": 450.84, "word": " zero", "probability": 0.5888671875}, {"start": 450.84, "end": 451.42, "word": " vector", "probability": 0.97216796875}, {"start": 451.42, "end": 452.12, "word": " هذا", "probability": 0.91015625}, {"start": 452.12, "end": 452.28, "word": " اللي", "probability": 0.953125}, {"start": 452.28, "end": 453.0, "word": " بنقصده", "probability": 0.94892578125}, {"start": 453.0, "end": 453.24, "word": " بال", "probability": 0.927734375}, {"start": 453.24, "end": 454.08, "word": " operations", "probability": 0.9189453125}, {"start": 454.08, "end": 454.74, "word": " on", "probability": 0.8896484375}, {"start": 454.74, "end": 455.26, "word": " vectors", "probability": 0.9580078125}, {"start": 455.26, "end": 456.34, "word": " بالعمليات", "probability": 0.9365234375}, {"start": 456.34, "end": 457.1, "word": " على", "probability": 0.9169921875}, {"start": 457.1, "end": 458.58, "word": " المتجهة", "probability": 0.96123046875}, {"start": 458.58, "end": 459.34, "word": " فبعدين", "probability": 0.75494384765625}, {"start": 459.34, "end": 459.64, "word": " بقول", "probability": 0.93017578125}, {"start": 459.64, "end": 459.92, "word": " لو", "probability": 0.9580078125}, {"start": 459.92, "end": 460.66, "word": " كاتبت", "probability": 0.9332275390625}, {"start": 460.66, "end": 460.82, "word": " ال", "probability": 0.9736328125}, {"start": 460.82, "end": 461.24, "word": " vector", "probability": 0.98046875}, {"start": 461.24, "end": 461.7, "word": " x", "probability": 0.541015625}, {"start": 461.7, "end": 463.0, "word": " بمركباته", "probability": 0.9331868489583334}, {"start": 463.0, "end": 463.22, "word": " و", "probability": 0.30126953125}, {"start": 463.22, "end": 463.34, "word": " ال", "probability": 0.88818359375}, {"start": 463.34, "end": 463.58, "word": " y", "probability": 0.802734375}, {"start": 463.58, "end": 464.78, "word": " بمركباته", "probability": 0.9838053385416666}], "temperature": 1.0}, {"id": 21, "seek": 48753, "start": 465.29, "end": 487.53, "text": "وكان عندنا c any real number موجة بسالب سفر ما بتفريقش عنها ضربت هذا c في ال vector يبقى بروح بضربه في كل مركبة من مركبات هذا ال vector فمثلا لما أقول c x يبقى ال c بدي أضربها في كل مركبة من هذه المركبات زي ما تشايفه", "tokens": [2407, 41361, 43242, 8315, 269, 604, 957, 1230, 3714, 29245, 3660, 4724, 3794, 6027, 3555, 8608, 5172, 2288, 19446, 39894, 5172, 16572, 4587, 8592, 18871, 11296, 48812, 25513, 2655, 23758, 269, 8978, 2423, 8062, 7251, 3555, 4587, 7578, 4724, 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"word": " موجة", "probability": 0.8141276041666666}, {"start": 468.35, "end": 468.79, "word": " بسالب", "probability": 0.6943359375}, {"start": 468.79, "end": 469.05, "word": " سفر", "probability": 0.7720540364583334}, {"start": 469.05, "end": 469.11, "word": " ما", "probability": 0.2440185546875}, {"start": 469.11, "end": 469.63, "word": " بتفريقش", "probability": 0.76513671875}, {"start": 469.63, "end": 470.01, "word": " عنها", "probability": 0.55712890625}, {"start": 470.01, "end": 471.15, "word": " ضربت", "probability": 0.9303385416666666}, {"start": 471.15, "end": 471.51, "word": " هذا", "probability": 0.8603515625}, {"start": 471.51, "end": 471.91, "word": " c", "probability": 0.5966796875}, {"start": 471.91, "end": 472.11, "word": " في", "probability": 0.95068359375}, {"start": 472.11, "end": 472.37, "word": " ال", "probability": 0.958984375}, {"start": 472.37, "end": 472.91, "word": " vector", "probability": 0.8896484375}, {"start": 472.91, "end": 473.59, "word": " يبقى", "probability": 0.9354248046875}, {"start": 473.59, "end": 473.95, "word": " بروح", "probability": 0.9248046875}, {"start": 473.95, "end": 474.67, "word": " بضربه", "probability": 0.8602294921875}, {"start": 474.67, "end": 474.91, "word": " في", "probability": 0.95751953125}, {"start": 474.91, "end": 475.45, "word": " كل", "probability": 0.98974609375}, {"start": 475.45, "end": 476.49, "word": " مركبة", "probability": 0.8268229166666666}, {"start": 476.49, "end": 476.93, "word": " من", "probability": 0.990234375}, {"start": 476.93, "end": 478.01, "word": " مركبات", "probability": 0.950927734375}, {"start": 478.01, "end": 478.41, "word": " هذا", "probability": 0.9638671875}, {"start": 478.41, "end": 478.61, "word": " ال", "probability": 0.978515625}, {"start": 478.61, "end": 479.01, "word": " vector", "probability": 0.97216796875}, {"start": 479.01, "end": 479.79, "word": " فمثلا", "probability": 0.9422607421875}, {"start": 479.79, "end": 480.77, "word": " لما", "probability": 0.898681640625}, {"start": 480.77, "end": 481.13, "word": " أقول", "probability": 0.78515625}, {"start": 481.13, "end": 481.59, "word": " c", "probability": 0.771484375}, {"start": 481.59, "end": 482.11, "word": " x", "probability": 0.469482421875}, {"start": 482.11, "end": 482.65, "word": " يبقى", "probability": 0.9808349609375}, {"start": 482.65, "end": 482.79, "word": " ال", "probability": 0.64111328125}, {"start": 482.79, "end": 482.95, "word": " c", "probability": 0.86962890625}, {"start": 482.95, "end": 483.27, "word": " بدي", "probability": 0.669189453125}, {"start": 483.27, "end": 483.79, "word": " أضربها", "probability": 0.9371337890625}, {"start": 483.79, "end": 484.01, "word": " في", "probability": 0.978515625}, {"start": 484.01, "end": 484.43, "word": " كل", "probability": 0.98681640625}, {"start": 484.43, "end": 485.15, "word": " مركبة", "probability": 0.98876953125}, {"start": 485.15, "end": 485.35, "word": " من", "probability": 0.9892578125}, {"start": 485.35, "end": 485.73, "word": " هذه", "probability": 0.96728515625}, {"start": 485.73, "end": 486.61, "word": " المركبات", "probability": 0.9639892578125}, {"start": 486.61, "end": 486.83, "word": " زي", "probability": 0.88330078125}, {"start": 486.83, "end": 486.95, "word": " ما", "probability": 0.91259765625}, {"start": 486.95, "end": 487.53, "word": " تشايفه", "probability": 0.718701171875}], "temperature": 1.0}, {"id": 22, "seek": 50221, "start": 487.67, "end": 502.21, "text": "يبقى بيصير المركبات الجديدة للـ vector CX هي من CX1, CX2, CX3 لغاية ما أوصل إلى CXN طب العملية العكسية", "tokens": [1829, 3555, 4587, 7578, 4724, 1829, 9381, 13546, 9673, 31747, 3555, 9307, 25724, 16254, 41891, 24976, 39184, 8062, 383, 55, 39896, 9154, 383, 55, 16, 11, 383, 55, 17, 11, 383, 55, 18, 5296, 17082, 995, 10632, 19446, 34051, 36520, 30731, 383, 55, 45, 23032, 3555, 18863, 42213, 10632, 18863, 4117, 3794, 10632], "avg_logprob": -0.19806134314448745, "compression_ratio": 1.2255639097744362, "no_speech_prob": 0.0, "words": [{"start": 487.67, "end": 488.31, "word": "يبقى", "probability": 0.7789306640625}, {"start": 488.31, "end": 488.97, "word": " بيصير", "probability": 0.854736328125}, {"start": 488.97, "end": 490.37, "word": " المركبات", "probability": 0.78875732421875}, {"start": 490.37, "end": 491.05, "word": " الجديدة", "probability": 0.9869791666666666}, {"start": 491.05, "end": 491.57, "word": " للـ", "probability": 0.61279296875}, {"start": 491.57, "end": 491.85, "word": " vector", "probability": 0.73583984375}, {"start": 491.85, "end": 492.77, "word": " CX", "probability": 0.688720703125}, {"start": 492.77, "end": 493.43, "word": " هي", "probability": 0.927734375}, {"start": 493.43, "end": 493.79, "word": " من", "probability": 0.5322265625}, {"start": 493.79, "end": 494.89, "word": " CX1,", "probability": 0.85205078125}, {"start": 495.07, "end": 495.83, "word": " CX2,", "probability": 0.92919921875}, {"start": 496.01, "end": 496.75, "word": " CX3", "probability": 0.9527994791666666}, {"start": 496.75, "end": 497.13, "word": " لغاية", "probability": 0.911376953125}, {"start": 497.13, "end": 497.27, "word": " ما", "probability": 0.8828125}, {"start": 497.27, "end": 497.55, "word": " أوصل", "probability": 0.728759765625}, {"start": 497.55, "end": 497.87, "word": " إلى", "probability": 0.7392578125}, {"start": 497.87, "end": 499.93, "word": " CXN", "probability": 0.8759765625}, {"start": 499.93, "end": 500.83, "word": " طب", "probability": 0.67041015625}, {"start": 500.83, "end": 501.29, "word": " العملية", "probability": 0.9698893229166666}, {"start": 501.29, "end": 502.21, "word": " العكسية", "probability": 0.9962158203125}], "temperature": 1.0}, {"id": 23, "seek": 52196, "start": 502.7, "end": 521.96, "text": "أيش العملية العكسية؟ لو كان عندي vector مُعطَب مُركّبته واطلعته بعيني اللي جيت فيه عمل مشترك ممكن أخده برا، إذا بقدر أاخده برا ال vector يبقى هذا يعتبر constant مضروب في من؟ في ال vector، برضه هذا الكلام صحيح", "tokens": [10721, 1829, 8592, 18863, 42213, 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"word": " مشترك", "probability": 0.9547526041666666}, {"start": 511.08, "end": 511.58, "word": " ممكن", "probability": 0.989501953125}, {"start": 511.58, "end": 512.12, "word": " أخده", "probability": 0.8350830078125}, {"start": 512.12, "end": 512.88, "word": " برا،", "probability": 0.808837890625}, {"start": 512.88, "end": 513.14, "word": " إذا", "probability": 0.86376953125}, {"start": 513.14, "end": 513.68, "word": " بقدر", "probability": 0.9737955729166666}, {"start": 513.68, "end": 514.22, "word": " أاخده", "probability": 0.81842041015625}, {"start": 514.22, "end": 515.38, "word": " برا", "probability": 0.61376953125}, {"start": 515.38, "end": 515.54, "word": " ال", "probability": 0.943359375}, {"start": 515.54, "end": 515.82, "word": " vector", "probability": 0.88623046875}, {"start": 515.82, "end": 516.18, "word": " يبقى", "probability": 0.8406982421875}, {"start": 516.18, "end": 516.46, "word": " هذا", "probability": 0.420654296875}, {"start": 516.46, "end": 517.0, "word": " يعتبر", "probability": 0.904296875}, {"start": 517.0, "end": 517.56, "word": " constant", "probability": 0.470458984375}, {"start": 517.56, "end": 518.12, "word": " مضروب", "probability": 0.90576171875}, {"start": 518.12, "end": 518.28, "word": " في", "probability": 0.9814453125}, {"start": 518.28, "end": 519.06, "word": " من؟", "probability": 0.62646484375}, {"start": 519.06, "end": 519.26, "word": " في", "probability": 0.8974609375}, {"start": 519.26, "end": 519.56, "word": " ال", "probability": 0.962890625}, {"start": 519.56, "end": 520.16, "word": " vector،", "probability": 0.8505859375}, {"start": 520.16, "end": 520.5, "word": " برضه", "probability": 0.94140625}, {"start": 520.5, "end": 520.74, "word": " هذا", "probability": 0.98388671875}, {"start": 520.74, "end": 521.42, "word": " الكلام", "probability": 0.9474283854166666}, {"start": 521.42, "end": 521.96, "word": " صحيح", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 24, "seek": 53995, "start": 523.19, "end": 539.95, "text": "الامر الثاني لو بدى اجمع two vectors مع بعض x زائد y الجمع component wise ايش المقصود بال component wise يعني كل مركبة جاها مع نظيرتها وماليش ده بالتانية يعني", "tokens": [6027, 10943, 2288, 6024, 104, 7649, 1829, 45164, 47525, 7578, 1975, 7435, 2304, 3615, 732, 18875, 20449, 45030, 11242, 2031, 30767, 16373, 3215, 288, 25724, 2304, 3615, 6542, 10829, 1975, 1829, 8592, 9673, 4587, 9381, 23328, 20666, 6542, 10829, 37495, 22653, 28242, 3714, 31747, 49401, 10874, 995, 11296, 20449, 8717, 19913, 13546, 2655, 11296, 4032, 2304, 6027, 1829, 8592, 11778, 3224, 20666, 2655, 7649, 10632, 37495, 22653], "avg_logprob": -0.19669117384097157, "compression_ratio": 1.537037037037037, "no_speech_prob": 0.0, "words": [{"start": 523.19, "end": 523.75, "word": "الامر", "probability": 0.6663411458333334}, {"start": 523.75, "end": 524.29, "word": " الثاني", "probability": 0.962646484375}, {"start": 524.29, "end": 524.87, "word": " لو", "probability": 0.427734375}, {"start": 524.87, "end": 525.19, "word": " بدى", "probability": 0.5504150390625}, {"start": 525.19, "end": 525.67, "word": " اجمع", "probability": 0.9111328125}, {"start": 525.67, "end": 526.05, "word": " two", "probability": 0.8212890625}, {"start": 526.05, "end": 526.65, "word": " vectors", "probability": 0.96826171875}, {"start": 526.65, "end": 526.89, "word": " مع", "probability": 0.9873046875}, {"start": 526.89, "end": 527.23, "word": " بعض", "probability": 0.997314453125}, {"start": 527.23, "end": 527.59, "word": " x", "probability": 0.50830078125}, {"start": 527.59, "end": 528.07, "word": " زائد", "probability": 0.7412923177083334}, {"start": 528.07, "end": 528.31, "word": " y", "probability": 0.9130859375}, {"start": 528.31, "end": 528.97, "word": " الجمع", "probability": 0.7377115885416666}, {"start": 528.97, "end": 530.19, "word": " component", "probability": 0.8818359375}, {"start": 530.19, "end": 530.91, "word": " wise", "probability": 0.58349609375}, {"start": 530.91, "end": 531.63, "word": " ايش", "probability": 0.7491861979166666}, {"start": 531.63, "end": 532.19, "word": " المقصود", "probability": 0.983154296875}, {"start": 532.19, "end": 532.35, "word": " بال", "probability": 0.92236328125}, {"start": 532.35, "end": 532.91, "word": " component", "probability": 0.94970703125}, {"start": 532.91, "end": 533.39, "word": " wise", "probability": 0.9306640625}, {"start": 533.39, "end": 533.73, "word": " يعني", "probability": 0.814208984375}, {"start": 533.73, "end": 534.27, "word": " كل", "probability": 0.86181640625}, {"start": 534.27, "end": 535.07, "word": " مركبة", "probability": 0.9005533854166666}, {"start": 535.07, "end": 535.71, "word": " جاها", "probability": 0.8795572916666666}, {"start": 535.71, "end": 536.07, "word": " مع", "probability": 0.9873046875}, {"start": 536.07, "end": 537.73, "word": " نظيرتها", "probability": 0.9654296875}, {"start": 537.73, "end": 538.63, "word": " وماليش", "probability": 0.73427734375}, {"start": 538.63, "end": 538.87, "word": " ده", "probability": 0.94677734375}, {"start": 538.87, "end": 539.51, "word": " بالتانية", "probability": 0.8861083984375}, {"start": 539.51, "end": 539.95, "word": " يعني", "probability": 0.7958984375}], "temperature": 1.0}, {"id": 25, "seek": 55608, "start": 540.62, "end": 556.08, "text": "لما يكون عندي two vectors هاي عنا X وهذا Y وبدي أجمعهم يبقى المركبة الأولى مع المركبة الأولى وتمثل المركبة الأولى في ال vector الناتج من عملية الجامعة", "tokens": [1211, 15042, 7251, 30544, 18871, 16254, 732, 18875, 8032, 47302, 6225, 8315, 1783, 37037, 15730, 398, 46599, 16254, 5551, 7435, 2304, 3615, 16095, 7251, 3555, 4587, 7578, 9673, 31747, 49401, 16247, 12610, 7578, 20449, 9673, 31747, 49401, 16247, 12610, 7578, 34683, 2304, 12984, 1211, 9673, 31747, 49401, 16247, 12610, 7578, 8978, 2423, 8062, 2423, 8315, 2655, 7435, 9154, 6225, 42213, 10632, 25724, 10943, 27884], "avg_logprob": -0.2032451923076923, "compression_ratio": 1.7586206896551724, "no_speech_prob": 0.0, "words": [{"start": 540.62, "end": 541.02, "word": "لما", "probability": 0.5584716796875}, {"start": 541.02, "end": 541.34, "word": " يكون", "probability": 0.893310546875}, {"start": 541.34, "end": 541.78, "word": " عندي", "probability": 0.6114501953125}, {"start": 541.78, "end": 542.12, "word": " two", "probability": 0.6513671875}, {"start": 542.12, "end": 542.86, "word": " vectors", "probability": 0.96923828125}, {"start": 542.86, "end": 543.28, "word": " هاي", "probability": 0.43505859375}, {"start": 543.28, "end": 543.68, "word": " عنا", "probability": 0.666748046875}, {"start": 543.68, "end": 544.14, "word": " X", "probability": 0.67333984375}, {"start": 544.14, "end": 544.92, "word": " وهذا", "probability": 0.7177734375}, {"start": 544.92, "end": 545.16, "word": " Y", "probability": 0.96484375}, {"start": 545.16, "end": 545.52, "word": " وبدي", "probability": 0.55548095703125}, {"start": 545.52, "end": 546.14, "word": " أجمعهم", "probability": 0.93828125}, {"start": 546.14, "end": 546.88, "word": " يبقى", "probability": 0.929931640625}, {"start": 546.88, "end": 547.46, "word": " المركبة", "probability": 0.8763020833333334}, {"start": 547.46, "end": 547.88, "word": " الأولى", "probability": 0.9856770833333334}, {"start": 547.88, "end": 548.04, "word": " مع", "probability": 0.9853515625}, {"start": 548.04, "end": 548.72, "word": " المركبة", "probability": 0.9923502604166666}, {"start": 548.72, "end": 549.24, "word": " الأولى", "probability": 0.9959309895833334}, {"start": 549.24, "end": 550.66, "word": " وتمثل", "probability": 0.91845703125}, {"start": 550.66, "end": 551.84, "word": " المركبة", "probability": 0.9881184895833334}, {"start": 551.84, "end": 552.74, "word": " الأولى", "probability": 0.9959309895833334}, {"start": 552.74, "end": 553.1, "word": " في", "probability": 0.89453125}, {"start": 553.1, "end": 553.26, "word": " ال", "probability": 0.9697265625}, {"start": 553.26, "end": 553.68, "word": " vector", "probability": 0.8955078125}, {"start": 553.68, "end": 554.32, "word": " الناتج", "probability": 0.7864990234375}, {"start": 554.32, "end": 554.56, "word": " من", "probability": 0.990234375}, {"start": 554.56, "end": 555.32, "word": " عملية", "probability": 0.9853515625}, {"start": 555.32, "end": 556.08, "word": " الجامعة", "probability": 0.7877604166666666}], "temperature": 1.0}, {"id": 26, "seek": 57329, "start": 556.28, "end": 573.3, "text": "إذا لما أقول X زائد Y يبقى X1 زائد Y1 المركبة الثانية X2 زائد Y2 المركبة الثانية من المتجه الأول زائد المركبة الثانية من المتجه التاني بتكون المركبة التانية في المتجه الجديد", "tokens": [28814, 15730, 5296, 15042, 5551, 39648, 1783, 30767, 16373, 3215, 398, 7251, 3555, 4587, 7578, 1783, 16, 30767, 16373, 3215, 398, 16, 9673, 31747, 49401, 6024, 104, 7649, 10632, 1783, 17, 30767, 16373, 3215, 398, 17, 9673, 31747, 49401, 6024, 104, 7649, 10632, 9154, 9673, 2655, 7435, 3224, 16247, 12610, 30767, 16373, 3215, 9673, 31747, 49401, 6024, 104, 7649, 10632, 9154, 9673, 2655, 7435, 3224, 16712, 7649, 1829, 39894, 30544, 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0.99072265625}, {"start": 560.42, "end": 561.52, "word": " المركبة", "probability": 0.81201171875}, {"start": 561.52, "end": 562.1, "word": " الثانية", "probability": 0.9276123046875}, {"start": 562.1, "end": 563.46, "word": " X2", "probability": 0.9140625}, {"start": 563.46, "end": 564.26, "word": " زائد", "probability": 0.9736328125}, {"start": 564.26, "end": 564.7, "word": " Y2", "probability": 0.9912109375}, {"start": 564.7, "end": 565.36, "word": " المركبة", "probability": 0.9830729166666666}, {"start": 565.36, "end": 565.82, "word": " الثانية", "probability": 0.9390869140625}, {"start": 565.82, "end": 566.02, "word": " من", "probability": 0.978515625}, {"start": 566.02, "end": 566.72, "word": " المتجه", "probability": 0.9609375}, {"start": 566.72, "end": 567.16, "word": " الأول", "probability": 0.992919921875}, {"start": 567.16, "end": 567.48, "word": " زائد", "probability": 0.9736328125}, {"start": 567.48, "end": 568.02, "word": " المركبة", "probability": 0.9912109375}, 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إذا عندي constant بضربه في جميع المركبات إذا عندي مجموعة vectors بجمع component Y", "tokens": [1829, 3555, 4587, 7578, 1783, 17, 30767, 1829, 398, 17, 37037, 4117, 15730, 4724, 14851, 29973, 5296, 17082, 995, 10632, 3714, 2407, 36520, 5296, 148, 95, 34740, 3714, 31747, 49401, 1783, 45, 30767, 1829, 398, 45, 7251, 3555, 4587, 7578, 35186, 4724, 8315, 31371, 11933, 15730, 18871, 16254, 5754, 4724, 11242, 25513, 3224, 8978, 10874, 2304, 40228, 9673, 31747, 3555, 9307, 11933, 15730, 18871, 16254, 3714, 7435, 2304, 2407, 27884, 18875, 4724, 7435, 2304, 3615, 6542, 398], "avg_logprob": -0.24158653292136315, "compression_ratio": 1.4319526627218935, "no_speech_prob": 0.0, "words": [{"start": 573.53, "end": 574.23, "word": "يبقى", "probability": 0.8079833984375}, {"start": 574.23, "end": 574.81, "word": " X2", "probability": 0.5946044921875}, {"start": 574.81, "end": 575.13, "word": " زي", "probability": 0.4560546875}, {"start": 575.13, "end": 575.53, "word": " Y2", "probability": 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"probability": 0.992431640625}, {"start": 609.45, "end": 609.67, "word": " و", "probability": 0.57568359375}, {"start": 609.67, "end": 610.31, "word": " هكذا", "probability": 0.9103190104166666}, {"start": 610.31, "end": 611.33, "word": " تمام", "probability": 0.961669921875}, {"start": 611.33, "end": 612.09, "word": " يبقى", "probability": 0.8607177734375}, {"start": 612.09, "end": 612.51, "word": " الجمع", "probability": 0.93603515625}, {"start": 612.51, "end": 612.63, "word": " في", "probability": 0.89697265625}, {"start": 612.63, "end": 612.93, "word": " هذه", "probability": 0.11871337890625}, {"start": 612.93, "end": 613.07, "word": " ال", "probability": 0.97265625}, {"start": 613.07, "end": 613.33, "word": " vector", "probability": 0.96826171875}, {"start": 613.33, "end": 613.67, "word": " هو", "probability": 0.96826171875}, {"start": 613.67, "end": 614.15, "word": " component", "probability": 0.93310546875}, {"start": 614.15, "end": 615.07, "word": " wise", "probability": 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اللى", "probability": 0.8759765625}, {"start": 622.86, "end": 623.44, "word": " مطول", "probability": 0.7753092447916666}, {"start": 623.44, "end": 624.08, "word": " شوية", "probability": 0.85498046875}, {"start": 624.08, "end": 624.5, "word": " هذا", "probability": 0.37451171875}, {"start": 624.5, "end": 625.64, "word": " وهذا", "probability": 0.7373046875}, {"start": 625.64, "end": 626.16, "word": " عبارة", "probability": 0.983154296875}, {"start": 626.16, "end": 626.38, "word": " عن", "probability": 0.97900390625}, {"start": 626.38, "end": 627.04, "word": " مجموعة", "probability": 0.9634765625}, {"start": 627.04, "end": 627.4, "word": " من", "probability": 0.97021484375}, {"start": 627.4, "end": 629.24, "word": " المركبات", "probability": 0.85394287109375}, {"start": 629.24, "end": 630.8, "word": " عدد", "probability": 0.8714192708333334}, {"start": 630.8, "end": 631.24, "word": " هذه", "probability": 0.97021484375}, {"start": 631.24, "end": 632.26, "word": " المركبات", "probability": 0.9910888671875}, {"start": 632.26, "end": 632.8, "word": " يسوى", "probability": 0.80804443359375}, {"start": 632.8, "end": 633.6, "word": " قداش", "probability": 0.7501627604166666}, {"start": 633.6, "end": 635.04, "word": " يسوى", "probability": 0.85595703125}, {"start": 635.04, "end": 635.46, "word": " n", "probability": 0.407470703125}, {"start": 635.46, "end": 635.76, "word": " اللى", "probability": 0.943603515625}, {"start": 635.76, "end": 636.32, "word": " عندنا", "probability": 0.986328125}, {"start": 636.32, "end": 636.72, "word": " هذه", "probability": 0.69091796875}, {"start": 636.72, "end": 636.86, "word": " و", "probability": 0.5419921875}, {"start": 636.86, "end": 637.28, "word": " الراحة", "probability": 0.3110758463541667}, {"start": 637.28, "end": 637.44, "word": " اللى", "probability": 0.754150390625}, {"start": 637.44, "end": 637.68, "word": " هى", "probability": 0.859619140625}, {"start": 637.68, "end": 638.06, "word": " n", "probability": 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" من", "probability": 0.734375}, {"start": 647.39, "end": 648.35, "word": " المراكبات", "probability": 0.87451171875}, {"start": 648.35, "end": 648.87, "word": " وكل", "probability": 0.75244140625}, {"start": 648.87, "end": 649.51, "word": " مراكبة", "probability": 0.959228515625}, {"start": 649.51, "end": 649.69, "word": " من", "probability": 0.966796875}, {"start": 649.69, "end": 649.95, "word": " هذه", "probability": 0.9033203125}, {"start": 649.95, "end": 650.73, "word": " المراكبات", "probability": 0.99013671875}, {"start": 650.73, "end": 650.99, "word": " هي", "probability": 0.89453125}, {"start": 650.99, "end": 651.67, "word": " zero", "probability": 0.642578125}, {"start": 651.67, "end": 652.67, "word": " كل", "probability": 0.80029296875}, {"start": 652.67, "end": 653.59, "word": " المراكبات", "probability": 0.99091796875}, {"start": 653.59, "end": 654.33, "word": " صفر", "probability": 0.9152018229166666}, {"start": 654.33, "end": 655.25, "word": " تمام", "probability": 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اجمع", "probability": 0.983154296875}, {"start": 741.69, "end": 742.11, "word": " هذه", "probability": 0.8388671875}, {"start": 742.11, "end": 742.33, "word": " مع", "probability": 0.970703125}, {"start": 742.33, "end": 742.73, "word": " هذه", "probability": 0.943359375}, {"start": 742.73, "end": 742.89, "word": " و", "probability": 0.459228515625}, {"start": 742.89, "end": 743.13, "word": " هذه", "probability": 0.86962890625}, {"start": 743.13, "end": 743.33, "word": " مع", "probability": 0.984375}, {"start": 743.33, "end": 743.57, "word": " هذه", "probability": 0.849609375}, {"start": 743.57, "end": 743.67, "word": " و", "probability": 0.60400390625}, {"start": 743.67, "end": 743.89, "word": " هذه", "probability": 0.8876953125}, {"start": 743.89, "end": 744.13, "word": " مع", "probability": 0.99169921875}, {"start": 744.13, "end": 745.11, "word": " مين؟", "probability": 0.849609375}], "temperature": 1.0}, {"id": 35, "seek": 77480, "start": 745.82, "end": 774.8, "text": "مافيش مكان يبقى للمعنى هنا في هاتفها does not exist يبقى انا بقدر اجمع two vectors اللي هما نفس العدد من ال components غير هيك بقدرش تمام طيب نيجي الان لل remark اللي عندنا هذه قبل مفوت لل remark حد بتسأل اي سؤال في الكلام اللي تحدثنا به قبل قليل اه مين بتحب تسأل؟", "tokens": [15042, 41185, 8592, 3714, 41361, 7251, 3555, 4587, 7578, 5296, 19528, 3615, 1863, 7578, 34105, 8978, 8032, 9307, 5172, 11296, 775, 406, 2514, 7251, 3555, 4587, 7578, 1975, 8315, 4724, 28543, 2288, 1975, 7435, 2304, 3615, 732, 18875, 13672, 1829, 8032, 15042, 8717, 36178, 18863, 3215, 3215, 9154, 2423, 6677, 32771, 13546, 39896, 4117, 4724, 28543, 2288, 8592, 46811, 10943, 23032, 1829, 3555, 8717, 1829, 7435, 1829, 2423, 7649, 24976, 7942, 13672, 1829, 43242, 8315, 29538, 12174, 36150, 3714, 5172, 35473, 24976, 7942, 11331, 3215, 39894, 3794, 10721, 1211, 1975, 1829, 8608, 33604, 6027, 8978, 2423, 28820, 10943, 13672, 1829, 6055, 24401, 12984, 8315, 39627, 12174, 36150, 12174, 20292, 1211, 1975, 3224, 3714, 9957, 39894, 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"end": 765.96, "word": " قبل", "probability": 0.92236328125}, {"start": 765.96, "end": 766.34, "word": " مفوت", "probability": 0.5938313802083334}, {"start": 766.34, "end": 766.48, "word": " لل", "probability": 0.25146484375}, {"start": 766.48, "end": 766.84, "word": " remark", "probability": 0.96826171875}, {"start": 766.84, "end": 767.22, "word": " حد", "probability": 0.69384765625}, {"start": 767.22, "end": 767.84, "word": " بتسأل", "probability": 0.895263671875}, {"start": 767.84, "end": 768.22, "word": " اي", "probability": 0.7392578125}, {"start": 768.22, "end": 768.74, "word": " سؤال", "probability": 0.99609375}, {"start": 768.74, "end": 768.88, "word": " في", "probability": 0.861328125}, {"start": 768.88, "end": 769.28, "word": " الكلام", "probability": 0.9075520833333334}, {"start": 769.28, "end": 769.54, "word": " اللي", "probability": 0.697509765625}, {"start": 769.54, "end": 770.24, "word": " تحدثنا", "probability": 0.95947265625}, {"start": 770.24, "end": 770.5, "word": " به", "probability": 0.77880859375}, {"start": 770.5, "end": 770.94, "word": " قبل", "probability": 0.997314453125}, {"start": 770.94, "end": 772.84, "word": " قليل", "probability": 0.9949544270833334}, {"start": 772.84, "end": 773.7, "word": " اه", "probability": 0.760986328125}, {"start": 773.7, "end": 773.9, "word": " مين", "probability": 0.56494140625}, {"start": 773.9, "end": 774.16, "word": " بتحب", "probability": 0.9674479166666666}, {"start": 774.16, "end": 774.8, "word": " تسأل؟", "probability": 0.93037109375}], "temperature": 1.0}, {"id": 36, "seek": 78061, "start": 776.27, "end": 780.61, "text": "مفهوم يعني واضح؟ ننتقل إلى الـ Remark", "tokens": [2304, 5172, 3224, 20498, 37495, 22653, 4032, 46958, 5016, 22807, 8717, 29399, 4587, 1211, 30731, 2423, 39184, 4080, 809], "avg_logprob": -0.25019530653953553, "compression_ratio": 0.8732394366197183, "no_speech_prob": 0.0, "words": [{"start": 776.27, "end": 776.81, "word": "مفهوم", "probability": 0.9014892578125}, {"start": 776.81, "end": 777.01, "word": " يعني", "probability": 0.924560546875}, {"start": 777.01, "end": 778.39, "word": " واضح؟", "probability": 0.843505859375}, {"start": 778.39, "end": 779.39, "word": " ننتقل", "probability": 0.8634033203125}, {"start": 779.39, "end": 779.83, "word": " إلى", "probability": 0.60400390625}, {"start": 779.83, "end": 780.29, "word": " الـ", "probability": 0.89111328125}, {"start": 780.29, "end": 780.61, "word": " Remark", "probability": 0.57861328125}], "temperature": 1.0}, {"id": 37, "seek": 80825, "start": 781.11, "end": 808.25, "text": "بقول الـ N dimensional raw vector أو الكون vector يبقى أنا عندي متجه صفي أو متجه عمودي عدد العناصر في كل واحد منهم يساوي M هذا بقدر اكتبه على شكل components ماله can be represented as N tuple يعني بقدر اكتبه على شكل tuple اللي هو vector بمركبات", "tokens": [3555, 39648, 2423, 39184, 426, 18795, 8936, 8062, 34051, 2423, 30544, 8062, 7251, 3555, 4587, 7578, 41850, 18871, 16254, 44650, 7435, 3224, 20328, 5172, 1829, 34051, 44650, 7435, 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vector", "probability": 0.9736328125}, {"start": 784.31, "end": 784.67, "word": " أو", "probability": 0.609375}, {"start": 784.67, "end": 785.31, "word": " الكون", "probability": 0.6856689453125}, {"start": 785.31, "end": 785.97, "word": " vector", "probability": 0.68310546875}, {"start": 785.97, "end": 786.87, "word": " يبقى", "probability": 0.96484375}, {"start": 786.87, "end": 787.15, "word": " أنا", "probability": 0.6806640625}, {"start": 787.15, "end": 787.57, "word": " عندي", "probability": 0.745361328125}, {"start": 787.57, "end": 788.19, "word": " متجه", "probability": 0.9680989583333334}, {"start": 788.19, "end": 788.81, "word": " صفي", "probability": 0.8206380208333334}, {"start": 788.81, "end": 789.07, "word": " أو", "probability": 0.7451171875}, {"start": 789.07, "end": 789.79, "word": " متجه", "probability": 0.9951171875}, {"start": 789.79, "end": 790.31, "word": " عمودي", "probability": 0.98388671875}, {"start": 790.31, "end": 790.81, "word": " عدد", "probability": 0.9373372395833334}, {"start": 790.81, "end": 791.39, "word": " العناصر", "probability": 0.97509765625}, {"start": 791.39, "end": 791.61, "word": " في", "probability": 0.96630859375}, {"start": 791.61, "end": 791.95, "word": " كل", "probability": 0.9775390625}, {"start": 791.95, "end": 792.33, "word": " واحد", "probability": 0.99609375}, {"start": 792.33, "end": 792.73, "word": " منهم", "probability": 0.98779296875}, {"start": 792.73, "end": 793.67, "word": " يساوي", "probability": 0.9632568359375}, {"start": 793.67, "end": 794.15, "word": " M", "probability": 0.84521484375}, {"start": 794.15, "end": 795.17, "word": " هذا", "probability": 0.92529296875}, {"start": 795.17, "end": 795.69, "word": " بقدر", "probability": 0.982421875}, {"start": 795.69, "end": 796.53, "word": " اكتبه", "probability": 0.9072265625}, {"start": 796.53, "end": 797.05, "word": " على", "probability": 0.9091796875}, {"start": 797.05, "end": 797.67, "word": " شكل", "probability": 0.97705078125}, {"start": 797.67, "end": 798.83, "word": " components", "probability": 0.66943359375}, {"start": 798.83, "end": 799.41, "word": " ماله", "probability": 0.8180338541666666}, {"start": 799.41, "end": 800.05, "word": " can", "probability": 0.6396484375}, {"start": 800.05, "end": 800.31, "word": " be", "probability": 0.921875}, {"start": 800.31, "end": 800.97, "word": " represented", "probability": 0.78515625}, {"start": 800.97, "end": 801.51, "word": " as", "probability": 0.92724609375}, {"start": 801.51, "end": 801.89, "word": " N", "probability": 0.4443359375}, {"start": 801.89, "end": 802.73, "word": " tuple", "probability": 0.723388671875}, {"start": 802.73, "end": 803.41, "word": " يعني", "probability": 0.94482421875}, {"start": 803.41, "end": 803.91, "word": " بقدر", "probability": 0.99365234375}, {"start": 803.91, "end": 804.49, "word": " اكتبه", "probability": 0.98857421875}, {"start": 804.49, "end": 804.67, "word": " على", "probability": 0.90380859375}, {"start": 804.67, "end": 805.11, "word": " شكل", "probability": 0.963623046875}, {"start": 805.11, "end": 805.85, "word": " tuple", "probability": 0.8544921875}, {"start": 805.85, "end": 806.47, "word": " اللي", "probability": 0.947021484375}, {"start": 806.47, "end": 806.61, "word": " هو", "probability": 0.9716796875}, {"start": 806.61, "end": 806.93, "word": " vector", "probability": 0.91455078125}, {"start": 806.93, "end": 808.25, "word": " بمركبات", "probability": 0.862548828125}], "temperature": 1.0}, {"id": 38, "seek": 83026, "start": 808.28, "end": 830.26, "text": "and vice versa و العكس بالعكس يعني لو عندي vector مكتوب على شكل الكمبوتر بقدر أكتبه متجه عمودي و بقدر أكتبه متجه صفي سواء كان هذا ولا هذا الأثنين أخرى فمثلا لو جاتي قولتلي في عندي الو X واحد X اتنين X اتنين ايش اسم هذا يا بنات؟", "tokens": [474, 11964, 25650, 4032, 18863, 4117, 3794, 20666, 3615, 4117, 3794, 37495, 22653, 45164, 18871, 16254, 8062, 3714, 4117, 2655, 37746, 15844, 13412, 28820, 2423, 24793, 3555, 35473, 2288, 4724, 28543, 2288, 5551, 4117, 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يبقى بصير هنا ستة و هنا سالب ستة و هنا سالب اتناشر", "tokens": [6027, 2655, 7649, 10632, 8717, 4587, 9381, 8608, 2655, 3660, 1975, 2655, 1863, 9957, 46811, 7649, 10632, 4032, 34105, 30767, 16373, 3215, 13412, 28820, 43242, 8315, 34105, 9673, 9381, 3224, 37746, 6156, 21292, 3215, 32887, 5016, 1975, 11242, 25513, 11296, 8978, 3714, 9957, 22807, 8978, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 34105, 8608, 2655, 3660, 4032, 34105, 8608, 6027, 3555, 8608, 2655, 3660, 4032, 34105, 8608, 6027, 3555, 1975, 2655, 1863, 33599, 2288], "avg_logprob": -0.23647103731225178, "compression_ratio": 1.8108108108108107, "no_speech_prob": 0.0, "words": [{"start": 1051.61, "end": 1052.51, "word": "التانية", "probability": 0.8426513671875}, {"start": 1052.51, "end": 1053.79, "word": " نقص", "probability": 0.64697265625}, {"start": 1053.79, "end": 1054.63, "word": " ستة", "probability": 0.752197265625}, {"start": 1054.63, "end": 1055.65, "word": " اتنين", 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"word": " و", "probability": 0.94580078125}, {"start": 1071.35, "end": 1071.75, "word": " هنا", "probability": 0.97314453125}, {"start": 1071.75, "end": 1072.79, "word": " سالب", "probability": 0.9915364583333334}, {"start": 1072.79, "end": 1074.25, "word": " اتناشر", "probability": 0.91875}], "temperature": 1.0}, {"id": 50, "seek": 108215, "start": 1074.61, "end": 1082.15, "text": "وهنا سالب تلاتة سالب تلاتة وهنا سالب تسعة بالشكل اللي عندنا هنا", "tokens": [2407, 3224, 8315, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 37037, 8315, 8608, 6027, 3555, 6055, 3794, 27884, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105], "avg_logprob": -0.20002297881771536, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1074.61, "end": 1075.17, "word": "وهنا", "probability": 0.5350748697916666}, {"start": 1075.17, "end": 1075.81, "word": " سالب", "probability": 0.6455891927083334}, {"start": 1075.81, "end": 1076.51, "word": " 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تمانية انتهينا من الصف الأول الصف الثاني ناقص 9 و ناقص 1 و هنا كمان ناقص 1 بالشكل اللي عندنا هنا نمر بيه", "tokens": [28814, 15730, 28239, 31371, 7435, 3660, 6055, 3794, 995, 45865, 9673, 9381, 5172, 38688, 3660, 16712, 6027, 10632, 31767, 5172, 16247, 12610, 44945, 7435, 2304, 3615, 6542, 390, 568, 4032, 1386, 46811, 7649, 10632, 4032, 34105, 8608, 6027, 3555, 1386, 9122, 15042, 39896, 4032, 34105, 8608, 6027, 3555, 46811, 7649, 10632, 16472, 47395, 1829, 8315, 9154, 31767, 5172, 16247, 12610, 31767, 5172, 6024, 104, 7649, 1829, 8717, 995, 4587, 9381, 1722, 4032, 8717, 995, 4587, 9381, 502, 4032, 34105, 9122, 2304, 7649, 8717, 995, 4587, 9381, 502, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105, 8717, 29973, 4724, 1829, 3224], "avg_logprob": -0.17837252062146025, "compression_ratio": 1.9210526315789473, "no_speech_prob": 0.0, "words": [{"start": 1082.82, "end": 1083.38, "word": "إذا", "probability": 0.565185546875}, {"start": 1083.38, "end": 1084.58, "word": " النتيجة", 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"probability": 0.82220458984375}, {"start": 1567.78, "end": 1569.06, "word": " واحد", "probability": 0.950927734375}, {"start": 1569.06, "end": 1570.06, "word": " ناقص", "probability": 0.876953125}, {"start": 1570.06, "end": 1570.74, "word": " تلاتة", "probability": 0.9256591796875}, {"start": 1570.74, "end": 1571.34, "word": " Zero", "probability": 0.360595703125}, {"start": 1571.34, "end": 1573.3, "word": " خمسة", "probability": 0.97607421875}, {"start": 1573.3, "end": 1574.22, "word": " Zero", "probability": 0.8134765625}, {"start": 1574.22, "end": 1574.76, "word": " Zero", "probability": 0.88671875}, {"start": 1574.76, "end": 1575.74, "word": " اتنين", "probability": 0.9388427734375}], "temperature": 1.0}, {"id": 73, "seek": 159588, "start": 1576.8, "end": 1595.88, "text": "زيرو واحد اربعة زيرو بالشكل اللي عندنا هنا سؤال مرة تانية", "tokens": [11622, 13546, 2407, 36764, 24401, 1975, 25513, 27884, 30767, 13546, 2407, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105, 8608, 33604, 6027, 3714, 25720, 6055, 7649, 10632], "avg_logprob": -0.22656249787126267, "compression_ratio": 1.2839506172839505, "no_speech_prob": 0.0, "words": [{"start": 1576.8, "end": 1577.88, "word": "زيرو", "probability": 0.5965983072916666}, {"start": 1577.88, "end": 1578.84, "word": " واحد", "probability": 0.87109375}, {"start": 1578.84, "end": 1579.82, "word": " اربعة", "probability": 0.8180338541666666}, {"start": 1579.82, "end": 1580.92, "word": " زيرو", "probability": 0.8129069010416666}, {"start": 1580.92, "end": 1581.5, "word": " بالشكل", "probability": 0.85205078125}, {"start": 1581.5, "end": 1581.7, "word": " اللي", "probability": 0.876708984375}, {"start": 1581.7, "end": 1582.3, "word": " عندنا", "probability": 0.87939453125}, {"start": 1582.3, "end": 1582.86, "word": " هنا", "probability": 0.9326171875}, {"start": 1582.86, "end": 1595.26, "word": " سؤال", "probability": 0.83740234375}, {"start": 1595.26, "end": 1595.52, "word": " مرة", "probability": 0.885009765625}, {"start": 1595.52, "end": 1595.88, "word": " تانية", "probability": 0.9646809895833334}], "temperature": 1.0}, {"id": 74, "seek": 162299, "start": 1597.15, "end": 1622.99, "text": "بقول لي هاتلي الـ column vectors المتجهات العمودية وال raw vectors المتجهات الصفية لماهم للمصوفة اللي عندنا هذه بدأ أبدا بالمتجهات العمودية فباجي بقول له the column vectors are بدي أجي لل V1", "tokens": [3555, 39648, 32239, 8032, 9307, 20292, 2423, 39184, 7738, 18875, 9673, 2655, 7435, 3224, 9307, 18863, 2304, 23328, 10632, 16070, 8936, 18875, 9673, 2655, 7435, 3224, 9307, 31767, 5172, 10632, 5296, 15042, 16095, 5296, 19528, 9381, 38688, 3660, 13672, 1829, 43242, 8315, 29538, 47525, 10721, 5551, 3555, 28259, 20666, 2304, 2655, 7435, 3224, 9307, 18863, 2304, 23328, 10632, 6156, 3555, 26108, 1829, 4724, 39648, 46740, 264, 7738, 18875, 366, 4724, 16254, 5551, 7435, 1829, 24976, 691, 16], "avg_logprob": -0.2896634584818131, "compression_ratio": 1.853658536585366, "no_speech_prob": 0.0, "words": [{"start": 1597.15, "end": 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"end": 1605.37, "word": " الصفية", "probability": 0.9733072916666666}, {"start": 1605.37, "end": 1605.99, "word": " لماهم", "probability": 0.4120279947916667}, {"start": 1605.99, "end": 1607.23, "word": " للمصوفة", "probability": 0.86455078125}, {"start": 1607.23, "end": 1607.39, "word": " اللي", "probability": 0.840087890625}, {"start": 1607.39, "end": 1607.89, "word": " عندنا", "probability": 0.915283203125}, {"start": 1607.89, "end": 1608.41, "word": " هذه", "probability": 0.6845703125}, {"start": 1608.41, "end": 1609.19, "word": " بدأ", "probability": 0.5316162109375}, {"start": 1609.19, "end": 1609.41, "word": " أبدا", "probability": 0.581298828125}, {"start": 1609.41, "end": 1610.53, "word": " بالمتجهات", "probability": 0.9752604166666666}, {"start": 1610.53, "end": 1611.31, "word": " العمودية", "probability": 0.9437255859375}, {"start": 1611.31, "end": 1611.85, "word": " فباجي", "probability": 0.7938232421875}, {"start": 1611.85, "end": 1612.31, "word": " بقول", "probability": 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"avg_logprob": -0.4449218764901161, "compression_ratio": 1.05, "no_speech_prob": 0.0, "words": [{"start": 1623.86, "end": 1625.18, "word": "U1", "probability": 0.5224609375}, {"start": 1625.18, "end": 1632.72, "word": " يساوي", "probability": 0.56488037109375}, {"start": 1632.72, "end": 1633.36, "word": " 2", "probability": 0.26953125}, {"start": 1633.36, "end": 1634.24, "word": " 5", "probability": 0.466064453125}, {"start": 1634.24, "end": 1635.08, "word": " 0", "probability": 0.9404296875}, {"start": 1635.08, "end": 1636.24, "word": " و", "probability": 0.37646484375}, {"start": 1636.24, "end": 1637.24, "word": " U2", "probability": 0.76318359375}, {"start": 1637.24, "end": 1638.74, "word": " يساوي", "probability": 0.9078369140625}, {"start": 1638.74, "end": 1640.04, "word": " 1", "probability": 0.67041015625}, {"start": 1640.04, "end": 1640.82, "word": " 0", "probability": 0.7744140625}, {"start": 1640.82, "end": 1641.34, "word": " 1", "probability": 0.98291015625}], "temperature": 1.0}, {"id": 76, "seek": 165685, "start": 1641.95, "end": 1656.85, "text": "و ال U3 بده يساوي سالب تلاتة Zero أربعة and U4 بده يساوي Zero اتنين Zero", "tokens": [2407, 2423, 624, 18, 47525, 3224, 7251, 3794, 995, 45865, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 17182, 5551, 25513, 27884, 293, 624, 19, 47525, 3224, 7251, 3794, 995, 45865, 17182, 1975, 2655, 1863, 9957, 17182], "avg_logprob": -0.36929897682086843, "compression_ratio": 1.25, "no_speech_prob": 0.0, "words": [{"start": 1641.95, "end": 1642.21, "word": "و", "probability": 0.7294921875}, {"start": 1642.21, "end": 1642.43, "word": " ال", "probability": 0.443115234375}, {"start": 1642.43, "end": 1643.45, "word": " U3", "probability": 0.7080078125}, {"start": 1643.45, "end": 1644.25, "word": " بده", "probability": 0.2851715087890625}, {"start": 1644.25, "end": 1644.55, "word": " يساوي", "probability": 0.8323974609375}, {"start": 1644.55, "end": 1645.21, "word": " سالب", "probability": 0.6158854166666666}, {"start": 1645.21, 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و U2 و U3 و U4 هذا ال column vectors بتروح أجيبله ال raw vectors فبجي بقوله they are raw vectors", "tokens": [1829, 3555, 4587, 7578, 29538, 2423, 39184, 2135, 2423, 39184, 7738, 18875, 7251, 3555, 4587, 7578, 9122, 28814, 1863, 9673, 9381, 38688, 3660, 13672, 1829, 43242, 8315, 29538, 4724, 28543, 2288, 5551, 4117, 2655, 3555, 11296, 47525, 1211, 6027, 31371, 2423, 624, 16, 4032, 624, 17, 4032, 624, 18, 4032, 624, 19, 23758, 2423, 7738, 18875, 39894, 32887, 5016, 5551, 7435, 1829, 3555, 43761, 2423, 8936, 18875, 6156, 3555, 7435, 1829, 4724, 39648, 3224, 436, 366, 8936, 18875], "avg_logprob": -0.29746835141242306, "compression_ratio": 1.5414364640883977, "no_speech_prob": 0.0, "words": [{"start": 1657.82, "end": 1658.34, "word": "يبقى", "probability": 0.84002685546875}, {"start": 1658.34, "end": 1658.62, "word": " هذه", "probability": 0.366455078125}, {"start": 1658.62, "end": 1659.0, "word": " الـ", "probability": 0.41943359375}, {"start": 1659.0, "end": 1659.0, "word": " main", 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1707.49, "text": "بدي اجيل ال V1 يبقى V1 بده يساوي صف الأول اتنين واحد سالب تلاتة زيرو وال V2 اللي هو صف الثاني خمسة زيرو زيرو اتنين and ال V3 بده يساوي زيرو واحد اربعة زيرو", "tokens": [3555, 16254, 1975, 7435, 26895, 2423, 691, 16, 7251, 3555, 4587, 7578, 691, 16, 47525, 3224, 7251, 3794, 995, 45865, 20328, 5172, 16247, 12610, 1975, 2655, 1863, 9957, 36764, 24401, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 30767, 13546, 2407, 16070, 691, 17, 13672, 1829, 31439, 20328, 5172, 6024, 104, 7649, 1829, 16490, 2304, 3794, 3660, 30767, 13546, 2407, 30767, 13546, 2407, 1975, 2655, 1863, 9957, 293, 2423, 691, 18, 47525, 3224, 7251, 3794, 995, 45865, 30767, 13546, 2407, 36764, 24401, 1975, 25513, 27884, 30767, 13546, 2407], "avg_logprob": -0.2068536884405396, "compression_ratio": 1.8095238095238095, "no_speech_prob": 0.0, "words": [{"start": 1681.17, "end": 1681.53, "word": "بدي", "probability": 0.19415283203125}, {"start": 1681.53, "end": 1681.83, "word": " اجيل", "probability": 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and", "probability": 0.4853515625}, {"start": 1700.47, "end": 1701.23, "word": " ال", "probability": 0.73046875}, {"start": 1701.23, "end": 1702.19, "word": " V3", "probability": 0.976318359375}, {"start": 1702.19, "end": 1703.05, "word": " بده", "probability": 0.91650390625}, {"start": 1703.05, "end": 1703.77, "word": " يساوي", "probability": 0.9893798828125}, {"start": 1703.77, "end": 1704.85, "word": " زيرو", "probability": 0.826171875}, {"start": 1704.85, "end": 1705.85, "word": " واحد", "probability": 0.97314453125}, {"start": 1705.85, "end": 1706.85, "word": " اربعة", "probability": 0.7652994791666666}, {"start": 1706.85, "end": 1707.49, "word": " زيرو", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 79, "seek": 173583, "start": 1708.47, "end": 1735.83, "text": "والعكس لو أنا ال core vectors أو ال raw vectors بقدر أجيب من المصوفة الأصلية لهم السؤال التالت display the elements display the elements", "tokens": [2407, 6027, 3615, 4117, 3794, 45164, 41850, 2423, 4965, 18875, 34051, 2423, 8936, 18875, 4724, 28543, 2288, 5551, 7435, 1829, 3555, 9154, 9673, 9381, 38688, 3660, 16247, 9381, 1211, 10632, 5296, 16095, 21136, 33604, 6027, 16712, 6027, 2655, 4674, 264, 4959, 4674, 264, 4959], "avg_logprob": -0.2614583280351427, "compression_ratio": 1.4222222222222223, "no_speech_prob": 0.0, "words": [{"start": 1708.47, "end": 1709.23, "word": "والعكس", "probability": 0.831005859375}, {"start": 1709.23, "end": 1709.97, "word": " لو", "probability": 0.703125}, {"start": 1709.97, "end": 1710.19, "word": " أنا", "probability": 0.35498046875}, {"start": 1710.19, "end": 1710.39, "word": " ال", "probability": 0.802734375}, {"start": 1710.39, "end": 1710.63, "word": " core", "probability": 0.05169677734375}, {"start": 1710.63, "end": 1711.15, "word": " vectors", "probability": 0.88720703125}, {"start": 1711.15, "end": 1711.43, "word": " أو", "probability": 0.708984375}, {"start": 1711.43, "end": 1711.61, "word": " ال", "probability": 0.94580078125}, {"start": 1711.61, "end": 1711.75, "word": " raw", "probability": 0.89794921875}, {"start": 1711.75, "end": 1712.21, "word": " vectors", "probability": 0.95947265625}, {"start": 1712.21, "end": 1712.71, "word": " بقدر", "probability": 0.9500325520833334}, {"start": 1712.71, "end": 1713.03, "word": " أجيب", "probability": 0.8819580078125}, {"start": 1713.03, "end": 1713.35, "word": " من", "probability": 0.59326171875}, {"start": 1713.35, "end": 1714.69, "word": " المصوفة", "probability": 0.9246826171875}, {"start": 1714.69, "end": 1715.61, "word": " الأصلية", "probability": 0.8084716796875}, {"start": 1715.61, "end": 1716.27, "word": " لهم", "probability": 0.85009765625}, {"start": 1716.27, "end": 1719.45, "word": " السؤال", "probability": 0.8036295572916666}, {"start": 1719.45, "end": 1720.21, "word": " التالت", "probability": 0.9791666666666666}, {"start": 1720.21, "end": 1725.45, "word": " display", "probability": 0.77734375}, {"start": 1725.45, "end": 1728.55, "word": " the", "probability": 0.7744140625}, {"start": 1728.55, "end": 1729.37, "word": " elements", "probability": 0.8828125}, {"start": 1729.37, "end": 1734.87, "word": " display", "probability": 0.81201171875}, {"start": 1734.87, "end": 1735.23, "word": " the", "probability": 0.91748046875}, {"start": 1735.23, "end": 1735.83, "word": " elements", "probability": 0.89892578125}], "temperature": 1.0}, {"id": 80, "seek": 176654, "start": 1739.02, "end": 1766.54, "text": "the matrix who's convictors who's convictors who convictors are ال U1 بدي الساوية واحد zero واحد أربعة و U2", "tokens": [3322, 8141, 567, 311, 3754, 985, 830, 567, 311, 3754, 985, 830, 567, 3754, 985, 830, 366, 2423, 624, 16, 4724, 16254, 21136, 995, 2407, 10632, 36764, 24401, 4018, 36764, 24401, 5551, 25513, 27884, 4032, 624, 17], "avg_logprob": -0.4646381602475518, "compression_ratio": 1.3571428571428572, "no_speech_prob": 0.0, "words": [{"start": 1739.0199999999998, "end": 1740.4199999999998, "word": "the", "probability": 0.364013671875}, {"start": 1740.4199999999998, "end": 1741.82, "word": " matrix", "probability": 0.9365234375}, {"start": 1741.82, "end": 1743.92, "word": " who's", "probability": 0.3056640625}, {"start": 1743.92, "end": 1744.92, "word": " convictors", "probability": 0.754638671875}, {"start": 1744.92, "end": 1746.24, "word": " who's", "probability": 0.57452392578125}, {"start": 1746.24, "end": 1750.84, "word": " convictors", "probability": 0.9527994791666666}, {"start": 1750.84, "end": 1752.44, "word": " who", "probability": 0.49951171875}, {"start": 1752.44, "end": 1753.92, "word": " convictors", "probability": 0.8450520833333334}, {"start": 1753.92, "end": 1754.78, "word": " are", "probability": 0.966796875}, {"start": 1754.78, "end": 1757.14, "word": " ال", "probability": 0.55615234375}, {"start": 1757.14, "end": 1757.82, "word": " U1", "probability": 0.55078125}, {"start": 1757.82, "end": 1759.08, "word": " بدي", "probability": 0.612060546875}, {"start": 1759.08, "end": 1759.68, "word": " الساوية", "probability": 0.591064453125}, {"start": 1759.68, "end": 1760.32, "word": " واحد", "probability": 0.853759765625}, {"start": 1760.32, "end": 1761.34, "word": " zero", "probability": 0.1412353515625}, {"start": 1761.34, "end": 1763.16, "word": " واحد", "probability": 0.866943359375}, {"start": 1763.16, "end": 1764.6, "word": " أربعة", "probability": 0.6988932291666666}, {"start": 1764.6, "end": 1765.86, "word": " و", "probability": 0.861328125}, {"start": 1765.86, "end": 1766.54, "word": " U2", "probability": 0.84619140625}], "temperature": 1.0}, {"id": 81, "seek": 178360, "start": 1767.52, "end": 1783.6, "text": "بتساوي اتنين واحد خمسة سالب واحد و U3 و U3 بتساوي واحد اتنين تلاتة اربع", "tokens": [3555, 2655, 3794, 995, 45865, 1975, 2655, 1863, 9957, 36764, 24401, 16490, 2304, 3794, 3660, 8608, 6027, 3555, 36764, 24401, 4032, 624, 18, 4032, 624, 18, 4724, 2655, 3794, 995, 45865, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 1975, 25513, 3615], "avg_logprob": 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{"start": 1779.88, "end": 1781.12, "word": " واحد", "probability": 0.86328125}, {"start": 1781.12, "end": 1781.94, "word": " اتنين", "probability": 0.989013671875}, {"start": 1781.94, "end": 1783.16, "word": " تلاتة", "probability": 0.9244384765625}, {"start": 1783.16, "end": 1783.6, "word": " اربع", "probability": 0.7900390625}], "temperature": 1.0}, {"id": 82, "seek": 183716, "start": 1815.92, "end": 1837.16, "text": "نرجع لسؤالنا مرة تانية السؤال بيقول لي display the elements of the matrix whose cone vectors are U1 و U2 و U3 كلمة display .. display إيش يعني يا بنات بالعربي؟", "tokens": [1863, 47341, 3615, 5296, 3794, 33604, 6027, 8315, 3714, 25720, 6055, 7649, 10632, 21136, 33604, 6027, 4724, 1829, 39648, 32239, 4674, 264, 4959, 295, 264, 8141, 6104, 19749, 18875, 366, 624, 16, 4032, 624, 17, 4032, 624, 18, 9122, 19528, 3660, 4674, 4386, 4674, 11933, 1829, 8592, 37495, 22653, 35186, 4724, 8315, 2655, 20666, 3615, 2288, 21292, 22807], "avg_logprob": -0.23172668784351672, 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{"start": 1834.02, "end": 1834.76, "word": " display", "probability": 0.9306640625}, {"start": 1834.76, "end": 1835.04, "word": " ..", "probability": 0.2734375}, {"start": 1835.04, "end": 1835.72, "word": " display", "probability": 0.51123046875}, {"start": 1835.72, "end": 1836.02, "word": " إيش", "probability": 0.78564453125}, {"start": 1836.02, "end": 1836.2, "word": " يعني", "probability": 0.9453125}, {"start": 1836.2, "end": 1836.4, "word": " يا", "probability": 0.4052734375}, {"start": 1836.4, "end": 1836.48, "word": " بنات", "probability": 0.93408203125}, {"start": 1836.48, "end": 1837.16, "word": " بالعربي؟", "probability": 0.88818359375}], "temperature": 1.0}, {"id": 83, "seek": 185797, "start": 1838.45, "end": 1857.97, "text": "إعرض، واضح، بيّن، شغلات زي ذلك يبقى إعرض أو بيّن يبقى إعرض العناصر تبعات المصروفة اللي ال column vectors على الشكل اللي عندنا هنا بقولك كويس المصروفة هذه يا بنات لو جيت رمز تلها الرمز A", "tokens": [28814, 3615, 43042, 12399, 4032, 46958, 5016, 12399, 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"text": "طلب مني find the vector 2x-3 هو كأنه طلب العمليتين في آن واحد، بدك تضرب رقم في vector ورقم تاني في vector ثم تقوم بعملية مين؟ عملية الجمع", "tokens": [9566, 46152, 9154, 1829, 915, 264, 8062, 568, 87, 12, 18, 31439, 9122, 33456, 3224, 23032, 46152, 18863, 42213, 36081, 9957, 8978, 19753, 1863, 36764, 24401, 12399, 47525, 4117, 6055, 11242, 25513, 12602, 4587, 2304, 8978, 8062, 4032, 2288, 4587, 2304, 6055, 7649, 1829, 8978, 8062, 38637, 2304, 6055, 4587, 20498, 4724, 25957, 1211, 10632, 3714, 9957, 22807, 6225, 42213, 10632, 25724, 2304, 3615], "avg_logprob": -0.2143028846153846, "compression_ratio": 1.4248366013071896, "no_speech_prob": 0.0, "words": [{"start": 2133.6, "end": 2134.08, "word": "طلب", "probability": 0.9013671875}, {"start": 2134.08, "end": 2134.72, "word": " مني", "probability": 0.80517578125}, {"start": 2134.72, "end": 2135.24, "word": " find", "probability": 0.544921875}, {"start": 2135.24, "end": 2135.48, "word": " the", "probability": 0.75341796875}, 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"probability": 0.9539388020833334}, {"start": 2149.04, "end": 2149.66, "word": " الجمع", "probability": 0.81396484375}], "temperature": 1.0}, {"id": 95, "seek": 217252, "start": 2150.28, "end": 2172.52, "text": "إذا أنا لما بداجي أقوله اتنين capital X ناقص تلاتة capital Y يساوي معناته بداجي أقوله اتنين في واحد تلاتة زيرو سالي باتنين ناقص تلاتة او زائد", "tokens": [28814, 15730, 41850, 5296, 15042, 4724, 28259, 7435, 1829, 5551, 39648, 3224, 1975, 2655, 1863, 9957, 4238, 1783, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 4238, 398, 7251, 3794, 995, 45865, 20449, 8315, 47395, 4724, 28259, 7435, 1829, 5551, 39648, 3224, 1975, 2655, 1863, 9957, 8978, 36764, 24401, 6055, 1211, 9307, 3660, 30767, 13546, 2407, 8608, 6027, 1829, 4724, 9307, 1863, 9957, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 1975, 2407, 30767, 16373, 3215], "avg_logprob": -0.18202110079975872, "compression_ratio": 1.7266187050359711, "no_speech_prob": 0.0, "words": [{"start": 2150.28, "end": 2150.64, "word": "إذا", "probability": 0.6412353515625}, {"start": 2150.64, "end": 2151.02, "word": " أنا", "probability": 0.61962890625}, {"start": 2151.02, "end": 2151.3, "word": " لما", "probability": 0.864990234375}, {"start": 2151.3, "end": 2151.92, "word": " بداجي", "probability": 0.6968994140625}, {"start": 2151.92, "end": 2152.78, "word": " أقوله", "probability": 0.74951171875}, {"start": 2152.78, "end": 2153.8, "word": " اتنين", "probability": 0.82073974609375}, {"start": 2153.8, "end": 2154.48, "word": " capital", "probability": 0.36376953125}, {"start": 2154.48, "end": 2155.22, "word": " X", "probability": 0.88037109375}, {"start": 2155.22, "end": 2156.02, "word": " ناقص", "probability": 0.9210205078125}, {"start": 2156.02, "end": 2156.7, "word": " تلاتة", "probability": 0.865234375}, {"start": 2156.7, "end": 2157.26, "word": " capital", "probability": 0.826171875}, {"start": 2157.26, "end": 2157.88, "word": " Y", "probability": 0.98828125}, {"start": 2157.88, "end": 2159.02, "word": " يساوي", "probability": 0.9156494140625}, {"start": 2159.02, "end": 2160.2, "word": " معناته", "probability": 0.8572591145833334}, {"start": 2160.2, "end": 2160.74, "word": " بداجي", "probability": 0.91357421875}, {"start": 2160.74, "end": 2161.48, "word": " أقوله", "probability": 0.8727213541666666}, {"start": 2161.48, "end": 2162.58, "word": " اتنين", "probability": 0.9656982421875}, {"start": 2162.58, "end": 2163.04, "word": " في", "probability": 0.9736328125}, {"start": 2163.04, "end": 2164.16, "word": " واحد", "probability": 0.98291015625}, {"start": 2164.16, "end": 2165.06, "word": " تلاتة", "probability": 0.9501953125}, {"start": 2165.06, "end": 2165.76, "word": " زيرو", "probability": 0.7120768229166666}, {"start": 2165.76, "end": 2166.62, "word": " سالي", "probability": 0.9278971354166666}, {"start": 2166.62, "end": 2167.26, "word": " باتنين", "probability": 0.80682373046875}, {"start": 2167.26, "end": 2169.52, "word": " ناقص", "probability": 0.9163818359375}, {"start": 2169.52, "end": 2170.3, "word": " تلاتة", "probability": 0.957275390625}, {"start": 2170.3, "end": 2171.1, "word": " او", "probability": 0.845703125}, {"start": 2171.1, "end": 2172.52, "word": " زائد", "probability": 0.8694661458333334}], "temperature": 1.0}, {"id": 96, "seek": 218376, "start": 2174.64, "end": 2183.76, "text": "لنقص تلاتة في ال vector التاني ال zero سالب واحد تلاتة سالب اربعة بالشكل اللي عندنا هذا", "tokens": [1211, 1863, 4587, 9381, 6055, 1211, 9307, 3660, 8978, 2423, 8062, 16712, 7649, 1829, 2423, 4018, 8608, 6027, 3555, 36764, 24401, 6055, 1211, 9307, 3660, 8608, 6027, 3555, 1975, 25513, 27884, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758], "avg_logprob": -0.25917969793081286, "compression_ratio": 1.3703703703703705, "no_speech_prob": 0.0, "words": [{"start": 2174.64, "end": 2175.6, "word": "لنقص", "probability": 0.70086669921875}, {"start": 2175.6, "end": 2176.56, "word": " تلاتة", "probability": 0.774658203125}, {"start": 2176.56, "end": 2177.0, "word": " في", "probability": 0.90234375}, {"start": 2177.0, "end": 2177.22, "word": " ال", "probability": 0.66845703125}, {"start": 2177.22, "end": 2177.62, "word": " vector", "probability": 0.416259765625}, {"start": 2177.62, "end": 2178.36, "word": " التاني", "probability": 0.8673502604166666}, {"start": 2178.36, "end": 2178.48, "word": " ال", "probability": 0.58154296875}, {"start": 2178.48, "end": 2178.92, "word": " zero", "probability": 0.458984375}, {"start": 2178.92, "end": 2179.88, "word": " سالب", "probability": 0.8069661458333334}, {"start": 2179.88, "end": 2180.36, "word": " واحد", "probability": 0.973876953125}, {"start": 2180.36, "end": 2181.4, "word": " تلاتة", "probability": 0.92138671875}, {"start": 2181.4, "end": 2182.0, "word": " سالب", "probability": 0.9401041666666666}, {"start": 2182.0, "end": 2182.52, "word": " اربعة", "probability": 0.7578125}, {"start": 2182.52, "end": 2183.08, "word": " بالشكل", "probability": 0.9283854166666666}, {"start": 2183.08, "end": 2183.2, "word": " اللي", "probability": 0.888427734375}, {"start": 2183.2, "end": 2183.54, "word": " عندنا", "probability": 0.93408203125}, {"start": 2183.54, "end": 2183.76, "word": " هذا", "probability": 0.69970703125}], "temperature": 1.0}, {"id": 97, "seek": 220852, "start": 2184.5, "end": 2208.52, "text": "يبقى هذا الكلام يساوي اخدنا اول خاصية انه اذا ضربنا constant فيه vector و بنضره في جميع مركبات هذا ال vector اذا ان ال vector هذا 2 6 0 سالب 4 ال vector التاني برضه 0 3 سالب 9 و هنا 12", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 7251, 3794, 995, 45865, 1975, 9778, 3215, 8315, 1975, 12610, 16490, 33546, 10632, 16472, 3224, 1975, 15730, 48812, 25513, 8315, 5754, 8978, 3224, 8062, 4032, 44945, 11242, 2288, 3224, 8978, 10874, 2304, 40228, 3714, 31747, 3555, 9307, 23758, 2423, 8062, 1975, 15730, 16472, 2423, 8062, 23758, 568, 1386, 1958, 8608, 6027, 3555, 1017, 2423, 8062, 16712, 7649, 1829, 4724, 43042, 3224, 1958, 805, 8608, 6027, 3555, 1722, 4032, 34105, 2272], "avg_logprob": 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0.517578125}, {"start": 2196.48, "end": 2196.58, "word": " ال", "probability": 0.9765625}, {"start": 2196.58, "end": 2196.94, "word": " vector", "probability": 0.97705078125}, {"start": 2196.94, "end": 2197.42, "word": " هذا", "probability": 0.833984375}, {"start": 2197.42, "end": 2198.04, "word": " 2", "probability": 0.533203125}, {"start": 2198.04, "end": 2198.96, "word": " 6", "probability": 0.73876953125}, {"start": 2198.96, "end": 2199.86, "word": " 0", "probability": 0.962890625}, {"start": 2199.86, "end": 2200.9, "word": " سالب", "probability": 0.666748046875}, {"start": 2200.9, "end": 2201.28, "word": " 4", "probability": 0.81396484375}, {"start": 2201.28, "end": 2201.52, "word": " ال", "probability": 0.7197265625}, {"start": 2201.52, "end": 2201.88, "word": " vector", "probability": 0.9697265625}, {"start": 2201.88, "end": 2202.56, "word": " التاني", "probability": 0.9425455729166666}, {"start": 2202.56, "end": 2203.56, "word": " برضه", "probability": 0.9514973958333334}, {"start": 2203.56, "end": 2204.14, "word": " 0", "probability": 0.55615234375}, {"start": 2204.14, "end": 2205.24, "word": " 3", "probability": 0.939453125}, {"start": 2205.24, "end": 2206.38, "word": " سالب", "probability": 0.9308268229166666}, {"start": 2206.38, "end": 2207.02, "word": " 9", "probability": 0.98046875}, {"start": 2207.02, "end": 2207.56, "word": " و", "probability": 0.66748046875}, {"start": 2207.56, "end": 2207.9, "word": " هنا", "probability": 0.9208984375}, {"start": 2207.9, "end": 2208.52, "word": " 12", "probability": 0.8935546875}], "temperature": 1.0}, {"id": 98, "seek": 223178, "start": 2209.48, "end": 2231.78, "text": "بعد ذلك اخذنا خاصية جمع two vectors يبقى بنجمع component wise كل مراكبة مع نظيرتها يبقى باجي بقوله اتنين زائد زيرو باتنين ستة و تلاتة تسعة زيرو ناقص تسعة بناقص تسعة ناقص اربعة و اتناشر بظل قداشر", "tokens": [3555, 22488, 29910, 23275, 1975, 9778, 8848, 8315, 16490, 33546, 10632, 10874, 2304, 3615, 732, 18875, 7251, 3555, 4587, 7578, 44945, 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"probability": 0.9595947265625}, {"start": 2219.58, "end": 2220.04, "word": " باجي", "probability": 0.857421875}, {"start": 2220.04, "end": 2220.66, "word": " بقوله", "probability": 0.7679036458333334}, {"start": 2220.66, "end": 2221.14, "word": " اتنين", "probability": 0.807373046875}, {"start": 2221.14, "end": 2221.62, "word": " زائد", "probability": 0.9661458333333334}, {"start": 2221.62, "end": 2222.06, "word": " زيرو", "probability": 0.6873372395833334}, {"start": 2222.06, "end": 2222.8, "word": " باتنين", "probability": 0.8443603515625}, {"start": 2222.8, "end": 2223.84, "word": " ستة", "probability": 0.9562174479166666}, {"start": 2223.84, "end": 2223.98, "word": " و", "probability": 0.5947265625}, {"start": 2223.98, "end": 2224.62, "word": " تلاتة", "probability": 0.9215087890625}, {"start": 2224.62, "end": 2225.22, "word": " تسعة", "probability": 0.9814453125}, {"start": 2225.22, "end": 2226.26, "word": " زيرو", "probability": 0.7211100260416666}, {"start": 2226.26, "end": 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تسعة ناقص تسعة تمانية و هكذا لحد هنا stop انتهى هذا ال section ولا يكون ال exercise اتنين اربعة", "tokens": [2655, 27842, 10632, 11933, 15730, 5551, 9381, 49628, 2423, 8062, 1975, 2655, 1863, 9957, 1975, 4117, 3794, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 4238, 398, 31439, 13672, 1829, 4724, 1829, 3794, 995, 45865, 1975, 2655, 1863, 9957, 6055, 3794, 27884, 8717, 995, 4587, 9381, 6055, 3794, 27884, 46811, 7649, 10632, 4032, 8032, 4117, 15730, 5296, 24401, 34105, 1590, 16472, 47395, 7578, 23758, 2423, 3541, 49429, 7251, 30544, 2423, 5380, 1975, 2655, 1863, 9957, 1975, 25513, 27884], "avg_logprob": -0.22804588305799267, "compression_ratio": 1.5706214689265536, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2232.14, "end": 2232.86, "word": "تمنية", "probability": 0.4817097981770833}, {"start": 2232.86, "end": 2233.58, "word": " إذا", "probability": 0.6663818359375}, {"start": 2233.58, "end": 2234.32, "word": " أصبح", "probability": 0.9650065104166666}, {"start": 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diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/QZepsKIgm9Y_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/QZepsKIgm9Y_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..40e32319fa510bf024fb331bdc98d3ff776602cb
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@@ -0,0 +1 @@
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9501, "start": 65.73, "end": 95.01, "text": "ثلاثة شروط الشرط الأول إن هذا الـ subset اللي أخدته is non-empty على الأقل بدي أثبت ولو عنصر واحد موجود في هذا ال subset اتنين لو أخدت scalar من R مع vector من U ضربت اتنين في بعض بدي أطلع ناتج vector جديد موجود في الـ U itself الأمر الثالث لو أخدت vectors من U وجمعت الاتنين", "tokens": [12984, 1211, 5718, 104, 3660, 13412, 32887, 9566, 25124, 2288, 9566, 16247, 12610, 36145, 23758, 2423, 39184, 25993, 13672, 1829, 5551, 9778, 3215, 47395, 307, 2107, 12, 4543, 88, 15844, 16247, 4587, 1211, 4724, 16254, 5551, 12984, 3555, 2655, 35525, 2407, 18871, 9381, 2288, 36764, 24401, 3714, 29245, 23328, 8978, 23758, 2423, 25993, 1975, 2655, 1863, 9957, 45164, 5551, 9778, 3215, 2655, 39684, 9154, 497, 20449, 8062, 9154, 624, 48812, 25513, 2655, 1975, 2655, 1863, 9957, 8978, 45030, 11242, 4724, 16254, 5551, 9566, 1211, 3615, 8717, 9307, 7435, 8062, 10874, 16254, 3215, 3714, 29245, 23328, 8978, 2423, 39184, 624, 2564, 16247, 29973, 6024, 104, 6027, 12984, 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77.13, "word": " هذا", "probability": 0.97021484375}, {"start": 77.13, "end": 77.39, "word": " ال", "probability": 0.9462890625}, {"start": 77.39, "end": 77.85, "word": " subset", "probability": 0.82177734375}, {"start": 77.85, "end": 78.97, "word": " اتنين", "probability": 0.838134765625}, {"start": 78.97, "end": 79.63, "word": " لو", "probability": 0.66064453125}, {"start": 79.63, "end": 80.11, "word": " أخدت", "probability": 0.96875}, {"start": 80.11, "end": 80.61, "word": " scalar", "probability": 0.83642578125}, {"start": 80.61, "end": 81.05, "word": " من", "probability": 0.98779296875}, {"start": 81.05, "end": 81.61, "word": " R", "probability": 0.76708984375}, {"start": 81.61, "end": 82.31, "word": " مع", "probability": 0.9765625}, {"start": 82.31, "end": 82.83, "word": " vector", "probability": 0.85205078125}, {"start": 82.83, "end": 83.17, "word": " من", "probability": 0.99365234375}, {"start": 83.17, "end": 83.33, "word": " U", "probability": 0.96728515625}, {"start": 83.33, 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"probability": 0.459228515625}, {"start": 88.67, "end": 89.43, "word": " itself", "probability": 0.30712890625}, {"start": 89.43, "end": 90.41, "word": " الأمر", "probability": 0.957763671875}, {"start": 90.41, "end": 90.95, "word": " الثالث", "probability": 0.963134765625}, {"start": 90.95, "end": 91.43, "word": " لو", "probability": 0.84765625}, {"start": 91.43, "end": 91.91, "word": " أخدت", "probability": 0.9715576171875}, {"start": 91.91, "end": 92.47, "word": " vectors", "probability": 0.14111328125}, {"start": 92.47, "end": 92.95, "word": " من", "probability": 0.98193359375}, {"start": 92.95, "end": 93.25, "word": " U", "probability": 0.98681640625}, {"start": 93.25, "end": 94.31, "word": " وجمعت", "probability": 0.7877604166666666}, {"start": 94.31, "end": 95.01, "word": " الاتنين", "probability": 0.77252197265625}], "temperature": 1.0}, {"id": 4, "seek": 11849, "start": 95.27, "end": 118.49, "text": "الجامعه دي بدى اثبت ان هذا المجموع موجود في U كذلك ان تحقق الشروط التلاته يبقى ال subset اللى اخدتها من V بتكون subspace اختل اي شرط من الشروط التلاته يبقى ماهياش subspace واخدنا على ذلك اربعة امثلة وهذا هو المثال الخامس", "tokens": [6027, 7435, 10943, 3615, 3224, 11778, 1829, 47525, 7578, 1975, 12984, 3555, 2655, 16472, 23758, 9673, 7435, 2304, 45367, 3714, 29245, 23328, 8978, 624, 9122, 8848, 23275, 16472, 6055, 5016, 4587, 4587, 25124, 32887, 9566, 16712, 1211, 9307, 3224, 7251, 3555, 4587, 7578, 2423, 2090, 302, 13672, 7578, 1975, 9778, 3215, 2655, 11296, 9154, 691, 39894, 30544, 2090, 17940, 1975, 46456, 1211, 1975, 1829, 13412, 2288, 9566, 9154, 25124, 32887, 9566, 16712, 1211, 9307, 3224, 7251, 3555, 4587, 7578, 19446, 3224, 1829, 33599, 2090, 17940, 4032, 47283, 3215, 8315, 15844, 29910, 23275, 1975, 25513, 27884, 1975, 2304, 12984, 37977, 37037, 15730, 31439, 9673, 12984, 6027, 33962, 10943, 3794], "avg_logprob": -0.182196099823768, "compression_ratio": 1.8472906403940887, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 95.27, "end": 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0.8264973958333334}, {"start": 115.17, "end": 115.73, "word": " امثلة", "probability": 0.9307861328125}, {"start": 115.73, "end": 116.19, "word": " وهذا", "probability": 0.828125}, {"start": 116.19, "end": 116.39, "word": " هو", "probability": 0.9521484375}, {"start": 116.39, "end": 117.23, "word": " المثال", "probability": 0.9597981770833334}, {"start": 117.23, "end": 118.49, "word": " الخامس", "probability": 0.8857421875}], "temperature": 1.0}, {"id": 5, "seek": 14205, "start": 119.07, "end": 142.05, "text": "يبقى المثال الخامس بقول let P بيبدأ تسوى PN مين هي ال PN؟ يبقى هي كثيرات الحدود اللي درجتها أقصى ما يكون هو N يعني يا إما N يا إما أقل من N وال N عدد صحيح موجب ال N is a positive integer تمام؟", "tokens": [1829, 3555, 4587, 7578, 9673, 12984, 6027, 33962, 10943, 3794, 4724, 39648, 718, 430, 4724, 1829, 44510, 10721, 6055, 3794, 2407, 7578, 430, 45, 3714, 9957, 39896, 2423, 430, 45, 22807, 7251, 3555, 4587, 7578, 39896, 9122, 12984, 13546, 9307, 21542, 3215, 23328, 13672, 1829, 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520.19, "end": 539.77, "text": "real number في ال X تربيها موجود في ال U أم لا يبقى هدف belongs to main to you إذا انت حققت الشروط التلاتة أم لا يبقى باجي بقوله so ال U is a subspace", "tokens": [9342, 1230, 8978, 2423, 1783, 6055, 2288, 21292, 11296, 3714, 29245, 23328, 8978, 2423, 624, 5551, 2304, 20193, 7251, 3555, 4587, 7578, 8032, 3215, 5172, 12953, 281, 2135, 281, 291, 11933, 15730, 16472, 2655, 11331, 4587, 38149, 25124, 32887, 9566, 16712, 1211, 9307, 3660, 5551, 2304, 20193, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 370, 2423, 624, 307, 257, 2090, 17940], "avg_logprob": -0.2935096153846154, "compression_ratio": 1.3703703703703705, "no_speech_prob": 0.0, "words": [{"start": 520.19, "end": 520.67, "word": "real", "probability": 0.333251953125}, {"start": 520.67, "end": 521.19, "word": " number", "probability": 0.9765625}, {"start": 521.19, "end": 521.39, "word": " في", "probability": 0.755859375}, {"start": 521.39, "end": 521.51, "word": " ال", "probability": 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" بقوله", "probability": 0.8190104166666666}, {"start": 534.85, "end": 535.31, "word": " so", "probability": 0.43310546875}, {"start": 535.31, "end": 536.25, "word": " ال", "probability": 0.65625}, {"start": 536.25, "end": 536.69, "word": " U", "probability": 0.9287109375}, {"start": 536.69, "end": 537.73, "word": " is", "probability": 0.9013671875}, {"start": 537.73, "end": 538.39, "word": " a", "probability": 0.9638671875}, {"start": 538.39, "end": 539.77, "word": " subspace", "probability": 0.916015625}], "temperature": 1.0}, {"id": 24, "seek": 56725, "start": 541.69, "end": 567.25, "text": "R V يبقى هذا subspace من V نكمل الأمثلة على نفس الموضوع يبقى هذا المثال رقم خمسة بدنا نروح للمثال رقم ستة يبقى example 6 بقول let V تساوي P تكيب let", "tokens": [49, 691, 7251, 3555, 4587, 7578, 23758, 2090, 17940, 9154, 691, 8717, 24793, 1211, 16247, 2304, 12984, 37977, 15844, 8717, 36178, 9673, 2407, 11242, 45367, 7251, 3555, 4587, 7578, 23758, 9673, 12984, 6027, 12602, 4587, 2304, 16490, 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all", "probability": 0.93896484375}, {"start": 575.4, "end": 579.42, "word": " طبعا", "probability": 0.83746337890625}, {"start": 579.42, "end": 579.76, "word": " اللي", "probability": 0.793701171875}, {"start": 579.76, "end": 579.96, "word": " هي", "probability": 0.89013671875}, {"start": 579.96, "end": 580.12, "word": " the", "probability": 0.349609375}, {"start": 580.12, "end": 580.38, "word": " set", "probability": 0.966796875}, {"start": 580.38, "end": 580.56, "word": " of", "probability": 0.9736328125}, {"start": 580.56, "end": 580.74, "word": " all", "probability": 0.88623046875}, {"start": 580.74, "end": 581.04, "word": " X", "probability": 0.8837890625}, {"start": 581.04, "end": 581.56, "word": " واحد", "probability": 0.71826171875}, {"start": 581.56, "end": 581.7, "word": " و", "probability": 0.9208984375}, {"start": 581.7, "end": 582.02, "word": " X", "probability": 0.93798828125}, {"start": 582.02, "end": 582.64, "word": " اتنين", "probability": 0.90234375}, {"start": 582.64, "end": 583.18, "word": " و", "probability": 0.91748046875}, {"start": 583.18, "end": 583.42, "word": " X", "probability": 0.95751953125}, {"start": 583.42, "end": 583.9, "word": " ثلاثة", "probability": 0.8677734375}, {"start": 583.9, "end": 584.28, "word": " و", "probability": 0.65966796875}, {"start": 584.28, "end": 584.28, "word": " X", "probability": 0.364501953125}, {"start": 584.28, "end": 585.4, "word": " واحد", "probability": 0.6397705078125}, {"start": 585.4, "end": 585.54, "word": " و", "probability": 0.9208984375}, {"start": 585.54, "end": 585.82, "word": " X", "probability": 0.97607421875}, {"start": 585.82, "end": 586.5, "word": " اتنين", "probability": 0.87939453125}, {"start": 586.5, "end": 587.06, "word": " و", "probability": 0.94775390625}, {"start": 587.06, "end": 587.32, "word": " X", "probability": 0.9638671875}, {"start": 587.32, "end": 587.84, "word": " ثلاثة", "probability": 0.95634765625}, {"start": 587.84, "end": 588.4, "word": " موجودة", "probability": 0.973876953125}, {"start": 588.4, "end": 588.54, "word": " في", "probability": 0.947265625}, {"start": 588.54, "end": 588.72, "word": " ال", "probability": 0.380615234375}, {"start": 588.72, "end": 588.98, "word": " set", "probability": 0.85888671875}, {"start": 588.98, "end": 589.28, "word": " of", "probability": 0.9638671875}, {"start": 589.28, "end": 589.72, "word": " real", "probability": 0.95654296875}, {"start": 589.72, "end": 590.76, "word": " numbers", "probability": 0.65283203125}, {"start": 590.76, "end": 592.32, "word": " Little", "probability": 0.42041015625}, {"start": 592.32, "end": 593.14, "word": " u", "probability": 0.568359375}, {"start": 593.14, "end": 593.88, "word": " و", "probability": 0.56005859375}, {"start": 593.88, "end": 594.12, "word": " دي", "probability": 0.6414794921875}, {"start": 594.12, "end": 594.34, "word": " لنا", "probability": 0.707275390625}, {"start": 594.34, "end": 594.56, "word": " ال", "probability": 0.9638671875}, {"start": 594.56, "end": 594.8, "word": " U", "probability": 0.568359375}, {"start": 594.8, "end": 595.72, "word": " تساوي", "probability": 0.9783935546875}], "temperature": 1.0}, {"id": 26, "seek": 61816, "start": 596.46, "end": 618.16, "text": "اللي هو the set of all elements x1 وx2 وx3 such that بحيث ان x3 يساوي x1 زائد x2 السؤال هو show that", "tokens": [6027, 20292, 31439, 264, 992, 295, 439, 4959, 2031, 16, 4032, 87, 17, 4032, 87, 18, 1270, 300, 4724, 5016, 1829, 12984, 16472, 2031, 18, 7251, 3794, 995, 45865, 2031, 16, 30767, 16373, 3215, 2031, 17, 21136, 33604, 6027, 31439, 855, 300], "avg_logprob": -0.2334665669951328, "compression_ratio": 1.1293103448275863, "no_speech_prob": 0.0, "words": [{"start": 596.46, "end": 598.0, "word": "اللي", "probability": 0.386962890625}, {"start": 598.0, "end": 598.16, "word": " هو", "probability": 0.97021484375}, {"start": 598.16, "end": 598.38, "word": " the", "probability": 0.474609375}, {"start": 598.38, "end": 598.72, "word": " set", "probability": 0.9677734375}, 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و قلت هدول vector space اللي هو V", "tokens": [40228, 22653, 41850, 10874, 36081, 15844, 2423, 957, 1622, 4032, 5551, 9778, 3215, 2655, 6156, 2655, 25720, 3714, 24401, 41891, 4032, 10874, 3555, 2655, 28242, 2423, 6828, 13672, 1829, 16490, 1211, 4587, 11296, 12602, 3555, 8315, 4032, 13672, 1829, 1975, 5016, 8315, 44945, 3615, 28480, 3224, 9673, 3615, 28480, 3660, 15844, 29538, 27188, 2655, 25720, 4032, 12174, 1211, 2655, 8032, 3215, 12610, 8062, 1901, 13672, 1829, 31439, 691], "avg_logprob": -0.1509284446204918, "compression_ratio": 1.5146198830409356, "no_speech_prob": 0.0, "words": [{"start": 1135.16, "end": 1135.58, "word": "يعني", "probability": 0.527130126953125}, {"start": 1135.58, "end": 1135.78, "word": " أنا", "probability": 0.7470703125}, {"start": 1135.78, "end": 1136.06, "word": " جيت", "probability": 0.98681640625}, {"start": 1136.06, "end": 1136.24, "word": " على", "probability": 0.86767578125}, {"start": 1136.24, "end": 1136.42, "word": " ال", "probability": 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{"start": 1863.58, "end": 1864.18, "word": " space", "probability": 0.9404296875}, {"start": 1864.18, "end": 1864.5, "word": " V", "probability": 0.91845703125}, {"start": 1864.5, "end": 1865.16, "word": " is", "probability": 0.94189453125}, {"start": 1865.16, "end": 1867.0, "word": " a", "probability": 0.92919921875}, {"start": 1867.0, "end": 1867.7, "word": " linear", "probability": 0.9521484375}, {"start": 1867.7, "end": 1870.34, "word": " combination", "probability": 0.97314453125}, {"start": 1870.34, "end": 1878.28, "word": " of", "probability": 0.29150390625}, {"start": 1878.28, "end": 1880.26, "word": " V1", "probability": 0.888427734375}], "temperature": 1.0}, {"id": 79, "seek": 190830, "start": 1881.22, "end": 1908.3, "text": "و V2 و V M We say that .. We say that .. بروح نقول We say that capital V هذا is Spannid .. is Spannid by ..", "tokens": [2407, 691, 17, 4032, 691, 376, 492, 584, 300, 4386, 492, 584, 300, 4386, 4724, 32887, 5016, 8717, 39648, 492, 584, 300, 4238, 691, 23758, 307, 1738, 969, 327, 4386, 307, 1738, 969, 327, 538, 4386], "avg_logprob": -0.397804044388436, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 1881.22, "end": 1881.52, "word": "و", "probability": 0.85595703125}, {"start": 1881.52, "end": 1882.32, "word": " V2", "probability": 0.5941162109375}, {"start": 1882.32, "end": 1883.34, "word": " و", "probability": 0.9658203125}, {"start": 1883.34, "end": 1883.74, "word": " V", "probability": 0.474609375}, {"start": 1883.74, "end": 1884.42, "word": " M", "probability": 0.65771484375}, {"start": 1884.42, "end": 1885.64, "word": " We", "probability": 0.26708984375}, {"start": 1885.64, "end": 1886.0, "word": " say", "probability": 0.84716796875}, {"start": 1886.0, "end": 1886.6, "word": " that", "probability": 0.95703125}, {"start": 1886.6, "end": 1886.68, "word": " ..", "probability": 0.303466796875}, {"start": 1886.68, "end": 1887.56, "word": " We", "probability": 0.53564453125}, {"start": 1887.56, "end": 1888.96, "word": " say", "probability": 0.9658203125}, {"start": 1888.96, "end": 1890.8, "word": " that", "probability": 0.9404296875}, {"start": 1890.8, "end": 1890.8, "word": " ..", "probability": 0.6171875}, {"start": 1890.8, "end": 1892.32, "word": " بروح", "probability": 0.7777506510416666}, {"start": 1892.32, "end": 1892.88, "word": " نقول", "probability": 0.965087890625}, {"start": 1892.88, "end": 1895.36, "word": " We", "probability": 0.5234375}, {"start": 1895.36, "end": 1895.8, "word": " say", "probability": 0.962890625}, {"start": 1895.8, "end": 1896.28, "word": " that", "probability": 0.9541015625}, {"start": 1896.28, "end": 1897.2, "word": " capital", "probability": 0.365478515625}, {"start": 1897.2, "end": 1897.82, "word": " V", "probability": 0.990234375}, {"start": 1897.82, "end": 1898.28, "word": " هذا", "probability": 0.587890625}, {"start": 1898.28, "end": 1899.16, "word": " is", "probability": 0.90576171875}, {"start": 1899.16, "end": 1901.48, "word": " Spannid", "probability": 0.4823404947916667}, {"start": 1901.48, "end": 1901.84, "word": " ..", "probability": 0.324462890625}, {"start": 1901.84, "end": 1905.94, "word": " is", "probability": 0.6337890625}, {"start": 1905.94, "end": 1907.04, "word": " Spannid", "probability": 0.9501953125}, {"start": 1907.04, "end": 1907.54, "word": " by", "probability": 0.62109375}, {"start": 1907.54, "end": 1908.3, "word": " ..", "probability": 0.96044921875}], "temperature": 1.0}, {"id": 80, "seek": 193837, "start": 1908.93, "end": 1938.37, "text": "this elements by this elements also وكذلك we say that we say that the elements اللي هو V واحد و V اتنين", "tokens": [11176, 4959, 538, 341, 4959, 611, 4032, 4117, 8848, 23275, 321, 584, 300, 321, 584, 300, 264, 4959, 13672, 1829, 31439, 691, 36764, 24401, 4032, 691, 1975, 2655, 1863, 9957], "avg_logprob": -0.2689012019864975, "compression_ratio": 1.305263157894737, "no_speech_prob": 0.0, "words": [{"start": 1908.93, "end": 1909.43, "word": "this", "probability": 0.1990966796875}, {"start": 1909.43, "end": 1911.73, "word": " elements", "probability": 0.7578125}, {"start": 1911.73, "end": 1914.11, "word": " by", "probability": 0.54443359375}, {"start": 1914.11, "end": 1914.85, "word": " this", "probability": 0.70703125}, {"start": 1914.85, "end": 1915.75, "word": " elements", "probability": 0.90380859375}, {"start": 1915.75, "end": 1917.57, "word": " also", "probability": 0.5576171875}, {"start": 1917.57, "end": 1921.17, "word": " وكذلك", "probability": 0.8704833984375}, {"start": 1921.17, "end": 1921.89, "word": " we", "probability": 0.728515625}, {"start": 1921.89, "end": 1922.27, "word": " say", "probability": 0.9287109375}, {"start": 1922.27, "end": 1922.83, "word": " that", "probability": 0.95654296875}, {"start": 1922.83, "end": 1923.87, "word": " we", "probability": 0.449462890625}, {"start": 1923.87, "end": 1925.45, "word": " say", "probability": 0.96337890625}, {"start": 1925.45, "end": 1927.59, "word": " that", "probability": 0.953125}, {"start": 1927.59, "end": 1929.37, "word": " the", "probability": 0.85791015625}, {"start": 1929.37, "end": 1930.31, "word": " elements", "probability": 0.90380859375}, {"start": 1930.31, "end": 1935.17, "word": " اللي", "probability": 0.88623046875}, {"start": 1935.17, "end": 1935.35, "word": " هو", "probability": 0.94921875}, {"start": 1935.35, "end": 1935.57, "word": " V", "probability": 0.4912109375}, {"start": 1935.57, "end": 1936.33, "word": " واحد", "probability": 0.72802734375}, {"start": 1936.33, "end": 1937.39, "word": " و", "probability": 0.73046875}, {"start": 1937.39, "end": 1937.69, "word": " V", "probability": 0.833984375}, {"start": 1937.69, "end": 1938.37, "word": " اتنين", "probability": 0.9395751953125}], "temperature": 1.0}, {"id": 81, "seek": 194502, "start": 1939.14, "end": 1945.02, "text": "و VM Span V", "tokens": [2407, 18038, 1738, 282, 691], "avg_logprob": -0.3434244791666667, "compression_ratio": 0.6, "no_speech_prob": 0.0, "words": [{"start": 1939.14, "end": 1939.48, "word": "و", "probability": 0.60986328125}, {"start": 1939.48, "end": 1940.32, "word": " VM", "probability": 0.55908203125}, {"start": 1940.32, "end": 1942.68, "word": " Span", "probability": 0.696533203125}, {"start": 1942.68, "end": 1945.02, "word": " V", "probability": 0.80517578125}], "temperature": 1.0}, {"id": 82, "seek": 202496, "start": 2015.58, "end": 2024.96, "text": "طيب نجي لل two definitions اللي احنا معرفينهم و بدأنا في الجد شوية اهدروا بالكم الآن", "tokens": [9566, 1829, 3555, 8717, 7435, 1829, 24976, 732, 21988, 13672, 1829, 1975, 5016, 8315, 20449, 28480, 9957, 16095, 4032, 47525, 10721, 8315, 8978, 25724, 3215, 13412, 2407, 10632, 1975, 3224, 3215, 2288, 14407, 20666, 24793, 6024, 48506], "avg_logprob": -0.22902960840024447, "compression_ratio": 1.1982758620689655, "no_speech_prob": 0.0, "words": [{"start": 2015.58, "end": 2016.62, "word": "طيب", "probability": 0.880859375}, {"start": 2016.62, "end": 2017.52, "word": " نجي", "probability": 0.8421223958333334}, {"start": 2017.52, "end": 2017.64, "word": " لل", "probability": 0.286376953125}, {"start": 2017.64, "end": 2017.8, "word": " two", "probability": 0.8193359375}, {"start": 2017.8, "end": 2018.48, "word": " definitions", "probability": 0.91943359375}, {"start": 2018.48, "end": 2019.2, "word": " اللي", "probability": 0.82373046875}, {"start": 2019.2, "end": 2019.54, "word": " احنا", "probability": 0.9313151041666666}, {"start": 2019.54, "end": 2020.64, "word": " معرفينهم", "probability": 0.9755859375}, {"start": 2020.64, "end": 2021.88, "word": " و", "probability": 0.8134765625}, {"start": 2021.88, "end": 2022.76, "word": " بدأنا", "probability": 0.7007649739583334}, {"start": 2022.76, "end": 2022.9, "word": " في", "probability": 0.86572265625}, {"start": 2022.9, "end": 2023.28, "word": " الجد", "probability": 0.93896484375}, {"start": 2023.28, "end": 2023.76, "word": " شوية", "probability": 0.8644205729166666}, {"start": 2023.76, "end": 2024.32, "word": " اهدروا", "probability": 0.791015625}, {"start": 2024.32, "end": 2024.64, "word": " بالكم", "probability": 0.712158203125}, {"start": 2024.64, "end": 2024.96, "word": " الآن", "probability": 0.6807861328125}], "temperature": 1.0}, {"id": 83, "seek": 204973, "start": 2025.4, "end": 2049.74, "text": "مع بداية التعريفات الاتنين دول بدأنا ندخش في صميم الموضوع كل الكلام اللى فات كله كلام بسيط يعتبر اللى هم بيقولوا يفترض ال V هو عبارة عن vector space أخدت مجموعة من ال vectors موجودة وين في V يعني أخدت خمسة ستة سبعة جد ما يكون عددهم V1 وV2 لغاية VM موجودة في capital V", "tokens": [2304, 3615, 4724, 28259, 10632, 16712, 3615, 16572, 5172, 9307, 2423, 9307, 1863, 9957, 11778, 12610, 47525, 10721, 8315, 8717, 3215, 9778, 8592, 8978, 20328, 2304, 32640, 9673, 2407, 11242, 45367, 28242, 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{"start": 2026.8, "end": 2027.24, "word": " الاتنين", "probability": 0.745849609375}, {"start": 2027.24, "end": 2027.52, "word": " دول", "probability": 0.659912109375}, {"start": 2027.52, "end": 2027.94, "word": " بدأنا", "probability": 0.8206380208333334}, {"start": 2027.94, "end": 2028.36, "word": " ندخش", "probability": 0.82861328125}, {"start": 2028.36, "end": 2028.54, "word": " في", "probability": 0.9345703125}, {"start": 2028.54, "end": 2029.04, "word": " صميم", "probability": 0.9747721354166666}, {"start": 2029.04, "end": 2029.82, "word": " الموضوع", "probability": 0.9844970703125}, {"start": 2029.82, "end": 2030.1, "word": " كل", "probability": 0.79296875}, {"start": 2030.1, "end": 2030.56, "word": " الكلام", "probability": 0.9010416666666666}, {"start": 2030.56, "end": 2030.76, "word": " اللى", "probability": 0.79931640625}, {"start": 2030.76, "end": 2030.98, "word": " فات", "probability": 0.980712890625}, {"start": 2030.98, "end": 2031.28, "word": " كله", "probability": 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{"start": 2042.78, "end": 2043.1, "word": " أخدت", "probability": 0.881591796875}, {"start": 2043.1, "end": 2043.72, "word": " خمسة", "probability": 0.9661865234375}, {"start": 2043.72, "end": 2044.32, "word": " ستة", "probability": 0.83740234375}, {"start": 2044.32, "end": 2044.58, "word": " سبعة", "probability": 0.9226888020833334}, {"start": 2044.58, "end": 2044.82, "word": " جد", "probability": 0.934326171875}, {"start": 2044.82, "end": 2044.94, "word": " ما", "probability": 0.63671875}, {"start": 2044.94, "end": 2045.26, "word": " يكون", "probability": 0.9755859375}, {"start": 2045.26, "end": 2045.8, "word": " عددهم", "probability": 0.9669189453125}, {"start": 2045.8, "end": 2046.72, "word": " V1", "probability": 0.6795654296875}, {"start": 2046.72, "end": 2047.36, "word": " وV2", "probability": 0.8268229166666666}, {"start": 2047.36, "end": 2047.8, "word": " لغاية", "probability": 0.9708251953125}, {"start": 2047.8, "end": 2048.26, "word": " VM", "probability": 0.55517578125}, {"start": 2048.26, "end": 2048.76, "word": " موجودة", "probability": 0.9842529296875}, {"start": 2048.76, "end": 2048.96, "word": " في", "probability": 0.95263671875}, {"start": 2048.96, "end": 2049.4, "word": " capital", "probability": 0.474365234375}, {"start": 2049.4, "end": 2049.74, "word": " V", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 84, "seek": 207327, "start": 2049.97, "end": 2073.27, "text": "يبقى الفيات هدول كلهم إيش؟ كلهم vectors داخل ال vector space يعني لو جيت قولت البنات هدول ال vector space أخدت من؟ أخدت أول خمسة يبقى أول خمسة يعتبروا vectors في من؟ في ال vector space مالهم الخمسة هدول؟ we say that منقول ال V is a linear combination of", "tokens": [1829, 3555, 4587, 7578, 27188, 1829, 9307, 8032, 3215, 12610, 28242, 16095, 11933, 1829, 8592, 22807, 28242, 16095, 18875, 11778, 47283, 1211, 2423, 8062, 1901, 37495, 22653, 45164, 10874, 36081, 12174, 12610, 2655, 29739, 8315, 2655, 8032, 3215, 12610, 2423, 8062, 1901, 5551, 9778, 3215, 2655, 9154, 22807, 5551, 9778, 3215, 2655, 5551, 12610, 16490, 2304, 3794, 3660, 7251, 3555, 4587, 7578, 5551, 12610, 16490, 2304, 3794, 3660, 7251, 34268, 26890, 14407, 18875, 8978, 9154, 22807, 8978, 2423, 8062, 1901, 3714, 6027, 16095, 33962, 2304, 3794, 3660, 8032, 3215, 12610, 22807, 321, 584, 300, 9154, 39648, 2423, 691, 307, 257, 8213, 6562, 295], "avg_logprob": -0.20988581329584122, "compression_ratio": 1.8349514563106797, "no_speech_prob": 0.0, "words": [{"start": 2049.97, "end": 2050.49, "word": "يبقى", "probability": 0.80108642578125}, {"start": 2050.49, "end": 2051.07, "word": " الفيات", "probability": 0.681640625}, {"start": 2051.07, "end": 2051.39, "word": " هدول", "probability": 0.5438232421875}, {"start": 2051.39, "end": 2051.85, "word": " كلهم", "probability": 0.8857421875}, {"start": 2051.85, "end": 2052.35, "word": " إيش؟", "probability": 0.6369171142578125}, {"start": 2052.35, "end": 2052.95, "word": " كلهم", "probability": 0.94189453125}, {"start": 2052.95, "end": 2053.57, "word": " vectors", "probability": 0.81884765625}, {"start": 2053.57, "end": 2054.63, "word": " داخل", "probability": 0.9767252604166666}, {"start": 2054.63, "end": 2054.73, "word": " ال", "probability": 0.8759765625}, {"start": 2054.73, "end": 2054.93, "word": " vector", "probability": 0.6865234375}, {"start": 2054.93, "end": 2055.37, "word": " space", "probability": 0.95654296875}, {"start": 2055.37, "end": 2055.99, "word": " يعني", "probability": 0.78173828125}, {"start": 2055.99, "end": 2056.63, "word": " لو", "probability": 0.92041015625}, {"start": 2056.63, "end": 2056.91, "word": " جيت", "probability": 0.947021484375}, {"start": 2056.91, "end": 2057.29, "word": " قولت", "probability": 0.7740885416666666}, {"start": 2057.29, "end": 2057.73, "word": " البنات", "probability": 0.8349609375}, {"start": 2057.73, "end": 2058.03, "word": " هدول", "probability": 0.9015299479166666}, {"start": 2058.03, "end": 2058.17, "word": " ال", "probability": 0.90673828125}, {"start": 2058.17, "end": 2058.41, "word": " vector", "probability": 0.98291015625}, {"start": 2058.41, "end": 2058.91, "word": " space", "probability": 0.96337890625}, {"start": 2058.91, "end": 2059.57, "word": " أخدت", "probability": 0.9381103515625}, {"start": 2059.57, "end": 2059.87, "word": " من؟", "probability": 0.592529296875}, {"start": 2059.87, "end": 2060.29, "word": " أخدت", "probability": 0.9635009765625}, {"start": 2060.29, "end": 2060.51, "word": " أول", "probability": 0.883544921875}, {"start": 2060.51, "end": 2061.19, "word": " خمسة", "probability": 0.965087890625}, {"start": 2061.19, "end": 2061.83, "word": " يبقى", "probability": 0.9259033203125}, {"start": 2061.83, "end": 2062.11, "word": " أول", "probability": 0.9580078125}, {"start": 2062.11, "end": 2062.53, "word": " خمسة", "probability": 0.989990234375}, {"start": 2062.53, "end": 2063.19, "word": " يعتبروا", "probability": 0.927001953125}, {"start": 2063.19, "end": 2063.59, "word": " vectors", "probability": 0.96484375}, {"start": 2063.59, "end": 2063.95, "word": " في", "probability": 0.748046875}, {"start": 2063.95, "end": 2064.21, "word": " من؟", "probability": 0.5537109375}, {"start": 2064.21, "end": 2064.27, "word": " في", "probability": 0.86865234375}, {"start": 2064.27, "end": 2064.37, "word": " ال", "probability": 0.97412109375}, {"start": 2064.37, "end": 2064.63, "word": " vector", "probability": 0.98974609375}, {"start": 2064.63, "end": 2065.09, "word": " space", "probability": 0.89501953125}, {"start": 2065.09, "end": 2066.11, "word": " مالهم", "probability": 0.7300618489583334}, {"start": 2066.11, "end": 2066.81, "word": " الخمسة", "probability": 0.984130859375}, {"start": 2066.81, "end": 2067.81, "word": " هدول؟", "probability": 0.8795166015625}, {"start": 2067.81, "end": 2067.97, "word": " we", "probability": 0.59423828125}, {"start": 2067.97, "end": 2068.43, "word": " say", "probability": 0.92919921875}, {"start": 2068.43, "end": 2068.87, "word": " that", "probability": 0.9521484375}, {"start": 2068.87, "end": 2069.55, "word": " منقول", "probability": 0.540771484375}, {"start": 2069.55, "end": 2069.87, "word": " ال", "probability": 0.8115234375}, {"start": 2069.87, "end": 2070.19, "word": " V", "probability": 0.80517578125}, {"start": 2070.19, "end": 2070.65, "word": " is", "probability": 0.92529296875}, {"start": 2070.65, "end": 2070.99, "word": " a", "probability": 0.966796875}, {"start": 2070.99, "end": 2071.37, "word": " linear", "probability": 0.939453125}, {"start": 2071.37, "end": 2072.45, "word": " combination", "probability": 0.951171875}, {"start": 2072.45, "end": 2073.27, "word": " of", "probability": 0.986328125}], "temperature": 1.0}, {"id": 85, "seek": 208955, "start": 2073.93, "end": 2089.55, "text": "أنا لو روحت و أخدت vector تاني و لاجئت ان ال vector التاني قدرت اكتبه بدلالة الخمسة هدول يعني اخدت اي vector من ال vector اسمه اذا قدرت اكتبه بدلالة الخمسة هدول", "tokens": [10721, 8315, 45164, 12602, 2407, 33753, 4032, 5551, 9778, 3215, 2655, 8062, 6055, 7649, 1829, 4032, 20193, 7435, 19986, 2655, 16472, 2423, 8062, 16712, 7649, 1829, 12174, 3215, 43500, 1975, 4117, 2655, 3555, 3224, 47525, 1211, 6027, 3660, 33962, 2304, 3794, 3660, 8032, 3215, 12610, 37495, 22653, 1975, 9778, 3215, 2655, 1975, 1829, 8062, 9154, 2423, 8062, 24525, 2304, 3224, 1975, 15730, 12174, 3215, 43500, 1975, 4117, 2655, 3555, 3224, 47525, 1211, 6027, 3660, 33962, 2304, 3794, 3660, 8032, 3215, 12610], "avg_logprob": -0.26981707426106055, "compression_ratio": 1.9343065693430657, "no_speech_prob": 0.017303466796875, "words": [{"start": 2073.93, "end": 2074.63, "word": "أنا", "probability": 0.23687744140625}, {"start": 2074.63, "end": 2074.83, "word": " لو", "probability": 0.88818359375}, {"start": 2074.83, "end": 2075.19, "word": " روحت", "probability": 0.7052408854166666}, {"start": 2075.19, "end": 2075.33, "word": " و", "probability": 0.320556640625}, {"start": 2075.33, "end": 2075.77, "word": " أخدت", "probability": 0.8275146484375}, {"start": 2075.77, "end": 2076.27, "word": " vector", "probability": 0.446044921875}, {"start": 2076.27, "end": 2077.15, "word": " تاني", "probability": 0.84716796875}, {"start": 2077.15, "end": 2077.65, "word": " و", "probability": 0.8037109375}, {"start": 2077.65, "end": 2078.45, "word": " لاجئت", "probability": 0.66259765625}, {"start": 2078.45, "end": 2078.69, "word": " ان", "probability": 0.42041015625}, {"start": 2078.69, "end": 2078.93, "word": " ال", "probability": 0.7099609375}, {"start": 2078.93, "end": 2079.37, "word": " vector", "probability": 0.9228515625}, {"start": 2079.37, "end": 2079.97, "word": " التاني", "probability": 0.9099934895833334}, {"start": 2079.97, "end": 2080.65, "word": " قدرت", "probability": 0.762451171875}, {"start": 2080.65, "end": 2081.39, "word": " اكتبه", "probability": 0.88642578125}, {"start": 2081.39, "end": 2082.07, "word": " بدلالة", "probability": 0.8753662109375}, {"start": 2082.07, "end": 2082.81, "word": " الخمسة", "probability": 0.8643798828125}, {"start": 2082.81, "end": 2083.23, "word": " هدول", "probability": 0.7098795572916666}, {"start": 2083.23, "end": 2083.79, "word": " يعني", "probability": 0.7568359375}, {"start": 2083.79, "end": 2084.27, "word": " اخدت", "probability": 0.8751220703125}, {"start": 2084.27, "end": 2084.57, "word": " اي", "probability": 0.833984375}, {"start": 2084.57, "end": 2085.01, "word": " vector", "probability": 0.98486328125}, {"start": 2085.01, "end": 2085.25, "word": " من", "probability": 0.98291015625}, {"start": 2085.25, "end": 2085.43, "word": " ال", "probability": 0.91064453125}, {"start": 2085.43, "end": 2085.69, "word": " vector", "probability": 0.9775390625}, {"start": 2085.69, "end": 2085.99, "word": " اسمه", "probability": 0.5537109375}, {"start": 2085.99, "end": 2086.11, "word": " اذا", "probability": 0.6910400390625}, {"start": 2086.11, "end": 2086.67, "word": " قدرت", "probability": 0.9615885416666666}, {"start": 2086.67, "end": 2087.45, "word": " اكتبه", "probability": 0.98359375}, {"start": 2087.45, "end": 2088.07, "word": " بدلالة", "probability": 0.98876953125}, {"start": 2088.07, "end": 2088.73, "word": " الخمسة", "probability": 0.9700927734375}, {"start": 2088.73, "end": 2089.55, "word": " هدول", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 86, "seek": 213269, "start": 2104.7, "end": 2132.7, "text": "ماشي يعني يعني لو جيت أخدت أخدت مجموعة من ال vector قولي خمسة زي ما قلنا هنا و الخمسة هدول روحت أخدت vector تاني لجيت ال vector هذا بقدر أكتب بدلالة الخمسة constant في ال vector الأول زاد constant في ال vector التاني زاد constant في ال vector التاني زاد constant في ال vector الخامس", "tokens": [2304, 33599, 1829, 37495, 22653, 37495, 22653, 45164, 10874, 36081, 5551, 9778, 3215, 2655, 5551, 9778, 3215, 2655, 3714, 7435, 2304, 2407, 27884, 9154, 2423, 8062, 12174, 12610, 1829, 16490, 2304, 3794, 3660, 30767, 1829, 19446, 12174, 1211, 8315, 34105, 4032, 33962, 2304, 3794, 3660, 8032, 3215, 12610, 12602, 2407, 33753, 5551, 9778, 3215, 2655, 8062, 6055, 7649, 1829, 5296, 7435, 36081, 2423, 8062, 23758, 4724, 28543, 2288, 5551, 4117, 2655, 3555, 47525, 1211, 6027, 3660, 33962, 2304, 3794, 3660, 5754, 8978, 2423, 8062, 16247, 12610, 30767, 18513, 5754, 8978, 2423, 8062, 16712, 7649, 1829, 30767, 18513, 5754, 8978, 2423, 8062, 16712, 7649, 1829, 30767, 18513, 5754, 8978, 2423, 8062, 33962, 10943, 3794], "avg_logprob": -0.15816885363637356, "compression_ratio": 2.422222222222222, "no_speech_prob": 0.0, "words": [{"start": 2104.7, "end": 2105.58, "word": "ماشي", "probability": 0.43487548828125}, {"start": 2105.58, "end": 2106.46, "word": " يعني", "probability": 0.899169921875}, {"start": 2106.46, "end": 2107.48, "word": " يعني", "probability": 0.77001953125}, {"start": 2107.48, "end": 2107.72, "word": " لو", "probability": 0.94677734375}, {"start": 2107.72, "end": 2108.06, "word": " جيت", "probability": 0.943603515625}, {"start": 2108.06, "end": 2108.82, "word": " أخدت", "probability": 0.8519287109375}, {"start": 2108.82, "end": 2109.52, "word": " أخدت", "probability": 0.848388671875}, {"start": 2109.52, "end": 2110.22, "word": " مجموعة", "probability": 0.912109375}, {"start": 2110.22, "end": 2110.88, "word": " من", "probability": 0.9931640625}, {"start": 2110.88, "end": 2111.4, "word": " ال", "probability": 0.93359375}, {"start": 2111.4, "end": 2111.76, "word": " vector", "probability": 0.74853515625}, {"start": 2111.76, "end": 2112.4, "word": " قولي", "probability": 0.8147786458333334}, {"start": 2112.4, "end": 2112.84, "word": " خمسة", "probability": 0.968017578125}, {"start": 2112.84, "end": 2113.06, "word": " زي", "probability": 0.970703125}, {"start": 2113.06, "end": 2113.18, "word": " ما", "probability": 0.982421875}, {"start": 2113.18, "end": 2113.54, "word": " قلنا", "probability": 0.92333984375}, {"start": 2113.54, "end": 2113.8, "word": " هنا", "probability": 0.9248046875}, {"start": 2113.8, "end": 2114.68, "word": " و", "probability": 0.583984375}, {"start": 2114.68, "end": 2115.3, "word": " الخمسة", "probability": 0.9381103515625}, {"start": 2115.3, "end": 2115.98, "word": " هدول", "probability": 0.890625}, {"start": 2115.98, "end": 2116.86, "word": " روحت", "probability": 0.89208984375}, {"start": 2116.86, "end": 2117.34, "word": " أخدت", "probability": 0.9630126953125}, {"start": 2117.34, "end": 2117.92, "word": " vector", "probability": 0.97021484375}, {"start": 2117.92, "end": 2118.78, "word": " تاني", "probability": 0.9664713541666666}, {"start": 2118.78, "end": 2119.82, "word": " لجيت", "probability": 0.8714192708333334}, {"start": 2119.82, "end": 2120.04, "word": " ال", "probability": 0.97216796875}, {"start": 2120.04, "end": 2120.44, "word": " vector", "probability": 0.98876953125}, {"start": 2120.44, "end": 2120.86, "word": " هذا", "probability": 0.51953125}, {"start": 2120.86, "end": 2121.38, "word": " بقدر", "probability": 0.9658203125}, {"start": 2121.38, "end": 2121.92, "word": " أكتب", "probability": 0.870849609375}, {"start": 2121.92, "end": 2122.66, "word": " بدلالة", "probability": 0.81842041015625}, {"start": 2122.66, "end": 2123.46, "word": " الخمسة", "probability": 0.98486328125}, {"start": 2123.46, "end": 2123.94, "word": " constant", "probability": 0.767578125}, {"start": 2123.94, "end": 2124.24, "word": " في", "probability": 0.91015625}, {"start": 2124.24, "end": 2124.36, "word": " ال", "probability": 0.982421875}, {"start": 2124.36, "end": 2124.64, "word": " vector", "probability": 0.98828125}, {"start": 2124.64, "end": 2125.18, "word": " الأول", "probability": 0.966796875}, {"start": 2125.18, "end": 2127.04, "word": " زاد", "probability": 0.72900390625}, {"start": 2127.04, "end": 2127.48, "word": " constant", "probability": 0.95556640625}, {"start": 2127.48, "end": 2127.76, "word": " في", "probability": 0.97802734375}, {"start": 2127.76, "end": 2127.88, "word": " ال", "probability": 0.97607421875}, {"start": 2127.88, "end": 2128.16, "word": " vector", "probability": 0.99365234375}, {"start": 2128.16, "end": 2128.66, "word": " التاني", "probability": 0.95068359375}, {"start": 2128.66, "end": 2128.96, "word": " زاد", "probability": 0.960205078125}, {"start": 2128.96, "end": 2129.32, "word": " constant", "probability": 0.97607421875}, {"start": 2129.32, "end": 2129.56, "word": " في", "probability": 0.94677734375}, {"start": 2129.56, "end": 2129.64, "word": " ال", "probability": 0.958984375}, {"start": 2129.64, "end": 2129.86, "word": " vector", "probability": 0.9931640625}, {"start": 2129.86, "end": 2130.2, "word": " التاني", "probability": 0.771484375}, {"start": 2130.2, "end": 2130.52, "word": " زاد", "probability": 0.6619873046875}, {"start": 2130.52, "end": 2131.5, "word": " constant", "probability": 0.97314453125}, {"start": 2131.5, "end": 2131.76, "word": " في", "probability": 0.8759765625}, {"start": 2131.76, "end": 2131.86, "word": " ال", "probability": 0.95751953125}, {"start": 2131.86, "end": 2132.1, "word": " vector", "probability": 0.9912109375}, {"start": 2132.1, "end": 2132.7, "word": " الخامس", "probability": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/XTSVi7CEhGg_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/XTSVi7CEhGg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..dc59c8c733bf0ded401c61ceadd2f7016307ca74
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/XTSVi7CEhGg_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4935, "start": 21.65, "end": 49.35, "text": "بسم الله الرحمن الرحيم يبقى نعود الان الى اكمال المحاضرة فى الفترة الصباحية حيث واخدنا ثلاث نظريات وذكرنا بالتعريفين التعريف الاول كان تعريف ال finite dimensional vector space او لو vector space عنده dimension ايه له يسوئن شو معناه معناه شغلتين وبعد ذلك روحنا لتعريف ال basis وقلنا ان مجموعا ال vector بسميهم basis اذا تحقق شرطان", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 7251, 3555, 4587, 7578, 8717, 3615, 23328, 2423, 7649, 2423, 7578, 1975, 24793, 6027, 9673, 5016, 46958, 25720, 6156, 7578, 27188, 2655, 25720, 31767, 3555, 39319, 10632, 11331, 1829, 12984, 4032, 47283, 3215, 8315, 38637, 1211, 5718, 104, 8717, 19913, 16572, 9307, 4032, 8848, 37983, 8315, 20666, 2655, 3615, 16572, 5172, 9957, 16712, 3615, 16572, 5172, 42963, 12610, 25961, 37279, 16572, 5172, 2423, 19362, 18795, 8062, 1901, 1975, 2407, 45164, 8062, 1901, 43242, 3224, 10139, 1975, 1829, 3224, 46740, 7251, 3794, 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زائد", "probability": 0.7369791666666666}, {"start": 890.9, "end": 892.12, "word": " A1X", "probability": 0.9388020833333334}, {"start": 892.12, "end": 893.02, "word": " زائد", "probability": 0.9734700520833334}, {"start": 893.02, "end": 894.16, "word": " A2X", "probability": 0.984375}, {"start": 894.16, "end": 894.74, "word": " تربية", "probability": 0.6678059895833334}, {"start": 894.74, "end": 895.76, "word": " زائد", "probability": 0.9754231770833334}, {"start": 895.76, "end": 897.3, "word": " ANXN", "probability": 0.9493815104166666}, {"start": 897.3, "end": 897.66, "word": " كل", "probability": 0.84375}, {"start": 897.66, "end": 897.92, "word": " هذا", "probability": 0.771484375}, {"start": 897.92, "end": 898.32, "word": " الكلام", "probability": 0.9103190104166666}, {"start": 898.32, "end": 898.78, "word": " بيساوي", "probability": 0.606884765625}, {"start": 898.78, "end": 899.58, "word": " كده؟", "probability": 0.75860595703125}, {"start": 899.58, "end": 900.56, "word": " 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احنا أجبنا حتى الآن على نصف السؤال و بقى النصف الآخر find a basis او جدنا له basis وطوله هو ال standard basis", "tokens": [2994, 430, 45, 23032, 3555, 31439, 8978, 21136, 33604, 6027, 50239, 32239, 8032, 9307, 20292, 4724, 1829, 11622, 11622, 4032, 8032, 9307, 20292, 2423, 10139, 24976, 8062, 1901, 430, 45, 37893, 39896, 4117, 8608, 33604, 6027, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 5551, 7435, 3555, 8315, 11331, 49975, 6024, 48506, 15844, 8717, 9381, 5172, 21136, 33604, 6027, 4032, 4724, 4587, 7578, 28239, 9381, 5172, 6024, 95, 34740, 915, 257, 5143, 1975, 2407, 10874, 3215, 8315, 46740, 5143, 4032, 9566, 12610, 3224, 31439, 2423, 3832, 5143], "avg_logprob": -0.29687499794466743, "compression_ratio": 1.5909090909090908, "no_speech_prob": 0.0, "words": [{"start": 1109.9299999999998, "end": 1110.8899999999999, "word": "for", "probability": 0.08331298828125}, {"start": 1110.8899999999999, "end": 1111.85, "word": " PN", "probability": 0.5648193359375}, {"start": 1111.85, "end": 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special cases حالات خاصة لهذه ال polynomial نمرة واحد", "tokens": [4117, 12984, 13546, 4724, 1829, 5016, 9566, 12610, 3224, 16472, 3224, 426, 5296, 7649, 12174, 36150, 12174, 3215, 20498, 11296, 5296, 17082, 995, 10632, 426, 7251, 3555, 4587, 7578, 23758, 426, 4032, 21292, 1863, 3794, 7578, 16472, 3224, 8978, 36764, 24401, 10874, 16758, 9673, 44510, 10721, 316, 20666, 1783, 7251, 3555, 4587, 7578, 31439, 426, 30767, 16373, 3215, 36764, 24401, 4032, 20292, 3794, 376, 5296, 9778, 41193, 2288, 1975, 9778, 3215, 2121, 3331, 9154, 29538, 2423, 26110, 7251, 3555, 4587, 7578, 20666, 3215, 47341, 3660, 1975, 9778, 3215, 2121, 3331, 11331, 6027, 9307, 16490, 33546, 3660, 46740, 24192, 2423, 26110, 8717, 2304, 25720, 36764, 24401], "avg_logprob": -0.252948116581395, "compression_ratio": 1.7358490566037736, "no_speech_prob": 0.0, "words": [{"start": 1207.59, "end": 1207.99, "word": "كثير", "probability": 0.6227213541666666}, {"start": 1207.99, "end": 1208.45, "word": " بيحطوله", "probability": 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"end": 1668.31, "word": " مثل", "probability": 0.98583984375}, {"start": 1668.31, "end": 1668.75, "word": " اللي", "probability": 0.9765625}, {"start": 1668.75, "end": 1668.83, "word": " هو", "probability": 0.88427734375}, {"start": 1668.83, "end": 1669.25, "word": " المثال", "probability": 0.96826171875}, {"start": 1669.25, "end": 1669.37, "word": " في", "probability": 0.4775390625}, {"start": 1669.37, "end": 1669.95, "word": " محاضرة", "probability": 0.9444580078125}, {"start": 1669.95, "end": 1670.31, "word": " الصبح", "probability": 0.961181640625}, {"start": 1670.31, "end": 1670.87, "word": " أخر", "probability": 0.820556640625}, {"start": 1670.87, "end": 1671.53, "word": " مثال", "probability": 0.951171875}, {"start": 1671.53, "end": 1672.05, "word": " لما", "probability": 0.91552734375}, {"start": 1672.05, "end": 1672.61, "word": " جيبنا", "probability": 0.97802734375}], "temperature": 1.0}, {"id": 70, "seek": 169937, "start": 1672.95, "end": 1699.37, "text": "للـ R2 أربعة basis غير ال standard يبقى طلعنا له خمسة كل basis اللي عدد فيه كده بده يساوي بده يساوي ال dimension تبع ال vector space R2 طلعنا كل basis فيه بس two elements جينا على P2 طلعنا ان ال dimension اللي هيساوي تلاتة و أي تلاتة مش أي تلاتة بعض ال vectors", "tokens": [1211, 1211, 39184, 497, 17, 5551, 25513, 27884, 5143, 32771, 13546, 2423, 3832, 7251, 3555, 4587, 7578, 23032, 1211, 3615, 8315, 46740, 16490, 2304, 3794, 3660, 28242, 5143, 13672, 1829, 6225, 3215, 3215, 8978, 3224, 9122, 3215, 3224, 47525, 3224, 7251, 3794, 995, 45865, 47525, 3224, 7251, 3794, 995, 45865, 2423, 10139, 6055, 3555, 3615, 2423, 8062, 1901, 497, 17, 23032, 1211, 3615, 8315, 28242, 5143, 8978, 3224, 4724, 3794, 732, 4959, 10874, 1829, 8315, 15844, 430, 17, 23032, 1211, 3615, 8315, 16472, 2423, 10139, 13672, 1829, 39896, 3794, 995, 45865, 6055, 1211, 9307, 3660, 4032, 36632, 6055, 1211, 9307, 3660, 37893, 36632, 6055, 1211, 9307, 3660, 45030, 11242, 2423, 18875], "avg_logprob": -0.19782365725508758, "compression_ratio": 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جينا", "probability": 0.9617513020833334}, {"start": 1690.13, "end": 1690.51, "word": " على", "probability": 0.91015625}, {"start": 1690.51, "end": 1691.63, "word": " P2", "probability": 0.984130859375}, {"start": 1691.63, "end": 1692.69, "word": " طلعنا", "probability": 0.9576416015625}, {"start": 1692.69, "end": 1693.05, "word": " ان", "probability": 0.6455078125}, {"start": 1693.05, "end": 1693.21, "word": " ال", "probability": 0.9345703125}, {"start": 1693.21, "end": 1693.63, "word": " dimension", "probability": 0.9775390625}, {"start": 1693.63, "end": 1693.93, "word": " اللي", "probability": 0.6275634765625}, {"start": 1693.93, "end": 1694.41, "word": " هيساوي", "probability": 0.795166015625}, {"start": 1694.41, "end": 1695.15, "word": " تلاتة", "probability": 0.9410400390625}, {"start": 1695.15, "end": 1695.67, "word": " و", "probability": 0.79541015625}, {"start": 1695.67, "end": 1695.99, "word": " أي", "probability": 0.625}, {"start": 1695.99, "end": 1696.85, "word": " تلاتة", "probability": 0.9896240234375}, {"start": 1696.85, "end": 1697.07, "word": " مش", "probability": 0.6611328125}, {"start": 1697.07, "end": 1697.29, "word": " أي", "probability": 0.63037109375}, {"start": 1697.29, "end": 1697.89, "word": " تلاتة", "probability": 0.99267578125}, {"start": 1697.89, "end": 1698.71, "word": " بعض", "probability": 0.899658203125}, {"start": 1698.71, "end": 1698.89, "word": " ال", "probability": 0.9833984375}, {"start": 1698.89, "end": 1699.37, "word": " vectors", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 71, "seek": 171839, "start": 1699.61, "end": 1718.39, "text": "الموادات في P2 are linearly independent اللي بنفع يكونوا basis لهذا ال vector space نعطي كمان مثال بس عادى بيختلف شوية عن ما سبق من الأمثلة لذلك بده تفكير شوية", "tokens": [45340, 2407, 18513, 9307, 8978, 430, 17, 366, 43586, 6695, 13672, 1829, 44945, 5172, 3615, 7251, 30544, 14407, 5143, 46740, 15730, 2423, 8062, 1901, 8717, 3615, 9566, 1829, 9122, 2304, 7649, 50113, 6027, 4724, 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"probability": 0.962890625}, {"start": 1712.45, "end": 1713.03, "word": " شوية", "probability": 0.9230143229166666}, {"start": 1713.03, "end": 1713.41, "word": " عن", "probability": 0.481689453125}, {"start": 1713.41, "end": 1713.57, "word": " ما", "probability": 0.814453125}, {"start": 1713.57, "end": 1714.15, "word": " سبق", "probability": 0.9724934895833334}, {"start": 1714.15, "end": 1714.55, "word": " من", "probability": 0.9755859375}, {"start": 1714.55, "end": 1715.79, "word": " الأمثلة", "probability": 0.9324951171875}, {"start": 1715.79, "end": 1716.89, "word": " لذلك", "probability": 0.8146158854166666}, {"start": 1716.89, "end": 1717.21, "word": " بده", "probability": 0.896240234375}, {"start": 1717.21, "end": 1717.77, "word": " تفكير", "probability": 0.99609375}, {"start": 1717.77, "end": 1718.39, "word": " شوية", "probability": 0.96630859375}], "temperature": 1.0}, {"id": 72, "seek": 175147, "start": 1728.83, "end": 1751.47, "text": "يبقى example four بيقول let ال V تساوي R3 طبعا من هذا مناطق احنا عارفين هي دي مشهورة عندنا let", "tokens": [1829, 3555, 4587, 7578, 1365, 1451, 4724, 1829, 39648, 718, 2423, 691, 6055, 3794, 995, 45865, 497, 18, 23032, 3555, 3615, 995, 9154, 23758, 9154, 41193, 4587, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 39896, 11778, 1829, 37893, 3224, 13063, 3660, 43242, 8315, 718], "avg_logprob": -0.34600695504082574, "compression_ratio": 1.192, "no_speech_prob": 0.0, "words": [{"start": 1728.83, "end": 1729.21, "word": "يبقى", "probability": 0.6446533203125}, {"start": 1729.21, "end": 1729.67, "word": " example", "probability": 0.317138671875}, {"start": 1729.67, "end": 1730.49, "word": " four", "probability": 0.407958984375}, {"start": 1730.49, "end": 1740.03, "word": " بيقول", "probability": 0.7975260416666666}, {"start": 1740.03, "end": 1740.57, "word": " let", "probability": 0.60546875}, {"start": 1740.57, "end": 1742.21, "word": " ال", "probability": 0.57275390625}, {"start": 1742.21, "end": 1742.63, "word": " V", 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"probability": 0.738525390625}, {"start": 1749.87, "end": 1751.47, "word": " let", "probability": 0.68896484375}], "temperature": 1.0}, {"id": 73, "seek": 177846, "start": 1752.92, "end": 1778.46, "text": "الـ U تساوي اللي هي the set of all elements X واحد و X اتنين و X تلاتة such that X تلاتة بده ساوي اتنين X واحد زائد X اتنين بالشكل اللي عندنا هنا find a basis", "tokens": [6027, 39184, 624, 6055, 3794, 995, 45865, 13672, 1829, 39896, 264, 992, 295, 439, 4959, 1783, 36764, 24401, 4032, 1783, 1975, 2655, 1863, 9957, 4032, 1783, 6055, 1211, 9307, 3660, 1270, 300, 1783, 6055, 1211, 9307, 3660, 47525, 3224, 8608, 995, 45865, 1975, 2655, 1863, 9957, 1783, 36764, 24401, 30767, 16373, 3215, 1783, 1975, 2655, 1863, 9957, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105, 915, 257, 5143], "avg_logprob": -0.2642662957094718, "compression_ratio": 1.5526315789473684, "no_speech_prob": 0.0, "words": [{"start": 1752.92, "end": 1753.4, "word": "الـ", "probability": 0.379150390625}, {"start": 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"word": " X", "probability": 0.96533203125}, {"start": 1768.26, "end": 1769.0, "word": " واحد", "probability": 0.991455078125}, {"start": 1769.0, "end": 1770.34, "word": " زائد", "probability": 0.9226888020833334}, {"start": 1770.34, "end": 1770.74, "word": " X", "probability": 0.990234375}, {"start": 1770.74, "end": 1771.3, "word": " اتنين", "probability": 0.978759765625}, {"start": 1771.3, "end": 1771.82, "word": " بالشكل", "probability": 0.96875}, {"start": 1771.82, "end": 1772.12, "word": " اللي", "probability": 0.71826171875}, {"start": 1772.12, "end": 1772.22, "word": " عندنا", "probability": 0.642822265625}, {"start": 1772.22, "end": 1772.56, "word": " هنا", "probability": 0.94970703125}, {"start": 1772.56, "end": 1774.5, "word": " find", "probability": 0.51171875}, {"start": 1774.5, "end": 1777.52, "word": " a", "probability": 0.638671875}, {"start": 1777.52, "end": 1778.46, "word": " basis", "probability": 0.5009765625}], "temperature": 1.0}, {"id": 74, "seek": 180253, "start": 1792.95, "end": 1802.53, "text": "والدمينشن لـ subspace U", "tokens": [2407, 6027, 3215, 2304, 9957, 8592, 1863, 5296, 39184, 2090, 17940, 624], "avg_logprob": -0.8124999816601093, "compression_ratio": 0.7906976744186046, "no_speech_prob": 0.0, "words": [{"start": 1792.9499999999998, "end": 1794.35, "word": "والدمينشن", "probability": 0.5016130719866071}, {"start": 1794.35, "end": 1795.75, "word": " لـ", "probability": 0.419921875}, {"start": 1795.75, "end": 1797.47, "word": " subspace", "probability": 0.593994140625}, {"start": 1797.47, "end": 1802.53, "word": " U", "probability": 0.650390625}], "temperature": 1.0}, {"id": 75, "seek": 184774, "start": 1819.88, "end": 1847.74, "text": "سؤال مرة تانية احنا عندنا ال vector space R3 اللي كل element فيه عبارة عن عنصر مكون من ثلاث مركبات X1 و X2 و X3 اللي موجودة في R3 هذا ال vector space R3 ال X1 و X2 و X3 عارية ال number روحنا أخدنا منه مجموعة من العناصر أو ال elements أو ال vector مين هم هدول؟", "tokens": [3794, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 1975, 5016, 8315, 43242, 8315, 2423, 8062, 1901, 497, 18, 13672, 1829, 28242, 4478, 8978, 3224, 6225, 3555, 9640, 3660, 18871, 18871, 9381, 2288, 3714, 30544, 9154, 38637, 1211, 5718, 104, 3714, 31747, 3555, 9307, 1783, 16, 4032, 1783, 17, 4032, 1783, 18, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 497, 18, 23758, 2423, 8062, 1901, 497, 18, 2423, 1783, 16, 4032, 1783, 17, 4032, 1783, 18, 6225, 9640, 10632, 2423, 1230, 12602, 2407, 5016, 8315, 5551, 9778, 3215, 8315, 9154, 3224, 3714, 7435, 2304, 2407, 27884, 9154, 18863, 1863, 33546, 2288, 34051, 2423, 4959, 34051, 2423, 8062, 3714, 9957, 8032, 2304, 8032, 3215, 12610, 22807], "avg_logprob": -0.15951086671456047, "compression_ratio": 1.7828054298642535, "no_speech_prob": 0.0, "words": [{"start": 1819.88, "end": 1820.34, "word": "سؤال", "probability": 0.8860677083333334}, {"start": 1820.34, "end": 1820.62, "word": " مرة", "probability": 0.93994140625}, {"start": 1820.62, "end": 1821.08, "word": " تانية", 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"probability": 0.69921875}, {"start": 2518.28, "end": 2518.44, "word": " ال", "probability": 0.447265625}, {"start": 2518.44, "end": 2518.9, "word": " V", "probability": 0.986328125}, {"start": 2518.9, "end": 2519.72, "word": " اللي", "probability": 0.765625}, {"start": 2519.72, "end": 2520.3, "word": " موجودة", "probability": 0.9842529296875}, {"start": 2520.3, "end": 2520.42, "word": " في", "probability": 0.9306640625}, {"start": 2520.42, "end": 2520.56, "word": " ال", "probability": 0.91552734375}, {"start": 2520.56, "end": 2520.82, "word": " vector", "probability": 0.80517578125}, {"start": 2520.82, "end": 2521.78, "word": " space", "probability": 0.8447265625}, {"start": 2521.78, "end": 2522.52, "word": " V", "probability": 0.9599609375}, {"start": 2522.52, "end": 2523.78, "word": " Note", "probability": 0.147705078125}, {"start": 2523.78, "end": 2528.08, "word": " V", "probability": 0.47021484375}, {"start": 2528.08, "end": 2529.88, "word": " above", "probability": 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"probability": 0.96435546875}, {"start": 2542.05, "end": 2543.63, "word": " written", "probability": 0.9169921875}, {"start": 2543.63, "end": 2545.57, "word": " as", "probability": 0.7294921875}, {"start": 2545.57, "end": 2550.81, "word": " one", "probability": 0.48193359375}, {"start": 2550.81, "end": 2552.95, "word": " property", "probability": 0.94775390625}, {"start": 2552.95, "end": 2558.81, "word": " as", "probability": 0.91455078125}, {"start": 2558.81, "end": 2559.47, "word": " follows", "probability": 0.35595703125}], "temperature": 1.0}, {"id": 104, "seek": 259155, "start": 2562.77, "end": 2591.55, "text": "إن الـ T of CU زائد V بده يساوي C في T of U زائد T of V والـ C موجودة في R and الـ U والـ V موجودة في الـ V كابتن example one", "tokens": [28814, 1863, 2423, 39184, 314, 295, 29777, 30767, 16373, 3215, 691, 47525, 3224, 7251, 3794, 995, 45865, 383, 8978, 314, 295, 624, 30767, 16373, 3215, 314, 295, 691, 16070, 39184, 383, 3714, 29245, 23328, 3660, 8978, 497, 293, 2423, 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2571.11, "word": " C", "probability": 0.84423828125}, {"start": 2571.11, "end": 2571.95, "word": " في", "probability": 0.876953125}, {"start": 2571.95, "end": 2572.43, "word": " T", "probability": 0.97021484375}, {"start": 2572.43, "end": 2572.99, "word": " of", "probability": 0.9814453125}, {"start": 2572.99, "end": 2573.45, "word": " U", "probability": 0.9931640625}, {"start": 2573.45, "end": 2574.85, "word": " زائد", "probability": 0.9611002604166666}, {"start": 2574.85, "end": 2575.95, "word": " T", "probability": 0.8525390625}, {"start": 2575.95, "end": 2576.65, "word": " of", "probability": 0.98388671875}, {"start": 2576.65, "end": 2577.23, "word": " V", "probability": 0.99462890625}, {"start": 2577.23, "end": 2578.37, "word": " والـ", "probability": 0.703857421875}, {"start": 2578.37, "end": 2578.73, "word": " C", "probability": 0.82666015625}, {"start": 2578.73, "end": 2580.11, "word": " موجودة", "probability": 0.9871826171875}, {"start": 2580.11, "end": 2580.45, "word": " في", "probability": 0.98388671875}, {"start": 2580.45, "end": 2580.99, "word": " R", "probability": 0.9521484375}, {"start": 2580.99, "end": 2582.35, "word": " and", "probability": 0.323486328125}, {"start": 2582.35, "end": 2583.83, "word": " الـ", "probability": 0.782958984375}, {"start": 2583.83, "end": 2584.23, "word": " U", "probability": 0.79052734375}, {"start": 2584.23, "end": 2585.01, "word": " والـ", "probability": 0.6331787109375}, {"start": 2585.01, "end": 2585.37, "word": " V", "probability": 0.8466796875}, {"start": 2585.37, "end": 2586.97, "word": " موجودة", "probability": 0.9910888671875}, {"start": 2586.97, "end": 2587.45, "word": " في", "probability": 0.99169921875}, {"start": 2587.45, "end": 2587.99, "word": " الـ", "probability": 0.6708984375}, {"start": 2587.99, "end": 2588.17, "word": " V", "probability": 0.85546875}, {"start": 2588.17, "end": 2588.83, "word": " كابتن", "probability": 0.76519775390625}, {"start": 2588.83, "end": 2590.79, "word": " example", "probability": 0.1778564453125}, {"start": 2590.79, "end": 2591.55, "word": " one", "probability": 0.70556640625}], "temperature": 1.0}, {"id": 105, "seek": 262265, "start": 2596.59, "end": 2622.65, "text": "لت الـ T من الـ M M في N إلى الـ M N في M بـ a mapping بـ a mapping defined by", "tokens": [1211, 2655, 2423, 39184, 314, 9154, 2423, 39184, 376, 376, 8978, 426, 30731, 2423, 39184, 376, 426, 8978, 376, 4724, 39184, 257, 18350, 4724, 39184, 257, 18350, 7642, 538], "avg_logprob": -0.4190104087193807, "compression_ratio": 1.36, "no_speech_prob": 0.0, "words": [{"start": 2596.59, "end": 2597.39, "word": "لت", "probability": 0.3814697265625}, {"start": 2597.39, "end": 2599.33, "word": " الـ", "probability": 0.5159912109375}, {"start": 2599.33, "end": 2599.73, "word": " T", "probability": 0.64111328125}, {"start": 2599.73, "end": 2600.97, "word": " من", "probability": 0.97802734375}, {"start": 2600.97, "end": 2602.15, "word": " الـ", "probability": 0.6470947265625}, {"start": 2602.15, 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"probability": 0.951171875}, {"start": 2615.41, "end": 2619.33, "word": " بـ", "probability": 0.482666015625}, {"start": 2619.33, "end": 2619.57, "word": " a", "probability": 0.96728515625}, {"start": 2619.57, "end": 2620.31, "word": " mapping", "probability": 0.97119140625}, {"start": 2620.31, "end": 2622.15, "word": " defined", "probability": 0.83056640625}, {"start": 2622.15, "end": 2622.65, "word": " by", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 106, "seek": 265541, "start": 2626.27, "end": 2655.41, "text": "معرّفة كالتالي T of A بديو يساوي ال A transpose for all A اللي موجودة في M M N السؤال هو is T a linear transformation؟", "tokens": [2304, 3615, 2288, 11703, 5172, 3660, 9122, 6027, 2655, 6027, 1829, 314, 295, 316, 4724, 16254, 2407, 7251, 3794, 995, 45865, 2423, 316, 25167, 337, 439, 316, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 376, 376, 426, 21136, 33604, 6027, 31439, 307, 314, 257, 8213, 9887, 22807], "avg_logprob": -0.28401692149539787, 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" a", "probability": 0.8330078125}, {"start": 2650.55, "end": 2651.29, "word": " linear", "probability": 0.92431640625}, {"start": 2651.29, "end": 2655.41, "word": " transformation؟", "probability": 0.853759765625}], "temperature": 1.0}, {"id": 107, "seek": 266777, "start": 2664.27, "end": 2667.77, "text": "هل التليانات تتغير أو لا؟", "tokens": [3224, 1211, 16712, 20292, 7649, 9307, 6055, 2655, 17082, 13546, 34051, 20193, 22807], "avg_logprob": -0.5393415135996682, "compression_ratio": 0.8846153846153846, "no_speech_prob": 0.0, "words": [{"start": 2664.27, "end": 2664.59, "word": "هل", "probability": 0.9404296875}, {"start": 2664.59, "end": 2665.39, "word": " التليانات", "probability": 0.52337646484375}, {"start": 2665.39, "end": 2666.29, "word": " تتغير", "probability": 0.5687255859375}, {"start": 2666.29, "end": 2666.93, "word": " أو", "probability": 0.22021484375}, {"start": 2666.93, "end": 2667.77, "word": " لا؟", "probability": 0.85595703125}], "temperature": 1.0}, {"id": 108, "seek": 271367, "start": 2712.15, "end": 2713.67, "text": "خلّيني أركب معايا العلماء البنات", "tokens": [9778, 1211, 11703, 9957, 1829, 5551, 31747, 3555, 20449, 995, 25528, 18863, 19528, 16606, 29739, 8315, 2655], "avg_logprob": -0.4800347155994839, "compression_ratio": 0.9375, "no_speech_prob": 0.0, "words": [{"start": 2712.15, "end": 2712.67, "word": "خلّيني", "probability": 0.74267578125}, {"start": 2712.67, "end": 2712.93, "word": " أركب", "probability": 0.6930338541666666}, {"start": 2712.93, "end": 2713.07, "word": " معايا", "probability": 0.603515625}, {"start": 2713.07, "end": 2713.33, "word": " العلماء", "probability": 0.6298828125}, {"start": 2713.33, "end": 2713.67, "word": " البنات", "probability": 0.550048828125}], "temperature": 1.0}, {"id": 109, "seek": 273911, "start": 2714.65, "end": 2739.11, "text": "في هذه الدقيقات المتبقيات الأخيرات من هذه المحاضرة نعطي تعريف الـLinear Transformation وتعطي مثال واحد والمرة الجاية ان شاء الله بنكمل بقية هذه الأمثلة بيقولي انا عندي two vector spaces V وW أخدنا T من V لW يبقى function او mapping من V لW", "tokens": [41185, 29538, 32748, 38436, 4587, 9307, 9673, 2655, 3555, 38436, 9307, 16247, 9778, 13546, 9307, 9154, 29538, 9673, 5016, 46958, 25720, 8717, 3615, 9566, 1829, 37279, 16572, 5172, 2423, 39184, 43, 533, 289, 6531, 8663, 34683, 3615, 9566, 1829, 50113, 6027, 36764, 24401, 4032, 45340, 25720, 25724, 995, 10632, 16472, 13412, 16606, 21984, 44945, 24793, 1211, 4724, 4587, 10632, 29538, 16247, 2304, 12984, 37977, 4724, 1829, 39648, 1829, 1975, 8315, 18871, 16254, 732, 8062, 7673, 691, 4032, 54, 5551, 9778, 3215, 8315, 314, 9154, 691, 5296, 54, 7251, 3555, 4587, 7578, 2445, 1975, 2407, 18350, 9154, 691, 5296, 54], "avg_logprob": -0.2804687529802322, "compression_ratio": 1.588235294117647, "no_speech_prob": 0.0, "words": [{"start": 2714.65, "end": 2714.89, "word": "في", "probability": 0.16796875}, {"start": 2714.89, "end": 2715.13, "word": " هذه", "probability": 0.59033203125}, {"start": 2715.13, "end": 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2913.64, "end": 2925.66, "text": "الـ C موجودة في الـ set of real numbers والـ A موجودة في الـ M الأولى", "tokens": [6027, 39184, 383, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 992, 295, 957, 3547, 16070, 39184, 316, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 376, 16247, 12610, 7578], "avg_logprob": -0.32327586617963067, "compression_ratio": 1.3866666666666667, "no_speech_prob": 0.0, "words": [{"start": 2913.64, "end": 2913.94, "word": "الـ", "probability": 0.342559814453125}, {"start": 2913.94, "end": 2914.26, "word": " C", "probability": 0.5830078125}, {"start": 2914.26, "end": 2915.6, "word": " موجودة", "probability": 0.984375}, {"start": 2915.6, "end": 2915.76, "word": " في", "probability": 0.9609375}, {"start": 2915.76, "end": 2916.0, "word": " الـ", "probability": 0.459228515625}, {"start": 2916.0, "end": 2916.28, "word": " set", "probability": 0.85302734375}, {"start": 2916.28, "end": 2916.6, "word": " of", "probability": 0.9658203125}, {"start": 2916.6, "end": 2916.94, 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جود فيه R يبقى ال C هذا بقوله خليك برا من خواص اللي أخدناها ل Transpose يبقى هذا C في A Transpose من خواص ل Transpose خليكم معايا سيبقوا من الفشر", "tokens": [3794, 1829, 9122, 11536, 14851, 7649, 2655, 12602, 4587, 2304, 3714, 47283, 2407, 10874, 23328, 8978, 3224, 497, 7251, 3555, 4587, 7578, 2423, 383, 23758, 4724, 39648, 3224, 16490, 20292, 4117, 4724, 23557, 9154, 16490, 2407, 33546, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 5296, 6531, 43501, 7251, 3555, 4587, 7578, 23758, 383, 8978, 316, 6531, 43501, 9154, 16490, 2407, 33546, 5296, 6531, 43501, 16490, 20292, 24793, 20449, 995, 25528, 8608, 1829, 3555, 4587, 14407, 9154, 27188, 8592, 2288], "avg_logprob": -0.31406251192092893, "compression_ratio": 1.6280487804878048, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2955.25, "end": 2955.65, "word": "سي", "probability": 0.3348388671875}, {"start": 2955.65, "end": 2956.63, "word": " كونستانت", "probability": 0.77890625}, {"start": 2956.63, "end": 2957.25, "word": " 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"probability": 0.60205078125}, {"start": 3057.59, "end": 3058.29, "word": " Definition", "probability": 0.875}, {"start": 3058.29, "end": 3058.71, "word": " T", "probability": 0.90185546875}, {"start": 3058.71, "end": 3059.23, "word": " of", "probability": 0.98095703125}, {"start": 3059.23, "end": 3059.91, "word": " A،", "probability": 0.5914306640625}, {"start": 3059.91, "end": 3060.33, "word": " B", "probability": 0.485595703125}, {"start": 3060.33, "end": 3061.35, "word": " Transpose", "probability": 0.950927734375}, {"start": 3061.35, "end": 3061.73, "word": " طبق", "probability": 0.9855143229166666}, {"start": 3061.73, "end": 3062.01, "word": " للـ", "probability": 0.92919921875}, {"start": 3062.01, "end": 3062.67, "word": " Definition", "probability": 0.941162109375}, {"start": 3062.67, "end": 3063.71, "word": " يبقى", "probability": 0.907958984375}, {"start": 3063.71, "end": 3064.35, "word": " T", "probability": 0.9580078125}, {"start": 3064.35, "end": 3065.15, "word": " of", "probability": 0.9814453125}, {"start": 3065.15, "end": 3066.07, "word": " B،", "probability": 0.75830078125}, {"start": 3066.07, "end": 3066.39, "word": " يبقى", "probability": 0.92041015625}, {"start": 3066.39, "end": 3067.03, "word": " تحقق", "probability": 0.90478515625}, {"start": 3067.03, "end": 3067.27, "word": " الـ", "probability": 0.715087890625}, {"start": 3067.27, "end": 3067.31, "word": " A", "probability": 0.76806640625}, {"start": 3067.31, "end": 3067.51, "word": " عن", "probability": 0.9814453125}, {"start": 3067.51, "end": 3067.63, "word": " ال", "probability": 0.94091796875}, {"start": 3067.63, "end": 3068.03, "word": " condition", "probability": 0.818359375}, {"start": 3068.03, "end": 3068.53, "word": " التاني", "probability": 0.9039713541666666}, {"start": 3068.53, "end": 3068.69, "word": " ولا", "probability": 0.76513671875}, {"start": 3068.69, "end": 3069.57, "word": " لا،", "probability": 0.751220703125}, {"start": 3069.57, "end": 3070.01, "word": " يبقى", "probability": 0.943603515625}, {"start": 3070.01, "end": 3070.29, "word": " معناه", "probability": 0.8414713541666666}, {"start": 3070.29, "end": 3070.51, "word": " يتكلم", "probability": 0.66375732421875}, {"start": 3070.51, "end": 3070.69, "word": " ان", "probability": 0.37109375}, {"start": 3070.69, "end": 3070.83, "word": " الـ", "probability": 0.6793212890625}, {"start": 3070.83, "end": 3070.95, "word": " T", "probability": 0.771484375}, {"start": 3070.95, "end": 3071.15, "word": " ما", "probability": 0.83447265625}, {"start": 3071.15, "end": 3071.47, "word": " لها", "probability": 0.793701171875}], "temperature": 1.0}, {"id": 125, "seek": 309378, "start": 3072.24, "end": 3093.78, "text": "لينير ترانسفورماشن يبقى سا تي از اي لينير ترانسفورماشن حد فيكم لايه تساول هنا؟ رب يا الله جهزولي خلصولي الورقة يا الله", "tokens": [1211, 9957, 13546, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 33599, 1863, 7251, 3555, 4587, 7578, 8608, 995, 6055, 1829, 1975, 11622, 1975, 1829, 5296, 9957, 13546, 6055, 2288, 7649, 3794, 5172, 13063, 2304, 33599, 1863, 11331, 3215, 8978, 24793, 20193, 1829, 3224, 6055, 3794, 995, 12610, 34105, 22807, 12602, 3555, 35186, 21984, 10874, 3224, 11622, 12610, 1829, 16490, 1211, 9381, 12610, 1829, 2423, 13063, 28671, 35186, 21984], "avg_logprob": -0.35303440819615906, "compression_ratio": 1.7479674796747968, "no_speech_prob": 0.0, "words": [{"start": 3072.24, "end": 3073.24, "word": "لينير", "probability": 0.586669921875}, {"start": 3073.24, "end": 3074.82, "word": " ترانسفورماشن", "probability": 0.7017686631944444}, {"start": 3074.82, "end": 3075.96, "word": " يبقى", "probability": 0.842041015625}, {"start": 3075.96, "end": 3076.48, "word": " سا", "probability": 0.442138671875}, {"start": 3076.48, "end": 3077.44, "word": " تي", "probability": 0.6033935546875}, {"start": 3077.44, "end": 3078.38, "word": " از", "probability": 0.5728759765625}, {"start": 3078.38, "end": 3078.98, "word": " اي", "probability": 0.72607421875}, {"start": 3078.98, "end": 3079.9, "word": " لينير", "probability": 0.8976236979166666}, {"start": 3079.9, "end": 3085.44, "word": " ترانسفورماشن", "probability": 0.9386935763888888}, {"start": 3085.44, "end": 3088.04, "word": " حد", "probability": 0.26885986328125}, {"start": 3088.04, "end": 3088.3, "word": " فيكم", "probability": 0.3961181640625}, {"start": 3088.3, "end": 3088.5, "word": " لايه", "probability": 0.5266927083333334}, {"start": 3088.5, "end": 3088.92, "word": " تساول", "probability": 0.8272705078125}, {"start": 3088.92, "end": 3090.8, "word": " هنا؟", "probability": 0.92724609375}, {"start": 3090.8, "end": 3091.8, "word": " رب", "probability": 0.5888671875}, {"start": 3091.8, "end": 3091.94, "word": " يا", "probability": 0.337646484375}, {"start": 3091.94, "end": 3092.04, "word": " الله", "probability": 0.93212890625}, {"start": 3092.04, "end": 3092.5, "word": " جهزولي", "probability": 0.9142578125}, {"start": 3092.5, "end": 3092.96, "word": " خلصولي", "probability": 0.93642578125}, {"start": 3092.96, "end": 3093.42, "word": " الورقة", "probability": 0.9259440104166666}, {"start": 3093.42, "end": 3093.64, "word": " يا", "probability": 0.53857421875}, {"start": 3093.64, "end": 3093.78, "word": " الله", "probability": 0.931640625}], "temperature": 1.0}, {"id": 126, "seek": 311085, "start": 3098.05, "end": 3110.85, "text": "احنا عليكي بكون انتهينا ولسه لازلنا في بداية هذا section اللي هو مليان زي ال dimension وال bases وهو أساسي لن يخلو أي امتحان ينسوان عليه", "tokens": [39319, 8315, 25894, 4117, 1829, 4724, 30544, 16472, 47395, 1829, 8315, 35525, 3794, 3224, 5296, 31377, 1211, 8315, 8978, 4724, 28259, 10632, 23758, 3541, 13672, 1829, 31439, 3714, 20292, 7649, 30767, 1829, 2423, 10139, 16070, 17949, 37037, 2407, 5551, 3794, 32277, 1829, 5296, 1863, 7251, 9778, 1211, 2407, 36632, 1975, 2304, 2655, 5016, 7649, 7251, 1863, 3794, 2407, 7649, 47356], "avg_logprob": -0.23936987411780436, "compression_ratio": 1.486842105263158, "no_speech_prob": 0.0, "words": [{"start": 3098.05, "end": 3098.47, "word": "احنا", "probability": 0.879150390625}, {"start": 3098.47, "end": 3098.89, "word": " عليكي", "probability": 0.5374348958333334}, {"start": 3098.89, "end": 3099.13, "word": " بكون", "probability": 0.645751953125}, {"start": 3099.13, "end": 3099.67, "word": " انتهينا", "probability": 0.9031982421875}, {"start": 3099.67, "end": 3100.23, "word": " ولسه", "probability": 0.71484375}, {"start": 3100.23, "end": 3100.83, "word": " لازلنا", "probability": 0.9468994140625}, {"start": 3100.83, "end": 3101.03, "word": " في", "probability": 0.70458984375}, {"start": 3101.03, "end": 3101.69, "word": " بداية", "probability": 0.9684244791666666}, {"start": 3101.69, "end": 3101.95, "word": " هذا", "probability": 0.88232421875}, {"start": 3101.95, "end": 3102.61, "word": " section", "probability": 0.53125}, {"start": 3102.61, "end": 3103.45, "word": " اللي", "probability": 0.9443359375}, {"start": 3103.45, "end": 3103.61, "word": " هو", "probability": 0.44189453125}, {"start": 3103.61, "end": 3104.47, "word": " مليان", "probability": 0.9381510416666666}, {"start": 3104.47, "end": 3104.79, "word": " زي", "probability": 0.883544921875}, {"start": 3104.79, "end": 3104.91, "word": " ال", "probability": 0.98681640625}, {"start": 3104.91, "end": 3105.35, "word": " dimension", "probability": 0.77734375}, {"start": 3105.35, "end": 3105.71, "word": " وال", "probability": 0.6318359375}, {"start": 3105.71, "end": 3106.21, "word": " bases", "probability": 0.52880859375}, {"start": 3106.21, "end": 3107.15, "word": " وهو", "probability": 0.77734375}, {"start": 3107.15, "end": 3108.05, "word": " أساسي", "probability": 0.9266357421875}, {"start": 3108.05, "end": 3108.47, "word": " لن", "probability": 0.97216796875}, {"start": 3108.47, "end": 3109.39, "word": " يخلو", "probability": 0.83905029296875}, {"start": 3109.39, "end": 3109.65, "word": " أي", "probability": 0.63818359375}, {"start": 3109.65, "end": 3110.11, "word": " امتحان", "probability": 0.97705078125}, {"start": 3110.11, "end": 3110.57, "word": " ينسوان", "probability": 0.5758544921875}, {"start": 3110.57, "end": 3110.85, "word": " عليه", "probability": 0.95166015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3112.82075, "duration_after_vad": 2895.352499999989}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f17b3e60db213bc22f5d4af55c861dc59b09e1ef
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/_E3ug1jsGaY_postprocess.srt
@@ -0,0 +1,1276 @@
+1
+00:00:27,790 --> 00:00:33,170
+الشبطر أشبه بالمراجعة لمدرس في الثانوية العامة
+
+2
+00:00:33,170 --> 00:00:38,450
+بنضيف عليه بعض الإضافات الشبطر هو عبارة عن
+
+3
+00:00:38,450 --> 00:00:43,710
+matrices and determinants المصفوفات والمحددات
+
+4
+00:00:43,710 --> 00:00:47,150
+matrices يا بنات هذه هي جامع matrix
+
+5
+00:00:50,130 --> 00:00:55,770
+يبقى مفردها matrix جمعها matrices بنجي أول section
+
+6
+00:00:55,770 --> 00:00:58,790
+في هذا ال chapter هو systems of linear equations
+
+7
+00:00:58,790 --> 00:01:05,550
+أنظمة المعادلات الخطية معادلات عادية مش تفاضلية
+
+8
+00:01:05,550 --> 00:01:10,880
+يبقى أنظمة المعادلات الخطيةهنقط مجموعة من الـ
+
+9
+00:01:10,880 --> 00:01:15,680
+definitions أول تعريف من هذه الـ definition هو a
+
+10
+00:01:15,680 --> 00:01:19,420
+non homogeneous system هذا اختصار non homogeneous
+
+11
+00:01:19,420 --> 00:01:23,900
+system of linear equations من المعادلات الخطية of
+
+12
+00:01:23,900 --> 00:01:30,480
+M equations في M من المعادلات و N من المجاهيل is a
+
+13
+00:01:30,480 --> 00:01:33,940
+system in the form يبقى أنا عندي مجموعة من
+
+14
+00:01:33,940 --> 00:01:41,190
+المعادلات عددها Mوعدد المجاهيل فيها N ممكن يتساوى
+
+15
+00:01:41,190 --> 00:01:49,150
+وممكن لا يتساوى ال system بيقول a11x1 زائد a12x2
+
+16
+00:01:49,150 --> 00:01:55,170
+زائد a13x3 زائد زايد بغير ما نوصل ل a1nxnb1
+
+17
+00:01:56,300 --> 00:02:09,480
+التانية A21X1 A22X2 A23X3 A2N B2 A31X1
+
+18
+00:02:09,480 --> 00:02:18,540
+A32X2 A33X3 A23X2 A33X3 A31X1 A32X2 A33X3 A31X1
+
+19
+00:02:18,540 --> 00:02:20,320
+A32X2 A33X3 A31X1 A32X2 A33X3 A31X1 A32X2 A33X3
+
+20
+00:02:20,320 --> 00:02:21,660
+A31X1 A32X2 A32X2 A33X3 A31X1 A32X2 A32X2 A32X2
+
+21
+00:02:21,660 --> 00:02:22,240
+A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2
+
+22
+00:02:22,240 --> 00:02:22,260
+A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2 A32X2
+
+23
+00:02:22,260 --> 00:02:27,490
+A32X2 A32Xويمكن خمس أو يمكن ست أو يمكن عشر أو يمكن
+
+24
+00:02:27,490 --> 00:02:32,250
+عشرين جد ما يكونوا يكونوا يبقى لما حطيت فراغ حطي
+
+25
+00:02:32,250 --> 00:02:37,810
+جد ما بدك معادلات على هذا الشكل بيقول لي حيث M في
+
+26
+00:02:37,810 --> 00:02:43,410
+N numbers AI هدول يا بنات M في N يعني مضربات في
+
+27
+00:02:43,410 --> 00:02:48,450
+بعض ضرباللي هو main AI اتطلع هدول كم واحدة واحدة
+
+28
+00:02:48,450 --> 00:02:55,310
+تنتين تلتة اربعة خمسة N هنا واحدة تنتين تلتة اربعة
+
+29
+00:02:55,310 --> 00:03:01,290
+M إذا لو ضربت M في N بيجيب لي كل ال A هات هدول كل
+
+30
+00:03:01,290 --> 00:03:07,330
+ال A11 و ال A12 و ال Aثلاث آخرينيبقى هدول عددهم M
+
+31
+00:03:07,330 --> 00:03:15,370
+في N وهو A I J والـ I تتغير من 1 إلى M 1 2 3 4 M
+
+32
+00:03:15,370 --> 00:03:21,710
+اللي هو الرمز الأول الرمز التاني J يتغير من 1
+
+33
+00:03:21,710 --> 00:03:32,520
+لغاية N 1 2 3 4 لغاية Mالمعاملات هم
+
+34
+00:03:32,520 --> 00:03:45,200
+ثوابت هذا النظام X1
+
+35
+00:03:45,200 --> 00:03:50,180
+و X2 و X3 و XN هم المجاهيل
+
+36
+00:03:51,980 --> 00:03:56,220
+طب والبهات بي واحد و بي اتنين و بي ام بسميهم
+
+37
+00:03:56,220 --> 00:04:00,820
+الثوابت يبقى انا في عند المعاملات و في عند
+
+38
+00:04:00,820 --> 00:04:06,580
+المجاهيل و في عند من الثوابت هذول القيم كلهم
+
+39
+00:04:06,580 --> 00:04:11,600
+بسميهم الثوابتالـ X's اللي عندنا هدول كلهم بسميهم
+
+40
+00:04:11,600 --> 00:04:17,680
+المجاهيل unknowns هاي هجيلك عليها ال unknowns اللي
+
+41
+00:04:17,680 --> 00:04:22,500
+هو ال X I و I من 1 إلى N ضالوا الإيهات اللي عندنا
+
+42
+00:04:22,500 --> 00:04:27,220
+ليه بسميهم مين المعاملات لهذا ال system يبقى عندي
+
+43
+00:04:27,220 --> 00:04:33,620
+معاملات عندي مجاهيل عندي ثوابت لل system starطيب
+
+44
+00:04:33,620 --> 00:04:38,260
+نأخد بعض أنواع من هذا ال system بعض أنواع من هذا
+
+45
+00:04:38,260 --> 00:04:43,220
+ال system ممكن يكون عندي معادلتين في مجهولين
+
+46
+00:04:43,220 --> 00:04:49,360
+المجهول x1 و x2 وماعنديش إلا معادلتين ممكن يكون
+
+47
+00:04:49,360 --> 00:04:54,880
+عندي تلت معادلات ومجهولين بس ممكن أربع معادلات
+
+48
+00:04:54,880 --> 00:05:00,420
+ومجهولين قد ما بدك ماعنديش مشكلةالنقطة الثانية الـ
+
+49
+00:05:00,420 --> 00:05:04,480
+linear system of the three unknowns يبقى هذا عندي
+
+50
+00:05:04,480 --> 00:05:08,800
+مجهولين هذا ال system فيه ثلاثة مجاهيل يمكن أن
+
+51
+00:05:08,800 --> 00:05:15,920
+يكون ثلاث معادلات في ثلاثة مجاهيلممكن يكون M من
+
+52
+00:05:15,920 --> 00:05:22,920
+المعادلات في ثلاثة مجاهيل فقط وهكذا يعني هذه بعض
+
+53
+00:05:22,920 --> 00:05:28,500
+أنواع من ال system start ممكن يكون أربع معادلات في
+
+54
+00:05:28,500 --> 00:05:32,940
+أربع مجاهيل ممكن يكون أربع معادلات في عشر مجاهيل و
+
+55
+00:05:32,940 --> 00:05:37,200
+و إلى آخرى يعني هذه بس أمثلة عملية على ال system
+
+56
+00:05:37,200 --> 00:05:42,780
+هذا كيف ممكن يكون شكله في حالات مختلفةطيب ال
+
+57
+00:05:42,780 --> 00:05:47,400
+system هذا ممكن نسميه homogeneous و ممكن نسميه non
+
+58
+00:05:47,400 --> 00:05:53,080
+homogeneous non homogeneous إذا هدول ماكانوش أسفار
+
+59
+00:05:53,080 --> 00:05:58,860
+طيب افترضي هدول عشرة تسعة منهم أسفار و واحدة لأ
+
+60
+00:05:58,860 --> 00:06:02,200
+أسميه homogeneous ولا non homogeneousnon
+
+61
+00:06:02,200 --> 00:06:07,260
+homogeneous لكن لو كانوا كلهم أصفر بسميه
+
+62
+00:06:07,260 --> 00:06:12,020
+homogeneous system يبقى system متجانس يبقى أنا
+
+63
+00:06:12,020 --> 00:06:19,320
+عندي two systems أحدهما متجانس والآخر غير متجانس
+
+64
+00:06:19,320 --> 00:06:24,120
+يبقى non homogeneous system هذا homogeneous if the
+
+65
+00:06:24,120 --> 00:06:28,400
+above constants دول are all zero the above systems
+
+66
+00:06:28,400 --> 00:06:34,270
+are called homogeneousإذا كان كل البيهات هذول اللي
+
+67
+00:06:34,270 --> 00:06:39,750
+عند مالها أصفر لكن لو كان واحدة بس على الأقل منهم
+
+68
+00:06:39,750 --> 00:06:44,670
+ليس صفر و الباقي كله أصفر يبقى هذا non-homogeneous
+
+69
+00:06:44,670 --> 00:06:49,810
+النقطة الرابعة ال system إذا كان ال system is not
+
+70
+00:06:49,810 --> 00:06:54,550
+of the form أستعارف يعني ليس على هذا الشكل كافي
+
+71
+00:06:54,550 --> 00:06:58,190
+يعني ليس على هذا الشكل يعني مش هلاجي x واحد دي
+
+72
+00:06:58,190 --> 00:07:03,420
+ممكن هلاجي x واحد تربيةيمكن أن ألاقي X تلاتة تكعيب
+
+73
+00:07:03,420 --> 00:07:10,160
+مثلا ممكن ألاقي X اتنين في X تلاتة ممكن ألاقي sign
+
+74
+00:07:10,160 --> 00:07:14,900
+X أربعة مثلا من حد ما ألاقي شغلات من هذا القبيل
+
+75
+00:07:14,900 --> 00:07:21,080
+يبقى هذا ليس linear system تمامفبعدين بقول if the
+
+76
+00:07:21,080 --> 00:07:25,160
+system is not in the above form أسطر إنه ماكانش
+
+77
+00:07:25,160 --> 00:07:29,920
+على الشكل هذه يعني الإكسات هذه تغير وضعها then it
+
+78
+00:07:29,920 --> 00:07:36,090
+is nonlinear يمكن بسميه system غير خاطي فمثلالو
+
+79
+00:07:36,090 --> 00:07:40,890
+قلت X1 تربية زياد خمسة X اتنين يساوي تلاتة اتنين X
+
+80
+00:07:40,890 --> 00:07:44,990
+واحد زيادين X اتنين يساوي اتنين طلعيلي في المعادلة
+
+81
+00:07:44,990 --> 00:07:49,390
+X واحد تربية لكن ال system هنا ماعنديش X واحد
+
+82
+00:07:49,390 --> 00:07:55,050
+تربية بالمرة نهائي ولا في اي معادلةإذا حتى لو كانت
+
+83
+00:07:55,050 --> 00:07:59,410
+التانية linear يبقى ال system على بعضه nonlinear
+
+84
+00:07:59,410 --> 00:08:04,470
+يعني لو لجيت معادلة واحدة شذت عن حكاية ال linear
+
+85
+00:08:04,470 --> 00:08:08,750
+هدول يبقى ال system على بعضه كله بقول nonlinear
+
+86
+00:08:08,750 --> 00:08:13,500
+system تمام؟هذا ليس شد بس بسبب X1 تربية لأ كمان
+
+87
+00:08:13,500 --> 00:08:19,380
+عندي لين X2 يبقى هذا ليس linear system لو جيت هنا
+
+88
+00:08:19,380 --> 00:08:24,780
+X1 في X2 اللي جت مضربات في بعض ضرب وليس بتربية
+
+89
+00:08:24,780 --> 00:08:29,280
+يبقى كمان هذا non linear system لو اللي جت E أوس
+
+90
+00:08:29,280 --> 00:08:34,640
+X1 exponential ليست linear يبقى هذه كمان non
+
+91
+00:08:34,640 --> 00:08:38,690
+linear cosine X2 و هكذاطلع المعادلة تالتة Linear
+
+92
+00:08:38,690 --> 00:08:43,430
+عادي جدا X1-X2 يساوي Zero عادي جدا المعادلة هذه
+
+93
+00:08:43,430 --> 00:08:47,590
+Linear لكن التنتين هذول Non-Linear يبقى ال system
+
+94
+00:08:47,590 --> 00:08:54,370
+على بعض بيقول عنه ماله Non-Linear System حد بتسأل
+
+95
+00:08:54,370 --> 00:08:57,950
+أي سؤال في هذه التعريفات؟
+
+96
+00:08:59,320 --> 00:09:04,340
+أصل هذه الساعة أو هذه المحاضرة أقرب إلى النظر منها
+
+97
+00:09:04,340 --> 00:09:11,800
+إلى الشغل العملي ناخد
+
+98
+00:09:11,800 --> 00:09:16,620
+الآن تعريف آخرالـ System اللي توستار يا بنات لو
+
+99
+00:09:16,620 --> 00:09:23,500
+حطيت الإيهات في مصوفة بسميها مصوفة المعاملات أضفت
+
+100
+00:09:23,500 --> 00:09:28,460
+عليها عمود ثواب بسميها المصوفة الموسعة زي الثانوية
+
+101
+00:09:28,460 --> 00:09:32,500
+بالضبط تماما فبعدين بحطيها ال definition التالي
+
+102
+00:09:32,500 --> 00:09:36,260
+definition for
+
+103
+00:09:36,260 --> 00:09:42,740
+the above system star for the above system
+
+104
+00:09:45,000 --> 00:09:54,860
+استعار اللي كان قبل قليل الـ matrix المصفوفة اللي
+
+105
+00:09:54,860 --> 00:10:11,700
+هي من a11, a12, a13, a1n, a21, a22, a23, a2n نفض
+
+106
+00:10:11,700 --> 00:10:24,380
+الماشيل لغاية am1am1 am2 am3 amn يبجى هذه بسميها
+
+107
+00:10:24,380 --> 00:10:34,500
+مصوفة المعاملات يبجى هذه is called the coefficient
+
+108
+00:10:34,500 --> 00:10:39,540
+matrix the
+
+109
+00:10:39,540 --> 00:10:41,980
+coefficient
+
+110
+00:10:45,550 --> 00:10:57,730
+a coefficients matrix يبقى مصوفة المعاملات and ال
+
+111
+00:10:57,730 --> 00:11:03,770
+matrix والمصوفة
+
+112
+00:11:03,770 --> 00:11:12,750
+اللي هي من a11 a12 a1n
+
+113
+00:11:12,750 --> 00:11:25,270
+a1nأو جيت ماشي اتون اتوتون اتون او ضليت ماشي لغاية
+
+114
+00:11:25,270 --> 00:11:34,550
+امون امتونامن و رحت اضفت لها عمود زيادة اللي هو
+
+115
+00:11:34,550 --> 00:11:42,110
+عمود ثوابت بي وان و بيتو وضلت ماشية لغاية بي ام
+
+116
+00:11:42,110 --> 00:11:50,910
+هذي بسميها المصوفة الموسعة is called the
+
+117
+00:11:50,910 --> 00:11:52,290
+augmented matrix
+
+118
+00:12:01,730 --> 00:12:09,890
+بعدها بسميها المصفوفة الموسعة definition آخر the
+
+119
+00:12:09,890 --> 00:12:15,650
+solution of
+
+120
+00:12:15,650 --> 00:12:21,370
+the system a
+
+121
+00:12:21,370 --> 00:12:29,390
+star is an entupel
+
+122
+00:12:30,850 --> 00:12:45,390
+نتيوفل of numbers من الأعداد X1 و X2 و لغاية XN
+
+123
+00:12:45,390 --> 00:12:54,670
+and satisfies the
+
+124
+00:12:54,670 --> 00:12:55,350
+system
+
+125
+00:13:05,180 --> 00:13:14,640
+remark for the solution of
+
+126
+00:13:14,640 --> 00:13:25,620
+the above system star there are three
+
+127
+00:13:25,620 --> 00:13:29,720
+possibilities there are
+
+128
+00:13:33,240 --> 00:13:40,800
+three possibilities يحد
+
+129
+00:13:40,800 --> 00:13:51,120
+ثلاثة احتمالات نمر واحد ال system has
+
+130
+00:13:51,120 --> 00:13:56,580
+no solution ال
+
+131
+00:13:56,580 --> 00:14:01,180
+system ممكن مايكونش له حل يعني
+
+132
+00:14:01,790 --> 00:14:06,690
+No intersection
+
+133
+00:14:06,690 --> 00:14:11,290
+of
+
+134
+00:14:11,290 --> 00:14:22,490
+lines or planes نمري
+
+135
+00:14:22,490 --> 00:14:30,010
+اتنين The system has one solution
+
+136
+00:14:32,590 --> 00:14:38,510
+الواحد فقط يبقى
+
+137
+00:14:38,510 --> 00:14:49,850
+all linear lines
+
+138
+00:14:49,850 --> 00:14:54,590
+intersect
+
+139
+00:14:54,590 --> 00:14:59,330
+in
+
+140
+00:14:59,330 --> 00:15:10,470
+one pointفي نقطة واحدة الاحتمال الثالث والاخير ال
+
+141
+00:15:10,470 --> 00:15:17,730
+system has infinite number
+
+142
+00:15:17,730 --> 00:15:22,090
+of
+
+143
+00:15:22,090 --> 00:15:27,750
+solutions infinite
+
+144
+00:15:27,750 --> 00:15:31,090
+number of solutions يعني
+
+145
+00:15:34,630 --> 00:15:38,170
+lines lines go inside
+
+146
+00:16:10,480 --> 00:16:20,560
+coincide or all the planes جميع المستويات
+
+147
+00:16:20,560 --> 00:16:25,920
+intersect in
+
+148
+00:16:25,920 --> 00:16:35,900
+a line تتقطع في خط مستقيم واحد or coincide
+
+149
+00:16:42,960 --> 00:16:50,240
+كوانصيف نوت for
+
+150
+00:16:50,240 --> 00:17:00,980
+the system star for the system star
+
+151
+00:17:00,980 --> 00:17:13,790
+there is no two solutions there isno two solutions
+
+152
+00:17:13,790 --> 00:17:19,610
+or three
+
+153
+00:17:19,610 --> 00:17:22,730
+solutions
+
+154
+00:17:22,730 --> 00:17:26,870
+or
+
+155
+00:17:26,870 --> 00:17:32,330
+but
+
+156
+00:17:32,330 --> 00:17:35,670
+one
+
+157
+00:17:36,760 --> 00:17:46,840
+solution or infinite number
+
+158
+00:17:46,840 --> 00:17:57,120
+of solutions division
+
+159
+00:17:57,120 --> 00:18:04,900
+the above system star
+
+160
+00:18:06,800 --> 00:18:16,540
+is called consistent if
+
+161
+00:18:16,540 --> 00:18:22,780
+it
+
+162
+00:18:22,780 --> 00:18:26,860
+has consistent
+
+163
+00:18:26,860 --> 00:18:31,480
+if
+
+164
+00:18:31,480 --> 00:18:32,240
+it has
+
+165
+00:18:36,720 --> 00:18:42,720
+one solution or
+
+166
+00:18:42,720 --> 00:18:54,160
+infinite number of solutions
+
+167
+00:18:54,160 --> 00:18:58,200
+نمرأ
+
+168
+00:18:58,200 --> 00:19:03,000
+نان دوا first semester
+
+169
+00:19:10,010 --> 00:19:18,470
+الشركة السابقة استارة اسمها ان
+
+170
+00:19:18,470 --> 00:19:35,210
+كون سيستانت ان كون سيستانت اذا كان لديه اذا
+
+171
+00:19:35,210 --> 00:19:38,630
+كان لديه لا حلول
+
+172
+00:19:41,490 --> 00:19:53,310
+تلاتة a set of all solutions a
+
+173
+00:19:53,310 --> 00:20:04,510
+set of all solutions of the system a star is
+
+174
+00:20:04,510 --> 00:20:06,450
+called
+
+175
+00:20:07,880 --> 00:20:15,000
+the general أو
+
+176
+00:20:15,000 --> 00:20:23,380
+complete solution
+
+177
+00:20:23,380 --> 00:20:27,840
+of
+
+178
+00:20:27,840 --> 00:20:34,700
+the system تعريف
+
+179
+00:20:34,700 --> 00:20:35,320
+الرابع
+
+180
+00:20:38,220 --> 00:20:44,800
+تو سيستام او
+
+181
+00:20:44,800 --> 00:20:56,460
+اكوايشن هم قادرين يكونوا اكوالينت
+
+182
+00:20:56,460 --> 00:21:01,960
+هم
+
+183
+00:21:01,960 --> 00:21:04,740
+قادرين يكونوا اكوالينت اذا كانوا
+
+184
+00:21:10,620 --> 00:21:17,480
+if they have exactly exactly
+
+185
+00:21:17,480 --> 00:21:23,060
+the same solutions
+
+186
+00:21:23,060 --> 00:21:26,980
+درجع لكلام اللي احنا كاتبينه هذا مرة تانية يا بنات
+
+187
+00:21:26,980 --> 00:21:31,740
+يبقى شوية تعريف وبها ننهي الجزء النظري وبعدين نبدأ
+
+188
+00:21:31,740 --> 00:21:36,120
+ناخد أمثلة التعريف يقول ال system المجموعة
+
+189
+00:21:36,120 --> 00:21:40,310
+المعادلة اللي كنا كاتبينها قبل قليللو أخدت
+
+190
+00:21:40,310 --> 00:21:45,370
+المعاملات بس و حطيتهم في مصوفة بجهد المصوفة بسميها
+
+191
+00:21:45,370 --> 00:21:50,370
+coefficient matrix of the system يعني اللي هم
+
+192
+00:21:50,370 --> 00:21:56,920
+مصوفة المعاملات لهذا النظاملو جيت مصوفة المعاملة
+
+193
+00:21:56,920 --> 00:22:02,200
+أضفت لها عمود واحد فقط هو عمود الثوابت يبقى بسميها
+
+194
+00:22:02,200 --> 00:22:06,680
+الـ Augmented Matrix يعني المصوفة الموسعة يعني
+
+195
+00:22:06,680 --> 00:22:11,460
+أضفناها عمود فوسعناها شوية من هما سميت المصوفة
+
+196
+00:22:11,460 --> 00:22:17,900
+الموسعة تمام؟ دي التعريف الثانيالحل تبع ال system
+
+197
+00:22:17,900 --> 00:22:22,820
+is star يبقى احنا بندور على حل هذا ال system هو
+
+198
+00:22:22,820 --> 00:22:26,880
+عبارة عن in a tuple لما اقول يا بنات انا عندي
+
+199
+00:22:26,880 --> 00:22:32,260
+معادلتين في مجهولين يبقى بطلع ليه قيم ال X واحد
+
+200
+00:22:32,260 --> 00:22:37,020
+وقيم ال X اتنين يبقى بقول هذا ordered pair زوج
+
+201
+00:22:37,020 --> 00:22:40,860
+مرتم X واحد هي القيمة الأولى و X اتنين هي من
+
+202
+00:22:40,860 --> 00:22:44,820
+القيمة الثانية و بقول هذا الحل طب لكن لو صارت تلت
+
+203
+00:22:44,820 --> 00:22:51,370
+مجهيلبقول عليها three tuple يعني كأنه تلت مركبات
+
+204
+00:22:51,370 --> 00:22:54,350
+موجودة يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1
+
+205
+00:22:54,350 --> 00:22:54,690
+و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى
+
+206
+00:22:54,690 --> 00:22:55,830
+X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3
+
+207
+00:22:55,830 --> 00:22:59,630
+يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و
+
+208
+00:22:59,630 --> 00:23:03,910
+X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و
+
+209
+00:23:03,910 --> 00:23:05,490
+X2 و X3 يبقى X1 و X2 و X3 يبقى X1 و X2 و X3 يبقى
+
+210
+00:23:05,490 --> 00:23:09,200
+X1 و X2اللي طلعت عندي Unsatisfy the system وهذه
+
+211
+00:23:09,200 --> 00:23:14,260
+القيم تحقق ال system يبقى حل هذا ال system هو
+
+212
+00:23:14,260 --> 00:23:20,920
+عبارة عن قيم X1 و X2 و X3 بحطها على شكل قوس و
+
+213
+00:23:20,920 --> 00:23:25,460
+فواصل بين هذه القيم X1 هي القيم الأولى X2 هي القيم
+
+214
+00:23:25,460 --> 00:23:32,030
+التالتة X3 هي القيم التالتة Xn هي القيم الرقموهذه
+
+215
+00:23:32,030 --> 00:23:37,330
+يجب أن تحقق هذا ال system طيب السؤال هو هل ال
+
+216
+00:23:37,330 --> 00:23:43,010
+system هذا دائما و أبدا إله حل؟ الإجابة قد يكون و
+
+217
+00:23:43,010 --> 00:23:47,590
+قد لا يكون طب إن كان هناك حل لهذا ال system حل
+
+218
+00:23:47,590 --> 00:23:51,330
+واحد و لا اتنين و لا تلاتة و لا اربع و لا ما لا
+
+219
+00:23:51,330 --> 00:23:57,330
+نهاية من الحلول هذا ما سنجيب عليهيبقى اي system من
+
+220
+00:23:57,330 --> 00:24:02,970
+المعادلة الخاطية له احد ثلاثة احتمالاتالاحتمال
+
+221
+00:24:02,970 --> 00:24:08,310
+الاول ان لا يكون هناك حل لا حل يحقق المعادلات مع
+
+222
+00:24:08,310 --> 00:24:13,990
+بعضها ال system has no solution no solution يعني
+
+223
+00:24:13,990 --> 00:24:19,390
+المعادلة إذا تعت خط مستقيمات لا يمكن للخطوط
+
+224
+00:24:19,390 --> 00:24:24,250
+المستقيمات كلها أن تتقاطع في نقطة واحدة وإن كانت
+
+225
+00:24:24,250 --> 00:24:29,360
+مستويات برضه المستويات هذه لا تتقاطعزي المستوى هذا
+
+226
+00:24:29,360 --> 00:24:34,220
+والمستوى هذا مافيش تقاطع تمام؟ ممكن يكونوا مستقيمة
+
+227
+00:24:34,220 --> 00:24:39,200
+و كل اتنين يتقاطعوا مع بعض لكن مايتقاطعوش كلهم في
+
+228
+00:24:39,200 --> 00:24:42,280
+نفس النقطة هذا و هذا يتقاطعوا في نقطة هذا و هذا في
+
+229
+00:24:42,280 --> 00:24:45,420
+نقطة هذا و هذا في نقطة تانية و اللي بعد ايه؟يبقى
+
+230
+00:24:45,420 --> 00:24:49,140
+هذا اللي لا يوجد حل في هذه الحالة يبقى في هذه
+
+231
+00:24:49,140 --> 00:24:52,720
+الحالة يبقى there is no solution كيف هذا مثلا
+
+232
+00:24:52,720 --> 00:24:57,420
+نعرفه بعد قليل من خلال الأمثلة طيب الأمر الثاني
+
+233
+00:24:57,420 --> 00:25:03,380
+ممكن يكون عندي حل وحيد فقطوهذا بيحصل إذا كانت
+
+234
+00:25:03,380 --> 00:25:07,700
+المعادلات هذه معادلات مستقيمات إذا انت تقاطع في
+
+235
+00:25:07,700 --> 00:25:13,580
+نقطة واحدة فقط لغيرها لأن المستويات إذا تقاطعت في
+
+236
+00:25:13,580 --> 00:25:17,020
+نقطة .. في .. إذا تقاطعت هذه المستقيمات فإن
+
+237
+00:25:17,020 --> 00:25:23,200
+تقاطعها يكون في خط مستقيم زي مستوى السقفو مستوى
+
+238
+00:25:23,200 --> 00:25:27,820
+الحقيقة اللي عندنا التقاطة في خط مستقيم والخط
+
+239
+00:25:27,820 --> 00:25:32,380
+مستقيم عبارة عن مهلة نهاية من النقط وليست نقطة
+
+240
+00:25:32,380 --> 00:25:38,070
+واحدةيبقى هنا ليس عندى إلا حل واحد يبقى الـ Linear
+
+241
+00:25:38,070 --> 00:25:42,770
+Loss تتخطى في نقطة واحدة وبالتالي لا يظهر إلا حل
+
+242
+00:25:42,770 --> 00:25:47,870
+واحد لهذا الـ system أو لمجموعة هذه المعادلات
+
+243
+00:25:47,870 --> 00:25:51,690
+الاحتمال يكون عندى infinite number of solutions
+
+244
+00:25:51,690 --> 00:25:57,790
+يبقى عندى عددلنهائي من الحلول في هذه الحلقة
+
+245
+00:25:57,790 --> 00:26:03,030
+المستويات كلها ممكن أنت تقاطع في نقطة واحدة زي ما
+
+246
+00:26:03,030 --> 00:26:07,410
+اقول هذا الملزم اللي بينك كلها مستويات و تقاطعة في
+
+247
+00:26:07,410 --> 00:26:11,160
+الحرارة زي الدفتر اللي عندككلها تقطعت في الحرف
+
+248
+00:26:11,160 --> 00:26:15,240
+الجانبي يبقى الحرف الجانبي هو خط التقطع كام نقطة
+
+249
+00:26:15,240 --> 00:26:19,740
+فيه يبقى مالة نهاية من النقاط ممكن مستويات تنطبق
+
+250
+00:26:19,740 --> 00:26:23,600
+زي ما تجه في الدفتر و كل ورقة بذاصير كانت مستوية
+
+251
+00:26:23,600 --> 00:26:27,500
+يبقى كلهم انطبقوا على بعض تمام الانطباق يبقى كلهم
+
+252
+00:26:27,500 --> 00:26:31,900
+اشتركوا في نفس النقاطيبقى في هذه الحلقة كام حل
+
+253
+00:26:31,900 --> 00:26:36,720
+عندي، عندي مالة نهاية من الحلول فبنقول في هذه
+
+254
+00:26:36,720 --> 00:26:42,060
+الحلقة the lines coincide الخطوط هذه بتنطبق أو ال
+
+255
+00:26:42,060 --> 00:26:46,580
+planes تتقاطع في خط أو تنطبق مع بعضها في هذه
+
+256
+00:26:46,580 --> 00:26:52,090
+الحلقةيبقى اي system يبقى نتقله احد ثلاثة احتمالات
+
+257
+00:26:52,090 --> 00:26:57,790
+يا اما مافيش حل يا اما حل واحد unique solution
+
+258
+00:26:57,790 --> 00:27:03,010
+مافيش غيره exactly one solution بالضبط يا اما عدد
+
+259
+00:27:03,010 --> 00:27:08,980
+لا نهائي من الحلول وبالتالي مافيش system له حلينأو
+
+260
+00:27:08,980 --> 00:27:12,620
+الـ system له ثلاث حلول أو الـ system له أربعة
+
+261
+00:27:12,620 --> 00:27:16,960
+حلول، لا يمكن أن يكون هناك نتيجة أو لا يوجد نتيجة
+
+262
+00:27:16,960 --> 00:27:18,360
+أو هناك نتيجة أو هناك نتيجة أو هناك نتيجة أو هناك
+
+263
+00:27:18,360 --> 00:27:23,650
+نتيجة أو هناك نتيجةكتبنا لك هذه الملاحظة كتبنا لك
+
+264
+00:27:23,650 --> 00:27:26,650
+هذه الملاحظة في الملاحظة التالية في الملاحظة
+
+265
+00:27:26,650 --> 00:27:27,290
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+266
+00:27:27,290 --> 00:27:28,010
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+267
+00:27:28,010 --> 00:27:33,110
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+268
+00:27:33,110 --> 00:27:36,230
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+269
+00:27:36,230 --> 00:27:36,810
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+270
+00:27:36,810 --> 00:27:40,090
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+271
+00:27:40,090 --> 00:27:40,790
+التالية في الملاحظة التالية في الملاحظة التالية في
+
+272
+00:27:40,790 --> 00:27:47,350
+الملاحظة التالية في الملاحظة التالية في الملاحظة
+
+273
+00:27:47,350 --> 00:27:52,010
+التالية في المفي عندي الأن أربع تعريفات ضروري أن
+
+274
+00:27:52,010 --> 00:27:57,350
+نكون ملمين بها و بتيجي أحيانا منها في الخيارات
+
+275
+00:27:57,350 --> 00:28:02,470
+المتعددة في الامتحانات يبقى صح صح كويسthe above
+
+276
+00:28:02,470 --> 00:28:07,290
+system star is called consistent يعني consistent
+
+277
+00:28:07,290 --> 00:28:15,350
+متطابق تمام if it has او متين يعني بالعربي if it
+
+278
+00:28:15,350 --> 00:28:19,390
+has one solution or infinite number of solutions
+
+279
+00:28:19,390 --> 00:28:24,990
+يعني ال system اللي بلاجئله حل وحيد او عدد لانهائي
+
+280
+00:28:24,990 --> 00:28:32,070
+من الحلول بسميه consistent طب وإذا مالوش حلولولا
+
+281
+00:28:32,070 --> 00:28:38,550
+حل بسمي inconsistent يعني نفيها تمام فبتجيب وقلت
+
+282
+00:28:38,550 --> 00:28:41,250
+لني that the above system is called inconsistent
+
+283
+00:28:41,250 --> 00:28:46,150
+if it has no solution مافيش ولا حل بسميه
+
+284
+00:28:46,150 --> 00:28:54,720
+inconsistent زي ايه ايش مقولالعدد الراشونال نمبر و
+
+285
+00:28:54,720 --> 00:29:00,600
+بقول irrational يعني ليس عددا نسبي راشونال نسبي
+
+286
+00:29:00,600 --> 00:29:05,240
+راشونال راشونال راشونال راشونال راشونال راشونال
+
+287
+00:29:05,240 --> 00:29:10,400
+راشونال راشونال راشونال
+
+288
+00:29:11,170 --> 00:29:17,030
+الأمر الثالث مجموعة الحلول هذه يابا ساميها ال
+
+289
+00:29:17,030 --> 00:29:20,990
+general solution الحل العام لهذا ال system يابا
+
+290
+00:29:20,990 --> 00:29:25,590
+ساميها ال complete solution الحل الكامل لهذا
+
+291
+00:29:25,590 --> 00:29:29,810
+النظام يابا ساميها ال general أو ال complete
+
+292
+00:29:29,810 --> 00:29:37,410
+solution لهذا ال systemفي كمان ضايلة عندنا ممكن
+
+293
+00:29:37,410 --> 00:29:42,630
+توصيه وهذا very important هنستخدمه في حل ال system
+
+294
+00:29:42,630 --> 00:29:47,510
+ايش هو هذا بيقول لي two systems of equations
+
+295
+00:29:47,510 --> 00:29:55,110
+مجموعة من systemو System هذا فيه equations وهذا
+
+296
+00:29:55,110 --> 00:29:59,090
+فيه equations لكن بيختلفوا عن بعض المعادلتين غير
+
+297
+00:29:59,090 --> 00:30:03,370
+المعادلتين لكن نفسي المجاهيل و نفسي المعادلتين
+
+298
+00:30:03,370 --> 00:30:07,950
+معادلتين تلاتة تلاتة عشرة عشرة و هكذا بيقول لي two
+
+299
+00:30:07,950 --> 00:30:12,630
+systems of equations are said to be equivalentبقول
+
+300
+00:30:12,630 --> 00:30:17,910
+هدول اتنين متكافئين if they have exactly the same
+
+301
+00:30:17,910 --> 00:30:22,590
+solutions اذا كان اللهم نفس الحل يعني انا عنده
+
+302
+00:30:22,590 --> 00:30:26,510
+system و عنده system اذا جيت على ال system الأول
+
+303
+00:30:26,510 --> 00:30:30,510
+اللي جيته طلعت الحل تبعه و جيت على ال system
+
+304
+00:30:30,510 --> 00:30:34,690
+التاني و طلعت الحل تبعه اللي جيت اتنين زي بعض بقول
+
+305
+00:30:34,690 --> 00:30:40,310
+two systems are equivalentاتنين متكافئين إذا هذا
+
+306
+00:30:40,310 --> 00:30:43,670
+عنده عدد لانهائي من الحلول و هذا عنده عدد لانهائي
+
+307
+00:30:43,670 --> 00:30:44,030
+من الحلول و هذا عنده عدد لانهائي من الحلول و هذا
+
+308
+00:30:44,030 --> 00:30:45,190
+عنده عدد لانهائي من الحلول و هذا عنده عدد لانهائي
+
+309
+00:30:45,190 --> 00:30:46,470
+من الحلول و هذا عنده عدد لانهائي من الحلول و هذا
+
+310
+00:30:46,470 --> 00:30:47,050
+عنده عدد لانهائي من الحلول و هذا عنده عدد لانهائي
+
+311
+00:30:47,050 --> 00:30:49,090
+من الحلول و هذا عنده عدد لانهائي من الحلول و هذا
+
+312
+00:30:49,090 --> 00:30:55,150
+عنده عدد لانهائي من الحلول و هذا عنده عدد لانهائي
+
+313
+00:30:55,150 --> 00:30:57,830
+من الحلول و هذا عنده عدد لانهائي من الحلول و هذا
+
+314
+00:30:57,830 --> 00:31:03,150
+عنده عدد لانهائي من الحلول و هذا عنده عددالحلول
+
+315
+00:31:03,150 --> 00:31:06,330
+متساوية في ال two systems بقول هدول are equivalent
+
+316
+00:31:06,330 --> 00:31:10,650
+ماشي شافة فرق شاسف ما بين ايه؟ ما بين الاتنين
+
+317
+00:31:10,650 --> 00:31:14,530
+المعلومات اللي اعطاناها هذه بدنا نبدأ ناخد أمثلة
+
+318
+00:31:14,530 --> 00:31:22,970
+تطبيقية عليها مرة جاية؟ قصد ايه بعد الظهر؟ طيب
+
+319
+00:31:22,970 --> 00:31:25,150
+يبقى وصلنا إلى الأمثلة
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0d2e516d4d65224c2c90f32603924a51a7ab2c17
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_postprocess.srt
@@ -0,0 +1,2172 @@
+1
+00:00:20,670 --> 00:00:27,070
+بسم الله الرحمن الرحيم يسعدنا أن نرحب بيكون في
+
+2
+00:00:27,070 --> 00:00:32,550
+بداية هذا الفصل الدراسي الجديد وهو الفصل الثاني من
+
+3
+00:00:32,550 --> 00:00:40,040
+العام 2012-2013هذه المادة اللي هي مادة معدلات وجبر
+
+4
+00:00:40,040 --> 00:00:47,920
+خط هي عبارة عن أربع ساعات يعني تسجل في كشف درجاتك
+
+5
+00:00:47,920 --> 00:00:52,140
+أربع ساعات طبعا اللي بتجيب فوق التسعين بتضمن أن
+
+6
+00:00:52,140 --> 00:00:56,720
+المعدل هيظل عالي دائما و أبدا لأن هذه أربع ساعات
+
+7
+00:00:56,720 --> 00:01:01,840
+مش ساعة ولا ساعتين فلما تجيب فيها فوق التسعين بتظل
+
+8
+00:01:01,840 --> 00:01:05,470
+المعدلها عالي دائما أو أبداوانتوا غالبكوا بنات
+
+9
+00:01:05,470 --> 00:01:10,150
+كلية الهندسة يبقى حرصى على ان تكونى في هذا المستوى
+
+10
+00:01:10,150 --> 00:01:13,590
+لإن مستواكوا في الثانوية العامة كان مستوى عالى
+
+11
+00:01:13,590 --> 00:01:16,530
+والشغل في الجامعة بيختلف عن الشغل في المرحلة
+
+12
+00:01:16,530 --> 00:01:21,130
+الثانوية وانتوا درستوا قبل هيك سنة عندنا وهذه هي
+
+13
+00:01:21,130 --> 00:01:25,230
+السنة الثانية او هذا هو الفصلة الرابع اللى كنا في
+
+14
+00:01:25,230 --> 00:01:30,600
+هذه الجامعة اللى لم يكن لبعض كنا اكثرمن ذلك لكن
+
+15
+00:01:30,600 --> 00:01:35,300
+هذه اللي هي الحالة المثالية لذلك أحرصنا على
+
+16
+00:01:35,300 --> 00:01:41,280
+الدراسة بشكل سليم أنا أحب أن أذكر من باب قول الله
+
+17
+00:01:41,280 --> 00:01:47,080
+تعالى واذكر فإن الذكرة تنفع المؤمنين أحب أن أذكر
+
+18
+00:01:47,080 --> 00:01:54,740
+بكيفية الدراسة أولا قبل أن نبدأ في الموضوعال ..
+
+19
+00:01:54,740 --> 00:01:59,500
+بالنسبة للدراسة حتى تدرسي دراسة سليمة و تجيبي
+
+20
+00:01:59,500 --> 00:02:04,980
+علامات أنا بشرح المحاضرة تفصيليا على اللوعبوأفتح
+
+21
+00:02:04,980 --> 00:02:09,940
+المجال للأسئلة لمن أرادت أن تسأل بل بطلب منكوا
+
+22
+00:02:09,940 --> 00:02:13,980
+أحيانا إنكوا تسألوا بقول من عندها سؤال من بتحب
+
+23
+00:02:13,980 --> 00:02:19,240
+تسأل ليه سؤال حتى نطلع وقد استفدنا أو فهمنا ما قيل
+
+24
+00:02:19,240 --> 00:02:24,140
+أمامنا على الصبورة هنا شرحنا الموضوع شرحا كاملا
+
+25
+00:02:24,140 --> 00:02:31,990
+مطلوب مننا ندرس المحاضرة فور الذهاب إلى البيتإن
+
+26
+00:02:31,990 --> 00:02:36,530
+أجلنا لبكرة بصير بدها وقت ضعف وإن أجلنا لآخر
+
+27
+00:02:36,530 --> 00:02:42,830
+الأسبوع بدنا وقت أضعاف الوقت الذي أخذناه أو الكلام
+
+28
+00:02:42,830 --> 00:02:46,410
+اللي بنذاكره اليوم يعني الأربع ساعات ممكن تروح في
+
+29
+00:02:46,410 --> 00:02:49,730
+البيت تجريها في نص ساعة أو في ساعة لربع و تكون
+
+30
+00:02:49,730 --> 00:02:53,970
+قرأتي المحاضرة كاملة و استوعبتيها لكن إذا بتخليها
+
+31
+00:02:53,970 --> 00:02:58,230
+لنهاية الأسبوع من نص ساعة أو ساعة لربع لعلها تحتاج
+
+32
+00:02:58,230 --> 00:03:04,150
+إلى أربع ساعاتيبقى لا تؤجلي عمل اليوم إلى الغد لإن
+
+33
+00:03:04,150 --> 00:03:08,910
+هذه الساعات مش تراكمة و أنا في الأسبوع أعطيكي أربع
+
+34
+00:03:08,910 --> 00:03:12,070
+ساعات في المادة فما بالك بغيرها لما يعطيكي أبو
+
+35
+00:03:12,070 --> 00:03:16,970
+ساعة و أبو ساعتين و أبو ثلاث ساعات و ربما يكون عند
+
+36
+00:03:16,970 --> 00:03:22,070
+بعضكوا أربع ساعات أخرى يبقى يتراكم الشيء علشان و
+
+37
+00:03:22,070 --> 00:03:27,290
+إذا تراكم بصير من الصعب الدراسة يبقى يجب أن ندرس
+
+38
+00:03:27,290 --> 00:03:33,060
+أولا بأولالنقطة الثانية الدراسة ليست ان نقرأ
+
+39
+00:03:33,060 --> 00:03:36,560
+المحاضرة و نقرأ الأمثلة و نقول احنا تمام لا مش
+
+40
+00:03:36,560 --> 00:03:42,000
+تمام يعني اذا اكتفيت بالمحاضرة و الأمثلة ربما
+
+41
+00:03:42,000 --> 00:03:46,940
+تنجحي ربما لا استطيع التأكيد لكن مشان تنجح و تجيب
+
+42
+00:03:46,940 --> 00:03:53,150
+درجات لازم تمسك القلم و تحلي بإيدك انتو .. و بعد
+
+43
+00:03:53,150 --> 00:03:56,470
+هيكده هتصعب عليك بعض الأسئلة ان تصعب عليك بعض
+
+44
+00:03:56,470 --> 00:04:00,550
+الأسئلة تعالوا نقشونا بنجاوبك طبعا عندي ساعات
+
+45
+00:04:00,550 --> 00:04:06,950
+مكتبية هقولك و هو ضرورةاللي هو دراسة المحاضرة فورا
+
+46
+00:04:06,950 --> 00:04:11,610
+العودة إلى البيت ثم حل الأسئلة و اللي بيصعب عليك
+
+47
+00:04:11,610 --> 00:04:16,270
+إحنا موجودين تعالى بنناقشك فيه و بتناقشنا فيه حتى
+
+48
+00:04:16,270 --> 00:04:20,810
+إذا نقطة ما فهمتيهاش برضه تعالى اسألي فيها يعني
+
+49
+00:04:20,810 --> 00:04:24,450
+إذا ماقدرتيش تساوع بيها هنا أو في البيت تعالى
+
+50
+00:04:24,450 --> 00:04:28,330
+اسألينا فيها إحنا بنجاوبك ان شاء الله و تعالى و
+
+51
+00:04:28,330 --> 00:04:32,570
+لنبخل عليكي بأي معلومة ان شاء الله و تباركه و
+
+52
+00:04:32,570 --> 00:04:39,360
+تعالىبعد هيك وصلنا للامتحان فلما نوصل للامتحان
+
+53
+00:04:39,360 --> 00:04:45,880
+علينا أن نأتي بنماذج من الامتحانات السابقة نطلع
+
+54
+00:04:45,880 --> 00:04:50,880
+عليها بس مشان نعرف كيف نماذج الامتحانات او كيف
+
+55
+00:04:50,880 --> 00:04:55,020
+يوضع نظام الامتحان وبالتالي ما نصير في صورة
+
+56
+00:04:55,020 --> 00:04:59,900
+الامتحان قبل ايه قبل أن ندخل الامتحان مش نتفاجأ
+
+57
+00:04:59,900 --> 00:05:04,540
+بشكله يوم الامتحانالذين يكونوا متدربين وماخدين
+
+58
+00:05:04,540 --> 00:05:08,380
+احتياطاتنا الله سبحانه وتعالى بيعيدنا على النجاح
+
+59
+00:05:08,380 --> 00:05:14,880
+لأن الله تبارك وتعالى لا يضيع أجر من أحسن عمله
+
+60
+00:05:14,880 --> 00:05:19,560
+اللي بيحسن العمل الله سبحانه وتعالى بيعطيه الأجر
+
+61
+00:05:19,560 --> 00:05:26,000
+ويرزقه النجاح بس بدك تعتمدي على الله أولا وأخيرا
+
+62
+00:05:26,000 --> 00:05:31,050
+مش على قرايتكالاجراية ضرورية وهي من جانب الأخذ
+
+63
+00:05:31,050 --> 00:05:35,630
+بالأسباب ثم الاعتماد على الله يعني أنا بدلت كل
+
+64
+00:05:35,630 --> 00:05:41,310
+جهدي وكل طاقتي في أني أستوعب أو أفهم أو أحل
+
+65
+00:05:41,310 --> 00:05:46,150
+المسائل وبعد ذلك برفع يدي إلى الله سبحانه وتعالى
+
+66
+00:05:46,150 --> 00:05:51,010
+وخاصة في دوري كل صلاة وأطلب من الله النجاح والله
+
+67
+00:05:51,010 --> 00:05:56,260
+سبحانه وتعالى لن يخيب دعائكلقوله تبارك ليس في مادة
+
+68
+00:05:56,260 --> 00:06:01,680
+معدلة تفاضلية وجبر خط وإنما في كل المساقات الأخرى
+
+69
+00:06:01,680 --> 00:06:07,120
+لأن هذا هو الأساس الصحيح للدراسة من خلال خبرتنا
+
+70
+00:06:07,120 --> 00:06:13,170
+السابقة على مدى أكثر من عشرينعاما في الجامعة
+
+71
+00:06:13,170 --> 00:06:18,010
+الإسلامية وعلى مدى أكثر من ثلاثين عاما في حقل
+
+72
+00:06:18,010 --> 00:06:23,370
+التدريسة بنعطيكي خبرتنا بسهولة بضيف شغلة بس لو قبل
+
+73
+00:06:23,370 --> 00:06:29,650
+تيجي حضرت الموضوع قرأتيه مثل قراءة الجريدةالواحد
+
+74
+00:06:29,650 --> 00:06:32,610
+ماجرال جنرال بيطلع معاه بس العناوين الرئيسية بس
+
+75
+00:06:32,610 --> 00:06:36,510
+التفاصيلات محفظهاش لكن العناوين الرئيسية بتضلها
+
+76
+00:06:36,510 --> 00:06:39,790
+راسخة .. يوم صار كذا كذا و كان الرد عليه كذا كذا
+
+77
+00:06:39,790 --> 00:06:44,970
+يبقى احنا بيناياكي بس مشان تكوني .. يعني يكون عندي
+
+78
+00:06:44,970 --> 00:06:48,350
+خلفية شو احنا بنحكي فانت لو جيتي جابة اللي تيجي
+
+79
+00:06:48,350 --> 00:06:53,780
+على المحاضرة و كنت يعني قرأتيهاقراءة مرور الكرام
+
+80
+00:06:53,780 --> 00:06:57,820
+قراءة الجريدة بيكون شيء جاهز بديش هيك تجيني حافظ
+
+81
+00:06:57,820 --> 00:07:02,320
+ولا حاجة بديك بس تعرف شو الموضوع اللي بناها نتحدث
+
+82
+00:07:02,320 --> 00:07:09,500
+فيه المتابعة لها دور أساسي في تواصل المعلومات
+
+83
+00:07:09,500 --> 00:07:14,780
+والبناء زي ما انت شايفها من خلال اسم المساق معادلة
+
+84
+00:07:14,780 --> 00:07:20,520
+تفاضلية وجبرخاطي يبقى النص المقرر معادلة تفاضلية
+
+85
+00:07:20,520 --> 00:07:28,700
+والنص في الآخر جبر خاطي هناخد six chapters تلاتة
+
+86
+00:07:28,700 --> 00:07:34,340
+معادلة تفاضلية وتلاتة جبر خاطي سنبدأ أول شي ب
+
+87
+00:07:34,340 --> 00:07:38,220
+chapter واحد معادلة تفاضلية وهي المعادلة التفاضلية
+
+88
+00:07:38,390 --> 00:07:44,150
+من الرتبة الأولى بأنواعها المختلفة ثم بعد ذلك إلى
+
+89
+00:07:44,150 --> 00:07:49,350
+ثلاثة شباتر جبر خطي بصير أربعة وبعد ذلك بنرجع إلى
+
+90
+00:07:49,350 --> 00:07:54,610
+شبترين معدلة تفاضلية بصير ستة وهذا هو المقرر في
+
+91
+00:07:54,610 --> 00:08:02,810
+هذا المسابقنأتي الآن لاسم المساق اسم الكتاب المؤلف
+
+92
+00:08:02,810 --> 00:08:07,750
+المساقات اللتي سندرسها في هذا الفصل ان شاء الله
+
+93
+00:08:07,750 --> 00:08:11,130
+تعالى الكتاب اسمه elementary differential
+
+94
+00:08:11,130 --> 00:08:17,390
+equations with linear algebra يبقى اسم الكتاب هو
+
+95
+00:08:17,390 --> 00:08:18,250
+elementary
+
+96
+00:08:27,420 --> 00:08:36,620
+Elementary Differential Equations
+
+97
+00:08:36,620 --> 00:08:42,740
+كلمة equations باختصرها إلى الأربع تعرف اللي عندنا
+
+98
+00:08:42,740 --> 00:08:48,380
+يبقى elementary differential equations with linear
+
+99
+00:08:48,380 --> 00:08:49,040
+algebra
+
+100
+00:08:57,860 --> 00:09:05,440
+اسم المؤلف البرت البرت
+
+101
+00:09:05,440 --> 00:09:07,140
+ال رامانستان
+
+102
+00:09:27,120 --> 00:09:34,760
+الان جايكي يبقى اسم الكتاب elementary differential
+
+103
+00:09:34,760 --> 00:09:40,200
+equations with linear algebra المؤلف اسمه البرت
+
+104
+00:09:40,200 --> 00:09:45,260
+رابانستين الطابعة الرابعة يبقى باجي بقول هنا
+
+105
+00:09:45,260 --> 00:09:51,880
+fourth edition يبقى
+
+106
+00:09:51,880 --> 00:09:58,510
+الطابعة الرابعةالكتاب موجود في مكتبة الطالب وهي
+
+107
+00:09:58,510 --> 00:10:03,450
+الشكل تبعه طبعا أنا مجلده hard cover لكن ماهواش
+
+108
+00:10:03,450 --> 00:10:07,730
+hard cover لأن hard cover بكلف ككتر فانت هي الكتاب
+
+109
+00:10:07,730 --> 00:10:11,850
+هي الجلدة الأساسية لبرا مش هالكل واحدة تشوفها بعد
+
+110
+00:10:11,850 --> 00:10:15,970
+المحاضرة ممكنك أنت تتوجهي إلى مكتبة الطالب وتشتري
+
+111
+00:10:15,970 --> 00:10:21,430
+هذا الكتاب لكن إن كانهناك أحد أقاربك أو واحدة من
+
+112
+00:10:21,430 --> 00:10:25,830
+قريباتك كانت بتدرس المادة العام الماضي فالكتاب هو
+
+113
+00:10:25,830 --> 00:10:29,970
+هو لم يتغير لا العام الماضي ولا العام اللي جابله
+
+114
+00:10:29,970 --> 00:10:32,890
+يبقى نفس الكتاب بس اللي جابله كانت الطابعة اللي
+
+115
+00:10:32,890 --> 00:10:36,510
+جابله لكن الطابعة الرابعة إن سنتين بندرس نفس
+
+116
+00:10:36,510 --> 00:10:40,290
+الطابعة الرابعة يبقى هاي الشكل العام طبعا أشكال
+
+117
+00:10:40,290 --> 00:10:44,590
+هندسية فرجار ومحايا وما بعرف إيه على الجلد هايم
+
+118
+00:10:44,590 --> 00:10:48,880
+تمام؟موجود في مكتبة طالب بعد المحاضرة بإمكانك
+
+119
+00:10:48,880 --> 00:10:53,260
+تروحي تشتري او ما هي لذلك يبقى هذا بالنسبة لمين؟
+
+120
+00:10:53,260 --> 00:10:58,620
+بالنسبة للكتاب نيجي ندخل الآن في صميم الموضوعات
+
+121
+00:10:58,620 --> 00:11:03,880
+الخاصة بهذا الكتابيبقى بدنا نيجي لأول chapter اللي
+
+122
+00:11:03,880 --> 00:11:06,940
+هو introduction to a differential equation يعني
+
+123
+00:11:06,940 --> 00:11:13,180
+مقدمة في المعادلات التفاضلية يبقى بعد ذلك بدنا
+
+124
+00:11:13,180 --> 00:11:18,420
+نيجي لأول chapter اللي هو chapter one بتكلم عن
+
+125
+00:11:18,420 --> 00:11:23,560
+introduction مقدمة
+
+126
+00:11:23,560 --> 00:11:28,880
+to differential equations
+
+127
+00:11:31,050 --> 00:11:36,230
+يبقى مقدمة في المعادلات التفاضلية حة نعطي صورة
+
+128
+00:11:36,230 --> 00:11:40,850
+عامة للمعادلات التفاضلية ونبدأ بأول نوع من هذه
+
+129
+00:11:40,850 --> 00:11:45,090
+المعادلات اللي هي المعادلات التفاضلية من الرتبة
+
+130
+00:11:45,090 --> 00:11:50,840
+الأولىfirst order differential equation من هذه
+
+131
+00:11:50,840 --> 00:11:55,580
+المعادلة او تحت الرتبة الأولى هناخد عدة معادلات
+
+132
+00:11:55,580 --> 00:12:00,200
+اول معادلة من هذه المعادلات اللى هى الـ separable
+
+133
+00:12:00,200 --> 00:12:08,330
+equationseparable equations يبقى المعادلات التي
+
+134
+00:12:08,330 --> 00:12:15,290
+يمكن فيها فصل المتغيرات ايش فصل المتغيرات؟ يعني
+
+135
+00:12:15,290 --> 00:12:20,690
+بنحاول نخل ال X في ناحية و ال Y في ناحية أخرى
+
+136
+00:12:20,690 --> 00:12:25,930
+وبالتالي هذا بنسميها فصل المتغيرات ثم نذهب إلى
+
+137
+00:12:25,930 --> 00:12:32,890
+التكاملإذا موضوع المعادلات التفضلية يعتمد فقط على
+
+138
+00:12:32,890 --> 00:12:38,910
+ما درسناه في calculus a و b في موضوع التكامل مش
+
+139
+00:12:38,910 --> 00:12:43,310
+تكاملات صعبة و معقدة لها تكاملات بسيطة و ما إلى
+
+140
+00:12:43,310 --> 00:12:47,670
+ذلك يعني اللي نجحت بجدارة في calculus a و b بتروح
+
+141
+00:12:47,670 --> 00:12:53,030
+تكامل a بسهولة يبقى الأساس تبع المادة هو موضوع
+
+142
+00:12:53,030 --> 00:12:57,000
+التكامللأن ما أقول differential equation معادلات
+
+143
+00:12:57,000 --> 00:13:01,300
+تفاضلية يعني فيها أن معادلة ظهر فيها المشتقة
+
+144
+00:13:01,300 --> 00:13:04,480
+الأولى أو المشتقة الثانية إذا اللي مابده رجعها إلى
+
+145
+00:13:04,480 --> 00:13:09,460
+أصلها معناته بده كامل مرة أو مرتين أو نحو ذلك إذا
+
+146
+00:13:09,460 --> 00:13:15,700
+بالزمن موضوع التكامل مش على هذه بس في كل شبتر
+
+147
+00:13:15,700 --> 00:13:19,860
+ساعات المعادلة التفاضلية بالزمن مين؟ بالزمن موضوع
+
+148
+00:13:19,860 --> 00:13:24,550
+التكاملبعد هيك بدنا نيجي لل homogenous equations
+
+149
+00:13:31,250 --> 00:13:37,210
+يبقى الـ homogeneous equations المعادلات المتجانسة
+
+150
+00:13:37,210 --> 00:13:42,670
+فيها نصيغة من خلالها بنقدر نحكم على المعادلة هل هي
+
+151
+00:13:42,670 --> 00:13:48,290
+separable و هل هي homogeneous طبعا سنقول هذا الشرط
+
+152
+00:13:48,290 --> 00:13:52,550
+في حينه ان شاء الله بعد ال homogeneous بدنا نيجي
+
+153
+00:13:52,550 --> 00:13:57,990
+لل exactical هذه exact equation طبعا كمان فيها شرط
+
+154
+00:13:58,210 --> 00:14:01,890
+الشرط هذا لو تحقق بقول ان المعادلة هذه ما لها
+
+155
+00:14:01,890 --> 00:14:07,010
+exact equation بعد ال exact equation بتداجي لمين؟
+
+156
+00:14:07,010 --> 00:14:15,270
+لل linear equations المعادلات الخطية يبقى إليها
+
+157
+00:14:15,270 --> 00:14:19,750
+شكل محدد بالشكل المحدد هذا لو شفتوا مجرد ما شوفوا
+
+158
+00:14:19,750 --> 00:14:23,270
+بقول هذه إيه معادلة خطية وبالتالي طريقة حل
+
+159
+00:14:23,270 --> 00:14:29,340
+المعادلة بالطريقة الفولانيةبعد هيك بدنا نيجي لـ
+
+160
+00:14:29,340 --> 00:14:37,840
+two types of
+
+161
+00:14:37,840 --> 00:14:45,720
+second order differential
+
+162
+00:14:45,720 --> 00:14:48,400
+equations
+
+163
+00:14:52,970 --> 00:14:58,670
+هذا بنات إجمال ما سندرسه في الشابتر الأول يبقى
+
+164
+00:14:58,670 --> 00:15:02,770
+الشابتر الأول عبارة عن مجموعة من ال sections طبعا
+
+165
+00:15:02,770 --> 00:15:07,270
+اكتر في الكتاب مش كلهم هندرسهم هندرس فقط اللي احنا
+
+166
+00:15:07,270 --> 00:15:11,770
+كاتبينه قدامنا على اللعبكل عنوان هنا يمثل section
+
+167
+00:15:11,770 --> 00:15:15,290
+في الكتاب وفي نهاية ال section فيه مجموعة من
+
+168
+00:15:15,290 --> 00:15:20,110
+الأسئلة هعطيكي أمثلة ان شاء الله من خلال الأسئلة
+
+169
+00:15:20,110 --> 00:15:23,350
+تبعتي التمرين و الأمثلة المحلولة في الكتاب هذه
+
+170
+00:15:23,350 --> 00:15:27,570
+هدية إليك تقريها براحتك من الكتابأنا بعطيكي أمثلة
+
+171
+00:15:27,570 --> 00:15:31,750
+من خلال الأسئلة تبع التمرين وبالتالي قللت عدد
+
+172
+00:15:31,750 --> 00:15:37,230
+الأسئلة المطلوب منك اتحليها وبحاول أغطيلي كل الفكر
+
+173
+00:15:37,230 --> 00:15:43,020
+اللي موجودة بحيث انت ماتلاقيش صعوبة أثناء الحليبقى
+
+174
+00:15:43,020 --> 00:15:47,360
+أول section separable equations المعادلات التي
+
+175
+00:15:47,360 --> 00:15:53,060
+يمكن فيها فصل المتغيرات بمعنى أخل ال X لحالي و ال
+
+176
+00:15:53,060 --> 00:15:56,820
+Y لحالي ثم أقوم بعملية التكامل ال homogeneous
+
+177
+00:15:56,820 --> 00:16:03,340
+equations المعادلات المتجانسة هنعطيها تعريف و نبين
+
+178
+00:16:03,340 --> 00:16:08,920
+كيف هنحل هذا النوع منالمعادلات بعد ذلك ال exact
+
+179
+00:16:08,920 --> 00:16:15,360
+equation المعادلات أتم برضه هيكون لها صيغة و هذه
+
+180
+00:16:15,360 --> 00:16:20,360
+الصيغة لها طريقة للحل ثم بعد ذلك cleaner equations
+
+181
+00:16:20,360 --> 00:16:25,220
+المعادلات الخطية برضه اللي هي شكل معين و عندها
+
+182
+00:16:25,220 --> 00:16:30,950
+صيغة للحلكله هدمنات كله معادلة من الرتبة الأولى
+
+183
+00:16:30,950 --> 00:16:34,530
+شوية عن الرتبة الأولى يعني ماعنديش إلا المعامل
+
+184
+00:16:34,530 --> 00:16:38,630
+التفاضل الأول يعني المشتقة الأولى هي اللي موجودة
+
+185
+00:16:38,630 --> 00:16:43,530
+وين؟ في المعادلة فقط لا غير ماعنديش لا مشتقة تانية
+
+186
+00:16:43,530 --> 00:16:48,030
+ولا تالتة ولا غير بس المشتقة الأولى ومن هنا سمنها
+
+187
+00:16:48,030 --> 00:16:53,280
+first order الرتبة الأولىكل واحدة من المعادلات
+
+188
+00:16:53,280 --> 00:16:57,740
+هدول كلهم هي الرتبة الأولى جانا سيكشن لحاله قال لي
+
+189
+00:16:57,740 --> 00:17:02,820
+two types نوعين من ال second order من الرتبة
+
+190
+00:17:02,820 --> 00:17:06,820
+التانية of differential equation هدول النوعين من
+
+191
+00:17:06,820 --> 00:17:12,180
+حد ما شوفهم بقول اه النوع الأول قد يكون المتغير
+
+192
+00:17:12,180 --> 00:17:17,910
+التابع غير ظاهر في المعادلةيعني Y غير ظاهرة في
+
+193
+00:17:17,910 --> 00:17:23,490
+المعادلة قد يكون النوع الثاني T missing يعني
+
+194
+00:17:23,490 --> 00:17:29,230
+المتغير المستقل T أو X مش ظاهر في المعادلة يبقى
+
+195
+00:17:29,230 --> 00:17:32,470
+هدول النوع الجدد المعادلة ممكن تكون من الرتبة
+
+196
+00:17:32,470 --> 00:17:36,990
+الثانية أو حاصل ضرب two derivatives أو ما إلى ذلك
+
+197
+00:17:36,990 --> 00:17:42,360
+هنشوف كيف نحل المعادلة هذا عن طريق تنزيل الرتبةمن
+
+198
+00:17:42,360 --> 00:17:46,300
+الرتبة الثانية إلى الرتبة الأولى ثم نقوم بعد ذلك
+
+199
+00:17:46,300 --> 00:17:50,880
+بعملية الحل وبالتالي بصير اه ماهياش مشكلة ومن هنا
+
+200
+00:17:50,880 --> 00:17:55,380
+ألحق بهذا الشبطر لأنه بنزل الرتبة من الرتبة
+
+201
+00:17:55,380 --> 00:17:58,760
+الثانية إلى الرتبة الأولى وبالتالي بصير كانها
+
+202
+00:17:58,760 --> 00:18:03,540
+first order differential equation هذا كل ما يتعلق
+
+203
+00:18:03,540 --> 00:18:07,760
+بالشبطر الأول اللي هو ال first order differential
+
+204
+00:18:07,760 --> 00:18:13,120
+equationبنجي الآن نخش في ال chapter الثاني وهو
+
+205
+00:18:13,120 --> 00:18:18,580
+بداية الجبر الخطي linear algebra يبقى بنجي لل
+
+206
+00:18:18,580 --> 00:18:23,300
+chapter التاني ال chapter التاني موضوعين أساسيين
+
+207
+00:18:23,300 --> 00:18:31,720
+matrices and determinants المصفوفات والمحددات يبقى
+
+208
+00:18:31,720 --> 00:18:36,820
+matrices and
+
+209
+00:18:39,250 --> 00:18:46,070
+data منين انت؟
+
+210
+00:18:46,070 --> 00:18:49,850
+يبقى
+
+211
+00:18:49,850 --> 00:18:58,400
+المصفوفات والمحددات طبعاالمصففات والمحددات لن يزيد
+
+212
+00:18:58,400 --> 00:19:02,360
+عما درستي في الثانوية العامة مش في الثانوية أخدت
+
+213
+00:19:02,360 --> 00:19:07,940
+المصففات والمحددات أو بقى تسموه الجبر الإضافي غير
+
+214
+00:19:07,940 --> 00:19:10,720
+الجبر العادي كان معاكوا الجبر الإضافي أو الجبر
+
+215
+00:19:10,720 --> 00:19:14,960
+القاطي في الثانوية العامة ولا في تانية ثانوية؟ في
+
+216
+00:19:14,960 --> 00:19:19,570
+تانية؟ اه يعني درست فيها مرتينعلى أي حال في
+
+217
+00:19:19,570 --> 00:19:23,410
+التانية ولا في التالتة بتفرقش عنها المهم أنه سبق
+
+218
+00:19:23,410 --> 00:19:28,150
+الدراسة التانية يبقى احنا بنذكرها من جديد وكأنك لم
+
+219
+00:19:28,150 --> 00:19:33,830
+تدرسيها من قبل طب السؤال هو شو بدنا ندرس في موضوع
+
+220
+00:19:33,830 --> 00:19:40,550
+المصفوفات يبقى هذا هو الشابتر الثاني زي ما كان هذا
+
+221
+00:19:40,550 --> 00:19:45,110
+هو الشابتر الأول يبقى أول موضوع سناخده في هذا
+
+222
+00:19:45,110 --> 00:19:57,360
+الشابتر هو systemsystems of linear equations
+
+223
+00:19:57,360 --> 00:20:00,460
+انظمة
+
+224
+00:20:00,460 --> 00:20:05,640
+المعادلات الخطية ايش يعني انظمة المعادلة الخطية
+
+225
+00:20:05,640 --> 00:20:11,960
+مثلا قد تكون المعادلة فيها مجهولين وقد يكون بثلاثة
+
+226
+00:20:11,960 --> 00:20:17,670
+مجاهيلوقد يكون باربعة مجهيل او نحو ذلك زي ايش مثلا
+
+227
+00:20:17,670 --> 00:20:26,650
+زي ماجي اقولك المعادلة هذه مثلا a1x زائد a2y زائد
+
+228
+00:20:26,650 --> 00:20:38,610
+a3z يساوي مثلا ال oneA2X أو B1X
+
+229
+00:20:38,610 --> 00:20:51,650
+زائد B2Y زائد B3Z بده يساوي L2 مثلا C1X زائد C2Y
+
+230
+00:20:51,650 --> 00:21:00,430
+زائد C3Z يساوي L3هذا النظام المعادلات بسميه system
+
+231
+00:21:00,430 --> 00:21:05,470
+of linear equations يعني معادلة خطية شوية في ال X
+
+232
+00:21:05,470 --> 00:21:10,790
+و Y و Z اللي هو المجاهيل كلها من الدرجات الأولى
+
+233
+00:21:10,790 --> 00:21:15,470
+يبقى هذه بسميها معادلة خطية المعادلات مع بعض كل
+
+234
+00:21:15,470 --> 00:21:19,510
+تلاتة مجموعة بسميها system of linear equations
+
+235
+00:21:19,510 --> 00:21:26,890
+يعني نظام مكون من مجموعة من المعادلات الخطيةالـ A1
+
+236
+00:21:26,890 --> 00:21:30,370
+والـ A2 والـ A3 والـ B1 والـ B2 والـ B3 والـ C وكل
+
+237
+00:21:30,370 --> 00:21:35,230
+هذه أرقام real numbers أرقام عادية لكن الـ X والـ
+
+238
+00:21:35,230 --> 00:21:39,850
+Y والـ Z هذه مجاهيل فلمان بده أحل ال system يعني
+
+239
+00:21:39,850 --> 00:21:44,670
+بده أجيب قيم هذه المجاهيل دير بالك ال system
+
+240
+00:21:44,670 --> 00:21:49,400
+المعادلات ليس بضرورة يكون ثلاث معادلات ويكونأربعة
+
+241
+00:21:49,400 --> 00:21:53,980
+معادلات في ثلاثة مجاهيل ممكن يكون أربعة معادلات في
+
+242
+00:21:53,980 --> 00:21:59,040
+أربعة مجاهيل ممكن يكون معادلتين في مجهولين ممكن
+
+243
+00:21:59,040 --> 00:22:06,480
+يكون معادلتين في مجهولين و هكذا يعني ليس بضرورة
+
+244
+00:22:06,480 --> 00:22:10,240
+تلات مجاهيل ممكن مجهولين ممكن تلاتة ممكن أربعة
+
+245
+00:22:10,240 --> 00:22:15,200
+ممكن خمسة إلى آخرى يبقى هذا كله system في عندي أحد
+
+246
+00:22:15,200 --> 00:22:21,170
+ثلاثة احتمالاتالاحتمال الاول يكون عندي حل واحدة
+
+247
+00:22:21,170 --> 00:22:26,510
+مافيش غيره حل واحد للتلت معادلات ممكن يكون عندي
+
+248
+00:22:26,510 --> 00:22:32,350
+عدد لانهائي من الحلول مش حل و اتنين و تلاتة او
+
+249
+00:22:32,350 --> 00:22:37,530
+اربعة لأ عدد لانهائي من الحلول الأمر الثالث no
+
+250
+00:22:37,530 --> 00:22:42,230
+solution او الحل does not exist يبقى ال system
+
+251
+00:22:42,230 --> 00:22:47,810
+المعادلة قد يكون حلا واحدةوقد يكون عدد ذانهائي من
+
+252
+00:22:47,810 --> 00:22:53,070
+الحلول وقد لا يوجد حل يبقى هي الاحتمالات التلاتة
+
+253
+00:22:53,070 --> 00:22:56,870
+بالنسبة لل system of linear equations وهذا ما
+
+254
+00:22:56,870 --> 00:23:02,310
+سنجدوه عند دراسة هذا النوع من المعادلات الخطية
+
+255
+00:23:02,310 --> 00:23:06,170
+النقطة الثانية اللي سندرسها هي ال homogeneous
+
+256
+00:23:06,170 --> 00:23:13,830
+systems بعد هيك بدنا نيجي لحاجة اسمهاHomo Genius
+
+257
+00:23:13,830 --> 00:23:16,090
+Systems
+
+258
+00:23:18,410 --> 00:23:21,650
+إيش يعني homogeneous system؟ طب ماهي homogeneous
+
+259
+00:23:21,650 --> 00:23:25,210
+system ماهي اللي فوق هذا system of linear
+
+260
+00:23:25,210 --> 00:23:28,470
+equations إيش يعني homogeneous system؟ باجي بقول
+
+261
+00:23:28,470 --> 00:23:34,530
+لو كانت الواحد و الاتنين و التلاتة بيقى صفر
+
+262
+00:23:34,530 --> 00:23:38,890
+المعادلة التلاتة أو التنتين أو الأربع كلها معادلة
+
+263
+00:23:38,890 --> 00:23:45,060
+صفرية بسمي هذا homogeneous systemيبقى لو كانت هذه
+
+264
+00:23:45,060 --> 00:23:51,420
+كلها بأصفار يبقى هذا بسميمين اللي هو ال homogenous
+
+265
+00:23:51,420 --> 00:23:59,220
+system ال system المتجانس تمام؟ يبقى هذه النقطة
+
+266
+00:23:59,220 --> 00:24:03,220
+الثانوية اللي سندرسها و بعد هيك بدنا نيجي لحاجة
+
+267
+00:24:03,220 --> 00:24:08,580
+اسمها matrices and
+
+268
+00:24:08,580 --> 00:24:10,320
+vectors
+
+269
+00:24:14,590 --> 00:24:22,560
+matrices يا بنات بنات مصوفات هي جامعة matrixMatrix
+
+270
+00:24:22,560 --> 00:24:30,080
+هي مصفوفة جمعها matrices بشيل ال X و بحط CES يبقى
+
+271
+00:24:30,080 --> 00:24:35,320
+matrices مصفوفات Matrix عبارة عن مصفوفة vectors
+
+272
+00:24:35,320 --> 00:24:42,420
+يعني متجهات الصف الأول أو الصف الواحد أو العمود
+
+273
+00:24:42,420 --> 00:24:47,420
+الواحد من عناصر مصفوفة بسميه vectorيبقى ال vector
+
+274
+00:24:47,420 --> 00:24:53,660
+هو عبارة عن مصوفة عمودية أو مصوفة أفوقية تمام؟
+
+275
+00:24:53,660 --> 00:24:58,880
+يبقى هذه بسميها .. بسميها اللي هو ال vector مش
+
+276
+00:24:58,880 --> 00:25:02,520
+vector اتنين I زي اتلات جيه زي اربعة كيه سوى مثلا
+
+277
+00:25:02,520 --> 00:25:07,420
+رقم زي ما أخدنا في ال calculus C لأ لأ لأ هذه ال
+
+278
+00:25:07,420 --> 00:25:10,580
+vector بيختلف عن ال vector هناك وليها دراستة
+
+279
+00:25:10,580 --> 00:25:16,970
+متعلقة بموضوع المصوفات والمحددةبعد هيك بدنا نيجي
+
+280
+00:25:16,970 --> 00:25:22,670
+لحاجة اسمها matrix multiplication
+
+281
+00:25:22,670 --> 00:25:28,530
+يبقى
+
+282
+00:25:28,530 --> 00:25:33,410
+عملية ضرب المصوفات طبعا أخدنا ضرب المصوفات في
+
+283
+00:25:33,410 --> 00:25:38,770
+الثانوية بدأينا نذكربه تاني ومشان أضرب مصوفتين في
+
+284
+00:25:38,770 --> 00:25:43,330
+بعض لازم أتحقق عندي شرط يعني مش أي مصوفتين بقوم
+
+285
+00:25:43,330 --> 00:25:48,370
+بضربهم في بعضلأ لابد يكون عدد الأعمدة في المصوفة
+
+286
+00:25:48,370 --> 00:25:54,270
+الأولى يسوى عدد الصفوف في المصوفة الثانية ان تحقق
+
+287
+00:25:54,270 --> 00:25:59,620
+ذلك بيكون بقدرأضرب المسلطين ما هدول في بعض
+
+288
+00:25:59,620 --> 00:26:03,860
+وبالتالي المسلطين ممكن ال system تبع الأولى يختلف
+
+289
+00:26:03,860 --> 00:26:07,620
+عن ال system تبع المصوفة لما أقول system بالنسبة
+
+290
+00:26:07,620 --> 00:26:12,600
+للمصوفة يعني عدد الصفوف في عدد الأعمدة يعني نوعية
+
+291
+00:26:12,600 --> 00:26:17,220
+المصوفة تلاتة صفوف و عمودين عمودين و أربعة صفوف
+
+292
+00:26:17,220 --> 00:26:23,700
+صفين و ثلاثة أعمدة صفين و أربعة أعمدة يبجي هذا هو
+
+293
+00:26:23,700 --> 00:26:29,500
+النظام تبع مينتبع المصوفة أو بيبقى نقول نوعها M في
+
+294
+00:26:29,500 --> 00:26:37,280
+N M رقم للعدد الصفوف N عدد الأعمدة و هكذا يبقى في
+
+295
+00:26:37,280 --> 00:26:41,600
+شرط لازم أتحقق مشان أقدر أضرب المصوفتين هدول في
+
+296
+00:26:41,600 --> 00:26:47,820
+بعض وبعد هيك some special matrices يبقى هنا some
+
+297
+00:26:47,820 --> 00:26:49,720
+special
+
+298
+00:26:52,090 --> 00:26:56,450
+بعض المصوفات الخاصة
+
+299
+00:26:58,850 --> 00:27:01,930
+ماذا عن بعض المصفوفات الخاصة؟ هذه في الثانوية
+
+300
+00:27:01,930 --> 00:27:07,630
+وكنتوا مذكرين بجينا نقول أنواع المصفوفات types of
+
+301
+00:27:07,630 --> 00:27:13,430
+matrices بجينا نقول المصفوفة الصفرية مصفوفة الوحدة
+
+302
+00:27:13,430 --> 00:27:19,170
+المصفوفة القياسية المصفوفة القطرية المصفوفة
+
+303
+00:27:19,170 --> 00:27:25,090
+المثلثة العليا المصفوفة المثلثة السفلة كل هدول
+
+304
+00:27:25,090 --> 00:27:29,000
+اللي بتسمعهم هذه هي أنواع المصفوفاتيبقى نحن لم
+
+305
+00:27:29,000 --> 00:27:33,000
+نأتي بجديد هو الكلام اللي عتيجي بس بنذكره و بدل ما
+
+306
+00:27:33,000 --> 00:27:37,340
+كنت تكتبيه بالعربي بنكتب هناكبالإنقليزي عادية يبقى
+
+307
+00:27:37,340 --> 00:27:43,160
+لا توجد أي صعوبة أثناء الدراسة وخاصة اللي بتابع
+
+308
+00:27:43,160 --> 00:27:47,720
+الأول بأول يبقى للمدور some special matrices بعض
+
+309
+00:27:47,720 --> 00:27:52,740
+المصفوفات الخاصة يعني المصفوفات اللي لها اسم محدد
+
+310
+00:27:52,740 --> 00:27:58,280
+مصفوفة صفرية مصفوفة قطرية مصفوفة قياسية مصفوفة
+
+311
+00:27:58,280 --> 00:28:03,140
+مربعة مصفوفة مستطيلة مصفوفة الوحدة مصفوفة مثلثة
+
+312
+00:28:03,140 --> 00:28:06,970
+عليا مصفوفة مثلثة ..so كله هنذكره و نعطي عليه
+
+313
+00:28:06,970 --> 00:28:12,410
+أمثلة ان شاء الله تعالى بعد ذلك بنجي ل
+
+314
+00:28:12,410 --> 00:28:15,370
+determinants المحددات
+
+315
+00:28:22,890 --> 00:28:28,550
+الفرق بين الإتنين الكتابة متشابهة قريبة من بعض إلى
+
+316
+00:28:28,550 --> 00:28:34,570
+حد بعيد لكن المصوفة لو ضربتيها في رقم أو ضربت
+
+317
+00:28:34,570 --> 00:28:39,970
+مصوفتين في البعض فالنتج هو مصوفة لكن المحدد له
+
+318
+00:28:39,970 --> 00:28:45,440
+قيمة عددية واحدة one real numberيعني المحدد له
+
+319
+00:28:45,440 --> 00:28:50,380
+قيمة حقيقية مافيش غيرها يعني بقدر أفك المحدد و
+
+320
+00:28:50,380 --> 00:28:53,700
+أطلع قد ياش قيمته العددية و من هنا هذا الفرق
+
+321
+00:28:53,700 --> 00:28:58,020
+الأساسي بينه وبين المصوفة المصوفات لها خواص
+
+322
+00:28:58,020 --> 00:29:04,420
+المحددات لها خواص تختلف كذلك عن خواص من المصوفات
+
+323
+00:29:04,700 --> 00:29:09,400
+يبقى المصوّات والمحددات كل واحدة فيهم لها خواص خاص
+
+324
+00:29:09,400 --> 00:29:15,060
+بها تختلف فيها عن الخواص الأخرى وفي الثانوية أخدتم
+
+325
+00:29:15,060 --> 00:29:20,380
+خواص المحددات و هنرجع نعطي خواص المحددات لـ
+
+326
+00:29:20,380 --> 00:29:25,220
+properties of determinants بعد هيك هنجي في
+
+327
+00:29:25,220 --> 00:29:29,300
+المحددات ناخد حاجة اسمها cofactors
+
+328
+00:29:32,500 --> 00:29:39,000
+يعني العوامل المرافقة شو العوامل المرافقة؟ نذكركم
+
+329
+00:29:39,000 --> 00:29:43,820
+لما جينا نفك المحدد مثلا نفكه باستخدام عناصر الصف
+
+330
+00:29:43,820 --> 00:29:47,600
+اللي اول اللي بنمسك هو العنصر نشطه بصفه و عموده
+
+331
+00:29:47,600 --> 00:29:54,320
+المحدد اللي بيظل بسميه المحدد الأصغر المناظر لهذا
+
+332
+00:29:54,320 --> 00:29:58,700
+العنصر يبقى هذا هو ال cofactorاللي هو العامل
+
+333
+00:29:58,700 --> 00:30:03,420
+المرافق لمين للعنصر اللي موجود في المحدد انا بس
+
+334
+00:30:03,420 --> 00:30:07,740
+مجرد تذكير ليس الا لكن عندما نوصله هنعطيه نشتغل
+
+335
+00:30:07,740 --> 00:30:12,800
+شغل تفصيلي و حسابات دقيقة ان شاء الله تبارك وتعالى
+
+336
+00:30:13,890 --> 00:30:20,230
+بعد هيك بدنا نيجي نتناول كرامر رول قاعدة كرامر لحل
+
+337
+00:30:20,230 --> 00:30:25,890
+المعادلات وكذلك طريقة معكوس المصفوفة نستخدمها في
+
+338
+00:30:25,890 --> 00:30:29,710
+حل ال system of linear equations يبقى بدنا نيجي
+
+339
+00:30:29,710 --> 00:30:40,410
+ناخد حاجة اسمها كرامر رول يبقى كرامر كرامر
+
+340
+00:30:40,410 --> 00:30:48,060
+رولقاعدة كرامر لحل المعادلات و بعد هيك بدنا ناخد
+
+341
+00:30:48,060 --> 00:30:59,420
+the inverse of a matrix يبقى معكوس المصوفة
+
+342
+00:30:59,420 --> 00:31:04,860
+واستخدام معكوس المصوفة في حل المعادلات التفاضلية
+
+343
+00:31:05,610 --> 00:31:10,710
+هذا بالنسبة لمين؟ للشبتر الثاني يبقى كل اللي سمعته
+
+344
+00:31:10,710 --> 00:31:16,270
+هو ملخص الشبتر الثاني الشبتر الثاني أكثر من عشر
+
+345
+00:31:16,270 --> 00:31:21,770
+سكاشن يعني طويل شوية مش زي الأول الأولاني الشبتر
+
+346
+00:31:21,770 --> 00:31:27,150
+الأول قصير هذا أطول منه كثيرا بعد هي كده بنجي
+
+347
+00:31:27,150 --> 00:31:33,830
+للشبتر التالت يبقى بدنا نجي لحاجة اسمها vector
+
+348
+00:31:34,910 --> 00:31:43,510
+spaces and linear transformations
+
+349
+00:32:05,280 --> 00:32:11,780
+الفضاءات الاتجاهية والتحويلات الخطية يبقى vector
+
+350
+00:32:11,780 --> 00:32:15,700
+spaces الفضاءات الاتجاهية linear transformations
+
+351
+00:32:15,700 --> 00:32:22,460
+التحويلات الخطية موضوع يام كل واحد مستقل عن الثاني
+
+352
+00:32:22,460 --> 00:32:27,980
+وهذا يعتبر ethical chapter موجود في المقرريعني
+
+353
+00:32:27,980 --> 00:32:33,940
+مليان شوية و بده متابعة أولا بأول هنعطي تعريف ال
+
+354
+00:32:33,940 --> 00:32:38,520
+vector space في هذا ال chapter هنبدأ أول حاجة بال
+
+355
+00:32:38,520 --> 00:32:48,000
+vectorspaces الفضاءات الاتجاهية بعدين ناخد مجموعات
+
+356
+00:32:48,000 --> 00:32:53,120
+جزئية من هذه الفضاءات اسمها ال sub-spaces يبقى
+
+357
+00:32:53,120 --> 00:32:58,340
+بدنا نيجي لحاجة اسمها sub-spaces الفضاءات
+
+358
+00:32:58,340 --> 00:33:02,640
+الاتجاهية يعني وقتش لما أخد مجموعة جزئية من ال
+
+359
+00:33:02,640 --> 00:33:07,520
+vector space بقدر أقول عنهاالـ subspace و ماكنتش
+
+360
+00:33:07,520 --> 00:33:11,200
+بقدر أقول عنها ما هي ال subspace يعني نفترض لو
+
+361
+00:33:11,200 --> 00:33:14,800
+قلنا البنات اللي قعدتها دول كلهم عبارة عن vector
+
+362
+00:33:14,800 --> 00:33:19,020
+space لو أخدت الشجة هذه هل هذه subspace ولا لا
+
+363
+00:33:19,020 --> 00:33:23,960
+الله أعلم يبقى في شروط ان تحققت هذه الشروط بقول
+
+364
+00:33:23,960 --> 00:33:27,870
+هذه subspaceإن اختل أي شرط من هذه الشروط يبقى ما
+
+365
+00:33:27,870 --> 00:33:31,150
+أقدرش أقول عن هذه subspace كل اللي بقدر أقول إنها
+
+366
+00:33:31,150 --> 00:33:36,250
+مجموعة جزئية subset مجموعة جزئية لكنها ليست
+
+367
+00:33:36,250 --> 00:33:47,070
+subspace طيب بعد هيك بنجي لحاجة اسمها linear بنجي
+
+368
+00:33:47,070 --> 00:33:51,450
+لحاجة اسمها linear dependence
+
+369
+00:33:56,360 --> 00:34:01,980
+and linear independence الاستقلال الخاطي والاعتماد
+
+370
+00:34:01,980 --> 00:34:02,980
+الخاطي
+
+371
+00:34:05,350 --> 00:34:11,590
+واجتيش مستقلات عن بعض خطيا او واجتيش معتمدات على
+
+372
+00:34:11,590 --> 00:34:17,810
+بعض خطيا يبقى هذا بالنسبالك كله متعلق بمين؟ متعلق
+
+373
+00:34:17,810 --> 00:34:23,470
+بال vector spaces الأثنين على حد سواء بدنا نيجي
+
+374
+00:34:23,470 --> 00:34:31,790
+لحاجة اسمها ال runnerskin ال
+
+375
+00:34:31,790 --> 00:34:37,130
+runnerskin دي بنت عبارة عن محددdeterminant بس
+
+376
+00:34:37,130 --> 00:34:40,590
+محدده بيجيبوهش عشوائي بيجيبه من ال vectors اللي
+
+377
+00:34:40,590 --> 00:34:46,490
+عندي ومن خلال الرونسكين هذا بقدر أحكم هل اللي عند
+
+378
+00:34:46,490 --> 00:34:50,990
+ال vectors هدول dependence ولا independence يعني
+
+379
+00:34:50,990 --> 00:34:56,490
+هناخد نظريات بواسطتها نقدر نحكم وبواسطة ال رونسكين
+
+380
+00:34:56,490 --> 00:35:01,680
+نقدر نحكم هل هدولlinearly independent ولا linearly
+
+381
+00:35:01,680 --> 00:35:06,440
+dependent هذا الكلام سنعرفه في حينه ان شاء الله
+
+382
+00:35:06,440 --> 00:35:11,900
+تعالى بعد ذلك بنجي لآخر نقطة في ال vector spaces
+
+383
+00:35:11,900 --> 00:35:19,840
+حاجة اسمها ال dimension او
+
+384
+00:35:19,840 --> 00:35:26,800
+dimensionsهنعطيلها تعريف و من خلال التعريف هذا نقل
+
+385
+00:35:26,800 --> 00:35:31,780
+لكل vector space قدش ال dimension له طبعا في حاجة
+
+386
+00:35:31,780 --> 00:35:36,960
+بنات اسمها ال bases اللي هو الأساس لل vector space
+
+387
+00:35:36,960 --> 00:35:41,460
+تمام ال dimension له علاقة بال bases أو له علاقة
+
+388
+00:35:41,460 --> 00:35:45,540
+بعدد ال vector في ال bases فإذا كان مثلا ال bases
+
+389
+00:35:45,540 --> 00:35:49,750
+يحتوي بس على two vectors بقول ال base له اتنينإن
+
+390
+00:35:49,750 --> 00:35:53,430
+كان يحتوي على تلاتة linear independent vectors
+
+391
+00:35:53,430 --> 00:35:58,510
+بقول ال basis له تلاتة و هكذا طبعا سنعرف الحين و
+
+392
+00:35:58,510 --> 00:36:02,890
+كيف نحسب هذا ال basis و من ثم نقدر نعرف قداش ال
+
+393
+00:36:02,890 --> 00:36:08,050
+dimension لكل vector space موجود انه بعد ذلك بنجي
+
+394
+00:36:08,050 --> 00:36:11,410
+للنصف الثاني من هذا ال chapter وهو ال linear
+
+395
+00:36:11,410 --> 00:36:17,530
+transformations يبقى بدنا نيجي لمن؟ لل linear
+
+396
+00:36:26,490 --> 00:36:29,810
+transformations التحويلات الخطية شو يعني تحويلة
+
+397
+00:36:29,810 --> 00:36:34,540
+خطية؟ هي عبارة عن functionمش دراسة الـ function في
+
+398
+00:36:34,540 --> 00:36:39,040
+calculus A بس الـ function أخدناها من set A إلى
+
+399
+00:36:39,040 --> 00:36:43,860
+set B لكن linear transformation من vector space
+
+400
+00:36:43,860 --> 00:36:48,220
+إلى vector space مش set عادية تمام؟ يبقى هي
+
+401
+00:36:48,220 --> 00:36:51,160
+function من ال vector space الأول إلى ال vector
+
+402
+00:36:51,160 --> 00:36:56,180
+space الثاني ولها شروط ان تحقق أو لها شرطين مش
+
+403
+00:36:56,180 --> 00:37:00,920
+أكتر ان تحقق هذان الشرطان بقول عن هذه هي linear
+
+404
+00:37:00,920 --> 00:37:05,490
+transformationو هاد ال linear transformation لها
+
+405
+00:37:05,490 --> 00:37:11,030
+خواص و شغل اللي هيكون منصب كله على الخواص يبقى
+
+406
+00:37:11,030 --> 00:37:14,930
+بدنا نيجي لآخر نقطة موجودة في هاد ال section و هي
+
+407
+00:37:14,930 --> 00:37:20,730
+properties of linear transformations
+
+408
+00:37:30,790 --> 00:37:41,430
+يبقى هذا كل ما سندرسه في ال chapter التالت برضه
+
+409
+00:37:41,430 --> 00:37:44,650
+ال chapter هذا طويل بنات يعني chapter اتنين و
+
+410
+00:37:44,650 --> 00:37:50,190
+تلاتة هما اطول two chapters في المقرر يبقى اخدنا
+
+411
+00:37:50,190 --> 00:37:54,470
+chapterين جبر خطي chapter اتنين و chapter تلاتة
+
+412
+00:37:54,470 --> 00:37:58,450
+ابنجي ل chapter اربع اللي هو ال diagonalization
+
+413
+00:38:07,780 --> 00:38:11,960
+ال chapter هذا مش هنكتر عليكم بس two sections مش
+
+414
+00:38:11,960 --> 00:38:17,140
+أكتر two sections طبعا هذا مرتبط بموضوع مين بموضوع
+
+415
+00:38:17,140 --> 00:38:22,200
+ال vector spaces اللي قبله يبقى two sections أول
+
+416
+00:38:22,200 --> 00:38:25,020
+حاجة بدنا نيجي للحاجة اسمها ال characteristic
+
+417
+00:38:25,020 --> 00:38:25,820
+values
+
+418
+00:38:34,130 --> 00:38:38,530
+القيم المميزة وبعد ذلك بنجي اليوميا لل
+
+419
+00:38:38,530 --> 00:38:46,670
+diagonalization ايه
+
+420
+00:38:46,670 --> 00:38:49,910
+ال two sections مافيش غيرهم ايش معناه دياجون
+
+421
+00:38:49,910 --> 00:38:56,350
+الليمانات قطر ممتاز جدا يبقى diagonalization كي
+
+422
+00:38:56,350 --> 00:39:01,870
+بدي اعمل مصفوفة قطريةقطرية يعني ايه؟ اشي يعني
+
+423
+00:39:01,870 --> 00:39:06,070
+مصوفة مثلثة عليا أو سفلة يعني اللي فوق القطر
+
+424
+00:39:06,070 --> 00:39:11,290
+الرئيسي أسفر أو اللي تحت القطر الرئيسي أسفر أو
+
+425
+00:39:11,290 --> 00:39:14,610
+اللي فوق أسفر و اللي تحت أسفر ومايضالش إلا من؟
+
+426
+00:39:14,610 --> 00:39:20,550
+عناصر القطر الرئيسيهذا كلمة دا هذا المعنى البلدي
+
+427
+00:39:20,550 --> 00:39:23,970
+القريب إلى الفهم لمعنى ال diagonalization لكن
+
+428
+00:39:23,970 --> 00:39:29,530
+تحتها بنشر خطوات رياضية كأني بدي أحول المصوفة اللي
+
+429
+00:39:29,530 --> 00:39:34,430
+عندنا إلى ال diagonal matrix في شغل بدنا نشتغله
+
+430
+00:39:34,430 --> 00:39:39,330
+هذا ومن خلاله بكون جيب ال diagonalization لمام
+
+431
+00:39:39,330 --> 00:39:43,700
+لهذه المصوفةمش كل مصوفة اللي هي diagonalization مش
+
+432
+00:39:43,700 --> 00:39:48,160
+كل واحدة بنفعلها تمام يبقى في شروط لازم تتحقق مشان
+
+433
+00:39:48,160 --> 00:39:53,180
+أقدر أعمل ال diagonalization لمصوفة قبل هذه بدي
+
+434
+00:39:53,180 --> 00:39:58,000
+أخد ال characteristic values اللي هي القيامة و ال
+
+435
+00:39:58,000 --> 00:40:03,740
+characteristic vectors يعني المتجهات المميزةوالقيم
+
+436
+00:40:03,740 --> 00:40:08,500
+المميزة لهذه المصوفة يبقى نقطتين فقط في هذا ال
+
+437
+00:40:08,500 --> 00:40:13,700
+chapter او two sections فقط في هذا ال chapter على
+
+438
+00:40:13,700 --> 00:40:18,280
+هيك بيكون انتهينا من الجبر الخاطي يبقى أخدنا
+
+439
+00:40:18,280 --> 00:40:24,060
+chapter معادلة تفاضلية و three chapters اللي هو
+
+440
+00:40:24,060 --> 00:40:29,400
+جبر خاطي يبقى هي قداش اربعة طايل قداشضايل اتنين
+
+441
+00:40:29,400 --> 00:40:33,040
+اللي هم عبارة عن معادلات تفاضلية في ال chapter
+
+442
+00:40:33,040 --> 00:40:37,940
+الأول بدأنا بالرتبة الأولى هنا بدنا نقش الرتبة
+
+443
+00:40:37,940 --> 00:40:43,100
+التانية التالتة الرابعة إلى آخرها يبقى لو جينا ل
+
+444
+00:40:43,100 --> 00:40:50,660
+chapter خمسة chapter خمسة اسمه linear differential
+
+445
+00:40:50,660 --> 00:40:57,660
+equations linear differential equationsطبعا يمكن
+
+446
+00:40:57,660 --> 00:41:01,180
+واحدة تقولي متوسعة كتبنا linear equations هذه ال
+
+447
+00:41:01,180 --> 00:41:04,900
+linear equations من ال first order هذي ال second
+
+448
+00:41:04,900 --> 00:41:09,300
+order، third order، fourth order، nth order دي
+
+449
+00:41:09,300 --> 00:41:11,840
+بيجمع الرتبة التانية، التالتة، الرابعة، الرتبة
+
+450
+00:41:11,840 --> 00:41:15,400
+النونية لكن ال linear اللي خدناها قبل شوية هذي هي
+
+451
+00:41:15,400 --> 00:41:21,040
+من؟ من ال first order فقط لغير تحت هذا العنوان
+
+452
+00:41:21,040 --> 00:41:26,850
+بدنا ندرس عدة شغلاتأول شيء بدنا ناخد هو الـ
+
+453
+00:41:26,850 --> 00:41:33,290
+Homogeneous Equations هذه اختصار لكلمة homogeneous
+
+454
+00:41:33,290 --> 00:41:38,470
+بدا المكتوبة بالشكل الطويل هذابقول هنا homogeneous
+
+455
+00:41:38,470 --> 00:41:45,630
+equations يبقى المعادلات المتجانسة المعادلات
+
+456
+00:41:45,630 --> 00:41:49,790
+المتجانسة مش المعادلات المتجانسة الأولانية لأ من
+
+457
+00:41:49,790 --> 00:41:53,570
+الرتبة التانية او التالتة الطرف اليميني يساوي صفرة
+
+458
+00:41:53,570 --> 00:41:58,850
+بقول المعادلة تساوي صفر من حد ما اشوف هيك بسميها
+
+459
+00:41:58,850 --> 00:42:03,700
+homogeneous طب لو ماكناش صفر كانت رقمبسميها الـ
+
+460
+00:42:03,700 --> 00:42:07,640
+Non-homogeneous differential equation يبقى الـ
+
+461
+00:42:07,640 --> 00:42:11,540
+homogeneous لها طريقة للحل والـ non-homogeneous
+
+462
+00:42:11,540 --> 00:42:17,080
+لها طريقة للحل الطريقة بتعتمد على حل ال
+
+463
+00:42:17,080 --> 00:42:23,750
+homogeneousطيب هنا هذه ال homogenous equations هذه
+
+464
+00:42:23,750 --> 00:42:31,090
+ممكن أكثر من طريقة لمعرفة حل هذه المعادلة من ذلك
+
+465
+00:42:31,090 --> 00:42:37,850
+طريقة ال complex root الجذور التخيلية يبقى بداجي
+
+466
+00:42:37,850 --> 00:42:44,710
+لحاجة اسمها complex solutions complex solutions
+
+467
+00:42:46,330 --> 00:42:52,310
+الحلول المُركّبة وممكن
+
+468
+00:42:52,310 --> 00:43:03,010
+المعادلة تبقى equations with constant coefficients
+
+469
+00:43:03,010 --> 00:43:07,570
+يعني
+
+470
+00:43:07,570 --> 00:43:13,550
+المعادلة التفاضلية مثلا الـ A1 والـ A2 والـ A3
+
+471
+00:43:13,550 --> 00:43:19,510
+هدول ثوابتممكن يكونوا ثوابت وممكن مايكونوش ثوابت
+
+472
+00:43:19,510 --> 00:43:25,330
+إن كانوا ثوابت يبقى بسميها equations with constant
+
+473
+00:43:25,330 --> 00:43:29,770
+coefficients بمعاملة ثابتة وبستخدمها ال complex
+
+474
+00:43:29,770 --> 00:43:36,380
+solutions بالإضافة إلى بعض الطرق الأخرىلكن لو كانت
+
+475
+00:43:36,380 --> 00:43:41,320
+هذه المعادلة homogeneous equation لكن المعادلات ما
+
+476
+00:43:41,320 --> 00:43:47,420
+هيش ثوابت يبقى ممكن تحوير المعادلة إن كانت بصيغة
+
+477
+00:43:47,420 --> 00:43:52,960
+محددة بحيث أضيع هذه المتغيرات وأقلبها إلى معادلة
+
+478
+00:43:52,960 --> 00:43:58,260
+بمعاملات ثابتة وهذه اسمها Cauchy-Euler equations
+
+479
+00:43:58,260 --> 00:44:02,960
+يبقى بدنا نيجي لحاجة اسمها Cauchy-Euler equations
+
+480
+00:44:03,670 --> 00:44:11,290
+كوشي كوشي
+
+481
+00:44:11,290 --> 00:44:13,810
+أيلر equations
+
+482
+00:44:19,450 --> 00:44:25,130
+معادلة مشهورة باسم الاتنين هذه المعادلة بيكون
+
+483
+00:44:25,130 --> 00:44:30,570
+مسبوقة المعامل تبعها بدلالة ال X الأس تبعه جد
+
+484
+00:44:30,570 --> 00:44:35,610
+الرتبة تبعت ال Y فنقول X تربيع Y Double Prime زائد
+
+485
+00:44:35,610 --> 00:44:40,230
+XY Prime زائد Constant يساوي مين؟ Constant في Y
+
+486
+00:44:40,230 --> 00:44:44,250
+يساوي Zero يبقى هذه اللي بيسمي الكوشيه Euler
+
+487
+00:44:44,250 --> 00:44:48,750
+Equation وحناخد طريقة كيف أحولها من معادلة
+
+488
+00:44:48,990 --> 00:44:53,610
+بالمعاملات تبعتها متغيرة إلى معادلة بمعاملة ثابتة
+
+489
+00:44:53,610 --> 00:44:59,710
+وبعدين كيف انحل هذا النوع من المعادلات بعد ذلك بدأ
+
+490
+00:44:59,710 --> 00:45:03,130
+نجي لـ Non-homogeneous يبقى أخدنا أول حاجة الـ
+
+491
+00:45:03,130 --> 00:45:08,750
+homogeneous بدأ أجي لـ Non-homogeneous
+
+492
+00:45:08,750 --> 00:45:12,310
+differential equations
+
+493
+00:45:15,460 --> 00:45:17,800
+هنا الـ Non-homogeneous differential اللي كنا
+
+494
+00:45:17,800 --> 00:45:24,400
+بياخد ثلاث طرق للحل ثلاث طرق لحل هذا النوع من
+
+495
+00:45:24,400 --> 00:45:30,320
+المعادلات الطريقة الأولى والطريقة الثانية والطريقة
+
+496
+00:45:30,320 --> 00:45:34,520
+الثالثة الطريقة الأولى اللى بناخدها طريقة
+
+497
+00:45:34,520 --> 00:45:40,700
+المعاملات الثابتة فأول طريقة من هذه الطرق اللي هي
+
+498
+00:45:40,700 --> 00:45:44,300
+الـ Undetermined
+
+499
+00:45:51,060 --> 00:45:56,620
+coefficients طريقة المعاملات المجهولة طريقة
+
+500
+00:45:56,620 --> 00:46:02,720
+الثانية variation of
+
+501
+00:46:02,720 --> 00:46:10,960
+parameters يعني
+
+502
+00:46:10,960 --> 00:46:18,080
+طريقة تغيير المتغيراتطريقة الثالثة reduction of
+
+503
+00:46:18,080 --> 00:46:28,440
+order reduction of order طريقة اختزال الرتبة يعني
+
+504
+00:46:28,440 --> 00:46:33,340
+كيف أنزل الرتبة من الرتبة الثانية إلى الرتبةالأولى
+
+505
+00:46:33,340 --> 00:46:39,420
+مثلا وبالتالي هي الطرق الثلاث في هذه الحالة يبقى
+
+506
+00:46:39,420 --> 00:46:42,780
+في هذا الشبط راح ناخد نوعين من المعادلات النوع
+
+507
+00:46:42,780 --> 00:46:47,660
+الأول المعادلات المعاملات ثوابت النوع الثاني
+
+508
+00:46:47,660 --> 00:46:52,780
+المعاملات متغيرةالمعاملات المتغيرة يمكن تحويلها
+
+509
+00:46:52,780 --> 00:46:58,120
+إلى معادلة homogeneous بمعاملات ثابتة وهذا لها
+
+510
+00:46:58,120 --> 00:47:02,740
+أكثر من طريقة للحل ال complex هو أحد العلوم بعد
+
+511
+00:47:02,740 --> 00:47:05,480
+ذلك يجب أن نصل إلى non homogeneous يعني الطرف اللي
+
+512
+00:47:05,480 --> 00:47:10,520
+بين المعادلة يجب أن يكون دالة وليس zero يبقى هذا
+
+513
+00:47:10,520 --> 00:47:15,040
+النوع من المعادلات له ثلاث طرق للحل الطريقة الأولى
+
+514
+00:47:15,040 --> 00:47:18,420
+طريقة ال undetermined coefficients المعاملات
+
+515
+00:47:18,420 --> 00:47:22,870
+المجهولةوطريقة الثانية طريقة ال variation of
+
+516
+00:47:22,870 --> 00:47:27,570
+parameters تغيير المتغيرات و الحصول على هذه
+
+517
+00:47:27,570 --> 00:47:31,430
+المتغيرات في قد إيش قيمتها الطريقة التالتة طريقة
+
+518
+00:47:31,430 --> 00:47:35,490
+اختزال الرتبة أو تنزيل الرتبة من الرتبة الثانية
+
+519
+00:47:35,490 --> 00:47:42,410
+إلى الرتبة الأولى يبقى هذا باختصار كل ما هو موجود
+
+520
+00:47:42,410 --> 00:47:48,950
+في chapter 5 بنجي ل chapter 6 اللي هو Laplace
+
+521
+00:47:51,030 --> 00:47:55,510
+هذا ليس شبتر ستة هذه المواحدة خمسة هذا بنفط لبعض و
+
+522
+00:47:55,510 --> 00:48:00,690
+بروح لشبتر تسعة يبقى الشبتر السادس هو شبتر تسعة
+
+523
+00:48:00,690 --> 00:48:07,770
+يبقى الشبتر تسعة اللي هو لابلاز ترانسفورمز
+
+524
+00:48:08,410 --> 00:48:15,950
+تحويلات لابلاس وما يتعلق بها وكيفية استخدامها في
+
+525
+00:48:15,950 --> 00:48:23,450
+حل المعادلات التفاضلية وبعد هيك using Laplace
+
+526
+00:48:23,450 --> 00:48:32,850
+transform to
+
+527
+00:48:32,850 --> 00:48:42,100
+solve secondorder differential
+
+528
+00:48:42,100 --> 00:48:48,350
+equationsيعني كيف بنستخدم ال place transform في حل
+
+529
+00:48:48,350 --> 00:48:52,310
+المعادلة التفاضلية من الرتبة الثانية أو حتى من
+
+530
+00:48:52,310 --> 00:48:57,450
+الرتبة الثالثة أو الرابعة حسب طبيعة المثلة لكن
+
+531
+00:48:57,450 --> 00:49:01,730
+الرتبة الثانية هي الدرجة أكثر يبقى هذا باختصار
+
+532
+00:49:01,730 --> 00:49:05,110
+مثلا يبقى هذا الشيء الجديد ال place transform
+
+533
+00:49:05,110 --> 00:49:09,630
+بيكون عندنا معادلة بنات جصدي function هذه ال
+
+534
+00:49:09,630 --> 00:49:14,710
+function صعبة التعامل معاها فبنجيب معادلةمكافئة
+
+535
+00:49:14,710 --> 00:49:20,550
+لها تقريبا و بنحاول نستخدمها في إيه في الحل طبعا و
+
+536
+00:49:20,550 --> 00:49:24,330
+في عندنا جدول كل معادلة شهولة بلاس ترانسفورم لها
+
+537
+00:49:24,330 --> 00:49:30,050
+وهذا يعتمد على التكامل اللي دراسناه في Calculus B
+
+538
+00:49:30,500 --> 00:49:36,400
+infinite integration تكامل من 0 إلى infinity أو من
+
+539
+00:49:36,400 --> 00:49:37,440
+رقم إلى انفنترال
+
+540
+00:49:46,480 --> 00:49:51,840
+يعتمد عليها place a transfer بهذا القدر ان اكتفي و
+
+541
+00:49:51,840 --> 00:49:56,320
+اظن اننا قد وصلنا الى نهاية المحاضرة فالمرة الجاية
+
+542
+00:49:56,320 --> 00:50:00,860
+ان شاء الله هندخل في صميم الموضوع من اول و جديد
+
+543
+00:50:00,860 --> 00:50:05,480
+هذا كلام عام حول المنهج بارك الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6537691310abac770dd6d3b4c3c3b3680c2c9441
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_raw.json
@@ -0,0 +1 @@
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{"start": 1184.77, "end": 1185.11, "word": " هذا", "probability": 0.97412109375}, {"start": 1185.11, "end": 1185.67, "word": " الشابتر", "probability": 0.94189453125}, {"start": 1185.67, "end": 1185.95, "word": " هو", "probability": 0.98291015625}, {"start": 1185.95, "end": 1186.75, "word": " system", "probability": 0.72705078125}], "temperature": 1.0}, {"id": 51, "seek": 121272, "start": 1188.86, "end": 1212.72, "text": "systems of linear equations انظمة المعادلات الخطية ايش يعني انظمة المعادلة الخطية مثلا قد تكون المعادلة فيها مجهولين وقد يكون بثلاثة مجاهيل", "tokens": [28215, 82, 295, 8213, 11787, 16472, 19913, 46007, 9673, 3615, 18513, 1211, 9307, 33962, 9566, 10632, 1975, 1829, 8592, 37495, 22653, 16472, 19913, 46007, 9673, 3615, 18513, 37977, 33962, 9566, 10632, 50113, 15040, 12174, 3215, 6055, 30544, 9673, 3615, 18513, 37977, 8978, 11296, 3714, 7435, 3224, 12610, 9957, 4032, 28543, 7251, 30544, 4724, 12984, 1211, 5718, 104, 3660, 3714, 7435, 40294, 26895], "avg_logprob": 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"probability": 0.9664306640625}, {"start": 1204.86, "end": 1205.64, "word": " الخطية", "probability": 0.9915364583333334}, {"start": 1205.64, "end": 1206.88, "word": " مثلا", "probability": 0.94091796875}, {"start": 1206.88, "end": 1207.24, "word": " قد", "probability": 0.97216796875}, {"start": 1207.24, "end": 1207.62, "word": " تكون", "probability": 0.98828125}, {"start": 1207.62, "end": 1208.26, "word": " المعادلة", "probability": 0.976318359375}, {"start": 1208.26, "end": 1208.7, "word": " فيها", "probability": 0.984619140625}, {"start": 1208.7, "end": 1209.84, "word": " مجهولين", "probability": 0.99638671875}, {"start": 1209.84, "end": 1210.7, "word": " وقد", "probability": 0.8359375}, {"start": 1210.7, "end": 1211.1, "word": " يكون", "probability": 0.977294921875}, {"start": 1211.1, "end": 1211.96, "word": " بثلاثة", "probability": 0.9021809895833334}, {"start": 1211.96, "end": 1212.72, "word": " مجاهيل", "probability": 0.9180908203125}], "temperature": 1.0}, {"id": 52, "seek": 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"word": " مثلا", "probability": 0.984375}, {"start": 1221.47, "end": 1223.25, "word": " a1x", "probability": 0.71142578125}, {"start": 1223.25, "end": 1224.45, "word": " زائد", "probability": 0.6591796875}, {"start": 1224.45, "end": 1225.97, "word": " a2y", "probability": 0.9630533854166666}, {"start": 1225.97, "end": 1226.65, "word": " زائد", "probability": 0.9466145833333334}, {"start": 1226.65, "end": 1228.21, "word": " a3z", "probability": 0.9939778645833334}, {"start": 1228.21, "end": 1229.43, "word": " يساوي", "probability": 0.952392578125}, {"start": 1229.43, "end": 1230.17, "word": " مثلا", "probability": 0.9609375}, {"start": 1230.17, "end": 1230.69, "word": " ال", "probability": 0.95703125}, {"start": 1230.69, "end": 1230.95, "word": " one", "probability": 0.387451171875}], "temperature": 1.0}, {"id": 53, "seek": 125547, "start": 1232.51, "end": 1255.47, "text": "A2X أو B1X زائد B2Y زائد B3Z بده يساوي L2 مثلا C1X زائد C2Y زائد C3Z يساوي L3", "tokens": [32, 17, 55, 34051, 363, 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النظام المعادلات بسميه system of linear equations يعني معادلة خطية شوية في ال X و Y و Z اللي هو المجاهيل كلها من الدرجات الأولى يبقى هذه بسميها معادلة خطية المعادلات مع بعض كل تلاتة مجموعة بسميها system of linear equations يعني نظام مكون من مجموعة من المعادلات الخطية", "tokens": [3224, 15730, 28239, 19913, 10943, 9673, 3615, 18513, 1211, 9307, 4724, 38251, 1829, 3224, 1185, 295, 8213, 11787, 37495, 22653, 20449, 18513, 37977, 16490, 9566, 10632, 13412, 2407, 10632, 8978, 2423, 1783, 4032, 398, 4032, 1176, 13672, 1829, 31439, 9673, 7435, 40294, 26895, 28242, 11296, 9154, 32748, 47341, 9307, 16247, 12610, 7578, 7251, 3555, 4587, 7578, 29538, 4724, 38251, 1829, 11296, 20449, 18513, 37977, 16490, 9566, 10632, 9673, 3615, 18513, 1211, 9307, 20449, 45030, 11242, 28242, 6055, 1211, 9307, 3660, 3714, 7435, 2304, 2407, 27884, 4724, 38251, 1829, 11296, 1185, 295, 8213, 11787, 37495, 22653, 8717, 19913, 10943, 3714, 30544, 9154, 3714, 7435, 2304, 2407, 27884, 9154, 9673, 3615, 18513, 1211, 9307, 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تمام؟ يبقى هذه النقطة الثانوية اللي سندرسها و بعد هيك بدنا نيجي لحاجة اسمها matrices and vectors", "tokens": [1829, 3555, 4587, 7578, 45164, 25961, 2655, 29538, 28242, 11296, 4724, 10721, 9381, 5172, 9640, 7251, 3555, 4587, 7578, 23758, 4724, 38251, 32640, 9957, 13672, 1829, 31439, 2423, 3655, 45519, 1185, 2423, 1185, 9673, 2655, 7435, 7649, 3794, 46811, 10943, 22807, 7251, 3555, 4587, 7578, 29538, 28239, 47432, 3660, 6024, 104, 7649, 2407, 10632, 13672, 1829, 8608, 41260, 2288, 3794, 11296, 4032, 39182, 39896, 4117, 47525, 8315, 8717, 1829, 7435, 1829, 5296, 5016, 26108, 3660, 24525, 2304, 11296, 32284, 293, 18875], "avg_logprob": -0.15786967081267658, "compression_ratio": 1.527363184079602, "no_speech_prob": 0.0, "words": [{"start": 1423.08, "end": 1423.76, "word": "يبقى", "probability": 0.8914794921875}, {"start": 1423.76, "end": 1424.02, "word": " لو", "probability": 0.96826171875}, {"start": 1424.02, "end": 1424.68, "word": " كانت", "probability": 0.91796875}, {"start": 1424.68, 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1433.34, "end": 1433.92, "word": " system", "probability": 0.87060546875}, {"start": 1433.92, "end": 1436.14, "word": " المتجانس", "probability": 0.98818359375}, {"start": 1436.14, "end": 1438.0, "word": " تمام؟", "probability": 0.80224609375}, {"start": 1438.0, "end": 1438.42, "word": " يبقى", "probability": 0.985595703125}, {"start": 1438.42, "end": 1438.66, "word": " هذه", "probability": 0.4052734375}, {"start": 1438.66, "end": 1439.22, "word": " النقطة", "probability": 0.9842122395833334}, {"start": 1439.22, "end": 1439.54, "word": " الثانوية", "probability": 0.8337890625}, {"start": 1439.54, "end": 1439.76, "word": " اللي", "probability": 0.71728515625}, {"start": 1439.76, "end": 1440.56, "word": " سندرسها", "probability": 0.8458984375}, {"start": 1440.56, "end": 1441.2, "word": " و", "probability": 0.52587890625}, {"start": 1441.2, "end": 1441.52, "word": " بعد", "probability": 0.923828125}, {"start": 1441.52, "end": 1441.92, "word": " هيك", "probability": 0.865478515625}, 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order، nth order دي بيجمع الرتبة التانية، التالتة، الرابعة، الرتبة النونية لكن ال linear اللي خدناها قبل شوية هذي هي من؟ من ال first order فقط لغير تحت هذا العنوان بدنا ندرس عدة شغلات", "tokens": [9566, 3555, 3615, 995, 7251, 43020, 36764, 24401, 3660, 6055, 39648, 1829, 44650, 41779, 27884, 9122, 2655, 3555, 8315, 8213, 11787, 29538, 2423, 8213, 11787, 9154, 2423, 700, 1668, 8032, 8848, 1829, 2423, 1150, 1668, 12399, 2636, 1668, 12399, 6409, 1668, 12399, 297, 392, 1668, 11778, 1829, 4724, 1829, 7435, 2304, 3615, 34892, 2655, 49401, 16712, 7649, 10632, 12399, 16712, 6027, 2655, 3660, 12399, 34892, 16758, 27884, 12399, 34892, 2655, 49401, 28239, 11536, 10632, 44381, 2423, 8213, 13672, 1829, 16490, 3215, 8315, 11296, 12174, 36150, 13412, 2407, 10632, 8032, 8848, 1829, 39896, 9154, 22807, 9154, 2423, 700, 1668, 6156, 47432, 5296, 17082, 13546, 6055, 33753, 23758, 18863, 1863, 2407, 7649, 47525, 8315, 8717, 3215, 2288, 3794, 6225, 41891, 13412, 17082, 1211, 9307], "avg_logprob": 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first", "probability": 0.9384765625}, {"start": 2476.8, "end": 2477.34, "word": " order", "probability": 0.9599609375}, {"start": 2477.34, "end": 2478.14, "word": " فقط", "probability": 0.983154296875}, {"start": 2478.14, "end": 2478.86, "word": " لغير", "probability": 0.7752278645833334}, {"start": 2478.86, "end": 2479.72, "word": " تحت", "probability": 0.956298828125}, {"start": 2479.72, "end": 2480.16, "word": " هذا", "probability": 0.9560546875}, {"start": 2480.16, "end": 2481.04, "word": " العنوان", "probability": 0.9698486328125}, {"start": 2481.04, "end": 2481.8, "word": " بدنا", "probability": 0.885986328125}, {"start": 2481.8, "end": 2482.42, "word": " ندرس", "probability": 0.9959716796875}, {"start": 2482.42, "end": 2482.98, "word": " عدة", "probability": 0.961669921875}, {"start": 2482.98, "end": 2483.56, "word": " شغلات", "probability": 0.9864501953125}], "temperature": 1.0}, {"id": 106, "seek": 249583, "start": 2484.17, "end": 2495.83, "text": "أول شيء بدنا ناخد هو الـ Homogeneous Equations هذه اختصار لكلمة homogeneous بدا المكتوبة بالشكل الطويل هذا", "tokens": [10721, 12610, 44049, 38207, 47525, 8315, 8717, 47283, 3215, 31439, 2423, 39184, 20903, 31112, 15624, 763, 29538, 1975, 46456, 9381, 9640, 5296, 4117, 19528, 3660, 3655, 664, 1450, 563, 4724, 28259, 9673, 4117, 2655, 37746, 3660, 20666, 8592, 28820, 41950, 2407, 26895, 23758], "avg_logprob": -0.29421166059645737, "compression_ratio": 1.2406015037593985, "no_speech_prob": 0.0, "words": [{"start": 2484.17, "end": 2484.59, "word": "أول", "probability": 0.819091796875}, {"start": 2484.59, "end": 2484.91, "word": " شيء", "probability": 0.5091552734375}, {"start": 2484.91, "end": 2485.15, "word": " بدنا", "probability": 0.735595703125}, {"start": 2485.15, "end": 2485.77, "word": " ناخد", "probability": 0.9788411458333334}, {"start": 2485.77, "end": 2486.31, "word": " هو", "probability": 0.78955078125}, {"start": 2486.31, "end": 2486.85, "word": " الـ", "probability": 0.824951171875}, {"start": 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2512.77, "end": 2513.21, "word": " يساوي", "probability": 0.78363037109375}, {"start": 2513.21, "end": 2513.57, "word": " صفرة", "probability": 0.7574869791666666}, {"start": 2513.57, "end": 2513.95, "word": " بقول", "probability": 0.920654296875}, {"start": 2513.95, "end": 2514.73, "word": " المعادلة", "probability": 0.9010009765625}, {"start": 2514.73, "end": 2515.71, "word": " تساوي", "probability": 0.972412109375}, {"start": 2515.71, "end": 2516.23, "word": " صفر", "probability": 0.9676106770833334}, {"start": 2516.23, "end": 2516.81, "word": " من", "probability": 0.912109375}, {"start": 2516.81, "end": 2517.11, "word": " حد", "probability": 0.986572265625}, {"start": 2517.11, "end": 2517.25, "word": " ما", "probability": 0.9443359375}, {"start": 2517.25, "end": 2517.53, "word": " اشوف", "probability": 0.7401529947916666}, {"start": 2517.53, "end": 2517.97, "word": " هيك", "probability": 0.855712890625}, {"start": 2517.97, "end": 2518.85, "word": " بسميها", "probability": 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0.846923828125}, {"start": 2527.64, "end": 2528.08, "word": " homogeneous", "probability": 0.79833984375}, {"start": 2528.08, "end": 2528.66, "word": " لها", "probability": 0.969482421875}, {"start": 2528.66, "end": 2529.2, "word": " طريقة", "probability": 0.9851888020833334}, {"start": 2529.2, "end": 2529.84, "word": " للحل", "probability": 0.9679361979166666}, {"start": 2529.84, "end": 2530.54, "word": " والـ", "probability": 0.6287841796875}, {"start": 2530.54, "end": 2530.76, "word": " non", "probability": 0.79345703125}, {"start": 2530.76, "end": 2531.54, "word": "-homogeneous", "probability": 0.8514404296875}, {"start": 2531.54, "end": 2532.3, "word": " لها", "probability": 0.982666015625}, {"start": 2532.3, "end": 2533.02, "word": " طريقة", "probability": 0.9928385416666666}, {"start": 2533.02, "end": 2533.84, "word": " للحل", "probability": 0.9752604166666666}, {"start": 2533.84, "end": 2534.96, "word": " الطريقة", "probability": 0.9510091145833334}, {"start": 2534.96, "end": 2535.76, "word": " بتعتمد", "probability": 0.92578125}, {"start": 2535.76, "end": 2536.02, "word": " على", "probability": 0.9130859375}, {"start": 2536.02, "end": 2536.62, "word": " حل", "probability": 0.952880859375}, {"start": 2536.62, "end": 2537.08, "word": " ال", "probability": 0.9970703125}, {"start": 2537.08, "end": 2537.64, "word": " homogeneous", "probability": 0.2509765625}], "temperature": 1.0}, {"id": 109, "seek": 256471, "start": 2538.35, "end": 2564.71, "text": "طيب هنا هذه ال homogenous equations هذه ممكن أكثر من طريقة لمعرفة حل هذه المعادلة من ذلك طريقة ال complex root الجذور التخيلية يبقى بداجي لحاجة اسمها complex solutions complex solutions", "tokens": [9566, 1829, 3555, 34105, 29538, 2423, 3655, 45519, 11787, 29538, 3714, 43020, 5551, 4117, 49115, 9154, 23032, 16572, 28671, 32767, 3615, 28480, 3660, 11331, 1211, 29538, 9673, 3615, 18513, 37977, 9154, 29910, 23275, 23032, 16572, 28671, 2423, 3997, 5593, 25724, 8848, 13063, 16712, 9778, 26895, 10632, 7251, 3555, 4587, 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من", "probability": 0.99609375}, {"start": 2546.07, "end": 2546.89, "word": " طريقة", "probability": 0.9952799479166666}, {"start": 2546.89, "end": 2547.95, "word": " لمعرفة", "probability": 0.9866943359375}, {"start": 2547.95, "end": 2548.51, "word": " حل", "probability": 0.96875}, {"start": 2548.51, "end": 2549.37, "word": " هذه", "probability": 0.9814453125}, {"start": 2549.37, "end": 2550.27, "word": " المعادلة", "probability": 0.9620361328125}, {"start": 2550.27, "end": 2550.61, "word": " من", "probability": 0.845703125}, {"start": 2550.61, "end": 2551.09, "word": " ذلك", "probability": 0.989990234375}, {"start": 2551.09, "end": 2551.99, "word": " طريقة", "probability": 0.9903971354166666}, {"start": 2551.99, "end": 2552.27, "word": " ال", "probability": 0.77587890625}, {"start": 2552.27, "end": 2552.79, "word": " complex", "probability": 0.90966796875}, {"start": 2552.79, "end": 2553.33, "word": " root", "probability": 0.7158203125}, {"start": 2553.33, "end": 2554.51, "word": " الجذور", "probability": 0.9558919270833334}, {"start": 2554.51, "end": 2556.35, "word": " التخيلية", "probability": 0.8775634765625}, {"start": 2556.35, "end": 2557.31, "word": " يبقى", "probability": 0.9554443359375}, {"start": 2557.31, "end": 2557.85, "word": " بداجي", "probability": 0.4593098958333333}, {"start": 2557.85, "end": 2558.37, "word": " لحاجة", "probability": 0.960693359375}, {"start": 2558.37, "end": 2558.85, "word": " اسمها", "probability": 0.8333333333333334}, {"start": 2558.85, "end": 2559.39, "word": " complex", "probability": 0.869140625}, {"start": 2559.39, "end": 2560.59, "word": " solutions", "probability": 0.8994140625}, {"start": 2560.59, "end": 2562.05, "word": " complex", "probability": 0.794921875}, {"start": 2562.05, "end": 2564.71, "word": " solutions", "probability": 0.943359375}], "temperature": 1.0}, {"id": 110, "seek": 259507, "start": 2566.33, "end": 2595.07, "text": "الحلول المُركّبة وممكن المعادلة تبقى equations with constant coefficients يعني المعادلة التفاضلية مثلا الـ A1 والـ A2 والـ A3 هدول ثوابت", "tokens": [6027, 5016, 1211, 12610, 9673, 10859, 31747, 11703, 49401, 4032, 2304, 43020, 9673, 3615, 18513, 37977, 6055, 3555, 4587, 7578, 11787, 365, 5754, 31994, 37495, 22653, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 50113, 15040, 2423, 39184, 316, 16, 16070, 39184, 316, 17, 16070, 39184, 316, 18, 8032, 3215, 12610, 38637, 14407, 3555, 2655], "avg_logprob": -0.18421052631578946, "compression_ratio": 1.3653846153846154, "no_speech_prob": 0.0, "words": [{"start": 2566.33, "end": 2567.59, "word": "الحلول", "probability": 0.8946533203125}, {"start": 2567.59, "end": 2568.81, "word": " المُركّبة", "probability": 0.7712890625}, {"start": 2568.81, "end": 2572.31, "word": " وممكن", "probability": 0.57421875}, {"start": 2572.31, "end": 2573.17, "word": " المعادلة", "probability": 0.949951171875}, {"start": 2573.17, "end": 2573.93, "word": " تبقى", "probability": 0.952392578125}, {"start": 2573.93, "end": 2574.99, "word": " equations", "probability": 0.7734375}, {"start": 2574.99, "end": 2577.05, "word": " with", "probability": 0.91845703125}, {"start": 2577.05, "end": 2579.95, "word": " constant", "probability": 0.91552734375}, {"start": 2579.95, "end": 2583.01, "word": " coefficients", "probability": 0.91357421875}, {"start": 2583.01, "end": 2587.57, "word": " يعني", "probability": 0.873046875}, {"start": 2587.57, "end": 2588.17, "word": " المعادلة", "probability": 0.9794921875}, {"start": 2588.17, "end": 2589.25, "word": " التفاضلية", "probability": 0.9359375}, {"start": 2589.25, "end": 2590.53, "word": " مثلا", "probability": 0.84423828125}, {"start": 2590.53, "end": 2591.47, "word": " الـ", "probability": 0.7099609375}, {"start": 2591.47, "end": 2592.03, "word": " A1", "probability": 0.6328125}, {"start": 2592.03, "end": 2592.43, "word": " والـ", "probability": 0.6505126953125}, {"start": 2592.43, "end": 2592.91, "word": " A2", "probability": 0.924072265625}, {"start": 2592.91, "end": 2593.15, "word": " والـ", "probability": 0.9326171875}, {"start": 2593.15, "end": 2593.55, "word": " A3", "probability": 0.940673828125}, {"start": 2593.55, "end": 2593.99, "word": " هدول", "probability": 0.8585611979166666}, {"start": 2593.99, "end": 2595.07, "word": " ثوابت", "probability": 0.82891845703125}], "temperature": 1.0}, {"id": 111, "seek": 261461, "start": 2595.47, "end": 2614.61, "text": "ممكن يكونوا ثوابت وممكن مايكونوش ثوابت إن كانوا ثوابت يبقى بسميها equations with constant coefficients بمعاملة ثابتة وبستخدمها ال complex solutions بالإضافة إلى بعض الطرق الأخرى", "tokens": [2304, 43020, 7251, 30544, 14407, 38637, 14407, 3555, 2655, 4032, 2304, 43020, 19446, 1829, 30544, 2407, 8592, 38637, 14407, 3555, 2655, 36145, 25961, 14407, 38637, 14407, 3555, 2655, 7251, 3555, 4587, 7578, 4724, 38251, 1829, 11296, 11787, 365, 5754, 31994, 4724, 2304, 3615, 10943, 37977, 38637, 16758, 2655, 3660, 46599, 14851, 9778, 40448, 11296, 2423, 3997, 6547, 20666, 28814, 11242, 31845, 3660, 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"probability": 0.883544921875}, {"start": 2601.69, "end": 2602.65, "word": " بسميها", "probability": 0.9781494140625}, {"start": 2602.65, "end": 2603.81, "word": " equations", "probability": 0.32568359375}, {"start": 2603.81, "end": 2604.57, "word": " with", "probability": 0.91796875}, {"start": 2604.57, "end": 2605.33, "word": " constant", "probability": 0.943359375}, {"start": 2605.33, "end": 2606.37, "word": " coefficients", "probability": 0.88037109375}, {"start": 2606.37, "end": 2607.23, "word": " بمعاملة", "probability": 0.9099609375}, {"start": 2607.23, "end": 2607.89, "word": " ثابتة", "probability": 0.9622802734375}, {"start": 2607.89, "end": 2609.09, "word": " وبستخدمها", "probability": 0.6888916015625}, {"start": 2609.09, "end": 2609.27, "word": " ال", "probability": 0.64990234375}, {"start": 2609.27, "end": 2609.77, "word": " complex", "probability": 0.73046875}, {"start": 2609.77, "end": 2610.73, "word": " solutions", "probability": 0.875}, {"start": 2610.73, "end": 2612.17, "word": " بالإضافة", "probability": 0.9181640625}, {"start": 2612.17, "end": 2612.69, "word": " إلى", "probability": 0.8740234375}, {"start": 2612.69, "end": 2613.15, "word": " بعض", "probability": 0.963623046875}, {"start": 2613.15, "end": 2613.95, "word": " الطرق", "probability": 0.96240234375}, {"start": 2613.95, "end": 2614.61, "word": " الأخرى", "probability": 0.9742838541666666}], "temperature": 1.0}, {"id": 112, "seek": 264296, "start": 2615.02, "end": 2642.96, "text": "لكن لو كانت هذه المعادلة homogeneous equation لكن المعادلات ما هيش ثوابت يبقى ممكن تحوير المعادلة إن كانت بصيغة محددة بحيث أضيع هذه المتغيرات وأقلبها إلى معادلة بمعاملات ثابتة وهذه اسمها Cauchy-Euler equations يبقى بدنا نيجي لحاجة اسمها Cauchy-Euler equations", "tokens": [1211, 19452, 45164, 25961, 2655, 29538, 9673, 3615, 18513, 37977, 42632, 5367, 44381, 9673, 3615, 18513, 1211, 9307, 19446, 39896, 8592, 38637, 14407, 3555, 2655, 7251, 3555, 4587, 7578, 3714, 43020, 6055, 5016, 2407, 13546, 9673, 3615, 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0.828125}, {"start": 2968.81, "end": 2969.71, "word": " Calculus", "probability": 0.59954833984375}, {"start": 2969.71, "end": 2970.05, "word": " B", "probability": 0.64599609375}], "temperature": 1.0}, {"id": 127, "seek": 297744, "start": 2970.5, "end": 2977.44, "text": "infinite integration تكامل من 0 إلى infinity أو من رقم إلى انفنترال", "tokens": [259, 5194, 642, 10980, 6055, 4117, 10943, 1211, 9154, 1958, 30731, 13202, 34051, 9154, 12602, 4587, 2304, 30731, 16472, 5172, 29399, 2288, 6027], "avg_logprob": -0.6321614682674408, "compression_ratio": 1.0795454545454546, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2970.5, "end": 2971.66, "word": "infinite", "probability": 0.66326904296875}, {"start": 2971.66, "end": 2972.4, "word": " integration", "probability": 0.9296875}, {"start": 2972.4, "end": 2974.2, "word": " تكامل", "probability": 0.63641357421875}, {"start": 2974.2, "end": 2974.36, "word": " من", "probability": 0.85205078125}, {"start": 2974.36, "end": 2974.7, 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0.72216796875}, {"start": 2988.92, "end": 2990.0, "word": " بهذا", "probability": 0.93994140625}, {"start": 2990.0, "end": 2990.66, "word": " القدر", "probability": 0.986328125}, {"start": 2990.66, "end": 2990.8, "word": " ان", "probability": 0.3203125}, {"start": 2990.8, "end": 2991.34, "word": " اكتفي", "probability": 0.882080078125}, {"start": 2991.34, "end": 2991.84, "word": " و", "probability": 0.87109375}, {"start": 2991.84, "end": 2992.18, "word": " اظن", "probability": 0.8771158854166666}, {"start": 2992.18, "end": 2992.54, "word": " اننا", "probability": 0.7890625}, {"start": 2992.54, "end": 2992.74, "word": " قد", "probability": 0.95751953125}, {"start": 2992.74, "end": 2993.28, "word": " وصلنا", "probability": 0.9938151041666666}, {"start": 2993.28, "end": 2993.58, "word": " الى", "probability": 0.8896484375}, {"start": 2993.58, "end": 2994.0, "word": " نهاية", "probability": 0.8260091145833334}, {"start": 2994.0, "end": 2994.76, "word": " المحاضرة", "probability": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0d2e516d4d65224c2c90f32603924a51a7ab2c17
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cLNYD9YMFlA_raw.srt
@@ -0,0 +1,2172 @@
+1
+00:00:20,670 --> 00:00:27,070
+بسم الله الرحمن الرحيم يسعدنا أن نرحب بيكون في
+
+2
+00:00:27,070 --> 00:00:32,550
+بداية هذا الفصل الدراسي الجديد وهو الفصل الثاني من
+
+3
+00:00:32,550 --> 00:00:40,040
+العام 2012-2013هذه المادة اللي هي مادة معدلات وجبر
+
+4
+00:00:40,040 --> 00:00:47,920
+خط هي عبارة عن أربع ساعات يعني تسجل في كشف درجاتك
+
+5
+00:00:47,920 --> 00:00:52,140
+أربع ساعات طبعا اللي بتجيب فوق التسعين بتضمن أن
+
+6
+00:00:52,140 --> 00:00:56,720
+المعدل هيظل عالي دائما و أبدا لأن هذه أربع ساعات
+
+7
+00:00:56,720 --> 00:01:01,840
+مش ساعة ولا ساعتين فلما تجيب فيها فوق التسعين بتظل
+
+8
+00:01:01,840 --> 00:01:05,470
+المعدلها عالي دائما أو أبداوانتوا غالبكوا بنات
+
+9
+00:01:05,470 --> 00:01:10,150
+كلية الهندسة يبقى حرصى على ان تكونى في هذا المستوى
+
+10
+00:01:10,150 --> 00:01:13,590
+لإن مستواكوا في الثانوية العامة كان مستوى عالى
+
+11
+00:01:13,590 --> 00:01:16,530
+والشغل في الجامعة بيختلف عن الشغل في المرحلة
+
+12
+00:01:16,530 --> 00:01:21,130
+الثانوية وانتوا درستوا قبل هيك سنة عندنا وهذه هي
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+13
+00:01:21,130 --> 00:01:25,230
+السنة الثانية او هذا هو الفصلة الرابع اللى كنا في
+
+14
+00:01:25,230 --> 00:01:30,600
+هذه الجامعة اللى لم يكن لبعض كنا اكثرمن ذلك لكن
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+15
+00:01:30,600 --> 00:01:35,300
+هذه اللي هي الحالة المثالية لذلك أحرصنا على
+
+16
+00:01:35,300 --> 00:01:41,280
+الدراسة بشكل سليم أنا أحب أن أذكر من باب قول الله
+
+17
+00:01:41,280 --> 00:01:47,080
+تعالى واذكر فإن الذكرة تنفع المؤمنين أحب أن أذكر
+
+18
+00:01:47,080 --> 00:01:54,740
+بكيفية الدراسة أولا قبل أن نبدأ في الموضوعال ..
+
+19
+00:01:54,740 --> 00:01:59,500
+بالنسبة للدراسة حتى تدرسي دراسة سليمة و تجيبي
+
+20
+00:01:59,500 --> 00:02:04,980
+علامات أنا بشرح المحاضرة تفصيليا على اللوعبوأفتح
+
+21
+00:02:04,980 --> 00:02:09,940
+المجال للأسئلة لمن أرادت أن تسأل بل بطلب منكوا
+
+22
+00:02:09,940 --> 00:02:13,980
+أحيانا إنكوا تسألوا بقول من عندها سؤال من بتحب
+
+23
+00:02:13,980 --> 00:02:19,240
+تسأل ليه سؤال حتى نطلع وقد استفدنا أو فهمنا ما قيل
+
+24
+00:02:19,240 --> 00:02:24,140
+أمامنا على الصبورة هنا شرحنا الموضوع شرحا كاملا
+
+25
+00:02:24,140 --> 00:02:31,990
+مطلوب مننا ندرس المحاضرة فور الذهاب إلى البيتإن
+
+26
+00:02:31,990 --> 00:02:36,530
+أجلنا لبكرة بصير بدها وقت ضعف وإن أجلنا لآخر
+
+27
+00:02:36,530 --> 00:02:42,830
+الأسبوع بدنا وقت أضعاف الوقت الذي أخذناه أو الكلام
+
+28
+00:02:42,830 --> 00:02:46,410
+اللي بنذاكره اليوم يعني الأربع ساعات ممكن تروح في
+
+29
+00:02:46,410 --> 00:02:49,730
+البيت تجريها في نص ساعة أو في ساعة لربع و تكون
+
+30
+00:02:49,730 --> 00:02:53,970
+قرأتي المحاضرة كاملة و استوعبتيها لكن إذا بتخليها
+
+31
+00:02:53,970 --> 00:02:58,230
+لنهاية الأسبوع من نص ساعة أو ساعة لربع لعلها تحتاج
+
+32
+00:02:58,230 --> 00:03:04,150
+إلى أربع ساعاتيبقى لا تؤجلي عمل اليوم إلى الغد لإن
+
+33
+00:03:04,150 --> 00:03:08,910
+هذه الساعات مش تراكمة و أنا في الأسبوع أعطيكي أربع
+
+34
+00:03:08,910 --> 00:03:12,070
+ساعات في المادة فما بالك بغيرها لما يعطيكي أبو
+
+35
+00:03:12,070 --> 00:03:16,970
+ساعة و أبو ساعتين و أبو ثلاث ساعات و ربما يكون عند
+
+36
+00:03:16,970 --> 00:03:22,070
+بعضكوا أربع ساعات أخرى يبقى يتراكم الشيء علشان و
+
+37
+00:03:22,070 --> 00:03:27,290
+إذا تراكم بصير من الصعب الدراسة يبقى يجب أن ندرس
+
+38
+00:03:27,290 --> 00:03:33,060
+أولا بأولالنقطة الثانية الدراسة ليست ان نقرأ
+
+39
+00:03:33,060 --> 00:03:36,560
+المحاضرة و نقرأ الأمثلة و نقول احنا تمام لا مش
+
+40
+00:03:36,560 --> 00:03:42,000
+تمام يعني اذا اكتفيت بالمحاضرة و الأمثلة ربما
+
+41
+00:03:42,000 --> 00:03:46,940
+تنجحي ربما لا استطيع التأكيد لكن مشان تنجح و تجيب
+
+42
+00:03:46,940 --> 00:03:53,150
+درجات لازم تمسك القلم و تحلي بإيدك انتو .. و بعد
+
+43
+00:03:53,150 --> 00:03:56,470
+هيكده هتصعب عليك بعض الأسئلة ان تصعب عليك بعض
+
+44
+00:03:56,470 --> 00:04:00,550
+الأسئلة تعالوا نقشونا بنجاوبك طبعا عندي ساعات
+
+45
+00:04:00,550 --> 00:04:06,950
+مكتبية هقولك و هو ضرورةاللي هو دراسة المحاضرة فورا
+
+46
+00:04:06,950 --> 00:04:11,610
+العودة إلى البيت ثم حل الأسئلة و اللي بيصعب عليك
+
+47
+00:04:11,610 --> 00:04:16,270
+إحنا موجودين تعالى بنناقشك فيه و بتناقشنا فيه حتى
+
+48
+00:04:16,270 --> 00:04:20,810
+إذا نقطة ما فهمتيهاش برضه تعالى اسألي فيها يعني
+
+49
+00:04:20,810 --> 00:04:24,450
+إذا ماقدرتيش تساوع بيها هنا أو في البيت تعالى
+
+50
+00:04:24,450 --> 00:04:28,330
+اسألينا فيها إحنا بنجاوبك ان شاء الله و تعالى و
+
+51
+00:04:28,330 --> 00:04:32,570
+لنبخل عليكي بأي معلومة ان شاء الله و تباركه و
+
+52
+00:04:32,570 --> 00:04:39,360
+تعالىبعد هيك وصلنا للامتحان فلما نوصل للامتحان
+
+53
+00:04:39,360 --> 00:04:45,880
+علينا أن نأتي بنماذج من الامتحانات السابقة نطلع
+
+54
+00:04:45,880 --> 00:04:50,880
+عليها بس مشان نعرف كيف نماذج الامتحانات او كيف
+
+55
+00:04:50,880 --> 00:04:55,020
+يوضع نظام الامتحان وبالتالي ما نصير في صورة
+
+56
+00:04:55,020 --> 00:04:59,900
+الامتحان قبل ايه قبل أن ندخل الامتحان مش نتفاجأ
+
+57
+00:04:59,900 --> 00:05:04,540
+بشكله يوم الامتحانالذين يكونوا متدربين وماخدين
+
+58
+00:05:04,540 --> 00:05:08,380
+احتياطاتنا الله سبحانه وتعالى بيعيدنا على النجاح
+
+59
+00:05:08,380 --> 00:05:14,880
+لأن الله تبارك وتعالى لا يضيع أجر من أحسن عمله
+
+60
+00:05:14,880 --> 00:05:19,560
+اللي بيحسن العمل الله سبحانه وتعالى بيعطيه الأجر
+
+61
+00:05:19,560 --> 00:05:26,000
+ويرزقه النجاح بس بدك تعتمدي على الله أولا وأخيرا
+
+62
+00:05:26,000 --> 00:05:31,050
+مش على قرايتكالاجراية ضرورية وهي من جانب الأخذ
+
+63
+00:05:31,050 --> 00:05:35,630
+بالأسباب ثم الاعتماد على الله يعني أنا بدلت كل
+
+64
+00:05:35,630 --> 00:05:41,310
+جهدي وكل طاقتي في أني أستوعب أو أفهم أو أحل
+
+65
+00:05:41,310 --> 00:05:46,150
+المسائل وبعد ذلك برفع يدي إلى الله سبحانه وتعالى
+
+66
+00:05:46,150 --> 00:05:51,010
+وخاصة في دوري كل صلاة وأطلب من الله النجاح والله
+
+67
+00:05:51,010 --> 00:05:56,260
+سبحانه وتعالى لن يخيب دعائكلقوله تبارك ليس في مادة
+
+68
+00:05:56,260 --> 00:06:01,680
+معدلة تفاضلية وجبر خط وإنما في كل المساقات الأخرى
+
+69
+00:06:01,680 --> 00:06:07,120
+لأن هذا هو الأساس الصحيح للدراسة من خلال خبرتنا
+
+70
+00:06:07,120 --> 00:06:13,170
+السابقة على مدى أكثر من عشرينعاما في الجامعة
+
+71
+00:06:13,170 --> 00:06:18,010
+الإسلامية وعلى مدى أكثر من ثلاثين عاما في حقل
+
+72
+00:06:18,010 --> 00:06:23,370
+التدريسة بنعطيكي خبرتنا بسهولة بضيف شغلة بس لو قبل
+
+73
+00:06:23,370 --> 00:06:29,650
+تيجي حضرت الموضوع قرأتيه مثل قراءة الجريدةالواحد
+
+74
+00:06:29,650 --> 00:06:32,610
+ماجرال جنرال بيطلع معاه بس العناوين الرئيسية بس
+
+75
+00:06:32,610 --> 00:06:36,510
+التفاصيلات محفظهاش لكن العناوين الرئيسية بتضلها
+
+76
+00:06:36,510 --> 00:06:39,790
+راسخة .. يوم صار كذا كذا و كان الرد عليه كذا كذا
+
+77
+00:06:39,790 --> 00:06:44,970
+يبقى احنا بيناياكي بس مشان تكوني .. يعني يكون عندي
+
+78
+00:06:44,970 --> 00:06:48,350
+خلفية شو احنا بنحكي فانت لو جيتي جابة اللي تيجي
+
+79
+00:06:48,350 --> 00:06:53,780
+على المحاضرة و كنت يعني قرأتيهاقراءة مرور الكرام
+
+80
+00:06:53,780 --> 00:06:57,820
+قراءة الجريدة بيكون شيء جاهز بديش هيك تجيني حافظ
+
+81
+00:06:57,820 --> 00:07:02,320
+ولا حاجة بديك بس تعرف شو الموضوع اللي بناها نتحدث
+
+82
+00:07:02,320 --> 00:07:09,500
+فيه المتابعة لها دور أساسي في تواصل المعلومات
+
+83
+00:07:09,500 --> 00:07:14,780
+والبناء زي ما انت شايفها من خلال اسم المساق معادلة
+
+84
+00:07:14,780 --> 00:07:20,520
+تفاضلية وجبرخاطي يبقى النص المقرر معادلة تفاضلية
+
+85
+00:07:20,520 --> 00:07:28,700
+والنص في الآخر جبر خاطي هناخد six chapters تلاتة
+
+86
+00:07:28,700 --> 00:07:34,340
+معادلة تفاضلية وتلاتة جبر خاطي سنبدأ أول شي ب
+
+87
+00:07:34,340 --> 00:07:38,220
+chapter واحد معادلة تفاضلية وهي المعادلة التفاضلية
+
+88
+00:07:38,390 --> 00:07:44,150
+من الرتبة الأولى بأنواعها المختلفة ثم بعد ذلك إلى
+
+89
+00:07:44,150 --> 00:07:49,350
+ثلاثة شباتر جبر خطي بصير أربعة وبعد ذلك بنرجع إلى
+
+90
+00:07:49,350 --> 00:07:54,610
+شبترين معدلة تفاضلية بصير ستة وهذا هو المقرر في
+
+91
+00:07:54,610 --> 00:08:02,810
+هذا المسابقنأتي الآن لاسم المساق اسم الكتاب المؤلف
+
+92
+00:08:02,810 --> 00:08:07,750
+المساقات اللتي سندرسها في هذا الفصل ان شاء الله
+
+93
+00:08:07,750 --> 00:08:11,130
+تعالى الكتاب اسمه elementary differential
+
+94
+00:08:11,130 --> 00:08:17,390
+equations with linear algebra يبقى اسم الكتاب هو
+
+95
+00:08:17,390 --> 00:08:18,250
+elementary
+
+96
+00:08:27,420 --> 00:08:36,620
+Elementary Differential Equations
+
+97
+00:08:36,620 --> 00:08:42,740
+كلمة equations باختصرها إلى الأربع تعرف اللي عندنا
+
+98
+00:08:42,740 --> 00:08:48,380
+يبقى elementary differential equations with linear
+
+99
+00:08:48,380 --> 00:08:49,040
+algebra
+
+100
+00:08:57,860 --> 00:09:05,440
+اسم المؤلف البرت البرت
+
+101
+00:09:05,440 --> 00:09:07,140
+ال رامانستان
+
+102
+00:09:27,120 --> 00:09:34,760
+الان جايكي يبقى اسم الكتاب elementary differential
+
+103
+00:09:34,760 --> 00:09:40,200
+equations with linear algebra المؤلف اسمه البرت
+
+104
+00:09:40,200 --> 00:09:45,260
+رابانستين الطابعة الرابعة يبقى باجي بقول هنا
+
+105
+00:09:45,260 --> 00:09:51,880
+fourth edition يبقى
+
+106
+00:09:51,880 --> 00:09:58,510
+الطابعة الرابعةالكتاب موجود في مكتبة الطالب وهي
+
+107
+00:09:58,510 --> 00:10:03,450
+الشكل تبعه طبعا أنا مجلده hard cover لكن ماهواش
+
+108
+00:10:03,450 --> 00:10:07,730
+hard cover لأن hard cover بكلف ككتر فانت هي الكتاب
+
+109
+00:10:07,730 --> 00:10:11,850
+هي الجلدة الأساسية لبرا مش هالكل واحدة تشوفها بعد
+
+110
+00:10:11,850 --> 00:10:15,970
+المحاضرة ممكنك أنت تتوجهي إلى مكتبة الطالب وتشتري
+
+111
+00:10:15,970 --> 00:10:21,430
+هذا الكتاب لكن إن كانهناك أحد أقاربك أو واحدة من
+
+112
+00:10:21,430 --> 00:10:25,830
+قريباتك كانت بتدرس المادة العام الماضي فالكتاب هو
+
+113
+00:10:25,830 --> 00:10:29,970
+هو لم يتغير لا العام الماضي ولا العام اللي جابله
+
+114
+00:10:29,970 --> 00:10:32,890
+يبقى نفس الكتاب بس اللي جابله كانت الطابعة اللي
+
+115
+00:10:32,890 --> 00:10:36,510
+جابله لكن الطابعة الرابعة إن سنتين بندرس نفس
+
+116
+00:10:36,510 --> 00:10:40,290
+الطابعة الرابعة يبقى هاي الشكل العام طبعا أشكال
+
+117
+00:10:40,290 --> 00:10:44,590
+هندسية فرجار ومحايا وما بعرف إيه على الجلد هايم
+
+118
+00:10:44,590 --> 00:10:48,880
+تمام؟موجود في مكتبة طالب بعد المحاضرة بإمكانك
+
+119
+00:10:48,880 --> 00:10:53,260
+تروحي تشتري او ما هي لذلك يبقى هذا بالنسبة لمين؟
+
+120
+00:10:53,260 --> 00:10:58,620
+بالنسبة للكتاب نيجي ندخل الآن في صميم الموضوعات
+
+121
+00:10:58,620 --> 00:11:03,880
+الخاصة بهذا الكتابيبقى بدنا نيجي لأول chapter اللي
+
+122
+00:11:03,880 --> 00:11:06,940
+هو introduction to a differential equation يعني
+
+123
+00:11:06,940 --> 00:11:13,180
+مقدمة في المعادلات التفاضلية يبقى بعد ذلك بدنا
+
+124
+00:11:13,180 --> 00:11:18,420
+نيجي لأول chapter اللي هو chapter one بتكلم عن
+
+125
+00:11:18,420 --> 00:11:23,560
+introduction مقدمة
+
+126
+00:11:23,560 --> 00:11:28,880
+to differential equations
+
+127
+00:11:31,050 --> 00:11:36,230
+يبقى مقدمة في المعادلات التفاضلية حة نعطي صورة
+
+128
+00:11:36,230 --> 00:11:40,850
+عامة للمعادلات التفاضلية ونبدأ بأول نوع من هذه
+
+129
+00:11:40,850 --> 00:11:45,090
+المعادلات اللي هي المعادلات التفاضلية من الرتبة
+
+130
+00:11:45,090 --> 00:11:50,840
+الأولىfirst order differential equation من هذه
+
+131
+00:11:50,840 --> 00:11:55,580
+المعادلة او تحت الرتبة الأولى هناخد عدة معادلات
+
+132
+00:11:55,580 --> 00:12:00,200
+اول معادلة من هذه المعادلات اللى هى الـ separable
+
+133
+00:12:00,200 --> 00:12:08,330
+equationseparable equations يبقى المعادلات التي
+
+134
+00:12:08,330 --> 00:12:15,290
+يمكن فيها فصل المتغيرات ايش فصل المتغيرات؟ يعني
+
+135
+00:12:15,290 --> 00:12:20,690
+بنحاول نخل ال X في ناحية و ال Y في ناحية أخرى
+
+136
+00:12:20,690 --> 00:12:25,930
+وبالتالي هذا بنسميها فصل المتغيرات ثم نذهب إلى
+
+137
+00:12:25,930 --> 00:12:32,890
+التكاملإذا موضوع المعادلات التفضلية يعتمد فقط على
+
+138
+00:12:32,890 --> 00:12:38,910
+ما درسناه في calculus a و b في موضوع التكامل مش
+
+139
+00:12:38,910 --> 00:12:43,310
+تكاملات صعبة و معقدة لها تكاملات بسيطة و ما إلى
+
+140
+00:12:43,310 --> 00:12:47,670
+ذلك يعني اللي نجحت بجدارة في calculus a و b بتروح
+
+141
+00:12:47,670 --> 00:12:53,030
+تكامل a بسهولة يبقى الأساس تبع المادة هو موضوع
+
+142
+00:12:53,030 --> 00:12:57,000
+التكامللأن ما أقول differential equation معادلات
+
+143
+00:12:57,000 --> 00:13:01,300
+تفاضلية يعني فيها أن معادلة ظهر فيها المشتقة
+
+144
+00:13:01,300 --> 00:13:04,480
+الأولى أو المشتقة الثانية إذا اللي مابده رجعها إلى
+
+145
+00:13:04,480 --> 00:13:09,460
+أصلها معناته بده كامل مرة أو مرتين أو نحو ذلك إذا
+
+146
+00:13:09,460 --> 00:13:15,700
+بالزمن موضوع التكامل مش على هذه بس في كل شبتر
+
+147
+00:13:15,700 --> 00:13:19,860
+ساعات المعادلة التفاضلية بالزمن مين؟ بالزمن موضوع
+
+148
+00:13:19,860 --> 00:13:24,550
+التكاملبعد هيك بدنا نيجي لل homogenous equations
+
+149
+00:13:31,250 --> 00:13:37,210
+يبقى الـ homogeneous equations المعادلات المتجانسة
+
+150
+00:13:37,210 --> 00:13:42,670
+فيها نصيغة من خلالها بنقدر نحكم على المعادلة هل هي
+
+151
+00:13:42,670 --> 00:13:48,290
+separable و هل هي homogeneous طبعا سنقول هذا الشرط
+
+152
+00:13:48,290 --> 00:13:52,550
+في حينه ان شاء الله بعد ال homogeneous بدنا نيجي
+
+153
+00:13:52,550 --> 00:13:57,990
+لل exactical هذه exact equation طبعا كمان فيها شرط
+
+154
+00:13:58,210 --> 00:14:01,890
+الشرط هذا لو تحقق بقول ان المعادلة هذه ما لها
+
+155
+00:14:01,890 --> 00:14:07,010
+exact equation بعد ال exact equation بتداجي لمين؟
+
+156
+00:14:07,010 --> 00:14:15,270
+لل linear equations المعادلات الخطية يبقى إليها
+
+157
+00:14:15,270 --> 00:14:19,750
+شكل محدد بالشكل المحدد هذا لو شفتوا مجرد ما شوفوا
+
+158
+00:14:19,750 --> 00:14:23,270
+بقول هذه إيه معادلة خطية وبالتالي طريقة حل
+
+159
+00:14:23,270 --> 00:14:29,340
+المعادلة بالطريقة الفولانيةبعد هيك بدنا نيجي لـ
+
+160
+00:14:29,340 --> 00:14:37,840
+two types of
+
+161
+00:14:37,840 --> 00:14:45,720
+second order differential
+
+162
+00:14:45,720 --> 00:14:48,400
+equations
+
+163
+00:14:52,970 --> 00:14:58,670
+هذا بنات إجمال ما سندرسه في الشابتر الأول يبقى
+
+164
+00:14:58,670 --> 00:15:02,770
+الشابتر الأول عبارة عن مجموعة من ال sections طبعا
+
+165
+00:15:02,770 --> 00:15:07,270
+اكتر في الكتاب مش كلهم هندرسهم هندرس فقط اللي احنا
+
+166
+00:15:07,270 --> 00:15:11,770
+كاتبينه قدامنا على اللعبكل عنوان هنا يمثل section
+
+167
+00:15:11,770 --> 00:15:15,290
+في الكتاب وفي نهاية ال section فيه مجموعة من
+
+168
+00:15:15,290 --> 00:15:20,110
+الأسئلة هعطيكي أمثلة ان شاء الله من خلال الأسئلة
+
+169
+00:15:20,110 --> 00:15:23,350
+تبعتي التمرين و الأمثلة المحلولة في الكتاب هذه
+
+170
+00:15:23,350 --> 00:15:27,570
+هدية إليك تقريها براحتك من الكتابأنا بعطيكي أمثلة
+
+171
+00:15:27,570 --> 00:15:31,750
+من خلال الأسئلة تبع التمرين وبالتالي قللت عدد
+
+172
+00:15:31,750 --> 00:15:37,230
+الأسئلة المطلوب منك اتحليها وبحاول أغطيلي كل الفكر
+
+173
+00:15:37,230 --> 00:15:43,020
+اللي موجودة بحيث انت ماتلاقيش صعوبة أثناء الحليبقى
+
+174
+00:15:43,020 --> 00:15:47,360
+أول section separable equations المعادلات التي
+
+175
+00:15:47,360 --> 00:15:53,060
+يمكن فيها فصل المتغيرات بمعنى أخل ال X لحالي و ال
+
+176
+00:15:53,060 --> 00:15:56,820
+Y لحالي ثم أقوم بعملية التكامل ال homogeneous
+
+177
+00:15:56,820 --> 00:16:03,340
+equations المعادلات المتجانسة هنعطيها تعريف و نبين
+
+178
+00:16:03,340 --> 00:16:08,920
+كيف هنحل هذا النوع منالمعادلات بعد ذلك ال exact
+
+179
+00:16:08,920 --> 00:16:15,360
+equation المعادلات أتم برضه هيكون لها صيغة و هذه
+
+180
+00:16:15,360 --> 00:16:20,360
+الصيغة لها طريقة للحل ثم بعد ذلك cleaner equations
+
+181
+00:16:20,360 --> 00:16:25,220
+المعادلات الخطية برضه اللي هي شكل معين و عندها
+
+182
+00:16:25,220 --> 00:16:30,950
+صيغة للحلكله هدمنات كله معادلة من الرتبة الأولى
+
+183
+00:16:30,950 --> 00:16:34,530
+شوية عن الرتبة الأولى يعني ماعنديش إلا المعامل
+
+184
+00:16:34,530 --> 00:16:38,630
+التفاضل الأول يعني المشتقة الأولى هي اللي موجودة
+
+185
+00:16:38,630 --> 00:16:43,530
+وين؟ في المعادلة فقط لا غير ماعنديش لا مشتقة تانية
+
+186
+00:16:43,530 --> 00:16:48,030
+ولا تالتة ولا غير بس المشتقة الأولى ومن هنا سمنها
+
+187
+00:16:48,030 --> 00:16:53,280
+first order الرتبة الأولىكل واحدة من المعادلات
+
+188
+00:16:53,280 --> 00:16:57,740
+هدول كلهم هي الرتبة الأولى جانا سيكشن لحاله قال لي
+
+189
+00:16:57,740 --> 00:17:02,820
+two types نوعين من ال second order من الرتبة
+
+190
+00:17:02,820 --> 00:17:06,820
+التانية of differential equation هدول النوعين من
+
+191
+00:17:06,820 --> 00:17:12,180
+حد ما شوفهم بقول اه النوع الأول قد يكون المتغير
+
+192
+00:17:12,180 --> 00:17:17,910
+التابع غير ظاهر في المعادلةيعني Y غير ظاهرة في
+
+193
+00:17:17,910 --> 00:17:23,490
+المعادلة قد يكون النوع الثاني T missing يعني
+
+194
+00:17:23,490 --> 00:17:29,230
+المتغير المستقل T أو X مش ظاهر في المعادلة يبقى
+
+195
+00:17:29,230 --> 00:17:32,470
+هدول النوع الجدد المعادلة ممكن تكون من الرتبة
+
+196
+00:17:32,470 --> 00:17:36,990
+الثانية أو حاصل ضرب two derivatives أو ما إلى ذلك
+
+197
+00:17:36,990 --> 00:17:42,360
+هنشوف كيف نحل المعادلة هذا عن طريق تنزيل الرتبةمن
+
+198
+00:17:42,360 --> 00:17:46,300
+الرتبة الثانية إلى الرتبة الأولى ثم نقوم بعد ذلك
+
+199
+00:17:46,300 --> 00:17:50,880
+بعملية الحل وبالتالي بصير اه ماهياش مشكلة ومن هنا
+
+200
+00:17:50,880 --> 00:17:55,380
+ألحق بهذا الشبطر لأنه بنزل الرتبة من الرتبة
+
+201
+00:17:55,380 --> 00:17:58,760
+الثانية إلى الرتبة الأولى وبالتالي بصير كانها
+
+202
+00:17:58,760 --> 00:18:03,540
+first order differential equation هذا كل ما يتعلق
+
+203
+00:18:03,540 --> 00:18:07,760
+بالشبطر الأول اللي هو ال first order differential
+
+204
+00:18:07,760 --> 00:18:13,120
+equationبنجي الآن نخش في ال chapter الثاني وهو
+
+205
+00:18:13,120 --> 00:18:18,580
+بداية الجبر الخطي linear algebra يبقى بنجي لل
+
+206
+00:18:18,580 --> 00:18:23,300
+chapter التاني ال chapter التاني موضوعين أساسيين
+
+207
+00:18:23,300 --> 00:18:31,720
+matrices and determinants المصفوفات والمحددات يبقى
+
+208
+00:18:31,720 --> 00:18:36,820
+matrices and
+
+209
+00:18:39,250 --> 00:18:46,070
+data منين انت؟
+
+210
+00:18:46,070 --> 00:18:49,850
+يبقى
+
+211
+00:18:49,850 --> 00:18:58,400
+المصفوفات والمحددات طبعاالمصففات والمحددات لن يزيد
+
+212
+00:18:58,400 --> 00:19:02,360
+عما درستي في الثانوية العامة مش في الثانوية أخدت
+
+213
+00:19:02,360 --> 00:19:07,940
+المصففات والمحددات أو بقى تسموه الجبر الإضافي غير
+
+214
+00:19:07,940 --> 00:19:10,720
+الجبر العادي كان معاكوا الجبر الإضافي أو الجبر
+
+215
+00:19:10,720 --> 00:19:14,960
+القاطي في الثانوية العامة ولا في تانية ثانوية؟ في
+
+216
+00:19:14,960 --> 00:19:19,570
+تانية؟ اه يعني درست فيها مرتينعلى أي حال في
+
+217
+00:19:19,570 --> 00:19:23,410
+التانية ولا في التالتة بتفرقش عنها المهم أنه سبق
+
+218
+00:19:23,410 --> 00:19:28,150
+الدراسة التانية يبقى احنا بنذكرها من جديد وكأنك لم
+
+219
+00:19:28,150 --> 00:19:33,830
+تدرسيها من قبل طب السؤال هو شو بدنا ندرس في موضوع
+
+220
+00:19:33,830 --> 00:19:40,550
+المصفوفات يبقى هذا هو الشابتر الثاني زي ما كان هذا
+
+221
+00:19:40,550 --> 00:19:45,110
+هو الشابتر الأول يبقى أول موضوع سناخده في هذا
+
+222
+00:19:45,110 --> 00:19:57,360
+الشابتر هو systemsystems of linear equations
+
+223
+00:19:57,360 --> 00:20:00,460
+انظمة
+
+224
+00:20:00,460 --> 00:20:05,640
+المعادلات الخطية ايش يعني انظمة المعادلة الخطية
+
+225
+00:20:05,640 --> 00:20:11,960
+مثلا قد تكون المعادلة فيها مجهولين وقد يكون بثلاثة
+
+226
+00:20:11,960 --> 00:20:17,670
+مجاهيلوقد يكون باربعة مجهيل او نحو ذلك زي ايش مثلا
+
+227
+00:20:17,670 --> 00:20:26,650
+زي ماجي اقولك المعادلة هذه مثلا a1x زائد a2y زائد
+
+228
+00:20:26,650 --> 00:20:38,610
+a3z يساوي مثلا ال oneA2X أو B1X
+
+229
+00:20:38,610 --> 00:20:51,650
+زائد B2Y زائد B3Z بده يساوي L2 مثلا C1X زائد C2Y
+
+230
+00:20:51,650 --> 00:21:00,430
+زائد C3Z يساوي L3هذا النظام المعادلات بسميه system
+
+231
+00:21:00,430 --> 00:21:05,470
+of linear equations يعني معادلة خطية شوية في ال X
+
+232
+00:21:05,470 --> 00:21:10,790
+و Y و Z اللي هو المجاهيل كلها من الدرجات الأولى
+
+233
+00:21:10,790 --> 00:21:15,470
+يبقى هذه بسميها معادلة خطية المعادلات مع بعض كل
+
+234
+00:21:15,470 --> 00:21:19,510
+تلاتة مجموعة بسميها system of linear equations
+
+235
+00:21:19,510 --> 00:21:26,890
+يعني نظام مكون من مجموعة من المعادلات الخطيةالـ A1
+
+236
+00:21:26,890 --> 00:21:30,370
+والـ A2 والـ A3 والـ B1 والـ B2 والـ B3 والـ C وكل
+
+237
+00:21:30,370 --> 00:21:35,230
+هذه أرقام real numbers أرقام عادية لكن الـ X والـ
+
+238
+00:21:35,230 --> 00:21:39,850
+Y والـ Z هذه مجاهيل فلمان بده أحل ال system يعني
+
+239
+00:21:39,850 --> 00:21:44,670
+بده أجيب قيم هذه المجاهيل دير بالك ال system
+
+240
+00:21:44,670 --> 00:21:49,400
+المعادلات ليس بضرورة يكون ثلاث معادلات ويكونأربعة
+
+241
+00:21:49,400 --> 00:21:53,980
+معادلات في ثلاثة مجاهيل ممكن يكون أربعة معادلات في
+
+242
+00:21:53,980 --> 00:21:59,040
+أربعة مجاهيل ممكن يكون معادلتين في مجهولين ممكن
+
+243
+00:21:59,040 --> 00:22:06,480
+يكون معادلتين في مجهولين و هكذا يعني ليس بضرورة
+
+244
+00:22:06,480 --> 00:22:10,240
+تلات مجاهيل ممكن مجهولين ممكن تلاتة ممكن أربعة
+
+245
+00:22:10,240 --> 00:22:15,200
+ممكن خمسة إلى آخرى يبقى هذا كله system في عندي أحد
+
+246
+00:22:15,200 --> 00:22:21,170
+ثلاثة احتمالاتالاحتمال الاول يكون عندي حل واحدة
+
+247
+00:22:21,170 --> 00:22:26,510
+مافيش غيره حل واحد للتلت معادلات ممكن يكون عندي
+
+248
+00:22:26,510 --> 00:22:32,350
+عدد لانهائي من الحلول مش حل و اتنين و تلاتة او
+
+249
+00:22:32,350 --> 00:22:37,530
+اربعة لأ عدد لانهائي من الحلول الأمر الثالث no
+
+250
+00:22:37,530 --> 00:22:42,230
+solution او الحل does not exist يبقى ال system
+
+251
+00:22:42,230 --> 00:22:47,810
+المعادلة قد يكون حلا واحدةوقد يكون عدد ذانهائي من
+
+252
+00:22:47,810 --> 00:22:53,070
+الحلول وقد لا يوجد حل يبقى هي الاحتمالات التلاتة
+
+253
+00:22:53,070 --> 00:22:56,870
+بالنسبة لل system of linear equations وهذا ما
+
+254
+00:22:56,870 --> 00:23:02,310
+سنجدوه عند دراسة هذا النوع من المعادلات الخطية
+
+255
+00:23:02,310 --> 00:23:06,170
+النقطة الثانية اللي سندرسها هي ال homogeneous
+
+256
+00:23:06,170 --> 00:23:13,830
+systems بعد هيك بدنا نيجي لحاجة اسمهاHomo Genius
+
+257
+00:23:13,830 --> 00:23:16,090
+Systems
+
+258
+00:23:18,410 --> 00:23:21,650
+إيش يعني homogeneous system؟ طب ماهي homogeneous
+
+259
+00:23:21,650 --> 00:23:25,210
+system ماهي اللي فوق هذا system of linear
+
+260
+00:23:25,210 --> 00:23:28,470
+equations إيش يعني homogeneous system؟ باجي بقول
+
+261
+00:23:28,470 --> 00:23:34,530
+لو كانت الواحد و الاتنين و التلاتة بيقى صفر
+
+262
+00:23:34,530 --> 00:23:38,890
+المعادلة التلاتة أو التنتين أو الأربع كلها معادلة
+
+263
+00:23:38,890 --> 00:23:45,060
+صفرية بسمي هذا homogeneous systemيبقى لو كانت هذه
+
+264
+00:23:45,060 --> 00:23:51,420
+كلها بأصفار يبقى هذا بسميمين اللي هو ال homogenous
+
+265
+00:23:51,420 --> 00:23:59,220
+system ال system المتجانس تمام؟ يبقى هذه النقطة
+
+266
+00:23:59,220 --> 00:24:03,220
+الثانوية اللي سندرسها و بعد هيك بدنا نيجي لحاجة
+
+267
+00:24:03,220 --> 00:24:08,580
+اسمها matrices and
+
+268
+00:24:08,580 --> 00:24:10,320
+vectors
+
+269
+00:24:14,590 --> 00:24:22,560
+matrices يا بنات بنات مصوفات هي جامعة matrixMatrix
+
+270
+00:24:22,560 --> 00:24:30,080
+هي مصفوفة جمعها matrices بشيل ال X و بحط CES يبقى
+
+271
+00:24:30,080 --> 00:24:35,320
+matrices مصفوفات Matrix عبارة عن مصفوفة vectors
+
+272
+00:24:35,320 --> 00:24:42,420
+يعني متجهات الصف الأول أو الصف الواحد أو العمود
+
+273
+00:24:42,420 --> 00:24:47,420
+الواحد من عناصر مصفوفة بسميه vectorيبقى ال vector
+
+274
+00:24:47,420 --> 00:24:53,660
+هو عبارة عن مصوفة عمودية أو مصوفة أفوقية تمام؟
+
+275
+00:24:53,660 --> 00:24:58,880
+يبقى هذه بسميها .. بسميها اللي هو ال vector مش
+
+276
+00:24:58,880 --> 00:25:02,520
+vector اتنين I زي اتلات جيه زي اربعة كيه سوى مثلا
+
+277
+00:25:02,520 --> 00:25:07,420
+رقم زي ما أخدنا في ال calculus C لأ لأ لأ هذه ال
+
+278
+00:25:07,420 --> 00:25:10,580
+vector بيختلف عن ال vector هناك وليها دراستة
+
+279
+00:25:10,580 --> 00:25:16,970
+متعلقة بموضوع المصوفات والمحددةبعد هيك بدنا نيجي
+
+280
+00:25:16,970 --> 00:25:22,670
+لحاجة اسمها matrix multiplication
+
+281
+00:25:22,670 --> 00:25:28,530
+يبقى
+
+282
+00:25:28,530 --> 00:25:33,410
+عملية ضرب المصوفات طبعا أخدنا ضرب المصوفات في
+
+283
+00:25:33,410 --> 00:25:38,770
+الثانوية بدأينا نذكربه تاني ومشان أضرب مصوفتين في
+
+284
+00:25:38,770 --> 00:25:43,330
+بعض لازم أتحقق عندي شرط يعني مش أي مصوفتين بقوم
+
+285
+00:25:43,330 --> 00:25:48,370
+بضربهم في بعضلأ لابد يكون عدد الأعمدة في المصوفة
+
+286
+00:25:48,370 --> 00:25:54,270
+الأولى يسوى عدد الصفوف في المصوفة الثانية ان تحقق
+
+287
+00:25:54,270 --> 00:25:59,620
+ذلك بيكون بقدرأضرب المسلطين ما هدول في بعض
+
+288
+00:25:59,620 --> 00:26:03,860
+وبالتالي المسلطين ممكن ال system تبع الأولى يختلف
+
+289
+00:26:03,860 --> 00:26:07,620
+عن ال system تبع المصوفة لما أقول system بالنسبة
+
+290
+00:26:07,620 --> 00:26:12,600
+للمصوفة يعني عدد الصفوف في عدد الأعمدة يعني نوعية
+
+291
+00:26:12,600 --> 00:26:17,220
+المصوفة تلاتة صفوف و عمودين عمودين و أربعة صفوف
+
+292
+00:26:17,220 --> 00:26:23,700
+صفين و ثلاثة أعمدة صفين و أربعة أعمدة يبجي هذا هو
+
+293
+00:26:23,700 --> 00:26:29,500
+النظام تبع مينتبع المصوفة أو بيبقى نقول نوعها M في
+
+294
+00:26:29,500 --> 00:26:37,280
+N M رقم للعدد الصفوف N عدد الأعمدة و هكذا يبقى في
+
+295
+00:26:37,280 --> 00:26:41,600
+شرط لازم أتحقق مشان أقدر أضرب المصوفتين هدول في
+
+296
+00:26:41,600 --> 00:26:47,820
+بعض وبعد هيك some special matrices يبقى هنا some
+
+297
+00:26:47,820 --> 00:26:49,720
+special
+
+298
+00:26:52,090 --> 00:26:56,450
+بعض المصوفات الخاصة
+
+299
+00:26:58,850 --> 00:27:01,930
+ماذا عن بعض المصفوفات الخاصة؟ هذه في الثانوية
+
+300
+00:27:01,930 --> 00:27:07,630
+وكنتوا مذكرين بجينا نقول أنواع المصفوفات types of
+
+301
+00:27:07,630 --> 00:27:13,430
+matrices بجينا نقول المصفوفة الصفرية مصفوفة الوحدة
+
+302
+00:27:13,430 --> 00:27:19,170
+المصفوفة القياسية المصفوفة القطرية المصفوفة
+
+303
+00:27:19,170 --> 00:27:25,090
+المثلثة العليا المصفوفة المثلثة السفلة كل هدول
+
+304
+00:27:25,090 --> 00:27:29,000
+اللي بتسمعهم هذه هي أنواع المصفوفاتيبقى نحن لم
+
+305
+00:27:29,000 --> 00:27:33,000
+نأتي بجديد هو الكلام اللي عتيجي بس بنذكره و بدل ما
+
+306
+00:27:33,000 --> 00:27:37,340
+كنت تكتبيه بالعربي بنكتب هناكبالإنقليزي عادية يبقى
+
+307
+00:27:37,340 --> 00:27:43,160
+لا توجد أي صعوبة أثناء الدراسة وخاصة اللي بتابع
+
+308
+00:27:43,160 --> 00:27:47,720
+الأول بأول يبقى للمدور some special matrices بعض
+
+309
+00:27:47,720 --> 00:27:52,740
+المصفوفات الخاصة يعني المصفوفات اللي لها اسم محدد
+
+310
+00:27:52,740 --> 00:27:58,280
+مصفوفة صفرية مصفوفة قطرية مصفوفة قياسية مصفوفة
+
+311
+00:27:58,280 --> 00:28:03,140
+مربعة مصفوفة مستطيلة مصفوفة الوحدة مصفوفة مثلثة
+
+312
+00:28:03,140 --> 00:28:06,970
+عليا مصفوفة مثلثة ..so كله هنذكره و نعطي عليه
+
+313
+00:28:06,970 --> 00:28:12,410
+أمثلة ان شاء الله تعالى بعد ذلك بنجي ل
+
+314
+00:28:12,410 --> 00:28:15,370
+determinants المحددات
+
+315
+00:28:22,890 --> 00:28:28,550
+الفرق بين الإتنين الكتابة متشابهة قريبة من بعض إلى
+
+316
+00:28:28,550 --> 00:28:34,570
+حد بعيد لكن المصوفة لو ضربتيها في رقم أو ضربت
+
+317
+00:28:34,570 --> 00:28:39,970
+مصوفتين في البعض فالنتج هو مصوفة لكن المحدد له
+
+318
+00:28:39,970 --> 00:28:45,440
+قيمة عددية واحدة one real numberيعني المحدد له
+
+319
+00:28:45,440 --> 00:28:50,380
+قيمة حقيقية مافيش غيرها يعني بقدر أفك المحدد و
+
+320
+00:28:50,380 --> 00:28:53,700
+أطلع قد ياش قيمته العددية و من هنا هذا الفرق
+
+321
+00:28:53,700 --> 00:28:58,020
+الأساسي بينه وبين المصوفة المصوفات لها خواص
+
+322
+00:28:58,020 --> 00:29:04,420
+المحددات لها خواص تختلف كذلك عن خواص من المصوفات
+
+323
+00:29:04,700 --> 00:29:09,400
+يبقى المصوّات والمحددات كل واحدة فيهم لها خواص خاص
+
+324
+00:29:09,400 --> 00:29:15,060
+بها تختلف فيها عن الخواص الأخرى وفي الثانوية أخدتم
+
+325
+00:29:15,060 --> 00:29:20,380
+خواص المحددات و هنرجع نعطي خواص المحددات لـ
+
+326
+00:29:20,380 --> 00:29:25,220
+properties of determinants بعد هيك هنجي في
+
+327
+00:29:25,220 --> 00:29:29,300
+المحددات ناخد حاجة اسمها cofactors
+
+328
+00:29:32,500 --> 00:29:39,000
+يعني العوامل المرافقة شو العوامل المرافقة؟ نذكركم
+
+329
+00:29:39,000 --> 00:29:43,820
+لما جينا نفك المحدد مثلا نفكه باستخدام عناصر الصف
+
+330
+00:29:43,820 --> 00:29:47,600
+اللي اول اللي بنمسك هو العنصر نشطه بصفه و عموده
+
+331
+00:29:47,600 --> 00:29:54,320
+المحدد اللي بيظل بسميه المحدد الأصغر المناظر لهذا
+
+332
+00:29:54,320 --> 00:29:58,700
+العنصر يبقى هذا هو ال cofactorاللي هو العامل
+
+333
+00:29:58,700 --> 00:30:03,420
+المرافق لمين للعنصر اللي موجود في المحدد انا بس
+
+334
+00:30:03,420 --> 00:30:07,740
+مجرد تذكير ليس الا لكن عندما نوصله هنعطيه نشتغل
+
+335
+00:30:07,740 --> 00:30:12,800
+شغل تفصيلي و حسابات دقيقة ان شاء الله تبارك وتعالى
+
+336
+00:30:13,890 --> 00:30:20,230
+بعد هيك بدنا نيجي نتناول كرامر رول قاعدة كرامر لحل
+
+337
+00:30:20,230 --> 00:30:25,890
+المعادلات وكذلك طريقة معكوس المصفوفة نستخدمها في
+
+338
+00:30:25,890 --> 00:30:29,710
+حل ال system of linear equations يبقى بدنا نيجي
+
+339
+00:30:29,710 --> 00:30:40,410
+ناخد حاجة اسمها كرامر رول يبقى كرامر كرامر
+
+340
+00:30:40,410 --> 00:30:48,060
+رولقاعدة كرامر لحل المعادلات و بعد هيك بدنا ناخد
+
+341
+00:30:48,060 --> 00:30:59,420
+the inverse of a matrix يبقى معكوس المصوفة
+
+342
+00:30:59,420 --> 00:31:04,860
+واستخدام معكوس المصوفة في حل المعادلات التفاضلية
+
+343
+00:31:05,610 --> 00:31:10,710
+هذا بالنسبة لمين؟ للشبتر الثاني يبقى كل اللي سمعته
+
+344
+00:31:10,710 --> 00:31:16,270
+هو ملخص الشبتر الثاني الشبتر الثاني أكثر من عشر
+
+345
+00:31:16,270 --> 00:31:21,770
+سكاشن يعني طويل شوية مش زي الأول الأولاني الشبتر
+
+346
+00:31:21,770 --> 00:31:27,150
+الأول قصير هذا أطول منه كثيرا بعد هي كده بنجي
+
+347
+00:31:27,150 --> 00:31:33,830
+للشبتر التالت يبقى بدنا نجي لحاجة اسمها vector
+
+348
+00:31:34,910 --> 00:31:43,510
+spaces and linear transformations
+
+349
+00:32:05,280 --> 00:32:11,780
+الفضاءات الاتجاهية والتحويلات الخطية يبقى vector
+
+350
+00:32:11,780 --> 00:32:15,700
+spaces الفضاءات الاتجاهية linear transformations
+
+351
+00:32:15,700 --> 00:32:22,460
+التحويلات الخطية موضوع يام كل واحد مستقل عن الثاني
+
+352
+00:32:22,460 --> 00:32:27,980
+وهذا يعتبر ethical chapter موجود في المقرريعني
+
+353
+00:32:27,980 --> 00:32:33,940
+مليان شوية و بده متابعة أولا بأول هنعطي تعريف ال
+
+354
+00:32:33,940 --> 00:32:38,520
+vector space في هذا ال chapter هنبدأ أول حاجة بال
+
+355
+00:32:38,520 --> 00:32:48,000
+vectorspaces الفضاءات الاتجاهية بعدين ناخد مجموعات
+
+356
+00:32:48,000 --> 00:32:53,120
+جزئية من هذه الفضاءات اسمها ال sub-spaces يبقى
+
+357
+00:32:53,120 --> 00:32:58,340
+بدنا نيجي لحاجة اسمها sub-spaces الفضاءات
+
+358
+00:32:58,340 --> 00:33:02,640
+الاتجاهية يعني وقتش لما أخد مجموعة جزئية من ال
+
+359
+00:33:02,640 --> 00:33:07,520
+vector space بقدر أقول عنهاالـ subspace و ماكنتش
+
+360
+00:33:07,520 --> 00:33:11,200
+بقدر أقول عنها ما هي ال subspace يعني نفترض لو
+
+361
+00:33:11,200 --> 00:33:14,800
+قلنا البنات اللي قعدتها دول كلهم عبارة عن vector
+
+362
+00:33:14,800 --> 00:33:19,020
+space لو أخدت الشجة هذه هل هذه subspace ولا لا
+
+363
+00:33:19,020 --> 00:33:23,960
+الله أعلم يبقى في شروط ان تحققت هذه الشروط بقول
+
+364
+00:33:23,960 --> 00:33:27,870
+هذه subspaceإن اختل أي شرط من هذه الشروط يبقى ما
+
+365
+00:33:27,870 --> 00:33:31,150
+أقدرش أقول عن هذه subspace كل اللي بقدر أقول إنها
+
+366
+00:33:31,150 --> 00:33:36,250
+مجموعة جزئية subset مجموعة جزئية لكنها ليست
+
+367
+00:33:36,250 --> 00:33:47,070
+subspace طيب بعد هيك بنجي لحاجة اسمها linear بنجي
+
+368
+00:33:47,070 --> 00:33:51,450
+لحاجة اسمها linear dependence
+
+369
+00:33:56,360 --> 00:34:01,980
+and linear independence الاستقلال الخاطي والاعتماد
+
+370
+00:34:01,980 --> 00:34:02,980
+الخاطي
+
+371
+00:34:05,350 --> 00:34:11,590
+واجتيش مستقلات عن بعض خطيا او واجتيش معتمدات على
+
+372
+00:34:11,590 --> 00:34:17,810
+بعض خطيا يبقى هذا بالنسبالك كله متعلق بمين؟ متعلق
+
+373
+00:34:17,810 --> 00:34:23,470
+بال vector spaces الأثنين على حد سواء بدنا نيجي
+
+374
+00:34:23,470 --> 00:34:31,790
+لحاجة اسمها ال runnerskin ال
+
+375
+00:34:31,790 --> 00:34:37,130
+runnerskin دي بنت عبارة عن محددdeterminant بس
+
+376
+00:34:37,130 --> 00:34:40,590
+محدده بيجيبوهش عشوائي بيجيبه من ال vectors اللي
+
+377
+00:34:40,590 --> 00:34:46,490
+عندي ومن خلال الرونسكين هذا بقدر أحكم هل اللي عند
+
+378
+00:34:46,490 --> 00:34:50,990
+ال vectors هدول dependence ولا independence يعني
+
+379
+00:34:50,990 --> 00:34:56,490
+هناخد نظريات بواسطتها نقدر نحكم وبواسطة ال رونسكين
+
+380
+00:34:56,490 --> 00:35:01,680
+نقدر نحكم هل هدولlinearly independent ولا linearly
+
+381
+00:35:01,680 --> 00:35:06,440
+dependent هذا الكلام سنعرفه في حينه ان شاء الله
+
+382
+00:35:06,440 --> 00:35:11,900
+تعالى بعد ذلك بنجي لآخر نقطة في ال vector spaces
+
+383
+00:35:11,900 --> 00:35:19,840
+حاجة اسمها ال dimension او
+
+384
+00:35:19,840 --> 00:35:26,800
+dimensionsهنعطيلها تعريف و من خلال التعريف هذا نقل
+
+385
+00:35:26,800 --> 00:35:31,780
+لكل vector space قدش ال dimension له طبعا في حاجة
+
+386
+00:35:31,780 --> 00:35:36,960
+بنات اسمها ال bases اللي هو الأساس لل vector space
+
+387
+00:35:36,960 --> 00:35:41,460
+تمام ال dimension له علاقة بال bases أو له علاقة
+
+388
+00:35:41,460 --> 00:35:45,540
+بعدد ال vector في ال bases فإذا كان مثلا ال bases
+
+389
+00:35:45,540 --> 00:35:49,750
+يحتوي بس على two vectors بقول ال base له اتنينإن
+
+390
+00:35:49,750 --> 00:35:53,430
+كان يحتوي على تلاتة linear independent vectors
+
+391
+00:35:53,430 --> 00:35:58,510
+بقول ال basis له تلاتة و هكذا طبعا سنعرف الحين و
+
+392
+00:35:58,510 --> 00:36:02,890
+كيف نحسب هذا ال basis و من ثم نقدر نعرف قداش ال
+
+393
+00:36:02,890 --> 00:36:08,050
+dimension لكل vector space موجود انه بعد ذلك بنجي
+
+394
+00:36:08,050 --> 00:36:11,410
+للنصف الثاني من هذا ال chapter وهو ال linear
+
+395
+00:36:11,410 --> 00:36:17,530
+transformations يبقى بدنا نيجي لمن؟ لل linear
+
+396
+00:36:26,490 --> 00:36:29,810
+transformations التحويلات الخطية شو يعني تحويلة
+
+397
+00:36:29,810 --> 00:36:34,540
+خطية؟ هي عبارة عن functionمش دراسة الـ function في
+
+398
+00:36:34,540 --> 00:36:39,040
+calculus A بس الـ function أخدناها من set A إلى
+
+399
+00:36:39,040 --> 00:36:43,860
+set B لكن linear transformation من vector space
+
+400
+00:36:43,860 --> 00:36:48,220
+إلى vector space مش set عادية تمام؟ يبقى هي
+
+401
+00:36:48,220 --> 00:36:51,160
+function من ال vector space الأول إلى ال vector
+
+402
+00:36:51,160 --> 00:36:56,180
+space الثاني ولها شروط ان تحقق أو لها شرطين مش
+
+403
+00:36:56,180 --> 00:37:00,920
+أكتر ان تحقق هذان الشرطان بقول عن هذه هي linear
+
+404
+00:37:00,920 --> 00:37:05,490
+transformationو هاد ال linear transformation لها
+
+405
+00:37:05,490 --> 00:37:11,030
+خواص و شغل اللي هيكون منصب كله على الخواص يبقى
+
+406
+00:37:11,030 --> 00:37:14,930
+بدنا نيجي لآخر نقطة موجودة في هاد ال section و هي
+
+407
+00:37:14,930 --> 00:37:20,730
+properties of linear transformations
+
+408
+00:37:30,790 --> 00:37:41,430
+يبقى هذا كل ما سندرسه في ال chapter التالت برضه
+
+409
+00:37:41,430 --> 00:37:44,650
+ال chapter هذا طويل بنات يعني chapter اتنين و
+
+410
+00:37:44,650 --> 00:37:50,190
+تلاتة هما اطول two chapters في المقرر يبقى اخدنا
+
+411
+00:37:50,190 --> 00:37:54,470
+chapterين جبر خطي chapter اتنين و chapter تلاتة
+
+412
+00:37:54,470 --> 00:37:58,450
+ابنجي ل chapter اربع اللي هو ال diagonalization
+
+413
+00:38:07,780 --> 00:38:11,960
+ال chapter هذا مش هنكتر عليكم بس two sections مش
+
+414
+00:38:11,960 --> 00:38:17,140
+أكتر two sections طبعا هذا مرتبط بموضوع مين بموضوع
+
+415
+00:38:17,140 --> 00:38:22,200
+ال vector spaces اللي قبله يبقى two sections أول
+
+416
+00:38:22,200 --> 00:38:25,020
+حاجة بدنا نيجي للحاجة اسمها ال characteristic
+
+417
+00:38:25,020 --> 00:38:25,820
+values
+
+418
+00:38:34,130 --> 00:38:38,530
+القيم المميزة وبعد ذلك بنجي اليوميا لل
+
+419
+00:38:38,530 --> 00:38:46,670
+diagonalization ايه
+
+420
+00:38:46,670 --> 00:38:49,910
+ال two sections مافيش غيرهم ايش معناه دياجون
+
+421
+00:38:49,910 --> 00:38:56,350
+الليمانات قطر ممتاز جدا يبقى diagonalization كي
+
+422
+00:38:56,350 --> 00:39:01,870
+بدي اعمل مصفوفة قطريةقطرية يعني ايه؟ اشي يعني
+
+423
+00:39:01,870 --> 00:39:06,070
+مصوفة مثلثة عليا أو سفلة يعني اللي فوق القطر
+
+424
+00:39:06,070 --> 00:39:11,290
+الرئيسي أسفر أو اللي تحت القطر الرئيسي أسفر أو
+
+425
+00:39:11,290 --> 00:39:14,610
+اللي فوق أسفر و اللي تحت أسفر ومايضالش إلا من؟
+
+426
+00:39:14,610 --> 00:39:20,550
+عناصر القطر الرئيسيهذا كلمة دا هذا المعنى البلدي
+
+427
+00:39:20,550 --> 00:39:23,970
+القريب إلى الفهم لمعنى ال diagonalization لكن
+
+428
+00:39:23,970 --> 00:39:29,530
+تحتها بنشر خطوات رياضية كأني بدي أحول المصوفة اللي
+
+429
+00:39:29,530 --> 00:39:34,430
+عندنا إلى ال diagonal matrix في شغل بدنا نشتغله
+
+430
+00:39:34,430 --> 00:39:39,330
+هذا ومن خلاله بكون جيب ال diagonalization لمام
+
+431
+00:39:39,330 --> 00:39:43,700
+لهذه المصوفةمش كل مصوفة اللي هي diagonalization مش
+
+432
+00:39:43,700 --> 00:39:48,160
+كل واحدة بنفعلها تمام يبقى في شروط لازم تتحقق مشان
+
+433
+00:39:48,160 --> 00:39:53,180
+أقدر أعمل ال diagonalization لمصوفة قبل هذه بدي
+
+434
+00:39:53,180 --> 00:39:58,000
+أخد ال characteristic values اللي هي القيامة و ال
+
+435
+00:39:58,000 --> 00:40:03,740
+characteristic vectors يعني المتجهات المميزةوالقيم
+
+436
+00:40:03,740 --> 00:40:08,500
+المميزة لهذه المصوفة يبقى نقطتين فقط في هذا ال
+
+437
+00:40:08,500 --> 00:40:13,700
+chapter او two sections فقط في هذا ال chapter على
+
+438
+00:40:13,700 --> 00:40:18,280
+هيك بيكون انتهينا من الجبر الخاطي يبقى أخدنا
+
+439
+00:40:18,280 --> 00:40:24,060
+chapter معادلة تفاضلية و three chapters اللي هو
+
+440
+00:40:24,060 --> 00:40:29,400
+جبر خاطي يبقى هي قداش اربعة طايل قداشضايل اتنين
+
+441
+00:40:29,400 --> 00:40:33,040
+اللي هم عبارة عن معادلات تفاضلية في ال chapter
+
+442
+00:40:33,040 --> 00:40:37,940
+الأول بدأنا بالرتبة الأولى هنا بدنا نقش الرتبة
+
+443
+00:40:37,940 --> 00:40:43,100
+التانية التالتة الرابعة إلى آخرها يبقى لو جينا ل
+
+444
+00:40:43,100 --> 00:40:50,660
+chapter خمسة chapter خمسة اسمه linear differential
+
+445
+00:40:50,660 --> 00:40:57,660
+equations linear differential equationsطبعا يمكن
+
+446
+00:40:57,660 --> 00:41:01,180
+واحدة تقولي متوسعة كتبنا linear equations هذه ال
+
+447
+00:41:01,180 --> 00:41:04,900
+linear equations من ال first order هذي ال second
+
+448
+00:41:04,900 --> 00:41:09,300
+order، third order، fourth order، nth order دي
+
+449
+00:41:09,300 --> 00:41:11,840
+بيجمع الرتبة التانية، التالتة، الرابعة، الرتبة
+
+450
+00:41:11,840 --> 00:41:15,400
+النونية لكن ال linear اللي خدناها قبل شوية هذي هي
+
+451
+00:41:15,400 --> 00:41:21,040
+من؟ من ال first order فقط لغير تحت هذا العنوان
+
+452
+00:41:21,040 --> 00:41:26,850
+بدنا ندرس عدة شغلاتأول شيء بدنا ناخد هو الـ
+
+453
+00:41:26,850 --> 00:41:33,290
+Homogeneous Equations هذه اختصار لكلمة homogeneous
+
+454
+00:41:33,290 --> 00:41:38,470
+بدا المكتوبة بالشكل الطويل هذابقول هنا homogeneous
+
+455
+00:41:38,470 --> 00:41:45,630
+equations يبقى المعادلات المتجانسة المعادلات
+
+456
+00:41:45,630 --> 00:41:49,790
+المتجانسة مش المعادلات المتجانسة الأولانية لأ من
+
+457
+00:41:49,790 --> 00:41:53,570
+الرتبة التانية او التالتة الطرف اليميني يساوي صفرة
+
+458
+00:41:53,570 --> 00:41:58,850
+بقول المعادلة تساوي صفر من حد ما اشوف هيك بسميها
+
+459
+00:41:58,850 --> 00:42:03,700
+homogeneous طب لو ماكناش صفر كانت رقمبسميها الـ
+
+460
+00:42:03,700 --> 00:42:07,640
+Non-homogeneous differential equation يبقى الـ
+
+461
+00:42:07,640 --> 00:42:11,540
+homogeneous لها طريقة للحل والـ non-homogeneous
+
+462
+00:42:11,540 --> 00:42:17,080
+لها طريقة للحل الطريقة بتعتمد على حل ال
+
+463
+00:42:17,080 --> 00:42:23,750
+homogeneousطيب هنا هذه ال homogenous equations هذه
+
+464
+00:42:23,750 --> 00:42:31,090
+ممكن أكثر من طريقة لمعرفة حل هذه المعادلة من ذلك
+
+465
+00:42:31,090 --> 00:42:37,850
+طريقة ال complex root الجذور التخيلية يبقى بداجي
+
+466
+00:42:37,850 --> 00:42:44,710
+لحاجة اسمها complex solutions complex solutions
+
+467
+00:42:46,330 --> 00:42:52,310
+الحلول المُركّبة وممكن
+
+468
+00:42:52,310 --> 00:43:03,010
+المعادلة تبقى equations with constant coefficients
+
+469
+00:43:03,010 --> 00:43:07,570
+يعني
+
+470
+00:43:07,570 --> 00:43:13,550
+المعادلة التفاضلية مثلا الـ A1 والـ A2 والـ A3
+
+471
+00:43:13,550 --> 00:43:19,510
+هدول ثوابتممكن يكونوا ثوابت وممكن مايكونوش ثوابت
+
+472
+00:43:19,510 --> 00:43:25,330
+إن كانوا ثوابت يبقى بسميها equations with constant
+
+473
+00:43:25,330 --> 00:43:29,770
+coefficients بمعاملة ثابتة وبستخدمها ال complex
+
+474
+00:43:29,770 --> 00:43:36,380
+solutions بالإضافة إلى بعض الطرق الأخرىلكن لو كانت
+
+475
+00:43:36,380 --> 00:43:41,320
+هذه المعادلة homogeneous equation لكن المعادلات ما
+
+476
+00:43:41,320 --> 00:43:47,420
+هيش ثوابت يبقى ممكن تحوير المعادلة إن كانت بصيغة
+
+477
+00:43:47,420 --> 00:43:52,960
+محددة بحيث أضيع هذه المتغيرات وأقلبها إلى معادلة
+
+478
+00:43:52,960 --> 00:43:58,260
+بمعاملات ثابتة وهذه اسمها Cauchy-Euler equations
+
+479
+00:43:58,260 --> 00:44:02,960
+يبقى بدنا نيجي لحاجة اسمها Cauchy-Euler equations
+
+480
+00:44:03,670 --> 00:44:11,290
+كوشي كوشي
+
+481
+00:44:11,290 --> 00:44:13,810
+أيلر equations
+
+482
+00:44:19,450 --> 00:44:25,130
+معادلة مشهورة باسم الاتنين هذه المعادلة بيكون
+
+483
+00:44:25,130 --> 00:44:30,570
+مسبوقة المعامل تبعها بدلالة ال X الأس تبعه جد
+
+484
+00:44:30,570 --> 00:44:35,610
+الرتبة تبعت ال Y فنقول X تربيع Y Double Prime زائد
+
+485
+00:44:35,610 --> 00:44:40,230
+XY Prime زائد Constant يساوي مين؟ Constant في Y
+
+486
+00:44:40,230 --> 00:44:44,250
+يساوي Zero يبقى هذه اللي بيسمي الكوشيه Euler
+
+487
+00:44:44,250 --> 00:44:48,750
+Equation وحناخد طريقة كيف أحولها من معادلة
+
+488
+00:44:48,990 --> 00:44:53,610
+بالمعاملات تبعتها متغيرة إلى معادلة بمعاملة ثابتة
+
+489
+00:44:53,610 --> 00:44:59,710
+وبعدين كيف انحل هذا النوع من المعادلات بعد ذلك بدأ
+
+490
+00:44:59,710 --> 00:45:03,130
+نجي لـ Non-homogeneous يبقى أخدنا أول حاجة الـ
+
+491
+00:45:03,130 --> 00:45:08,750
+homogeneous بدأ أجي لـ Non-homogeneous
+
+492
+00:45:08,750 --> 00:45:12,310
+differential equations
+
+493
+00:45:15,460 --> 00:45:17,800
+هنا الـ Non-homogeneous differential اللي كنا
+
+494
+00:45:17,800 --> 00:45:24,400
+بياخد ثلاث طرق للحل ثلاث طرق لحل هذا النوع من
+
+495
+00:45:24,400 --> 00:45:30,320
+المعادلات الطريقة الأولى والطريقة الثانية والطريقة
+
+496
+00:45:30,320 --> 00:45:34,520
+الثالثة الطريقة الأولى اللى بناخدها طريقة
+
+497
+00:45:34,520 --> 00:45:40,700
+المعاملات الثابتة فأول طريقة من هذه الطرق اللي هي
+
+498
+00:45:40,700 --> 00:45:44,300
+الـ Undetermined
+
+499
+00:45:51,060 --> 00:45:56,620
+coefficients طريقة المعاملات المجهولة طريقة
+
+500
+00:45:56,620 --> 00:46:02,720
+الثانية variation of
+
+501
+00:46:02,720 --> 00:46:10,960
+parameters يعني
+
+502
+00:46:10,960 --> 00:46:18,080
+طريقة تغيير المتغيراتطريقة الثالثة reduction of
+
+503
+00:46:18,080 --> 00:46:28,440
+order reduction of order طريقة اختزال الرتبة يعني
+
+504
+00:46:28,440 --> 00:46:33,340
+كيف أنزل الرتبة من الرتبة الثانية إلى الرتبةالأولى
+
+505
+00:46:33,340 --> 00:46:39,420
+مثلا وبالتالي هي الطرق الثلاث في هذه الحالة يبقى
+
+506
+00:46:39,420 --> 00:46:42,780
+في هذا الشبط راح ناخد نوعين من المعادلات النوع
+
+507
+00:46:42,780 --> 00:46:47,660
+الأول المعادلات المعاملات ثوابت النوع الثاني
+
+508
+00:46:47,660 --> 00:46:52,780
+المعاملات متغيرةالمعاملات المتغيرة يمكن تحويلها
+
+509
+00:46:52,780 --> 00:46:58,120
+إلى معادلة homogeneous بمعاملات ثابتة وهذا لها
+
+510
+00:46:58,120 --> 00:47:02,740
+أكثر من طريقة للحل ال complex هو أحد العلوم بعد
+
+511
+00:47:02,740 --> 00:47:05,480
+ذلك يجب أن نصل إلى non homogeneous يعني الطرف اللي
+
+512
+00:47:05,480 --> 00:47:10,520
+بين المعادلة يجب أن يكون دالة وليس zero يبقى هذا
+
+513
+00:47:10,520 --> 00:47:15,040
+النوع من المعادلات له ثلاث طرق للحل الطريقة الأولى
+
+514
+00:47:15,040 --> 00:47:18,420
+طريقة ال undetermined coefficients المعاملات
+
+515
+00:47:18,420 --> 00:47:22,870
+المجهولةوطريقة الثانية طريقة ال variation of
+
+516
+00:47:22,870 --> 00:47:27,570
+parameters تغيير المتغيرات و الحصول على هذه
+
+517
+00:47:27,570 --> 00:47:31,430
+المتغيرات في قد إيش قيمتها الطريقة التالتة طريقة
+
+518
+00:47:31,430 --> 00:47:35,490
+اختزال الرتبة أو تنزيل الرتبة من الرتبة الثانية
+
+519
+00:47:35,490 --> 00:47:42,410
+إلى الرتبة الأولى يبقى هذا باختصار كل ما هو موجود
+
+520
+00:47:42,410 --> 00:47:48,950
+في chapter 5 بنجي ل chapter 6 اللي هو Laplace
+
+521
+00:47:51,030 --> 00:47:55,510
+هذا ليس شبتر ستة هذه المواحدة خمسة هذا بنفط لبعض و
+
+522
+00:47:55,510 --> 00:48:00,690
+بروح لشبتر تسعة يبقى الشبتر السادس هو شبتر تسعة
+
+523
+00:48:00,690 --> 00:48:07,770
+يبقى الشبتر تسعة اللي هو لابلاز ترانسفورمز
+
+524
+00:48:08,410 --> 00:48:15,950
+تحويلات لابلاس وما يتعلق بها وكيفية استخدامها في
+
+525
+00:48:15,950 --> 00:48:23,450
+حل المعادلات التفاضلية وبعد هيك using Laplace
+
+526
+00:48:23,450 --> 00:48:32,850
+transform to
+
+527
+00:48:32,850 --> 00:48:42,100
+solve secondorder differential
+
+528
+00:48:42,100 --> 00:48:48,350
+equationsيعني كيف بنستخدم ال place transform في حل
+
+529
+00:48:48,350 --> 00:48:52,310
+المعادلة التفاضلية من الرتبة الثانية أو حتى من
+
+530
+00:48:52,310 --> 00:48:57,450
+الرتبة الثالثة أو الرابعة حسب طبيعة المثلة لكن
+
+531
+00:48:57,450 --> 00:49:01,730
+الرتبة الثانية هي الدرجة أكثر يبقى هذا باختصار
+
+532
+00:49:01,730 --> 00:49:05,110
+مثلا يبقى هذا الشيء الجديد ال place transform
+
+533
+00:49:05,110 --> 00:49:09,630
+بيكون عندنا معادلة بنات جصدي function هذه ال
+
+534
+00:49:09,630 --> 00:49:14,710
+function صعبة التعامل معاها فبنجيب معادلةمكافئة
+
+535
+00:49:14,710 --> 00:49:20,550
+لها تقريبا و بنحاول نستخدمها في إيه في الحل طبعا و
+
+536
+00:49:20,550 --> 00:49:24,330
+في عندنا جدول كل معادلة شهولة بلاس ترانسفورم لها
+
+537
+00:49:24,330 --> 00:49:30,050
+وهذا يعتمد على التكامل اللي دراسناه في Calculus B
+
+538
+00:49:30,500 --> 00:49:36,400
+infinite integration تكامل من 0 إلى infinity أو من
+
+539
+00:49:36,400 --> 00:49:37,440
+رقم إلى انفنترال
+
+540
+00:49:46,480 --> 00:49:51,840
+يعتمد عليها place a transfer بهذا القدر ان اكتفي و
+
+541
+00:49:51,840 --> 00:49:56,320
+اظن اننا قد وصلنا الى نهاية المحاضرة فالمرة الجاية
+
+542
+00:49:56,320 --> 00:50:00,860
+ان شاء الله هندخل في صميم الموضوع من اول و جديد
+
+543
+00:50:00,860 --> 00:50:05,480
+هذا كلام عام حول المنهج بارك الله
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..68e2fb9683e2bde3b43831456ec576485df05e60
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ.srt
@@ -0,0 +1,1560 @@
+1
+00:00:20,700 --> 00:00:24,720
+بسم الله الرحمن الرحيم، بنرجع لـ section ثلاثة
+
+2
+00:00:24,720 --> 00:00:29,240
+سبعة اللي ابتدأنا به المرة الماضية وهو يتحدث عن ال
+
+3
+00:00:29,240 --> 00:00:35,700
+linear transformations التحويلات الخطية طبعًا
+
+4
+00:00:35,700 --> 00:00:40,840
+أعطينا تعريفًا للتحويلة الخطية ثم أعطينا مثالًا واحدًا فقط 
+
+5
+00:00:40,840 --> 00:00:45,360
+في المرة الماضية، واليوم بنكمل الأمثلة وبنكمل نفس
+
+6
+00:00:45,360 --> 00:00:49,700
+الموضوع إن شاء الله تعالى، طبعًا حابب أذكر قبل أن
+
+7
+00:00:49,700 --> 00:00:54,820
+نبدأ بـlinear transformation هي عبارة عن function
+
+8
+00:00:54,820 --> 00:00:59,960
+أو mapping من vector space V إلى vector space W
+
+9
+00:00:59,960 --> 00:01:06,420
+بحيث هذه الـ function تحقق خاصيتين، الخاصية الأولى T
+
+10
+00:01:06,420 --> 00:01:13,360
+of C في V يساوي C في T of V حيث C is a scalar يعني عدد 
+
+11
+00:01:13,360 --> 00:01:18,810
+حقيقي، والـ V هو فيكتور موجود في الـ vector space V
+
+12
+00:01:18,810 --> 00:01:23,070
+هذه الخاصية الأولى، الخاصية الثانية T لما يتأثر على 
+
+13
+00:01:23,070 --> 00:01:30,170
+مجموع  vectors V1 زائد V2 بيكون T of V1 زائد T of V2
+
+14
+00:01:30,450 --> 00:01:34,390
+يبقى هذه الخاصية، إن لو تحققوا بقول عن الـ mapping
+
+15
+00:01:34,390 --> 00:01:37,730
+اللي عندنا أو الـ function هي عبارة عن linear
+
+16
+00:01:37,730 --> 00:01:41,870
+transformation، يبقى هذا اللي تكلمنا عنه المرة الماضية 
+
+17
+00:01:41,870 --> 00:01:47,530
+وعطينا على ذلك مثالًا واحدًا، وهذا هو المثال رقم 2
+
+18
+00:01:48,270 --> 00:01:52,790
+يبقى المثال رقم 2 بيقول افترض أنه عندي mapping أو 
+
+19
+00:01:52,790 --> 00:01:57,430
+function T من الـ vector space R3 إلى الـ vector
+
+20
+00:01:57,430 --> 00:02:03,810
+space R2، هذه الـ function معرفة على الشكل التالي T 
+
+21
+00:02:03,810 --> 00:02:08,650
+لما تتأثر على العناصر الموجودة في R3، اللي هو X1 و X2 و
+
+22
+00:02:08,650 --> 00:02:15,460
+X3 صورتها بتبقى موجودة في R2 وهي على الشكل اللي هو
+
+23
+00:02:15,460 --> 00:02:20,740
+element of two components مركبتين وليس ثلاثة
+
+24
+00:02:20,740 --> 00:02:26,640
+لأن هذا الـ R3 مركبتين، لمين؟ لأن هذا R2، طيب ما هو 
+
+25
+00:02:26,640 --> 00:02:31,260
+شكل العناصر؟ شكله هو المركبة الثالثة اللي عندنا
+
+26
+00:02:31,260 --> 00:02:34,600
+بتخليه هنا، المركبة الأولى في الـ vector space اللي 
+
+27
+00:02:34,600 --> 00:02:39,940
+جديد، وهنا واحد صحيح، هو يسأل هل هذه T linear 
+
+28
+00:02:39,940 --> 00:02:44,900
+transformation أم لا؟ يعني الجواب ليس نقول نعم أو 
+
+29
+00:02:44,900 --> 00:02:49,140
+لا، نعم أو لا مبني على المعلومات التي سأتحدث عنها
+
+30
+00:02:49,140 --> 00:02:53,140
+و why؟ إذا قلتِ linear transformation ستقولين ليش؟
+
+31
+00:02:53,140 --> 00:02:55,640
+وإذا قلتِ لي تينا ماهيّش linear transformation
+
+32
+00:02:55,640 --> 00:03:02,230
+ستقولين ليه؟ إذا نحن بنروح ندور على الخاصيتين، هل
+
+33
+00:03:02,230 --> 00:03:06,590
+الخاصيتين محققتين ولا لأ، بدي أمسك الخاصية الأولى
+
+34
+00:03:06,590 --> 00:03:11,590
+لو تحققت الخاصية الأولى بروح لمين؟ للخاصية الثانية
+
+35
+00:03:11,590 --> 00:03:16,290
+لو ما تحققتش ما في داعي أروح لمين؟ للتانية حتى لو
+
+36
+00:03:16,290 --> 00:03:20,310
+بدأتِ بالتانية ثم بالأولى، ما في مشكلة، المهم أنا بدي
+
+37
+00:03:20,310 --> 00:03:29,650
+الخاصيتين أن يتحققا في آن واحد، فبدي أقوله هنا if C
+
+38
+00:03:29,650 --> 00:03:36,070
+موجود في الـ set of real number  و الـ V بده يساوي
+
+39
+00:03:36,070 --> 00:03:43,170
+X واحد و X اثنين و X ثلاثة، X واحد و X اثنين و X 
+
+40
+00:03:43,170 --> 00:03:52,770
+ثلاثة، هذا كله موجود في R3، then بدي آخذ T of C في الـ
+
+41
+00:03:52,770 --> 00:04:00,030
+V، يبقى هذا بدي يساوي T of C في الـ V اللي عبارة عن X
+
+42
+00:04:00,030 --> 00:04:07,710
+واحد و X اثنين و X ثلاثة بهذا الشكل، هذا 
+
+43
+00:04:07,710 --> 00:04:13,340
+بدي يعطيني T of، حاضروا الكون، الصندوق هذا في كل 
+
+44
+00:04:13,340 --> 00:04:21,240
+component من المركبات الثلاثة، يبقى CX1، CX2، CX3
+
+45
+00:04:21,240 --> 00:04:26,960
+بالشكل اللي عندنا هذا، طبقا للتعريف اللي عطيتيني إياه
+
+46
+00:04:26,960 --> 00:04:31,240
+يعني يبقى هذا الكلام بدي يساوي المركبة الأخيرة 
+
+47
+00:04:31,240 --> 00:04:38,500
+وقدرش واحد صحيح، طيب بدي آخذ C برا وأشوف شو بيصير
+
+48
+00:04:38,500 --> 00:04:44,160
+معايا، يمكن لو أخذت C برا بيصير عندي هذا C في X
+
+49
+00:04:44,160 --> 00:04:51,570
+ثلاثة وواحد على Z، هل الـ element هذا موجود في R2؟ 
+
+50
+00:04:51,570 --> 00:04:55,750
+موجود في R2 الصحيح، لكن هل هو على الشكل اللي عندنا 
+
+51
+00:04:55,750 --> 00:05:00,290
+هذا؟ لأ، ما هوّاش على الشكل اللي عندنا هذا، يبقى هذا 
+
+52
+00:05:00,290 --> 00:05:08,550
+لا يساوي C في T R V
+
+53
+00:05:10,600 --> 00:05:14,960
+ما بيساويش الكلام هذا طبعًا، مادام ما بيساويش يبقى T هذه
+
+54
+00:05:14,960 --> 00:05:17,180
+linear transformation ولا ما هيّش linear
+
+55
+00:05:17,180 --> 00:05:25,560
+transformation؟ يعني يبقى هنا بقوله C so it is not
+
+56
+00:05:25,560 --> 00:05:28,200
+a linear transformation
+
+57
+00:05:31,980 --> 00:05:35,800
+طب كان بإمكان أي واحدة فيكن تبدأ من مين؟ من الـ
+
+58
+00:05:35,800 --> 00:05:40,380
+condition الثاني وليس من الـ condition الأول ونشوف
+
+59
+00:05:40,380 --> 00:05:44,940
+هل يتحقق، والله ما يتحقق، أما حتى هيك انتهينا من
+
+60
+00:05:44,940 --> 00:05:48,540
+الحل خلصنا يعني لو اجينا حل تاني واحدة ابتدأت
+
+61
+00:05:48,540 --> 00:05:53,520
+بالخطوة الثانية وليست بالخطوة الأولى، وراحت قالت لي
+
+62
+00:05:53,520 --> 00:06:00,940
+أنا بدي آخذ V واحد بده يساوي X واحد و X اثنين و X
+
+63
+00:06:00,940 --> 00:06:08,560
+ثلاثة، والـ V اثنين بده يساوي Y واحد و Y اثنين و Y 
+
+64
+00:06:08,560 --> 00:06:12,660
+ثلاثة اللي موجودة في R3
+
+65
+00:06:32,220 --> 00:06:35,020
+النتيجة تساوي
+
+66
+00:06:44,260 --> 00:06:48,260
+التعريف بيقول المركبة الأخيرة والأخر واحد
+
+67
+00:06:48,260 --> 00:06:52,880
+يبقى المركبة الأخيرة ليه؟ X ثلاثة زائد Y 
+
+68
+00:06:52,880 --> 00:06:58,760
+ثلاثة ومين؟ وواحد، بدي أشوف هل هذا يساوي T of V واحد 
+
+69
+00:06:58,760 --> 00:07:04,180
+زائد T of V اثنين ولا لأ؟ بقوله كويس، إذا بدي أحط هذا
+
+70
+00:07:04,180 --> 00:07:09,200
+على شكل مجموع اللي هو two vectors يبقى بقدر أقول 
+
+71
+00:07:09,200 --> 00:07:16,500
+هذا X ثلاثة واحد زائد Y ثلاثة وقداش؟ و Zero، هذا من
+
+72
+00:07:16,500 --> 00:07:23,480
+الأول T of V واحد، وهذا زي ما هو، يبقى هذا الكلام 
+
+73
+00:07:23,480 --> 00:07:30,220
+بدي أساويه T of V واحد زائد هل هذا T of V اثنين؟ لأ
+
+74
+00:07:30,220 --> 00:07:35,880
+يبقى بحطه زي ما هو يبقى هذا زائد Y ثلاثة و Zero
+
+75
+00:07:35,880 --> 00:07:43,200
+وهذا الكلام لا يساوي T of V واحد زائد T of V اثنين
+
+76
+00:07:44,620 --> 00:07:50,580
+لأن T of V2 عبارة عن Y3 و 1 وليس Y3 و 0، يبقى كمان 
+
+77
+00:07:50,580 --> 00:07:55,580
+الـ condition الثاني مش متحقق is not satisfied يبقى 
+
+78
+00:07:55,580 --> 00:08:00,140
+بناء عليه برضه T not linear transformation، يبقى 
+
+79
+00:08:00,140 --> 00:08:08,390
+بروح بقوله T is not a linear transformation، يبقى 
+
+80
+00:08:08,390 --> 00:08:14,190
+معناها كلام اللي أخذت الخاصية الأولى ولاقتها غير
+
+81
+00:08:14,190 --> 00:08:18,490
+متحققة وقالت T not linear transformations صحيح، اللي راحت 
+
+82
+00:08:18,490 --> 00:08:23,090
+على الخاصية الثانية مباشرة ولاقتها غير متحققة برضه 
+
+83
+00:08:23,090 --> 00:08:28,890
+كلامها صحيح، يبقى هدول حلين وليس حلًا واحدًا يعني
+
+84
+00:08:28,890 --> 00:08:35,990
+يكفيني أحدهما، طب نيجي لـ المثال اللي بعده، example 3
+
+85
+00:08:41,890 --> 00:08:52,810
+تقول define a mapping، define a mapping، a mapping T
+
+86
+00:08:52,810 --> 00:09:02,290
+من R2 إلى R2 by T
+
+87
+00:09:02,290 --> 00:09:11,880
+of X1 و X2 بده يساوي الأول اثنين X واحد ناقص X
+
+88
+00:09:11,880 --> 00:09:21,300
+اثنين، وX واحد زائد X اثنين، السؤال هو prove or
+
+89
+00:09:21,300 --> 00:09:31,840
+disprove، prove or disprove that T is a linear
+
+90
+00:09:31,840 --> 00:09:33,200
+transformation
+
+91
+00:09:59,840 --> 00:10:03,840
+بنرجع لسؤالنا ثاني، يبقى أنا في عندي mapping أو 
+
+92
+00:10:03,840 --> 00:10:08,980
+function معرفة من R2 لـ R2 نفسها بالضبط
+
+93
+00:10:08,980 --> 00:10:16,460
+تمامًا، معرفة كيف؟ T of X1 و X2 يساوي اثنين المركبة
+
+94
+00:10:16,460 --> 00:10:19,620
+الأولى ناقص المركبة الثانية، هذا بيعطيني الـ
+
+95
+00:10:19,620 --> 00:10:24,660
+component الأولى، الـ component الثانية هي مجموع 
+
+96
+00:10:24,660 --> 00:10:28,960
+المركبات الاثنين هدول، يبقى عرفنا function بهذا
+
+97
+00:10:28,960 --> 00:10:34,300
+الشكل، سؤالنا هو هل هذه الـ function ممكن تكون linear
+
+98
+00:10:34,300 --> 00:10:38,740
+transformation أم لا؟ بنقوله الله أعلم تعالى نشوف
+
+99
+00:10:38,740 --> 00:10:42,840
+نتأكد، جالي probe or disprobe يعني إذا بتقدر تثبت
+
+100
+00:10:42,840 --> 00:10:46,020
+إنها linear transformation وإذا ما قدرتِ خلاص نعفي الله عنك
+
+101
+00:10:49,350 --> 00:10:55,770
+النقطة الأولى، بدي آخذ C موجودة في الـ set of real
+
+102
+00:10:55,770 --> 00:11:01,690
+numbers، والـ V اللي يساوي X واحد و X اثنين
+
+103
+00:11:01,690 --> 00:11:11,150
+موجودة في الـ R اثنين، then بدي آخذ T of C في الـ V
+
+104
+00:11:11,830 --> 00:11:20,690
+يبقى هذه T في C of V لـ X واحد و X اثنين، يبقى هذا
+
+105
+00:11:20,690 --> 00:11:27,470
+الكلام T of، ده فك الجثة ده، يبقى C X واحد و C X
+
+106
+00:11:27,470 --> 00:11:33,130
+اثنين بهذا الشكل، Y يساوي، الآن بدي أجي أطبق التعريف اللي
+
+107
+00:11:33,130 --> 00:11:36,730
+عندنا اللي إحنا قايلينه، يبقى هذا الكلام بده يساوي 
+
+108
+00:11:36,730 --> 00:11:46,950
+اثنين CX1 ناقص CX2، هيّا تمام، يبقى اثنين المركبة
+
+109
+00:11:46,950 --> 00:11:52,770
+الأولى ناقص المركبة الثانية، المركبة الأولى زائد
+
+110
+00:11:52,770 --> 00:11:58,160
+المركبة الثانية اللي عندنا، طيب أجت بصرت بالشكل اللي
+
+111
+00:11:58,160 --> 00:12:03,590
+عندنا هذا، لحظة يا بنات إن الـ C موجودة وين؟ موجودة
+
+112
+00:12:03,590 --> 00:12:07,850
+في كل مركبة، يبقى بقدر آخذها برا عامل مشترك من 
+
+113
+00:12:07,850 --> 00:12:14,990
+الكون، يبقى بقدر أقول هذا الكلام يساوي C، 2 X1 ناقص 
+
+114
+00:12:14,990 --> 00:12:22,830
+X2، وX1 زائد X2 بهذا الشكل، طب اللي بينجو سين هذا 
+
+115
+00:12:22,830 --> 00:12:30,310
+مش هو عبارة عن T of X1 و X2؟ يعني كأن هذا الكلام
+
+116
+00:12:30,310 --> 00:12:35,750
+يساوي C في T أو V اللي بدأنا فيها، إذا الـ condition 
+
+117
+00:12:35,750 --> 00:12:41,150
+الأول ماله؟ متحقق، بدي أجي للـ condition الثاني، الـ
+
+118
+00:12:41,150 --> 00:12:45,230
+condition الثاني بدي آخذ two vectors موجودات وين؟
+
+119
+00:12:45,230 --> 00:12:51,920
+في الـ R2 ويبقى باشي بجولة اللي هو الـ V1 بده يساوي 
+
+120
+00:12:51,920 --> 00:13:02,300
+X1 و X2، و V2 بده يساوي Y1 و Y2، الاثنين هدول
+
+121
+00:13:02,300 --> 00:13:04,940
+موجودات في R2
+
+122
+00:13:08,310 --> 00:13:17,070
+بدي آخذ T of الـ V1 زائد V2، يبقى T of بدي أجمع الـ
+
+123
+00:13:17,070 --> 00:13:26,830
+two vectors هدول، يبقى X1 زائد Y1 و X2 زائد Y2، يبقى
+
+124
+00:13:26,830 --> 00:13:34,110
+ايه جمعهم مرة واحدة، طب الآن هذا كله كله 
+
+125
+00:13:34,110 --> 00:13:58,890
+element موجود في الـ R2 كله
+
+126
+00:13:58,890 --> 00:14:00,550
+element موجود في الـ R2 كله، element موجود في 
+
+127
+00:14:00,550 --> 00:14:00,770
+الـ R2 كله، element موجود في الـ R2 كله، element
+
+128
+00:14:00,770 --> 00:14:00,850
+element موجود في الـ R2 كله، element موجود في
+
+129
+00:14:00,850 --> 00:14:04,270
+الـ R2 بتداجي لمين؟ بتداجي للمركبة الثانية 
+
+130
+00:14:04,270 --> 00:14:09,390
+المركبة الثانية اللي هي الأولى زائد الثانية يبقى
+
+131
+00:14:09,390 --> 00:14:18,430
+X واحد زائد Y واحد زائد X اثنين زائد Y اثنين بهذا
+
+132
+00:14:18,430 --> 00:14:24,320
+الشكل، طبعًا يبقى هذه كتابة العنصر اللي عندنا بدالي 
+
+133
+00:14:24,320 --> 00:14:28,940
+أفك الجوس هذا، يبقى لو جيت فكيت الجوس هذا بيصير على 
+
+134
+00:14:28,940 --> 00:14:34,200
+الشكل التالي اثنين X واحد زائد اثنين Y واحد
+
+135
+00:14:34,200 --> 00:14:39,040
+ناقص X اثنين ناقص Y اثنين، هذه المركبة الأولى
+
+136
+00:14:39,040 --> 00:14:43,700
+المركبة الثانية كما هي، X واحد زائد Y واحد 
+
+137
+00:14:43,700 --> 00:14:50,460
+زائد X اثنين زائد Y اثنين، هذا الكلام يساوي هذا
+
+138
+00:14:50,460 --> 00:14:55,780
+كله يعتبر عنصر واحد، بدي أحاول أكتبه على شكل عنصرين
+
+139
+00:14:55,780 --> 00:15:02,200
+وأشوف هل ممكن ولا لأ؟ بدي آخذ 2X1 مع الـ X يعني بدي 
+
+140
+00:15:02,200 --> 00:15:09,920
+آخذ الـ X مع بعضها والـ Y مع بعضها، يبقى هذا 2X1 نقص
+
+141
+00:15:09,920 --> 00:15:17,630
+X2 وهنا X1 زائد X2، زائد بقى اللي عندي هنا مين؟
+
+142
+00:15:17,630 --> 00:15:24,990
+اثنين Y واحد ناقص Y اثنين، وY واحد زائد Y اثنين 
+
+143
+00:15:24,990 --> 00:15:29,690
+بالشكل اللي عندنا، لو جمعت اللي هو الـ two vectors 
+
+144
+00:15:29,690 --> 00:15:33,350
+هدول بطلع مين؟ بطلع الـ vector اللي فوق بالضبط 
+
+145
+00:15:33,350 --> 00:15:39,430
+تمامًا، طيب هذا مين؟ مش T of X واحد و X اثنين يبقى
+
+146
+00:15:39,430 --> 00:15:46,910
+هذا الكلام يساوي T of X واحد و X اثنين زائد الثاني
+
+147
+00:15:46,910 --> 00:15:55,890
+T of Y واحد و Y اثنين، يعني هذا كأنه T of V1 زائد T
+
+148
+00:15:55,890 --> 00:16:01,290
+of V2 بالضبط تمامًا، إذا تحققت الخاصية الثانية ولا
+
+149
+00:16:01,290 --> 00:16:11,100
+لا؟ يبقى هنا T is a linear transformation، يبقى هنا T is a
+
+150
+00:16:11,100 --> 00:16:13,340
+linear transformation
+
+151
+00:16:35,780 --> 00:16:41,440
+نأخذ ملاحظة if 
+
+152
+00:16:41,440 --> 00:16:49,480
+الـ
+
+153
+00:16:49,480 --> 00:16:57,020
+V and الـ W are two vector spaces
+
+154
+00:17:10,000 --> 00:17:21,060
+و T من V إلى W هو
+
+155
+00:17:21,060 --> 00:17:24,400
+تحويل 
+
+156
+00:17:24,400 --> 00:17:29,960
+خطي من T 
+
+157
+00:17:29,960 --> 00:17:39,190
+من V إلى W، الـ Zero بتاع الـ V يساوي الـ Zero بتاع الـ W 
+
+158
+00:17:39,190 --> 00:17:48,010
+لأخطر
+
+159
+00:17:48,010 --> 00:17:53,410
+نثبتها بس 
+
+160
+00:17:53,410 --> 00:18:00,260
+لأخطر نفهمها قبل أن نثبتها، مين تقول أيش معناها؟ T 
+
+161
+00:18:00,260 --> 00:18:03,500
+of Zero بتاع الـ V يبدو يساوي الـ Zero بتاع الـ W، شو
+
+162
+00:18:03,500 --> 00:18:08,400
+يعني المعنى هذا بتاعه واحد
+
+163
+00:18:08,400 --> 00:18:13,000
+يحكي ولو غلط بس يحكوا، تعودوا تفهموا الكلام اللي 
+
+164
+00:18:13,000 --> 00:18:17,860
+مكتوب، T
+
+165
+00:18:17,860 --> 00:18:23,180
+function ده اللي عادي، أثرت على العنصر هذا خلى صوت 
+
+166
+00:18:23,180 --> 00:18:26,380
+العنصر، ايش يعني يا دي، ايش معناها؟
+
+167
+00:18:29,110 --> 00:18:31,330
+بدي واحدة تقول لي بس اللي بتحكي، بس اللي رفعت إيدها دي 
+
+168
+00:18:31,330 --> 00:18:36,650
+ناس ما بعرف بتقول ولا واحدة، بطلوا خلاص someone بقوا
+
+169
+00:18:36,650 --> 00:18:42,470
+نعمل انفهم، لا يعقلون؟ ها أيوة، قولي ممكن يعني أنه
+
+170
+00:18:42,470 --> 00:18:45,030
+على أساس إن الـ people اللي قدامي يقول لي متولد أو 
+
+171
+00:18:45,030 --> 00:18:48,530
+ما تش من الدين، تأثر عليا، فهنا بيقول لكِ إنه
+
+172
+00:19:04,680 --> 00:19:09,320
+بالبلدي هي كلمتين صغيرة، يعني صورة Zero بتاع الـ
+
+173
+00:19:09
+
+201
+00:21:23,900 --> 00:21:31,800
+color برا التأثير، مظبوط؟ إذا هذا بده يساوي 0 أو 
+
+202
+00:21:31,800 --> 00:21:39,420
+هذا بده يساوي 0 scalar في T of V، الشكل اللي عندنا
+
+203
+00:21:39,420 --> 00:21:46,890
+هنا T of V موجود وين؟ في الـ V ولا في الـ W؟ في الـ
+
+204
+00:21:46,890 --> 00:21:53,070
+W يبقى لما أضربه في Zero بيطلع من؟ الـ zero تبع من؟
+
+205
+00:21:53,070 --> 00:21:58,930
+تبع الـ W يبقى هذا يقدر يعطينا الـ zero تبع الـ W
+
+206
+00:21:58,930 --> 00:22:05,190
+والكلام صحيح لكل الـ V الموجود في الـ vector space V
+
+207
+00:22:05,190 --> 00:22:10,170
+يعني ما أخذتش vector بعينيه وإنما أي vector موجود،
+
+208
+00:22:10,170 --> 00:22:16,270
+إذا بناء عليه بتكون T of 0 V بتساوى من؟ الـ 0 W من
+
+209
+00:22:16,270 --> 00:22:20,490
+الرفة ساعدا بديك تعرفيه لإنه source العنصر الصفري
+
+210
+00:22:20,490 --> 00:22:24,090
+في الـ vector space V هو العنصر الصفري في الـ vector 
+
+211
+00:22:24,090 --> 00:22:31,470
+space W نأخد تعريفين مهمين very important يبقى
+
+212
+00:22:31,470 --> 00:22:41,130
+التعريف الأول بيقول ما يأتي let الـ T من V إلى الـ W
+
+213
+00:22:50,560 --> 00:23:03,240
+كبتل K كمجلد من جميع الأشياء كمجلد من جميع الأشياء
+
+214
+00:23:03,240 --> 00:23:08,340
+كمجلد
+
+215
+00:23:08,340 --> 00:23:09,080
+من جميع الأشياء
+
+216
+00:23:12,920 --> 00:23:32,370
+ذات مابس تو الـ Zero W Zero W ذات is I N كبتل K بدي
+
+217
+00:23:32,370 --> 00:23:39,350
+يساوي كل العناصر V اللي موجودة في capital V such
+
+218
+00:23:39,350 --> 00:23:46,730
+that T of V بدي يساوي الـ zero تبع الـ W بالشكل اللي
+
+219
+00:23:46,730 --> 00:23:56,550
+عندنا هنا then K then K is called
+
+220
+00:24:00,670 --> 00:24:06,050
+Kernel of T
+
+221
+00:24:06,050 --> 00:24:15,170
+يبقى بنسميه كيرنل تي كمان Definition بيقول
+
+222
+00:24:15,170 --> 00:24:24,510
+الـ T من الـ V إلى الـ W بإي لينير ترانسفورماشن
+
+223
+00:24:24,510 --> 00:24:29,590
+بإي لينير ترانسفورماشن
+
+224
+00:24:30,920 --> 00:24:34,540
+then the
+
+225
+00:24:34,540 --> 00:24:49,600
+range of T is defined by بروح
+
+226
+00:24:49,600 --> 00:24:56,430
+بنعرفه على ان الـ R of T أو الـ range تبع الـ T بد
+
+227
+00:24:56,430 --> 00:25:02,090
+يساوي كل الـ W اللي موجودة في الـ vector space W
+
+228
+00:25:02,090 --> 00:25:14,030
+كابتل such that الـ W بد يساوي T of V for some V
+
+229
+00:25:14,030 --> 00:25:17,550
+اللي موجودة في كابتل V
+
+230
+00:25:42,630 --> 00:25:55,830
+بنجي لأول نظرية على هذا الموضوع F T
+
+231
+00:25:55,830 --> 00:26:06,390
+من V لـ W is a linear transformation is a linear
+
+232
+00:26:06,390 --> 00:26:09,310
+transformation
+
+233
+00:26:20,680 --> 00:26:30,440
+النقطة الأولى is the kernel of
+
+234
+00:26:30,440 --> 00:26:34,520
+T is a subspace of V
+
+235
+00:26:45,000 --> 00:26:54,960
+النقطة الثانية the range of T is
+
+236
+00:26:54,960 --> 00:27:02,240
+a subspace of
+
+237
+00:27:02,240 --> 00:27:04,020
+W
+
+238
+00:27:25,500 --> 00:27:31,700
+احنا عندنا هنا تعريفين وعندنا نظرية بدنا نقرأ هذين
+
+239
+00:27:31,700 --> 00:27:38,260
+التعريفين قراءة رياضية سليمة ومن ثم نذهب للنظرية
+
+240
+00:27:38,260 --> 00:27:44,340
+بشقيها ونحاول نثبت هذه النظرية نجي للتعريف الأول
+
+241
+00:27:44,340 --> 00:27:48,360
+اللي هو متحدث عن حاجة اسمها الـ kernel of T يعني
+
+242
+00:27:48,360 --> 00:27:53,080
+النواة تبع من؟ تبع الـ kernel الترجمة العرفية لها
+
+243
+00:27:53,080 --> 00:27:59,520
+نواة بعدها بقول التعريف الأول بقول خلّي T من V لـ W
+
+244
+00:27:59,520 --> 00:28:06,920
+Linear Transformation خلّي 6K مين هذه؟ كل العناصر
+
+245
+00:28:06,920 --> 00:28:13,440
+LV اللي ذات maps domain to 0W يعني كل العناصر اللي
+
+246
+00:28:13,440 --> 00:28:18,060
+في الـ vector space V اللي صورتها هي من؟ هي الصفر
+
+247
+00:28:18,060 --> 00:28:22,990
+كل اللي بتروحله الـ that is الـ Kernel K هو كل الـ V
+
+248
+00:28:22,990 --> 00:28:27,730
+اللي موجود فيه capital V such that T of V بده يسوي
+
+249
+00:28:27,730 --> 00:28:34,510
+0 W يبقى ذنب الـ K is called the kernel of T طب
+
+250
+00:28:34,510 --> 00:28:38,250
+بناءً على هذا التاريخ بده أسهل السؤال التالي هل الـ
+
+251
+00:28:38,250 --> 00:28:44,910
+kernel هذا subset من V ولا من الـ W subset من مين
+
+252
+00:28:44,910 --> 00:28:52,820
+يا بنات؟ كل الـ V الموجودة في V يبقى subset من V
+
+253
+00:28:52,820 --> 00:28:58,860
+بصرتها مش بتكون الـ zero تبع الـ W نجي أي function
+
+254
+00:28:58,860 --> 00:29:04,200
+إلها domain و إلها range يبقى الـ kernel هو جزء من
+
+255
+00:29:04,200 --> 00:29:08,800
+الـ domain و لا جزء من الـ range جزء من الـ domain
+
+256
+00:29:08,800 --> 00:29:14,100
+كلام كويس إذا بدنا نروح للـ range جالي الـ range تبع
+
+257
+00:29:14,100 --> 00:29:18,520
+ال Lena transformation T اللي من فيه W الـ range
+
+258
+00:29:18,520 --> 00:29:23,320
+تبعها هديله رمز R of T يبقى R of T هو الـ range
+
+259
+00:29:23,320 --> 00:29:28,540
+لـ Lena transformation V هو مهم كل الـ W اللي موجودة
+
+260
+00:29:28,540 --> 00:29:35,770
+وين في الـ W و اللي إلها أصل وين في V يعني أنا لما
+
+261
+00:29:35,770 --> 00:29:39,930
+أجي على الـ code domain يا بنات ليس بالضرورة أن الـ
+
+262
+00:29:39,930 --> 00:29:43,890
+function تغطي كل عناصر الـ code domain بس لازم تغطي
+
+263
+00:29:43,890 --> 00:29:46,610
+جميع عناصر الـ domain يعني تأثر على جميع عناصر الـ
+
+264
+00:29:46,610 --> 00:29:51,590
+domain لكن صورهم ليس بالضرورة كل الـ code domain بعض
+
+265
+00:29:51,590 --> 00:29:56,330
+العناصر و يمكن يطلعوا كلهم أحيانا مش دايما تمام
+
+266
+00:29:56,330 --> 00:29:59,870
+يبقى الصورة اللي طلعت هذي بسميها الـ range بدي أخد
+
+267
+00:29:59,870 --> 00:30:04,830
+الصورة اللي طلعت هذول اللي هو mean R of T كل الـ W
+
+268
+00:30:04,830 --> 00:30:11,640
+اللي موجودة في الـ W و اللي إلها أصل في الـ domain
+
+269
+00:30:11,640 --> 00:30:16,060
+يبقى كل الـ W اللي موجودة في الـ W يعني الـ W هذه
+
+270
+00:30:16,060 --> 00:30:22,400
+تساوي T of V for some V اللي موجودة في V يعني V
+
+271
+00:30:22,400 --> 00:30:28,240
+هذا element موجود في V صورة الـ V هي من؟ هي الـ W
+
+272
+00:30:28,240 --> 00:30:32,980
+يبقى كل الصور اللي ظهرت في من؟ في الـ W إذا الـ W
+
+273
+00:30:32,980 --> 00:30:39,910
+هذه الـ range تبع الـ T هو جزء من الـ vector space V
+
+274
+00:30:39,910 --> 00:30:44,630
+والله جزء من الـ vector space W من الـ W اللي بيهدف
+
+275
+00:30:44,630 --> 00:30:50,750
+الـ range لإن الـ W هو الـ code domain المجال المصاحب
+
+276
+00:30:50,750 --> 00:30:56,470
+تمام الـ range هذا قد يسوى الـ W كلها وقد يكون جزء
+
+277
+00:30:56,470 --> 00:31:02,110
+منها لو كانت الدالة on to يعني دالة فوقيا بصير الـ
+
+278
+00:31:02,110 --> 00:31:06,440
+domain هو الـ الـ code domain هو الـ range ماكنتش on
+
+279
+00:31:06,440 --> 00:31:09,920
+two يبقى ليه؟ يمكن للـ code main انه يساوي من؟
+
+280
+00:31:09,920 --> 00:31:15,500
+يساوي الـ range طيب يبقى احنا لان صار عندنا K
+
+281
+00:31:15,500 --> 00:31:25,700
+subset من الـ vector space V و R of T subset من الـ W
+
+282
+00:31:27,030 --> 00:31:32,630
+الحين أنا ادعي ان الـ K هذي الـ subspace و الـ R of T
+
+283
+00:31:32,630 --> 00:31:36,590
+subspace، يعني النظرية بتقول لو كان T من V إلى
+
+284
+00:31:36,590 --> 00:31:40,390
+W، linear transformation يبقى الـ kernel of T اللي
+
+285
+00:31:40,390 --> 00:31:45,250
+هو الـ data الرمز capital K subspace من V وكذلك الـ
+
+286
+00:31:45,250 --> 00:31:48,370
+range تبع الـ T اللي Data الرمز R of T هو subspace
+
+287
+00:31:48,370 --> 00:31:53,910
+من من الـ W، إذا بدي أثبت ان كل واحد فيهم subspace
+
+288
+00:31:53,910 --> 00:32:02,710
+من الـ W نرجع بالذاكرة إلى section 3-1 اللي كان الـ
+
+289
+00:32:02,710 --> 00:32:07,050
+vector space والتلاتة اتنين كانت الـ subspace صحيح
+
+290
+00:32:07,050 --> 00:32:10,350
+ولا لأ يبقى أنا بدي أثبت هدول subspace قولنا مش
+
+291
+00:32:10,350 --> 00:32:13,970
+هناخد الـ subset من الـ vector space وانه اثبت ان الـ
+
+292
+00:32:13,970 --> 00:32:20,030
+subspace بدي أثبت كام شغلة تلاتة الشغلة الأولى على
+
+293
+00:32:20,030 --> 00:32:24,310
+الأقل بدي أثبت أنه في عنصر واحد لعمر الثاني لو
+
+294
+00:32:24,310 --> 00:32:27,950
+أخدت element من R و element من الـ vector من الـ
+
+295
+00:32:27,950 --> 00:32:32,620
+subset هذا و ضربتهم في بعض بدي أجيه داخل لو أخدت
+
+296
+00:32:32,620 --> 00:32:35,960
+مجموع two elements من الـ subset هذا بدي أجيب
+
+297
+00:32:35,960 --> 00:32:39,420
+موجودة في الـ subset ان حدث ذلك يظهر الـ subset بقول
+
+298
+00:32:39,420 --> 00:32:44,520
+هذه عبارة عن name subspace تمام؟ إذا أنا بدي أروح
+
+299
+00:32:44,520 --> 00:32:49,480
+أحقق لكل من k و r of t لي three conditions هدول
+
+300
+00:32:49,480 --> 00:32:53,020
+إذا بدي أجي لمن؟ للنقطة الأولى و بدي أجي للـ
+
+301
+00:32:53,020 --> 00:32:56,980
+condition الأول الـ condition الأول أو قبل ما بدي
+
+302
+00:32:56,980 --> 00:33:03,020
+أجي أقول الـ kernel هو كل الـ V اللي موجودة في
+
+303
+00:33:03,020 --> 00:33:09,020
+capital V بحيث ان T of V بده يساوي Zero مش هذا
+
+304
+00:33:09,020 --> 00:33:17,700
+تعريف الـ kernel يبقى هذا is the kernel of T هذا هو
+
+305
+00:33:17,700 --> 00:33:21,860
+الـ kernel اللي عندي الـ zero هذا هو الـ zero تبع الـ
+
+306
+00:33:21,860 --> 00:33:27,120
+W معناه مش الـ zero scalar يبقى الـ zero تبع من تبع
+
+307
+00:33:27,120 --> 00:33:34,820
+الـ W طيب كويس الآن بدي أبينه هذا على الأقل في ولو
+
+308
+00:33:34,820 --> 00:33:41,340
+عنصر واحد تمام؟ الآن عشان احنا عندنا في عندي
+
+309
+00:33:41,340 --> 00:33:50,820
+element هنا الـ kernel is non-empty ايش السبب؟
+
+310
+00:33:50,820 --> 00:34:01,050
+because هي موجودة عندي، مظبوط؟ because الـ T0V بدي
+
+311
+00:34:01,050 --> 00:34:08,130
+يساوي الـ 0 تبع الـ W هذا يعني ان الـ 0 تبع الـ V
+
+312
+00:34:08,130 --> 00:34:14,530
+موجود في الكيرن الـ K يبقى هذا non-empty يبقى هذه
+
+313
+00:34:14,530 --> 00:34:20,150
+هي main الخاصية الأولى الخاصية الثانية بدي أخد
+
+314
+00:34:20,150 --> 00:34:25,610
+element من R و element من الـ vector S P أو من الـ
+
+315
+00:34:25,610 --> 00:34:30,790
+kernel يبقى let C belongs to set of real numbers
+
+316
+00:34:30,790 --> 00:34:37,430
+and الـ V موجود في الـ kernel مدام الـ move V موجود
+
+317
+00:34:37,430 --> 00:34:42,750
+في الـ kernel يبقى فنتي لو أثرت على V قدش بتعطينا؟
+
+318
+00:34:42,750 --> 00:34:51,040
+Zero W يبقى Zero W تمام تمام يبقى أنا بدي أثبت انه
+
+319
+00:34:51,040 --> 00:34:58,040
+C في V موجودة يعني بدي أثبت ان الصورة T او T لما
+
+320
+00:34:58,040 --> 00:35:02,420
+تأثر على CV بدي تعطينا الـ Zero التبادل ان حدث ذلك
+
+321
+00:35:02,420 --> 00:35:06,120
+يبقى بقول الـ C في الـ V موجودة وين؟ في الـ kernel
+
+322
+00:35:06,120 --> 00:35:15,620
+يبقى بدي أخد T of C في الـ V هذا الكلام يساوي أنا
+
+323
+00:35:15,620 --> 00:35:20,360
+فرض انه T عبارة عن ايش؟ هذا من خواصة لينا
+
+324
+00:35:20,360 --> 00:35:26,260
+Transformation بصير C في T of V يبقى هذا الكلام
+
+325
+00:35:26,260 --> 00:35:33,980
+بده يساوي C في T of V اليمين Zero W ايش بيعطينا؟
+
+326
+00:35:33,980 --> 00:35:39,820
+ايش تفسيرك لهذا الكلام؟ ان الـ C في الـ V موجودة
+
+327
+00:35:39,820 --> 00:35:45,380
+وين؟ في الـ kernel يبقى أخدت element من الـ kernel
+
+328
+00:35:45,380 --> 00:35:49,320
+وأخدت real number ضربت اتنين في بعض لجيتهم موجودة
+
+329
+00:35:49,320 --> 00:35:53,040
+في الـ kernel يعني لجيتهم صورتهم متساومهم الـ zero
+
+330
+00:35:53,040 --> 00:36:01,260
+تبع الـ W بداجي للخطوة الثالثة بداجي اقول ت V1 و V2
+
+331
+00:36:01,260 --> 00:36:09,760
+موجودة في الـ kernel طب هذا ايش معناها؟ لما تكون في
+
+332
+00:36:09,760 --> 00:36:18,080
+الـ kernel المعناته T of V1 جداش بده يساوي Zero W يبقى
+
+333
+00:36:18,080 --> 00:36:27,160
+Zero تبع الـ W and T of V2 بده يساوي مين كمان؟ Zero
+
+334
+00:36:27,160 --> 00:36:33,300
+تبع الـ W بالشكل اللي عندنا طيب أنا بدي اشوف T لما
+
+335
+00:36:33,300 --> 00:36:41,120
+أتأثر على V1 زائد V2 ان اعطتنا Zero تبع الـ W وتم
+
+336
+00:36:41,120 --> 00:36:49,040
+المطلوب يبقى باجي بقوله هذا الكلام بده يساوي T
+
+337
+00:36:49,040 --> 00:36:54,960
+of V1 زائد T of V2 ليش؟ لأنه T Linear
+
+338
+00:36:54,960 --> 00:37:02,390
+Transformation T of V1 هي Zero تبع الـ W الـ T of V2
+
+339
+00:37:02,390 --> 00:37:07,990
+هي الـ Zero تبع الـ W Zero زائد Zero بيعطيني Zero
+
+340
+00:37:07,990 --> 00:37:16,070
+تبع الـ W يبقى هنا معنى هذا الكلام ان V1 زائد V2 في
+
+341
+00:37:16,070 --> 00:37:20,310
+الـ Kernel لأن صيرتها تساوي الـ 0 التابعة الـ W إذا
+
+342
+00:37:20,310 --> 00:37:24,410
+انتحقت الشروط الثلاثة للـ subspace ولا لا يبقى
+
+343
+00:37:24,410 --> 00:37:30,650
+بناءنا عليه من الآن فصاعدا بقوله يبقى الـ Kernel K
+
+344
+00:37:30,650 --> 00:37:39,850
+is a subspace of الـ vector space اللي هو main V
+
+345
+00:37:44,760 --> 00:37:49,700
+الآن بدنا نجي للشطر الثاني من النظرية بدنا نثبت ان
+
+346
+00:37:49,700 --> 00:37:57,400
+الـ range التي هو عبارة عن subspace كذلك باجي بقوله
+
+347
+00:37:57,400 --> 00:38:05,120
+النقطة الثانية احنا عندنا الـ R of T بده يساوي كل W
+
+348
+00:38:05,120 --> 00:38:11,740
+اللي موجودة في الـ vector space W بحيث ان الـ W هذه
+
+349
+00:38:11,740 --> 00:38:20,400
+بدها تساوي T of V for some V اللي موجودة في الـ
+
+350
+00:38:20,400 --> 00:38:24,590
+vector space V بالشكل اللي عندنا هنابدي أثبت إن
+
+351
+00:38:24,590 --> 00:38:31,210
+هذا كمان sub space بدي أثبت إن هذا non-empty كذلك
+
+352
+00:38:31,210 --> 00:38:38,830
+يبقى النقطة الأولى الـ R of T is non-empty شو السبب
+
+353
+00:38:38,830 --> 00:38:46,360
+في ذلك؟ because الـ zero تبع الـ W مش الـ zero هذا
+
+354
+00:38:46,360 --> 00:38:50,700
+الموجود في الـ vector space W بقدر اكتبه بال remark
+
+355
+00:38:50,700 --> 00:38:59,480
+اللي قبل قليل T of zero V، مظبوط؟ طيب هاي الـ zero
+
+356
+00:38:59,480 --> 00:39:04,990
+V وين موجود؟ في الـ V يبقى انطباق التعريف ولا لا
+
+357
+00:39:04,990 --> 00:39:11,710
+يبقى هذا بده يستوي اللي هو موجود وين؟ موجود في الـ
+
+358
+00:39:11,710 --> 00:39:18,230
+W أو هذا موجود في الـ R of T هذا موجود في الـ range
+
+359
+00:39:18,230 --> 00:39:24,790
+تبع الـ T يبقى الـ R of T is non-empty بدي أجي للخطوة
+
+360
+00:39:24,790 --> 00:39:33,890
+الثانية if الـ C موجود في الـ R and الـ W موجود في الـ
+
+361
+00:39:33,890 --> 00:39:40,930
+R of T then الـ
+
+362
+00:39:40,930 --> 00:39:50,710
+W بده يساوي الـ T of V for some V اللي موجودة في V
+
+363
+00:39:50,710 --> 00:39:56,730
+capital يبقى أنا بدي أثبت ان الـ CW موجودة في الـ
+
+364
+00:39:56,730 --> 00:40:04,270
+range يبقى بالدرجة اقوله CW تساوي الـ C في الـ W
+
+365
+00:40:04,270 --> 00:40:13,370
+اليمين TAV التي اشجعين عليهالينيرا ترانسفورماشن،
+
+366
+00:40:13,370 --> 00:40:19,290
+إذا الـ C تدخل وين؟ تدخل جوا، يبقى هذا بصير T of
+
+367
+00:40:19,290 --> 00:40:24,790
+CV، صار هذا element موجود في الـ range ولا لا؟ يبقى
+
+368
+00:40:24,790 --> 00:40:30,870
+هذا موجود كله في الـ R of T يعني صار الـ C في الـ W
+
+369
+00:40:30,870 --> 00:40:35,190
+موجودة في الـ R of T إذا انتحقق الـ condition الثاني
+
+370
+00:40:35,190 --> 00:40:40,090
+بده يروح لوين؟ للـ condition الثالث بده يقوله let
+
+371
+00:40:40,090 --> 00:40:52,350
+W1 و W2 موجود في الـ R of T then there exist V1 و V2
+
+372
+
+401
+00:45:07,490 --> 00:45:10,090
+بدي أثبت الـ two properties تبع Linear
+
+402
+00:45:10,090 --> 00:45:16,390
+Transformation يبقى بداجي للخاصية الأولى بداجي 
+
+403
+00:45:16,390 --> 00:45:25,000
+أقوله لو كانت الـ C موجودة في الـ R and الـ A موجودة
+
+404
+00:45:25,000 --> 00:45:31,980
+في الـ M<sub>2</sub><sub>2</sub> to them بدأ
+
+405
+00:45:31,980 --> 00:45:39,480
+أخد اللي هو T of C في الـ A حسب الـ definition
+
+406
+00:45:39,480 --> 00:45:47,620
+المناشي بده يساوي الـ A بده يساوي اللي هو CA زائد CA
+
+407
+00:45:47,620 --> 00:45:48,800
+transpose
+
+408
+00:45:52,090 --> 00:45:59,150
+التعريف يبقى كويس هذي بيظهر يساوي CA زائد لما نيجي
+
+409
+00:45:59,150 --> 00:46:04,130
+لهذا لو رجعنا لخواص Transpose مش هذا بيظهر يساوي C
+
+410
+00:46:04,130 --> 00:46:09,270
+itself في A Transpose كذلك يعني هذا بقدر أخد C
+
+411
+00:46:09,270 --> 00:46:15,270
+عامل مشترك مضروب A زائد A Transpose طيب نكمل سؤالنا
+
+412
+00:46:16,110 --> 00:46:20,630
+يبقى أثبتنا النقطة الأولى بدنا نروح للنقطة الثانية
+
+413
+00:46:20,630 --> 00:46:24,370
+جالي افترض أن الـ A و الـ B موجودة في الـ M<sub>2</sub><sub>2</sub>
+
+414
+00:46:24,370 --> 00:46:31,680
+then بدي أخد T of الـ A زائد الـ B حسب الـ definition
+
+415
+00:46:31,680 --> 00:46:37,660
+هذا بدي يعطينا مين؟ بدي يعطينا A زائد الـ B زائد الـ
+
+416
+00:46:37,660 --> 00:46:41,900
+A زائد الـ B transpose تعريف الـ linear 
+
+417
+00:46:41,900 --> 00:46:46,280
+transformation تمام؟ يبقى هذا الكلام بديه يساوي
+
+418
+00:46:46,280 --> 00:46:52,020
+مين؟ بديه يساوي الـ A زائد الـ B زائد هذه من خواص الـ
+
+419
+00:46:52,020 --> 00:46:57,920
+transpose A transpose زائد B transpose ممكن أجزيها 
+
+420
+00:46:57,920 --> 00:47:04,860
+لجزئين أخد A زائد A transpose زائد B زائد B
+
+421
+00:47:04,860 --> 00:47:11,040
+transpose يبقى هذا يعطيني الأول T of A و الثاني من
+
+422
+00:47:11,040 --> 00:47:21,220
+T of B يبقى هنا Sir T is a linear transformation
+
+423
+00:47:22,390 --> 00:47:26,530
+بدي آجي للمطلوب الثاني Nimra B، Nimra B قالي هاتلي
+
+424
+00:47:26,530 --> 00:47:35,190
+الـ kernel بقوله اه يبقى الـ kernel تبع الـ T اللي هو
+
+425
+00:47:35,190 --> 00:47:42,580
+بده يساوي الـ kernel للـ T، بده يساوي كل المصفوفات A 
+
+426
+00:47:42,580 --> 00:47:50,920
+اللي موجودة في الـ M<sub>2</sub><sub>2</sub> بحيث أن T of A بده يساوي
+
+427
+00:47:50,920 --> 00:47:56,500
+المصفوفة الصفرية مش شايف تعريف الـ kernel؟ كل
+
+428
+00:47:56,500 --> 00:48:00,460
+المصفوفات اللي موجودة في الـ vector space و اللي 
+
+429
+00:48:00,460 --> 00:48:05,600
+صورتها بدها تساوي مين؟ بدها تساوي zero بقوله كويس
+
+430
+00:48:05,600 --> 00:48:11,740
+يبقى هذا الكلام بده يساوي كل المصفوفات اللي موجودة 
+
+431
+00:48:11,740 --> 00:48:16,960
+في الـ M<sub>2</sub><sub>2</sub> such that الـ T of A حسب الـ
+
+432
+00:48:16,960 --> 00:48:23,470
+definition اللي هو الـ A زائد الـ A transpose 
+
+433
+00:48:23,470 --> 00:48:31,590
+بده يساوي من؟ بده يساوي الـ zero مظبوط هيك؟ طيب شو
+
+434
+00:48:31,590 --> 00:48:37,470
+رأيك هذا؟ هو كل المصفوفات A اللي موجودة في الـ M<sub>2</sub><sub>2</sub>
+
+435
+00:48:37,470 --> 00:48:45,930
+such that الـ A transpose بده يساوي سالب A مظبوط؟
+
+436
+00:48:45,930 --> 00:48:52,440
+يعني ايش؟ يعني ايش؟ مين هم المصفوفات هدول؟ شو اسمها؟
+
+437
+00:48:52,440 --> 00:48:58,580
+أدرى بتحقق من الخاصية هذي؟ مين؟ الـ skew symmetric
+
+438
+00:48:58,580 --> 00:49:04,040
+يبقى كل skew symmetric matrices يبقى هذا الكلام
+
+439
+00:49:04,040 --> 00:49:16,100
+بده يساوي the set of all skew symmetric matrices
+
+440
+00:49:18,830 --> 00:49:27,390
+in M<sub>2</sub><sub>2</sub> يبقى كل المصفوفات اللي بتكون main بتكون
+
+441
+00:49:27,390 --> 00:49:33,150
+skew symmetric يبقى ضايل علينا ايش؟ C good
+
+442
+00:49:33,150 --> 00:49:37,670
+exercise لك فكري فيه و حاولي تجيبي له و إن شاء
+
+443
+00:49:37,670 --> 00:49:42,030
+الله يوم السبت بنشوفكوا جيبتوا ولا لأ ماشي؟
+
+444
+00:49:42,030 --> 00:49:45,410
+يرفعلكوا هذا جيبتوا سؤال في إحدى الامتحانات
+
+445
+00:49:45,410 --> 00:49:46,830
+النصفية
+
+446
+00:49:48,590 --> 00:49:51,470
+هذا السؤال مثل اللي قدامك هذا 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..612913c0df658c0995319f41b60852527c6e8964
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/cNO7P2MEKSQ_raw.json
@@ -0,0 +1 @@
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لو أجينا حل تاني واحدة ابتدت بالخطوة الثانية وليست بالخطوة الأولى", "tokens": [9566, 3555, 25961, 4724, 28814, 2304, 41361, 36632, 36764, 24401, 3660, 8978, 4117, 14407, 6055, 44510, 10721, 9154, 3714, 9957, 22807, 9154, 2423, 4188, 16712, 7649, 1829, 4032, 20292, 3794, 9154, 2423, 4188, 16247, 12610, 4032, 1863, 8592, 38688, 8032, 1211, 7251, 2655, 5016, 4587, 4587, 16070, 43761, 20193, 7251, 2655, 5016, 4587, 4587, 5551, 15042, 11331, 31371, 39896, 4117, 16472, 47395, 1829, 8315, 9154, 21542, 1211, 16490, 1211, 9381, 8315, 37495, 22653, 45164, 5551, 7435, 1829, 8315, 11331, 1211, 6055, 7649, 1829, 36764, 24401, 3660, 48127, 2655, 3215, 2655, 20666, 9778, 9566, 2407, 3660, 6024, 104, 7649, 10632, 4032, 20292, 14851, 20666, 9778, 9566, 2407, 3660, 16247, 12610, 7578], "avg_logprob": -0.18003941253498867, "compression_ratio": 1.96, "no_speech_prob": 0.0, "words": [{"start": 331.98, "end": 332.26, "word": "طب", "probability": 0.4951171875}, {"start": 332.26, "end": 332.56, "word": " 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{"start": 415.28, "end": 415.98, "word": " بدي", "probability": 0.31744384765625}, {"start": 415.98, "end": 416.26, "word": " أشوف", "probability": 0.8626302083333334}, {"start": 416.26, "end": 416.5, "word": " هل", "probability": 0.9609375}, {"start": 416.5, "end": 416.78, "word": " هذا", "probability": 0.89501953125}, {"start": 416.78, "end": 417.38, "word": " بيسوي", "probability": 0.710693359375}, {"start": 417.38, "end": 417.74, "word": " T", "probability": 0.81689453125}, {"start": 417.74, "end": 418.08, "word": " of", "probability": 0.8896484375}, {"start": 418.08, "end": 418.26, "word": " V", "probability": 0.8994140625}, {"start": 418.26, "end": 418.76, "word": " واحد", "probability": 0.987060546875}, {"start": 418.76, "end": 419.18, "word": " زائد", "probability": 0.9117838541666666}, {"start": 419.18, "end": 419.44, "word": " T", "probability": 0.912109375}, {"start": 419.44, "end": 419.64, "word": " of", "probability": 0.9658203125}, {"start": 419.64, "end": 419.8, "word": 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"probability": 0.96728515625}, {"start": 440.1, "end": 440.84, "word": " وهذا", "probability": 0.728271484375}, {"start": 440.84, "end": 441.16, "word": " زي", "probability": 0.7388916015625}, {"start": 441.16, "end": 441.34, "word": " ما", "probability": 0.953125}, {"start": 441.34, "end": 441.58, "word": " هو", "probability": 0.97412109375}, {"start": 441.58, "end": 442.58, "word": " يبقى", "probability": 0.9755859375}, {"start": 442.58, "end": 442.94, "word": " هذا", "probability": 0.96923828125}, {"start": 442.94, "end": 443.48, "word": " الكلام", "probability": 0.9679361979166666}, {"start": 443.48, "end": 443.78, "word": " بدي", "probability": 0.71337890625}, {"start": 443.78, "end": 444.3, "word": " أساوي", "probability": 0.74444580078125}, {"start": 444.3, "end": 445.04, "word": " T", "probability": 0.87353515625}, {"start": 445.04, "end": 445.62, "word": " of", "probability": 0.95947265625}, {"start": 445.62, "end": 445.84, "word": " V", "probability": 0.9892578125}, {"start": 445.84, "end": 446.36, "word": " واحد", "probability": 0.990234375}, {"start": 446.36, "end": 446.82, "word": " زائد", "probability": 0.9417317708333334}, {"start": 446.82, "end": 447.52, "word": " هل", "probability": 0.954833984375}, {"start": 447.52, "end": 447.86, "word": " هذا", "probability": 0.943359375}, {"start": 447.86, "end": 448.24, "word": " T", "probability": 0.943359375}, {"start": 448.24, "end": 448.56, "word": " of", "probability": 0.97705078125}, {"start": 448.56, "end": 448.78, "word": " V", "probability": 0.9931640625}, {"start": 448.78, "end": 449.32, "word": " اتنين", "probability": 0.9298095703125}], "temperature": 1.0}, {"id": 20, "seek": 46320, "start": 449.84, "end": 463.2, "text": "لا يبقى بحطه زي ما هو يبقى هذا زائد Y تلاتة و Zero وهذا الكلام لا يساوي T of V واحد زائد T of V اتنين", "tokens": [15040, 7251, 3555, 4587, 7578, 4724, 5016, 9566, 3224, 30767, 1829, 19446, 31439, 7251, 3555, 4587, 7578, 23758, 30767, 16373, 3215, 398, 6055, 1211, 9307, 3660, 4032, 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{"start": 454.08, "end": 454.46, "word": " Y", "probability": 0.468017578125}, {"start": 454.46, "end": 455.3, "word": " تلاتة", "probability": 0.850341796875}, {"start": 455.3, "end": 455.4, "word": " و", "probability": 0.90478515625}, {"start": 455.4, "end": 455.88, "word": " Zero", "probability": 0.371826171875}, {"start": 455.88, "end": 456.76, "word": " وهذا", "probability": 0.825439453125}, {"start": 456.76, "end": 457.4, "word": " الكلام", "probability": 0.9444986979166666}, {"start": 457.4, "end": 457.82, "word": " لا", "probability": 0.783203125}, {"start": 457.82, "end": 458.92, "word": " يساوي", "probability": 0.9486083984375}, {"start": 458.92, "end": 459.62, "word": " T", "probability": 0.87109375}, {"start": 459.62, "end": 460.08, "word": " of", "probability": 0.892578125}, {"start": 460.08, "end": 460.26, "word": " V", "probability": 0.9462890625}, {"start": 460.26, "end": 460.84, "word": " واحد", "probability": 0.967529296875}, {"start": 460.84, "end": 461.46, "word": " زائد", "probability": 0.9619140625}, {"start": 461.46, "end": 461.94, "word": " T", "probability": 0.943359375}, {"start": 461.94, "end": 462.46, "word": " of", "probability": 0.97412109375}, {"start": 462.46, "end": 462.68, "word": " V", "probability": 0.99560546875}, {"start": 462.68, "end": 463.2, "word": " اتنين", "probability": 0.9403076171875}], "temperature": 1.0}, {"id": 21, "seek": 48686, "start": 464.62, "end": 486.86, "text": "لأن T of V2 عبارة عن Y3 و 1 و ليس Y3 و 0 يبقى كمان ال condition التاني مش متحقق is not satisfied يبقى بناء عليه برضه T not linear transformation يبقى بروح بقوله CT is not a linear transformation", "tokens": [1211, 33456, 314, 295, 691, 17, 6225, 3555, 9640, 3660, 18871, 398, 18, 4032, 502, 4032, 32239, 3794, 398, 18, 4032, 1958, 7251, 3555, 4587, 7578, 9122, 2304, 7649, 2423, 4188, 16712, 7649, 1829, 37893, 44650, 5016, 4587, 4587, 307, 406, 11239, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 4724, 43042, 3224, 314, 406, 8213, 9887, 7251, 3555, 4587, 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468.32, "word": " ليس", "probability": 0.8896484375}, {"start": 468.32, "end": 469.12, "word": " Y3", "probability": 0.94921875}, {"start": 469.12, "end": 469.38, "word": " و", "probability": 0.80712890625}, {"start": 469.38, "end": 469.62, "word": " 0", "probability": 0.8115234375}, {"start": 469.62, "end": 470.22, "word": " يبقى", "probability": 0.87841796875}, {"start": 470.22, "end": 470.58, "word": " كمان", "probability": 0.9007161458333334}, {"start": 470.58, "end": 470.74, "word": " ال", "probability": 0.927734375}, {"start": 470.74, "end": 471.2, "word": " condition", "probability": 0.94775390625}, {"start": 471.2, "end": 472.04, "word": " التاني", "probability": 0.94482421875}, {"start": 472.04, "end": 472.68, "word": " مش", "probability": 0.90283203125}, {"start": 472.68, "end": 473.54, "word": " متحقق", "probability": 0.9842529296875}, {"start": 473.54, "end": 473.72, "word": " is", "probability": 0.7109375}, {"start": 473.72, "end": 474.0, "word": " not", "probability": 0.9521484375}, {"start": 474.0, "end": 474.84, "word": " satisfied", "probability": 0.8662109375}, {"start": 474.84, "end": 475.58, "word": " يبقى", "probability": 0.960693359375}, {"start": 475.58, "end": 475.94, "word": " بناء", "probability": 0.908203125}, {"start": 475.94, "end": 476.4, "word": " عليه", "probability": 0.96484375}, {"start": 476.4, "end": 476.96, "word": " برضه", "probability": 0.8720703125}, {"start": 476.96, "end": 477.26, "word": " T", "probability": 0.8193359375}, {"start": 477.26, "end": 477.68, "word": " not", "probability": 0.5}, {"start": 477.68, "end": 478.16, "word": " linear", "probability": 0.87548828125}, {"start": 478.16, "end": 479.3, "word": " transformation", "probability": 0.8505859375}, {"start": 479.3, "end": 480.14, "word": " يبقى", "probability": 0.9736328125}, {"start": 480.14, "end": 480.48, "word": " بروح", "probability": 0.9016927083333334}, {"start": 480.48, "end": 481.12, "word": " بقوله", "probability": 0.8274739583333334}, {"start": 481.12, "end": 481.64, "word": " CT", "probability": 0.5634765625}, {"start": 481.64, "end": 483.06, "word": " is", "probability": 0.88623046875}, {"start": 483.06, "end": 484.3, "word": " not", "probability": 0.9541015625}, {"start": 484.3, "end": 485.24, "word": " a", "probability": 0.767578125}, {"start": 485.24, "end": 485.74, "word": " linear", "probability": 0.90869140625}, {"start": 485.74, "end": 486.86, "word": " transformation", "probability": 0.86181640625}], "temperature": 1.0}, {"id": 22, "seek": 51599, "start": 487.87, "end": 515.99, "text": "يبقى معناها كلام اللي أخدت الخاصية الأولى ولاجتها غير متحققة وقالت 120 transformations صحيح اللي راحت على الخاصية التانية مباشرة ولاجتها غير متحققة برضه كلامها صحيح يبقى هدول حلين وليس حلا واحدا يعني يكفيني أحدهما طب نيجي لالمثال اللي بعده example 3", "tokens": [1829, 3555, 4587, 7578, 20449, 8315, 11296, 28242, 10943, 13672, 1829, 5551, 9778, 3215, 2655, 33962, 33546, 10632, 16247, 12610, 7578, 4032, 15040, 7435, 2655, 11296, 32771, 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"end": 498.49, "word": " راحت", "probability": 0.810302734375}, {"start": 498.49, "end": 498.65, "word": " على", "probability": 0.8212890625}, {"start": 498.65, "end": 499.23, "word": " الخاصية", "probability": 0.9899088541666666}, {"start": 499.23, "end": 499.61, "word": " التانية", "probability": 0.9763997395833334}, {"start": 499.61, "end": 500.67, "word": " مباشرة", "probability": 0.9913330078125}, {"start": 500.67, "end": 501.75, "word": " ولاجتها", "probability": 0.95751953125}, {"start": 501.75, "end": 501.93, "word": " غير", "probability": 0.99609375}, {"start": 501.93, "end": 502.57, "word": " متحققة", "probability": 0.954833984375}, {"start": 502.57, "end": 503.09, "word": " برضه", "probability": 0.8994140625}, {"start": 503.09, "end": 503.75, "word": " كلامها", "probability": 0.9640299479166666}, {"start": 503.75, "end": 504.39, "word": " صحيح", "probability": 0.99609375}, {"start": 504.39, "end": 505.01, "word": " يبقى", "probability": 0.9578857421875}, {"start": 505.01, "end": 505.29, "word": " هدول", "probability": 0.85693359375}, {"start": 505.29, "end": 505.83, "word": " حلين", "probability": 0.8776041666666666}, {"start": 505.83, "end": 506.35, "word": " وليس", "probability": 0.9820963541666666}, {"start": 506.35, "end": 507.03, "word": " حلا", "probability": 0.7127278645833334}, {"start": 507.03, "end": 508.23, "word": " واحدا", "probability": 0.8815104166666666}, {"start": 508.23, "end": 508.89, "word": " يعني", "probability": 0.932373046875}, {"start": 508.89, "end": 509.81, "word": " يكفيني", "probability": 0.8880859375}, {"start": 509.81, "end": 511.19, "word": " أحدهما", "probability": 0.8089599609375}, {"start": 511.19, "end": 512.13, "word": " طب", "probability": 0.635498046875}, {"start": 512.13, "end": 512.55, "word": " نيجي", "probability": 0.8409423828125}, {"start": 512.55, "end": 513.73, "word": " لالمثال", "probability": 0.8538818359375}, {"start": 513.73, "end": 513.93, "word": " اللي", "probability": 0.96337890625}, {"start": 513.93, "end": 514.45, "word": " بعده", "probability": 0.891845703125}, {"start": 514.45, "end": 515.49, "word": " example", "probability": 0.9033203125}, {"start": 515.49, "end": 515.99, "word": " 3", "probability": 0.397705078125}], "temperature": 1.0}, {"id": 23, "seek": 54687, "start": 521.89, "end": 546.87, "text": "تقول define a mapping define a mapping a mapping T من R2 إلى R2 by T of X1 و X2 بده يساوي", "tokens": [2655, 39648, 6964, 257, 18350, 6964, 257, 18350, 257, 18350, 314, 9154, 497, 17, 30731, 497, 17, 538, 314, 295, 1783, 16, 4032, 1783, 17, 47525, 3224, 7251, 3794, 995, 45865], "avg_logprob": -0.31567383743822575, "compression_ratio": 1.2159090909090908, "no_speech_prob": 0.0, "words": [{"start": 521.89, "end": 522.29, "word": "تقول", "probability": 0.5347900390625}, {"start": 522.29, "end": 522.79, "word": " define", "probability": 0.529296875}, {"start": 522.79, "end": 523.07, "word": " a", "probability": 0.62353515625}, {"start": 523.07, "end": 523.49, "word": " mapping", "probability": 0.96240234375}, {"start": 523.49, "end": 526.23, "word": " define", "probability": 0.2069091796875}, {"start": 526.23, "end": 527.55, "word": " a", "probability": 0.95361328125}, {"start": 527.55, "end": 528.73, "word": " mapping", "probability": 0.96484375}, {"start": 528.73, "end": 530.91, "word": " a", "probability": 0.3701171875}, {"start": 530.91, "end": 531.67, "word": " mapping", "probability": 0.9677734375}, {"start": 531.67, "end": 532.81, "word": " T", "probability": 0.70947265625}, {"start": 532.81, "end": 534.25, "word": " من", "probability": 0.9833984375}, {"start": 534.25, "end": 535.53, "word": " R2", "probability": 0.940673828125}, {"start": 535.53, "end": 536.19, "word": " إلى", "probability": 0.7041015625}, {"start": 536.19, "end": 537.87, "word": " R2", "probability": 0.98388671875}, {"start": 537.87, "end": 538.75, "word": " by", "probability": 0.68115234375}, {"start": 538.75, "end": 542.29, "word": " T", "probability": 0.421142578125}, {"start": 542.29, "end": 542.79, "word": " of", "probability": 0.88720703125}, {"start": 542.79, "end": 544.05, "word": " X1", "probability": 0.791748046875}, {"start": 544.05, "end": 544.67, "word": " و", "probability": 0.88671875}, {"start": 544.67, "end": 545.69, "word": " X2", "probability": 0.90478515625}, {"start": 545.69, "end": 546.33, "word": " بده", "probability": 0.6524658203125}, {"start": 546.33, "end": 546.87, "word": " يساوي", "probability": 0.9715576171875}], "temperature": 1.0}, {"id": 24, "seek": 57320, "start": 547.68, "end": 573.2, "text": "الأول اتنين x واحد ناقص x اتنين وx واحد زائد x اتنين السؤال هو prove or disprove prove or disprove that T is a linear transformation", "tokens": [6027, 10721, 12610, 1975, 2655, 1863, 9957, 2031, 36764, 24401, 8717, 995, 4587, 9381, 2031, 1975, 2655, 1863, 9957, 4032, 87, 36764, 24401, 30767, 16373, 3215, 2031, 1975, 2655, 1863, 9957, 21136, 33604, 6027, 31439, 7081, 420, 717, 46955, 7081, 420, 717, 46955, 300, 314, 307, 257, 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"end": 604.28, "word": " function", "probability": 0.61572265625}, {"start": 604.28, "end": 604.84, "word": " معرفة", "probability": 0.9222005208333334}, {"start": 604.84, "end": 605.0, "word": " من", "probability": 0.986328125}, {"start": 605.0, "end": 605.6, "word": " R2", "probability": 0.824462890625}, {"start": 605.6, "end": 605.86, "word": " ل", "probability": 0.96142578125}, {"start": 605.86, "end": 606.9, "word": " R2", "probability": 0.80078125}, {"start": 606.9, "end": 607.6, "word": " itself", "probability": 0.53759765625}, {"start": 607.6, "end": 608.54, "word": " نفسها", "probability": 0.8361002604166666}, {"start": 608.54, "end": 608.98, "word": " بالضبط", "probability": 0.9666748046875}, {"start": 608.98, "end": 609.5, "word": " تماما", "probability": 0.92626953125}, {"start": 609.5, "end": 610.76, "word": " معرفة", "probability": 0.88330078125}, {"start": 610.76, "end": 611.52, "word": " كيف؟", "probability": 0.7818196614583334}, {"start": 611.52, "end": 611.74, "word": " T", "probability": 0.833984375}, {"start": 611.74, "end": 612.04, "word": " of", "probability": 0.79345703125}, {"start": 612.04, "end": 612.7, "word": " X1", "probability": 0.924072265625}, {"start": 612.7, "end": 613.18, "word": " و", "probability": 0.8046875}, {"start": 613.18, "end": 613.78, "word": " X2", "probability": 0.968994140625}, {"start": 613.78, "end": 614.74, "word": " يساوي", "probability": 0.930908203125}, {"start": 614.74, "end": 615.74, "word": " اتنين", "probability": 0.9405517578125}, {"start": 615.74, "end": 616.46, "word": " المركبة", "probability": 0.8601888020833334}, {"start": 616.46, "end": 616.96, "word": " الأولى", "probability": 0.8946940104166666}, {"start": 616.96, "end": 617.6, "word": " ناقص", "probability": 0.9688720703125}, {"start": 617.6, "end": 618.36, "word": " المركبة", "probability": 0.9860026041666666}, {"start": 618.36, "end": 618.76, "word": " الثانية", "probability": 0.935791015625}, {"start": 618.76, "end": 619.0, "word": " هذه", "probability": 0.37744140625}, {"start": 619.0, "end": 619.48, "word": " بيعطيني", "probability": 0.8083984375}, {"start": 619.48, "end": 619.62, "word": " ال", "probability": 0.80126953125}, {"start": 619.62, "end": 620.2, "word": " component", "probability": 0.96435546875}, {"start": 620.2, "end": 621.54, "word": " الأولى", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 26, "seek": 64602, "start": 621.82, "end": 646.02, "text": "الكمبوننت الثانية هي مجموع من المراكبات اللي اتنين هدول يبقى عرفنا function بهذا الشكل سؤالنا هو هل هذه ال function ممكن تكون لنا transformation ام لا بنقوله الله أعلم تعالى نشوف نتأكد جالي probe or disprobe يعني اذا بتقدر تبره انها كان بها ماجدرتش خلاص نعفى الله عنك", "tokens": [6027, 24793, 3555, 11536, 29399, 6024, 104, 7649, 10632, 39896, 3714, 7435, 2304, 45367, 9154, 9673, 23557, 4117, 3555, 9307, 13672, 1829, 1975, 2655, 1863, 9957, 8032, 3215, 12610, 7251, 3555, 4587, 7578, 6225, 28480, 8315, 2445, 39627, 15730, 25124, 28820, 8608, 33604, 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1931.07, "end": 1931.59, "word": " subset", "probability": 0.69970703125}, {"start": 1931.59, "end": 1932.13, "word": " من", "probability": 0.953125}, {"start": 1932.13, "end": 1932.23, "word": " ال", "probability": 0.982421875}, {"start": 1932.23, "end": 1932.49, "word": " vector", "probability": 0.98046875}, {"start": 1932.49, "end": 1932.87, "word": " space", "probability": 0.9462890625}, {"start": 1932.87, "end": 1933.19, "word": " وانه", "probability": 0.7682291666666666}, {"start": 1933.19, "end": 1933.67, "word": " اثبت", "probability": 0.9375}, {"start": 1933.67, "end": 1933.79, "word": " ان", "probability": 0.54638671875}, {"start": 1933.79, "end": 1933.97, "word": " ال", "probability": 0.67236328125}, {"start": 1933.97, "end": 1934.41, "word": " subspace", "probability": 0.960205078125}, {"start": 1934.41, "end": 1934.67, "word": " بدي", "probability": 0.759765625}, {"start": 1934.67, "end": 1934.97, "word": " اثبت", "probability": 0.9676513671875}, {"start": 1934.97, "end": 1935.21, "word": " كام", "probability": 0.73779296875}, {"start": 1935.21, "end": 1935.83, "word": " شغلة", "probability": 0.9620768229166666}, {"start": 1935.83, "end": 1936.87, "word": " تلاتة", "probability": 0.89111328125}, {"start": 1936.87, "end": 1937.27, "word": " الشغلة", "probability": 0.8746744791666666}, {"start": 1937.27, "end": 1937.81, "word": " الأولى", "probability": 0.8621419270833334}], "temperature": 1.0}, {"id": 79, "seek": 195075, "start": 1939.31, "end": 1950.75, "text": "على الأقل بدي أثبت أنه في عنصر واحد لعمر الثاني لو أخدت element من R و element من ال vector من ال subset هذا و ضربتهم في بعض بدي أجيه داخل", "tokens": [3615, 23942, 16247, 4587, 1211, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 3224, 8978, 18871, 9381, 2288, 36764, 24401, 5296, 25957, 2288, 6024, 104, 7649, 1829, 45164, 5551, 9778, 3215, 2655, 4478, 9154, 497, 4032, 4478, 9154, 2423, 8062, 9154, 2423, 25993, 23758, 4032, 48812, 25513, 2655, 16095, 8978, 45030, 11242, 4724, 16254, 5551, 7435, 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{"start": 1947.95, "end": 1948.37, "word": " subset", "probability": 0.91455078125}, {"start": 1948.37, "end": 1948.67, "word": " هذا", "probability": 0.478271484375}, {"start": 1948.67, "end": 1948.77, "word": " و", "probability": 0.8984375}, {"start": 1948.77, "end": 1949.19, "word": " ضربتهم", "probability": 0.7716064453125}, {"start": 1949.19, "end": 1949.33, "word": " في", "probability": 0.9365234375}, {"start": 1949.33, "end": 1949.57, "word": " بعض", "probability": 0.9892578125}, {"start": 1949.57, "end": 1949.81, "word": " بدي", "probability": 0.592041015625}, {"start": 1949.81, "end": 1950.15, "word": " أجيه", "probability": 0.779296875}, {"start": 1950.15, "end": 1950.75, "word": " داخل", "probability": 0.9715169270833334}], "temperature": 1.0}, {"id": 80, "seek": 197912, "start": 1951.44, "end": 1979.12, "text": "لو أخدت مجموع two elements من ال subset هذا بدي أجيب موجودة في ال subset ان حدث ذلك يظهر ال subset بقول هذه عبارة عن name subspace تمام؟ اذا انا بدي أروح أحقق لكل 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اثبت ان الصورة T او T لما تأثر على CV بدي تعطينا الـ Zero التبادل ان حدث ذلك يبقى بقول الـC في الـV موجودة وين؟ في ال kernel يبقى بدي اخد T of C في الـV هذا الكلام يساوي انا فرض انه T عبارة عن ايش؟", "tokens": [1829, 3555, 4587, 7578, 1975, 8315, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 3224, 383, 8978, 691, 3714, 29245, 23328, 3660, 37495, 22653, 4724, 16254, 1975, 12984, 3555, 2655, 16472, 31767, 13063, 3660, 314, 1975, 2407, 314, 5296, 15042, 6055, 10721, 49115, 15844, 383, 53, 4724, 16254, 6055, 3615, 9566, 1829, 8315, 2423, 39184, 17182, 16712, 3555, 18513, 1211, 16472, 11331, 3215, 12984, 29910, 23275, 7251, 3555, 4587, 7578, 4724, 39648, 2423, 39184, 34, 8978, 2423, 39184, 53, 3714, 29245, 23328, 3660, 4032, 9957, 22807, 8978, 2423, 28256, 7251, 3555, 4587, 7578, 4724, 16254, 1975, 9778, 3215, 314, 295, 383, 8978, 2423, 39184, 53, 23758, 2423, 28820, 10943, 7251, 3794, 995, 45865, 1975, 8315, 6156, 43042, 16472, 3224, 314, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 8592, 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{"start": 2110.98, "end": 2113.84, "word": " هذا", "probability": 0.97119140625}, {"start": 2113.84, "end": 2114.34, "word": " الكلام", "probability": 0.98193359375}, {"start": 2114.34, "end": 2114.98, "word": " يساوي", "probability": 0.90478515625}, {"start": 2114.98, "end": 2115.62, "word": " انا", "probability": 0.840576171875}, {"start": 2115.62, "end": 2116.04, "word": " فرض", "probability": 0.813232421875}, {"start": 2116.04, "end": 2116.38, "word": " انه", "probability": 0.6881103515625}, {"start": 2116.38, "end": 2116.5, "word": " T", "probability": 0.9404296875}, {"start": 2116.5, "end": 2116.84, "word": " عبارة", "probability": 0.958740234375}, {"start": 2116.84, "end": 2117.0, "word": " عن", "probability": 0.97119140625}, {"start": 2117.0, "end": 2117.2, "word": " ايش؟", "probability": 0.6297607421875}], "temperature": 1.0}, {"id": 86, "seek": 214190, "start": 2118.96, "end": 2141.9, "text": "هذا من خواصة لينا Transformation بصير C في T of V يبقى هذا الكلام بده يساوي C في T of V اليمين Zero W ايش بيعطينا؟ ايش تفسيرك لهذا الكلام؟ ان ال C في ال V موجودة وين؟ في ال kernel", "tokens": [3224, 15730, 9154, 16490, 2407, 33546, 3660, 32239, 8315, 6531, 8663, 4724, 9381, 13546, 383, 8978, 314, 295, 691, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 383, 8978, 314, 295, 691, 2423, 32640, 9957, 17182, 343, 1975, 1829, 8592, 4724, 1829, 3615, 9566, 1829, 8315, 22807, 1975, 1829, 8592, 6055, 36178, 13546, 4117, 46740, 15730, 2423, 28820, 10943, 22807, 16472, 2423, 383, 8978, 2423, 691, 3714, 29245, 23328, 3660, 4032, 9957, 22807, 8978, 2423, 28256], "avg_logprob": -0.2848268079470439, "compression_ratio": 1.5611111111111111, "no_speech_prob": 0.0, "words": [{"start": 2118.96, "end": 2119.3, "word": "هذا", "probability": 0.5147705078125}, {"start": 2119.3, "end": 2119.48, "word": " من", "probability": 0.50927734375}, {"start": 2119.48, "end": 2120.1, "word": " خواصة", "probability": 0.8173828125}, {"start": 2120.1, "end": 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{"start": 2469.71, "end": 2470.47, "word": " T", "probability": 0.97216796875}, {"start": 2470.47, "end": 2471.21, "word": " of", "probability": 0.97412109375}, {"start": 2471.21, "end": 2472.37, "word": " V2", "probability": 0.995849609375}, {"start": 2472.37, "end": 2474.61, "word": " بالداخل", "probability": 0.6607666015625}, {"start": 2474.61, "end": 2474.83, "word": " ال", "probability": 0.91748046875}, {"start": 2474.83, "end": 2475.83, "word": " W1", "probability": 0.947265625}, {"start": 2475.83, "end": 2476.73, "word": " زائد", "probability": 0.73681640625}, {"start": 2476.73, "end": 2477.75, "word": " W2", "probability": 0.907470703125}], "temperature": 1.0}, {"id": 102, "seek": 250680, "start": 2478.4, "end": 2506.8, "text": "بدي اثبت ان هذا موجود وين في ال range يعني بدي اثبت ان هذا صورة لعمصر موجود وين في ال domain بقوله بسيطة هذا عبارة عن T of V1 وهذا T of V2 طيب ال T Linear Transformation الخاصية التالتة منها بتقول هذا سوى T of V1 زي V2", "tokens": [3555, 16254, 1975, 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"word": " kernel", "probability": 0.91357421875}, {"start": 2857.15, "end": 2857.83, "word": " لل", "probability": 0.70556640625}, {"start": 2857.83, "end": 2858.41, "word": " T،", "probability": 0.826904296875}, {"start": 2858.41, "end": 2858.73, "word": " بده", "probability": 0.936279296875}, {"start": 2858.73, "end": 2859.35, "word": " يساوي", "probability": 0.9898681640625}], "temperature": 1.0}, {"id": 117, "seek": 287566, "start": 2859.86, "end": 2875.66, "text": "كل المصفوفات A اللى موجودة فى ال M22 بحيث أن T of A بده ساوى المصفوفة الصفرية مش شايف تعريف ال kernel؟", "tokens": [28820, 9673, 9381, 5172, 38688, 9307, 316, 13672, 7578, 3714, 29245, 23328, 3660, 6156, 7578, 2423, 376, 7490, 4724, 5016, 1829, 12984, 14739, 314, 295, 316, 47525, 3224, 8608, 995, 2407, 7578, 9673, 9381, 5172, 38688, 3660, 31767, 5172, 2288, 10632, 37893, 13412, 995, 33911, 37279, 16572, 5172, 2423, 28256, 22807], "avg_logprob": -0.24113582074642181, "compression_ratio": 1.2611940298507462, "no_speech_prob": 0.0, "words": [{"start": 2859.86, "end": 2860.36, "word": "كل", "probability": 0.44921875}, {"start": 2860.36, "end": 2862.1, "word": " المصفوفات", "probability": 0.9318359375}, {"start": 2862.1, "end": 2862.58, "word": " A", "probability": 0.52880859375}, {"start": 2862.58, "end": 2863.48, "word": " اللى", "probability": 0.5142822265625}, {"start": 2863.48, "end": 2864.22, "word": " موجودة", "probability": 0.9775390625}, {"start": 2864.22, "end": 2864.48, "word": " فى", "probability": 0.728759765625}, {"start": 2864.48, "end": 2864.58, "word": " ال", "probability": 0.720703125}, {"start": 2864.58, "end": 2865.74, "word": " M22", "probability": 0.718505859375}, {"start": 2865.74, "end": 2867.26, "word": " بحيث", "probability": 0.9835205078125}, {"start": 2867.26, "end": 2867.72, "word": " أن", "probability": 0.408447265625}, {"start": 2867.72, "end": 2868.42, "word": " T", "probability": 0.62744140625}, {"start": 2868.42, "end": 2869.0, "word": " of", "probability": 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تساوي مين بدها تساوي zero بقوله كويس يبقى هذا الكلام بده يساوي كل المصففات اللى موجودة في ال M to to such that ال T of A حسب ال definition اللى هو ال A", "tokens": [28820, 9673, 9381, 5172, 5172, 9307, 13672, 7578, 3714, 29245, 23328, 3660, 8978, 2423, 8062, 1901, 4032, 13672, 7578, 20328, 13063, 2655, 11296, 47525, 11296, 6055, 3794, 995, 45865, 3714, 9957, 47525, 11296, 6055, 3794, 995, 45865, 4018, 4724, 39648, 3224, 9122, 45865, 3794, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 28242, 9673, 9381, 5172, 5172, 9307, 13672, 7578, 3714, 29245, 23328, 3660, 8978, 2423, 376, 281, 281, 1270, 300, 2423, 314, 295, 316, 11331, 35457, 2423, 7123, 13672, 7578, 31439, 2423, 316], "avg_logprob": -0.17196085590582627, "compression_ratio": 1.8074866310160427, "no_speech_prob": 0.0, "words": [{"start": 2876.04, "end": 2876.5, "word": "كل", "probability": 0.393798828125}, {"start": 2876.5, "end": 2877.66, "word": " المصففات", "probability": 0.81806640625}, 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"end": 2983.31, "word": " جيبتوا", "probability": 0.8302734375}, {"start": 2983.31, "end": 2983.67, "word": " سؤال", "probability": 0.97900390625}, {"start": 2983.67, "end": 2983.83, "word": " في", "probability": 0.9853515625}, {"start": 2983.83, "end": 2984.11, "word": " إحدى", "probability": 0.7845865885416666}, {"start": 2984.11, "end": 2985.41, "word": " الامتحانات", "probability": 0.9423014322916666}, {"start": 2985.41, "end": 2986.83, "word": " النصفية", "probability": 0.945068359375}], "temperature": 1.0}, {"id": 122, "seek": 299147, "start": 2988.59, "end": 2991.47, "text": "هذا السؤال مثل اللي قدامك هذا", "tokens": [3224, 15730, 21136, 33604, 6027, 50113, 1211, 13672, 1829, 12174, 3215, 10943, 4117, 23758], "avg_logprob": -0.21171875596046447, "compression_ratio": 1.0392156862745099, "no_speech_prob": 0.0, "words": [{"start": 2988.59, "end": 2989.39, "word": "هذا", "probability": 0.69384765625}, {"start": 2989.39, "end": 2989.97, "word": " السؤال", "probability": 0.9635416666666666}, {"start": 2989.97, "end": 2990.49, "word": " مثل", "probability": 0.814208984375}, {"start": 2990.49, "end": 2990.59, "word": " اللي", "probability": 0.7027587890625}, {"start": 2990.59, "end": 2991.19, "word": " قدامك", "probability": 0.9420166015625}, {"start": 2991.19, "end": 2991.47, "word": " هذا", "probability": 0.8603515625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2992.309, "duration_after_vad": 2766.8499999999885}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/czq6xxZJyIg_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/czq6xxZJyIg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..78cbc93171f47bc2b9ce7621c7e8cca78b01feba
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/czq6xxZJyIg_postprocess.srt
@@ -0,0 +1,1784 @@
+1
+00:00:21,800 --> 00:00:27,080
+بسم الله الرحمن الرحيم نبدأ اليوم بأول محاضرة
+
+2
+00:00:27,080 --> 00:00:33,120
+فعلية في صميم المنهج المقرر لهذا الفصل وهو مادة
+
+3
+00:00:33,120 --> 00:00:39,930
+معادلة .. مادة مساق معادلات تفاضلية وجبر خطيهذا
+
+4
+00:00:39,930 --> 00:00:43,570
+المساق كما قلنا في المرة الماضية تكون من جزء يعني
+
+5
+00:00:43,570 --> 00:00:47,750
+جزء معادلات تفاضلية وجزء اللي هو جابر خطي three
+
+6
+00:00:47,750 --> 00:00:51,090
+chapters في المعادلات التفاضلية و three chapters
+
+7
+00:00:51,090 --> 00:00:55,950
+في الجابر الخطي أو ال linear algebra نبدأ بأول
+
+8
+00:00:55,950 --> 00:00:59,450
+section اللي كله بتحدث عن المعادلات التفاضلية
+
+9
+00:00:59,450 --> 00:01:03,050
+العنوان introduction to differential equations
+
+10
+00:01:03,050 --> 00:01:08,690
+يعني مقدمة للمعادلات التفاضليةنعطي بعض ال
+
+11
+00:01:08,690 --> 00:01:13,850
+definitions الأساسية اللي لازم نعرفها حتى ندخل في
+
+12
+00:01:13,850 --> 00:01:19,310
+صميم هذا المثال في عندي نوعين من المعادلات
+
+13
+00:01:19,310 --> 00:01:23,150
+التفاضلية معادلة تفاضلية نسميها ordinary
+
+14
+00:01:23,150 --> 00:01:27,750
+differential equation معادلة تفاضلية عادية وفي
+
+15
+00:01:27,750 --> 00:01:32,290
+partial differential equation معادلة تفاضلية جزئية
+
+16
+00:01:32,830 --> 00:01:36,530
+المعادلة التفاضلية الجزيرة تعتمد على ما دُرس في
+
+17
+00:01:36,530 --> 00:01:40,430
+Calculus C وهي دراسة الـ function of several
+
+18
+00:01:40,430 --> 00:01:45,570
+variables طبعا هذه خارج نطاق دراستنا في هذا المساق
+
+19
+00:01:45,570 --> 00:01:49,910
+و فقط ستقتصر دراستنا على ال ordinary differential
+
+20
+00:01:49,910 --> 00:01:55,400
+equations اللي هي المعادلات التفاضلية العاديةبنبدأ
+
+21
+00:01:55,400 --> 00:01:59,120
+بتعريف المعادلة التفاضلية فبجي بقول the ordinary
+
+22
+00:01:59,120 --> 00:02:03,960
+differential equation is an equation هي عبارة عن
+
+23
+00:02:03,960 --> 00:02:09,080
+معادلة that involves تشتمل أو تحتوي على single
+
+24
+00:02:09,080 --> 00:02:14,920
+unknown function دالة واحدة مجهولة فيها مجهول واحد
+
+25
+00:02:14,920 --> 00:02:20,500
+of a single variable في متغير واحد يعني ايه؟عندها
+
+26
+00:02:20,500 --> 00:02:27,060
+متغير دالة في متغيرة Y تساوي F of X يبقى Y هو
+
+27
+00:02:27,060 --> 00:02:32,340
+المتغير التابع و X هو المتغير المستقل يبقى Y
+
+28
+00:02:32,340 --> 00:02:37,560
+function في X هذه لما أقول دالة في متغيرين واحد
+
+29
+00:02:38,010 --> 00:02:43,410
+يبقى هنا المعادلة اللي عندي تجتمل على متغير واحد
+
+30
+00:02:43,410 --> 00:02:49,790
+في متغير واحد آخر and some finite number of its
+
+31
+00:02:49,790 --> 00:02:50,410
+derivative
+
+32
+00:02:53,660 --> 00:02:57,900
+فيها أو تحتوي أو المعادلة تحتوي على مجموعة من
+
+33
+00:02:57,900 --> 00:03:02,320
+المشتقات المشتقة الأولى أو المشتقة الأولى والثانية
+
+34
+00:03:02,320 --> 00:03:06,240
+أو المشتقة الأولى والتانية والتالتة أو التالتة
+
+35
+00:03:06,240 --> 00:03:10,980
+والتانية فقط لغير أو ما إلى ذلك يبقى احنا عندنا y
+
+36
+00:03:10,980 --> 00:03:15,580
+function في x اشتقناها مرة واتنين وتلاتة كونا منها
+
+37
+00:03:15,580 --> 00:03:20,800
+اربع خمسة جد ما يكون كونا منها معادلة هذه المعادلة
+
+38
+00:03:20,800 --> 00:03:26,020
+بسميها معادلة تفاضليةنعطي بعض الأمثلة لأنواع
+
+39
+00:03:26,020 --> 00:03:31,880
+المعادلات التفاضلية فمثلا المتغير الواحد اللي هو y
+
+40
+00:03:31,880 --> 00:03:35,780
+function في x لكن المعادلة احتوت على what you mean
+
+41
+00:03:35,780 --> 00:03:41,020
+مشتقتها لأن قلنا هنا finite number of its
+
+42
+00:03:41,020 --> 00:03:44,680
+derivatives يبقى هي عند المشتقة الأولى موجودة لو
+
+43
+00:03:44,680 --> 00:03:48,140
+جينا للمعادلة التانية تحتوي على المشتقة الأولى
+
+44
+00:03:48,140 --> 00:03:52,980
+والثانية هو الدالة بدون اشتقاق تمام؟إذا المعادلة
+
+45
+00:03:52,980 --> 00:03:56,940
+تحتوي على المشتقة الأولى والثانية لو جيت للمعادلة
+
+46
+00:03:56,940 --> 00:04:01,900
+التالتة تحتوي على المشتقة الثالثة والتانية والأولى
+
+47
+00:04:01,900 --> 00:04:06,300
+مش موجودة ماعنديش مشكلة المعادلة موجودة with بعض
+
+48
+00:04:06,300 --> 00:04:09,900
+ال derivatives ماقلتش كل ال derivatives قلت some
+
+49
+00:04:09,900 --> 00:04:14,520
+يبقى بعض ال derivatives موجودة يبقى كل مثل هذه
+
+50
+00:04:14,520 --> 00:04:20,540
+الأنواعبقول عنها معادلة تفاضلية عادية طيب في عندنا
+
+51
+00:04:20,540 --> 00:04:24,060
+بنات لما ندرسنا في المرحلة الإعدادية والثانوية بقى
+
+52
+00:04:24,060 --> 00:04:30,220
+نقول درجة المعادلة العادية لكن احنا هنا في فرق بين
+
+53
+00:04:30,220 --> 00:04:36,260
+الرتبة والدرجةالدرجة بنحطها للأسس تبع المعادلة
+
+54
+00:04:36,260 --> 00:04:41,540
+اللى موجودة عندى لكن إذا معادلة تفاضلية وفيها
+
+55
+00:04:41,540 --> 00:04:48,820
+مشتقت فبقول رتبتي المعادلة التفاضلية هي أعلى مشتقة
+
+56
+00:04:48,820 --> 00:04:53,760
+موجودة عندنا هذا أنا مكتوب قداميبيقولي the order
+
+57
+00:04:53,760 --> 00:04:58,820
+of a differential equation يعني رتبة المعادلة
+
+58
+00:04:58,820 --> 00:05:03,240
+التفاضلية is the order of the highest derivative
+
+59
+00:05:03,240 --> 00:05:10,220
+يبقى هي رتبة أعلى معامل
+
+60
+00:05:10,220 --> 00:05:17,320
+تفاضلي موجود في هذه المعادلة فمثلا هنا أعلى معامل
+
+61
+00:05:17,320 --> 00:05:22,340
+تفاضلي كده؟واحد مشتقة الأولى يبقى هذه معادلة من
+
+62
+00:05:22,340 --> 00:05:27,880
+الرتبة الأولى المعادلة التانية أعلى معامل تفاضل
+
+63
+00:05:27,880 --> 00:05:33,960
+يقداش يبقى هذه معادلة من الرتبة الثانية هذه أعلى
+
+64
+00:05:33,960 --> 00:05:39,640
+مشتقة يقداش يبقى المعادلة هذه من الرتبة الثالثة
+
+65
+00:05:39,640 --> 00:05:43,640
+يبقى بنفرق بين الدرجة و الرتبة الدرجة هي الأسس
+
+66
+00:05:43,640 --> 00:05:46,860
+اللي بتكون مرفوعة اليها المعادلة سواء كانت تفاضلية
+
+67
+00:05:46,860 --> 00:05:50,050
+ولا غير تفاضلية ماعيش علاقة فيهايبقى أنا بتكلم
+
+68
+00:05:50,050 --> 00:05:58,360
+بالرتبة وليس على الدرجة طيب فمثلاالـ order for
+
+69
+00:05:58,360 --> 00:06:02,720
+example the differential equation خمسة y triple
+
+70
+00:06:02,720 --> 00:06:06,800
+prime زائد تلاتة x y double prime ناقص اتنين y
+
+71
+00:06:06,800 --> 00:06:13,180
+prime أس خمسة زائد y يساوي x أس أربعة يا ترى رتبة
+
+72
+00:06:13,180 --> 00:06:18,960
+المعادلة هل هي أربعة ولا خمسة ولا اتنين ولا تلاتة
+
+73
+00:06:18,960 --> 00:06:25,160
+تلاتةلأن أعلى رتبة معامل تفاضل هي جداش المعادلة
+
+74
+00:06:25,160 --> 00:06:30,740
+فيها المشتقة التالتة يبقى هذه is of order three
+
+75
+00:06:30,740 --> 00:06:36,020
+يبقى هنا الرتبة تلاتة لا خمسة ولا أربعة ولا اتنين
+
+76
+00:06:36,020 --> 00:06:43,710
+وإنما هي من تلاتةبنجي كمال معلومة جديدة اللي هو حل
+
+77
+00:06:43,710 --> 00:06:46,910
+المعادلة التفاضلية شو يعني حل المعادلة التفاضلية
+
+78
+00:06:46,910 --> 00:06:51,450
+لما اقول المعادلة هذه موجودة فيها عند المشتقة
+
+79
+00:06:51,450 --> 00:06:56,710
+الأولى يبقى انا بدي الاصل قبل الاشتقاء يعني بدي y
+
+80
+00:06:56,710 --> 00:07:02,710
+as a function of x هذا اللي بسميه حل المعادلة
+
+81
+00:07:02,710 --> 00:07:07,870
+التفاضلية هذه ههه لو بدي أحلها معناته بدي أكمل
+
+82
+00:07:07,870 --> 00:07:12,020
+مرتينلو كمان مرتين ينتهي الـ derivative وبالتالي
+
+83
+00:07:12,020 --> 00:07:16,300
+يحصل عالمين حل المعادلة التفاضلية هذه نفس القصة
+
+84
+00:07:16,300 --> 00:07:21,140
+وهكذا إذا بدنا نيجي إلى تعريف حل المعادلة
+
+85
+00:07:21,140 --> 00:07:24,820
+التفاضلية the solution of a differential equation
+
+86
+00:07:24,820 --> 00:07:30,300
+هو عبارة عن function هذه ال function نظريا بقول هي
+
+87
+00:07:30,300 --> 00:07:35,560
+Phi of X يبقى الحل هو Y تساوي Phi of X ما له هذا
+
+88
+00:07:35,560 --> 00:07:41,160
+الحل؟معرف على فترة ما that is defined on an
+
+89
+00:07:41,160 --> 00:07:46,040
+intervalهذا الحل لازم يكون معرف على فترة يعني صحيح
+
+90
+00:07:46,040 --> 00:07:49,580
+على فترة and satisfying the given differential
+
+91
+00:07:49,580 --> 00:07:54,640
+equation وفي نفس الوقت يحقق المعادلة التفاضلية
+
+92
+00:07:54,640 --> 00:08:00,020
+الموجودة مشان يكون حل بدي يكون معرف على فترة تمام
+
+93
+00:08:00,020 --> 00:08:05,080
+اثنين لو جيت ع وطب في المعادلة التفاضلية بدي يحقق
+
+94
+00:08:05,080 --> 00:08:11,300
+هذه المعادلةنعطي مثال عملي لما نقول باجي بقول for
+
+95
+00:08:11,300 --> 00:08:14,440
+example the solution of the differential equation
+
+96
+00:08:14,440 --> 00:08:21,780
+هذه واحد is y يسوى E أس ناقص اتنالك لش هذا حل باجي
+
+97
+00:08:21,780 --> 00:08:26,540
+بشوف والله إذا حقق المعادلة التفاضل اللي عند رقم
+
+98
+00:08:26,540 --> 00:08:30,900
+واحد بيكون حل ماحققش يبقى كلامنا ماله غير صحيح
+
+99
+00:08:30,900 --> 00:08:36,000
+يبقى هذا حل because لو بدي أجي أخد y prime يا بنات
+
+100
+00:08:36,630 --> 00:08:41,310
+يبقى الـ exponential مشتقتها كما هي زي ما أخدنا في
+
+101
+00:08:41,310 --> 00:08:48,790
+كل قلص بي ضرب مشتقت الأس يبقى هاي ناقص اتنين بدنا
+
+102
+00:08:48,790 --> 00:08:56,370
+مين كمان؟ YW primeيبقى هذا يعطيك Y'' يبقى اشتق
+
+103
+00:08:56,370 --> 00:09:00,910
+كمان مرة يبقى ال X وهذا مقدر ثابت مالوش دعوة وهذا
+
+104
+00:09:00,910 --> 00:09:05,310
+نشتقه كمان مرة بيجينا ناقص اتنين فناقص اتنين بقداش
+
+105
+00:09:05,310 --> 00:09:12,510
+اربعة E أس ناقص اتنين X الان بدي اعوض في المعادلة
+
+106
+00:09:12,510 --> 00:09:19,090
+عن ال Y وY' وY'' في المعادلة لرقم واحد انشوف هنحصل
+
+107
+00:09:19,090 --> 00:09:27,970
+على ايشيبقى لو جيت للـ yw' زائد y' ناقص 2y لو جيت
+
+108
+00:09:27,970 --> 00:09:32,650
+عوط بهذه الحلول إن طلع الناتج يسوى الصفر يبقى
+
+109
+00:09:32,650 --> 00:09:37,930
+كلامنا صحيح ما طلع يسوى الصفر يبقى كلامنا ماله غير
+
+110
+00:09:37,930 --> 00:09:45,920
+صحيحيبقى نعوض YW' هي أربعة E أص ناقص اتنين X يبقى
+
+111
+00:09:45,920 --> 00:09:48,420
+نعوض YW' هي أربعة E أص ناقص اتنين X يبقى نعوض YW'
+
+112
+00:09:48,760 --> 00:09:51,100
+هي أربعة E أص ناقص اتنين X يبقى نعوض YW' هي أربعة
+
+113
+00:09:51,100 --> 00:09:58,000
+E أص ناقص اتنين X يبقى نعوض
+
+114
+00:09:58,000 --> 00:10:05,340
+YW' هي أربعة E أص ناقص اتنين Xطلعيلي أربعة بالموجة
+
+115
+00:10:05,340 --> 00:10:10,680
+يا ابو هدول قداش؟ أربعة سالب يبقى ناتج يساوي Zero
+
+116
+00:10:10,680 --> 00:10:17,000
+يبقى ناتج يساوي Zero معناتهدا فعلا هو عبارة عن
+
+117
+00:10:17,000 --> 00:10:22,540
+حلمين لهذه المعادلة بدي أخليك تمرني إيدك check
+
+118
+00:10:22,540 --> 00:10:23,420
+that
+
+119
+00:10:27,380 --> 00:10:38,120
+إن Y تساوي constant C E أُص ناقص 2X is a solution
+
+120
+00:10:38,120 --> 00:10:49,160
+of the differential equation 1 اتحققيلي أو اتأكدي
+
+121
+00:10:49,160 --> 00:10:56,120
+ان هذا كمان عبارة عن حل آخر للمعادلة التفاضلية شو
+
+122
+00:10:56,120 --> 00:11:03,490
+يعني معناه؟معناته ان المعادلة التفاضلية ممكن
+
+123
+00:11:03,490 --> 00:11:08,750
+لجيلها عدة حلول و ليس حلا واحدا
+
+124
+00:11:10,320 --> 00:11:15,340
+من هنا بعد قليل هروح اقولك في ان حاجة اسم ال
+
+125
+00:11:15,340 --> 00:11:20,720
+general solution للمعادلة التفاضلية يبقى هذا انت
+
+126
+00:11:20,720 --> 00:11:25,160
+بتمرني ايدك فيه في البيت تتأكد ان هذا عبارة عن حل
+
+127
+00:11:25,160 --> 00:11:31,700
+المعادلة التفاضلية كذلك نعطي ال definition الكلام
+
+128
+00:11:31,700 --> 00:11:37,580
+اللي قلته الشفوي بدنا نحطه على شكل تعريف the set
+
+129
+00:11:37,580 --> 00:11:39,840
+of
+
+130
+00:11:40,610 --> 00:11:51,330
+all solutions مجموعة كل الحلول of a differential
+
+131
+00:11:51,330 --> 00:12:00,010
+equation للمعادلة التفاضلية is called بنروح نسميه
+
+132
+00:12:00,010 --> 00:12:07,270
+the general solution الحل
+
+133
+00:12:07,270 --> 00:12:12,480
+العام of the differential equationof the
+
+134
+00:12:12,480 --> 00:12:18,380
+differential equation الحل العام للمعادلة
+
+135
+00:12:18,380 --> 00:12:25,740
+التفاضلية نعطي مثال example find
+
+136
+00:12:25,740 --> 00:12:30,080
+the general solution of the
+
+137
+00:12:41,300 --> 00:12:50,920
+Differential equations اتالية نمرا واحد f w prime
+
+138
+00:12:50,920 --> 00:13:01,200
+of x يساوى اتناشر x تربيع زائد ستة x ناقص تمانية
+
+139
+00:13:01,200 --> 00:13:03,660
+solution
+
+140
+00:13:23,180 --> 00:13:30,580
+مرة تانية اقول لو جات للمعادلة التفاضلية او جات
+
+141
+00:13:30,580 --> 00:13:35,600
+الحل الأول والثاني والثالث فمثلا اللي كتبناه قبل
+
+142
+00:13:35,600 --> 00:13:39,720
+قليل ماكنتشك that see هذا كنص تاني اتنين تلاتة
+
+143
+00:13:39,720 --> 00:13:44,140
+اربعة مص خمس جدر اتنين زي ما بدك كويسيك بقى كم حل
+
+144
+00:13:44,140 --> 00:13:49,170
+بصير عندىمال نهاية من الحلول إذا هذا الحل اللي
+
+145
+00:13:49,170 --> 00:13:55,030
+بيطلع هو صيغة الحل العام الذي يستمل على بقية
+
+146
+00:13:55,030 --> 00:14:01,290
+الحلول تمام؟ إذا في عندي حاجة اسمه الحل العام يبقى
+
+147
+00:14:01,290 --> 00:14:05,550
+مجموعة الحلول كلها بيسميها مين؟ الحل العام فمثلا
+
+148
+00:14:05,550 --> 00:14:09,930
+بدنا نروح نجيب الحل العام لهذه المعادلة المعادلة
+
+149
+00:14:09,930 --> 00:14:11,790
+تحتوي على المشتقة الثانية
+
+150
+00:14:17,920 --> 00:14:23,390
+يبقى مشان أحصل على ال F of X شكليش بدي أعملواضروحة
+
+151
+00:14:23,390 --> 00:14:30,630
+كامل مرتين صحيح ولا لأ؟ إذا لو جيت كاملت f double
+
+152
+00:14:30,630 --> 00:14:39,390
+prime of x dx بدي يسوي تكامل للـ 12x تربية زائد 6x
+
+153
+00:14:39,390 --> 00:14:45,130
+ناقص تمانية كله بالنسبة لمن؟ الاد إكستكامل مرة
+
+154
+00:14:45,130 --> 00:14:51,970
+واحدة بيعطينا ماذا؟ f prime of x يساوي اربعة x
+
+155
+00:14:51,970 --> 00:14:58,890
+تكيب زائد تلاتة x تربية ناقص تمانية x التكامل هذا
+
+156
+00:14:58,890 --> 00:15:04,330
+تكامل غير محدود مشاناك ايش بعمل؟ بقول زائد
+
+157
+00:15:04,330 --> 00:15:12,140
+constant c زائد constant cطيب كويس الان لكي أجيب
+
+158
+00:15:12,140 --> 00:15:17,660
+شكل ال F of X بدي أروحها كامل كمان مرة إذا لو كملت
+
+159
+00:15:17,660 --> 00:15:26,280
+كمان مرة بصير عند مين F of X يساوي X أص أربعة زائد
+
+160
+00:15:26,280 --> 00:15:35,280
+X تكيب ناقص أربعة X تربية زائد CX زائد C1
+
+161
+00:15:37,220 --> 00:15:41,640
+إذاً هذا البنات اللي حصلت عليه بيكون هو ال general
+
+162
+00:15:41,640 --> 00:15:48,080
+solution للمعادلة اللي عندنا هذه وبالتالي قدرت
+
+163
+00:15:48,080 --> 00:15:55,320
+أجيب اللي هو شكل الحل العام لهذه المعادلة نعطيكي
+
+164
+00:15:55,320 --> 00:16:04,410
+معادلة تانية نمر اتنين لو جيت قلتلك why w primeبدو
+
+165
+00:16:04,410 --> 00:16:14,330
+يساوي سك ال X في تان ال X زائد سك تربيع ال X و
+
+166
+00:16:14,330 --> 00:16:18,890
+بدنا نروح نحل هذه المعادلة هذه معادلة مشتملة
+
+167
+00:16:18,890 --> 00:16:25,090
+عالميا على المشتقة الثانية إذا مشان أروح أحلها
+
+168
+00:16:25,090 --> 00:16:31,680
+بدروح أكامل كم مرة مرتينكل تكامل بيجيب لي كنصة
+
+169
+00:16:31,680 --> 00:16:35,340
+الكنصة اللي أنا بحطه من عندي ممكن يكون أي قيمة
+
+170
+00:16:35,340 --> 00:16:39,180
+تيجي في بالنا ومن هنا صار اللي اللي في المستطيل
+
+171
+00:16:39,180 --> 00:16:43,200
+هذا هو ال general solution لماذا؟ للمعادلة الأولى
+
+172
+00:16:43,200 --> 00:16:46,880
+بنفس الطريقة بنحاول نجيب ال general solution
+
+173
+00:16:46,880 --> 00:16:51,620
+للمعادلة الثانية إذا لو كملت مرة بيصير عندنا هنا
+
+174
+00:16:51,620 --> 00:17:01,560
+كده؟ وايه؟ تكامل سكتانمقدش؟ سك مهم ده زي ده لإن
+
+175
+00:17:01,560 --> 00:17:08,340
+مشتقة السك هي سك ال X تان ال X يبقى سك ال X زائد
+
+176
+00:17:08,340 --> 00:17:15,900
+مشتقتي تان سك تربيع إذا انت كامل السك تربيع بتان
+
+177
+00:17:15,900 --> 00:17:25,360
+ال X يبقى هذه تان ال X زائد constant C نكامل كمان
+
+178
+00:17:25,360 --> 00:17:31,580
+مرةبيكون حصلنا على الحل العام الكامل كمان مرة يبقى
+
+179
+00:17:31,580 --> 00:17:36,200
+Y تساوي حدا
+
+180
+00:17:36,200 --> 00:17:41,060
+ماذا ذاكرة فيك وقداش تكامل السك؟ اه مين ماذا ذاكرة
+
+181
+00:17:41,060 --> 00:17:49,040
+يا بنات؟ calculus B اه احنا عندنا ست دواي المثلثية
+
+182
+00:17:49,040 --> 00:17:52,580
+وانا قلتلك المحاضرة الماضية لازم تروح تراجعي
+
+183
+00:17:52,580 --> 00:17:58,710
+التكامل بسيط هم ستةتنتين أخدناهم في calculus A
+
+184
+00:17:58,710 --> 00:18:03,310
+والباقي الأربعة التانية في calculus B مظبوط خدنا
+
+185
+00:18:03,310 --> 00:18:07,030
+تكامل ال cosine بالsine تكامل ال sine بالسالب
+
+186
+00:18:07,030 --> 00:18:10,950
+cosine و بعد ذلك انتقلنا على calculus B قلنا
+
+187
+00:18:10,950 --> 00:18:18,950
+تكاملتان فيجينابنكتب sin على cos البسط هو تفضل
+
+188
+00:18:18,950 --> 00:18:23,730
+مقام بس بده إشارة سالب يبقى الجواب سالب لم cos
+
+189
+00:18:23,730 --> 00:18:28,110
+السك هذه الصعبة بروح بضرب في سك زائد تان و بجسم
+
+190
+00:18:28,110 --> 00:18:33,210
+على سك زائد تان بصير البس هو تفضل مقام يبقى لين
+
+191
+00:18:33,210 --> 00:18:38,430
+absolute value لسك ال X زائد تان ال X ترجع من حد
+
+192
+00:18:38,430 --> 00:18:44,180
+ما تروح اليوم تروح تراجعها في كل كلص بيهيبقى هذا
+
+193
+00:18:44,180 --> 00:18:54,880
+الان absolute value لسك ال X زي التان ال X تكامل
+
+194
+00:18:54,880 --> 00:18:59,780
+التان بكتوبها sin على cos البص هو تفاضل مقام بس
+
+195
+00:18:59,780 --> 00:19:06,980
+بده إشارةسالب يبقى الجواب سالب لين absolute value
+
+196
+00:19:06,980 --> 00:19:17,580
+لكو صين ال X زائد CX زائد C1 يبقى هذا يعتبر حل
+
+197
+00:19:17,580 --> 00:19:22,580
+المعادلة التفاضلية التانية وزي ما انت شايفه اجتمل
+
+198
+00:19:22,580 --> 00:19:26,850
+على ثوابت اتنينمن هنا سمناها ال general solution
+
+199
+00:19:26,850 --> 00:19:32,750
+لإنه يحتوي على أي حل آخر تقدر تواجدي يبقى هذا صيغة
+
+200
+00:19:32,750 --> 00:19:38,050
+أو صورة الحل العام لهذه المعادلة في حاجة منتظرة
+
+201
+00:19:38,050 --> 00:19:41,330
+اسمها ال initial value problem شو هو initial value
+
+202
+00:19:41,330 --> 00:19:45,840
+problem؟يعني انا عندي معادلة تفاضلية مثل هذه
+
+203
+00:19:45,840 --> 00:19:50,780
+المعادلة بروح بحط عليها شرط او شرطين او تلاتة او
+
+204
+00:19:50,780 --> 00:19:56,440
+غيره حسب طبيعة المثلة من خلال هذه الشروط يمكن
+
+205
+00:19:56,440 --> 00:20:01,220
+الحصول على الثوابت اللي عندنا هذهفلما أحصل على ثوت
+
+206
+00:20:01,220 --> 00:20:06,060
+ببطلي الصيري عندي ثوابت وبالتالي بجيب شكل الحل
+
+207
+00:20:06,060 --> 00:20:11,000
+الفعلي لمين للمعادلة هذه ومن هنا بسميه initial
+
+208
+00:20:11,000 --> 00:20:16,980
+value problem يعني نظرية القيمة الأساسية أو السؤال
+
+209
+00:20:16,980 --> 00:20:21,840
+اللي يعتمد على القيم الأساسية نعطيكي definition
+
+210
+00:20:21,840 --> 00:20:31,230
+ومثال يبقى definitionThe initial
+
+211
+00:20:31,230 --> 00:20:37,170
+value
+
+212
+00:20:37,170 --> 00:20:41,990
+problem اللي
+
+213
+00:20:41,990 --> 00:20:55,250
+حديها الرمز IVP is a differential equationيبقى هي
+
+214
+00:20:55,250 --> 00:21:05,870
+عبارة عن معادلة تفاضلية with initial conditions مع
+
+215
+00:21:05,870 --> 00:21:14,870
+شروط ابتدائية موجودة على المثلة example solve
+
+216
+00:21:14,870 --> 00:21:25,400
+the initial value problemY triple A prime يسوى
+
+217
+00:21:25,400 --> 00:21:32,980
+تسعة E أس ناقص تلاتة X والـ Y عند الـ Zero بده
+
+218
+00:21:32,980 --> 00:21:37,740
+يسوى الواحد والـ Y prime عند الـ Zero بده يسوى
+
+219
+00:21:37,740 --> 00:21:40,980
+اتنين
+
+220
+00:21:48,470 --> 00:21:53,950
+بنرجع للتعريف اللي احنا كتبناه نقرأ هذا التعريف
+
+221
+00:21:53,950 --> 00:22:00,070
+نحاول ان نفهم كل كلمة في هذا التعريف ثم بعد ذلك
+
+222
+00:22:00,070 --> 00:22:07,610
+ناخد مثال كتطبيق مباشر على هذا التعريف التعريف
+
+223
+00:22:07,610 --> 00:22:14,990
+بيقول ال initial value problemهأختصرها إلى IVP مش
+
+224
+00:22:14,990 --> 00:22:19,110
+زي التصريح اللي باخده الناس اللي كانت حالهم عمره
+
+225
+00:22:19,110 --> 00:22:26,130
+اي يوم Vip لأ IVP هداك very important person يعني
+
+226
+00:22:26,130 --> 00:22:32,570
+شخص مهم جدا سهل مروره عن الحواجز لأ لأ هدا IVP بقى
+
+227
+00:22:32,570 --> 00:22:37,070
+مثلة و عليها شرورThe initial value problem is a
+
+228
+00:22:37,070 --> 00:22:41,350
+differential equation يبقى هي معادلة فاضلية with
+
+229
+00:22:41,350 --> 00:22:45,790
+initial conditions عليها شروط بسمي هذه الشروط هي
+
+230
+00:22:45,790 --> 00:22:51,510
+الشروط الإبتدائية نعطي مثال على ذلكبقول solve the
+
+231
+00:22:51,510 --> 00:22:55,230
+initial value problem yw prime يسوى تسعة e و اص
+
+232
+00:22:55,230 --> 00:23:00,750
+ناقص تلاتة x وروحنا حاطين عليها شروط ابتدائية هذه
+
+233
+00:23:00,750 --> 00:23:05,750
+بسميها ال initial condition وهدول اتنين هم السبب
+
+234
+00:23:05,750 --> 00:23:10,210
+في ان اسميت المعادلة اللى عندنا هذه initial value
+
+235
+00:23:10,210 --> 00:23:15,110
+problemطيب بنشوف كيف بنحلها يبقى نفس التكتيك اللى
+
+236
+00:23:15,110 --> 00:23:20,190
+اتبعناه عند حل السؤالين قبل قليل مع الفارق ان
+
+237
+00:23:20,190 --> 00:23:26,350
+ثوابت هدول هجيب قدرش القيم العددية عندهم طبقا لهذه
+
+238
+00:23:26,350 --> 00:23:34,150
+الشروط يبقى لما اقول انا عندي y'' يسوى تسعة اي أس
+
+239
+00:23:34,150 --> 00:23:42,340
+ناقص ثلاثة اكس لو كملت مرة واحدة يا بناتيبقى احد
+
+240
+00:23:42,340 --> 00:23:47,920
+المشتقات تبقى مشتقة واحدة هذه تسعة زي ما هي وهي E
+
+241
+00:23:47,920 --> 00:23:55,760
+أس ناقص تلاتة X مقسوما على مشتقة الأس إن كان الأس
+
+242
+00:23:55,760 --> 00:24:01,030
+من الدرجة الأولىطبعاً تلاتة X من الدرجة الأولى
+
+243
+00:24:01,030 --> 00:24:08,390
+يبقى مقسم على سالب تلاتة زائد constant C1 يبقى
+
+244
+00:24:08,390 --> 00:24:16,970
+الجواب سالب تلاتة E وسالب تلاتة X زائد C1الان انا
+
+245
+00:24:16,970 --> 00:24:20,890
+عندي initial condition هى و بدى استخدمه ايش
+
+246
+00:24:20,890 --> 00:24:25,170
+بيقوللي في ال initial condition بيقوللي y prime
+
+247
+00:24:25,170 --> 00:24:29,450
+عند ال zero بدى يساوي اتنين اذا بدى اجي على
+
+248
+00:24:29,450 --> 00:24:33,190
+المعادلة اللى عندها دي y prime عند ال zero بدى
+
+249
+00:24:33,190 --> 00:24:39,850
+يساوي قداش اتنين اذا بدى اشيل كل x و احط مكانه
+
+250
+00:24:39,850 --> 00:24:49,200
+قداش zero زائد constant c oneE0 بقداش يا بنات يعني
+
+251
+00:24:49,200 --> 00:24:55,960
+معناها كلام ان الـ C1 بدى يسوي كداش خمسة E0 بواحدة
+
+252
+00:24:55,960 --> 00:25:01,640
+سلب تلاتة تلاتة و اتنين خمسة يبقى صارة المعادلة
+
+253
+00:25:01,640 --> 00:25:07,860
+اللى عندى Y prime يسوى ناقص تلاتة E اص ناقص تلاتة
+
+254
+00:25:07,860 --> 00:25:14,860
+X زائد خمسة انا مابدي Y prime بدي Y يبقاش بعملبروح
+
+255
+00:25:14,860 --> 00:25:20,200
+كامل كمان مرة اذا لو روحنا كمان كاملنا كمان مرة
+
+256
+00:25:20,200 --> 00:25:26,720
+بنحصل على y يساوي ناقص ثلاثة ايص ناقص ثلاث اكس على
+
+257
+00:25:26,720 --> 00:25:35,360
+جداش على سالب تلاتة زائد خمس زائد خمس اكس زائد c
+
+258
+00:25:35,360 --> 00:25:43,200
+two constant جديد يعني هذاهذا بيعطيك ان الـ y اللي
+
+259
+00:25:43,200 --> 00:25:50,500
+بندور عليها بيبقى اي اص ناقص تلاتة x زائد خمسة x
+
+260
+00:25:50,500 --> 00:25:55,780
+زائد c2 في عندنا لا يزال initial condition ما
+
+261
+00:25:55,780 --> 00:26:01,210
+استخدمنهش اللي هو mainy عند ال zero تساوي واحد
+
+262
+00:26:01,210 --> 00:26:07,950
+الان y عند ال zero تساوي واحد implies يعني هشيل كل
+
+263
+00:26:07,950 --> 00:26:12,250
+y و أحط مكانها واحد و أشيل كل x و أعوض عنها ب zero
+
+264
+00:26:12,250 --> 00:26:16,750
+يبقى بصير عندنا واحد يساوي ايه و ال zero بقداش يا
+
+265
+00:26:16,750 --> 00:26:25,540
+بنات بواحد زائد خمسة في zero ب zeroزائد C2 هذا
+
+266
+00:26:25,540 --> 00:26:30,620
+معناته انه C2 بده ساوى قداش يبقى بناء انا عليه
+
+267
+00:26:30,620 --> 00:26:39,240
+بروح بقوله the solution of the given
+
+268
+00:26:40,460 --> 00:26:50,760
+initial value problem is y تساوي e أس ناقص ثلاثة x
+
+269
+00:26:50,760 --> 00:26:58,860
+زائد خمسة x فقط لغير لإيش لأن c2 عندنا راح ب zero
+
+270
+00:26:58,860 --> 00:27:06,880
+وبالتالي انتهينا من مشكلته هذه طيب نيجي لآخر تعريف
+
+271
+00:27:06,880 --> 00:27:13,700
+في محاضرة اليومتعريف definition و هذا التعريف
+
+272
+00:27:13,700 --> 00:27:17,920
+أساسي للدراسة المستفيدة في ال differential
+
+273
+00:27:17,920 --> 00:27:22,280
+equations بعد ذلك بيقول لي the linear differential
+
+274
+00:27:22,280 --> 00:27:30,220
+equation ال معادلة
+
+275
+00:27:30,220 --> 00:27:37,500
+التفاضلية الخطية is an equation هي عبارة عن معادلة
+
+276
+00:27:37,500 --> 00:27:47,320
+in the formفي الشكل التالي اللي هي a0 as a
+
+277
+00:27:47,320 --> 00:27:53,600
+function of x في الـ y to the derivative n الشكل
+
+278
+00:27:53,600 --> 00:28:01,320
+اللي عندنا هذا to the derivative n زائد a1 as a
+
+279
+00:28:01,320 --> 00:28:07,680
+function of x to the derivative n minus ال 1 زائد
+
+280
+00:28:07,820 --> 00:28:12,420
+اكتشف الـ a2 as a function of x في الـ y to the
+
+281
+00:28:12,420 --> 00:28:18,990
+derivative of n minus 2 زائد زائدأنضل ماشيين لغاية
+
+282
+00:28:18,990 --> 00:28:25,830
+ما نوصل لل a n minus ال one as a function of x في
+
+283
+00:28:25,830 --> 00:28:33,950
+ال y prime زائد a n as a function of x في ال y بده
+
+284
+00:28:33,950 --> 00:28:41,230
+يساوي ال f of x وهذه سامحالي المعادلة star where
+
+285
+00:28:41,230 --> 00:28:50,490
+حيثالـ a0 of x والـ a1 of x والـ a2 of x ونظل
+
+286
+00:28:50,490 --> 00:28:57,710
+ماشيين والـ a n minus one as a function of x والـ
+
+287
+00:28:57,710 --> 00:29:08,410
+a n and ال f of x كلهم هدول are functions are
+
+288
+00:29:08,410 --> 00:29:20,140
+functions ofx only يبقى هدول دوال في x فقط if the
+
+289
+00:29:20,140 --> 00:29:28,000
+differential equation is not in the form star is
+
+290
+00:29:28,000 --> 00:29:36,680
+not in the form star لو ماكنتش على الشكل star it
+
+291
+00:29:36,680 --> 00:29:49,480
+is calledit is called بنروح نسميها a nonlinear
+
+292
+00:29:49,480 --> 00:29:52,960
+differential
+
+293
+00:29:52,960 --> 00:29:56,040
+equation
+
+294
+00:29:56,040 --> 00:29:59,580
+example
+
+295
+00:29:59,580 --> 00:30:06,320
+equations
+
+296
+00:30:06,320 --> 00:30:09,300
+المعادلات
+
+297
+00:30:10,210 --> 00:30:20,030
+نمر آي يساوي
+
+298
+00:30:20,030 --> 00:30:28,490
+تلاتة X تربيع أو نمر بإتنين
+
+299
+00:30:28,490 --> 00:30:34,530
+Y to the derivative of fiveزائد تلاتة y triple
+
+300
+00:30:34,530 --> 00:30:42,330
+prime زائد y prime بده يساوي zero كلهم هدول are
+
+301
+00:30:42,330 --> 00:30:55,610
+linear differential equations but the equations
+
+302
+00:30:55,610 --> 00:31:08,790
+ولكن المعادلات نمر ا2y prime زائد 3 لإن الواي لإن
+
+303
+00:31:08,790 --> 00:31:19,620
+الواي بده يساوي x ونمر بيه y double primeزائد Y في
+
+304
+00:31:19,620 --> 00:31:28,340
+الـ Y Prime زائد X في الـ Y يساوي واحد نمره C Y
+
+305
+00:31:28,340 --> 00:31:39,320
+Triple Prime زائد X تربيع Y Prime الكل تكيب زائد Y
+
+306
+00:31:39,320 --> 00:31:50,170
+يساوي Zero هدول كلهم are nonelinear differential
+
+307
+00:31:50,170 --> 00:31:52,390
+equations
+
+308
+00:32:21,620 --> 00:32:27,640
+نرجع تعريفنا هذا مرة تانية هذا التعريف بنات يفرق
+
+309
+00:32:27,640 --> 00:32:31,780
+فقط ما بين ال linear differential equations وما
+
+310
+00:32:31,780 --> 00:32:35,000
+بين ال non-linear differential equations يعني
+
+311
+00:32:35,000 --> 00:32:38,720
+وقتاش لو شفت المعادلة بقول عليها ال linear
+
+312
+00:32:38,720 --> 00:32:42,290
+differential equations ووقتاش لو شفتهابقول ماهياش
+
+313
+00:32:42,290 --> 00:32:47,310
+linear equation يعني ليست معادلة تفاضلية خطية بغض
+
+314
+00:32:47,310 --> 00:32:49,850
+النظر عن الرتبة الأولى أو التانية أو التالتة أو
+
+315
+00:32:49,850 --> 00:32:54,730
+الرابعة أو حتى رتبة أنونية تعريف بقولاش the linear
+
+316
+00:32:54,730 --> 00:32:59,730
+differential equation المعادلة التفاضلية الخطية هي
+
+317
+00:32:59,730 --> 00:33:06,180
+عبارة عن equation في الشكل التاليa node of x في y
+
+318
+00:33:06,180 --> 00:33:11,260
+to the derivative n من حد ما نشوف y بناته فوقه عدد
+
+319
+00:33:11,260 --> 00:33:16,920
+إذا بين قوسين معناته مشتقة بدون أقواس معناته أُس
+
+320
+00:33:16,920 --> 00:33:23,880
+تمام اطلع كل رمز من هذه الرموز حتى تقولك ايه بين
+
+321
+00:33:23,880 --> 00:33:29,470
+قوسين عشان نعرف إن هذا معناه اشتقاءيبقى هذا a node
+
+322
+00:33:29,470 --> 00:33:34,150
+of x y to the derivative n يعني المشتقة النونية لـ
+
+323
+00:33:34,150 --> 00:33:43,530
+y زائد a1x في y to the derivative n-1 زائد a2 of x
+
+324
+00:33:43,530 --> 00:33:47,930
+y to the derivative n-2 زائد زائد الله باللحظة
+
+325
+00:33:47,930 --> 00:33:51,790
+المشتقة قاعدة بتنزل أنه نية أنه نية نقص واحد أنه
+
+326
+00:33:51,790 --> 00:33:56,610
+نية نقص اتنين وكذا لغاية ما أوصل للمشتقة الأولى
+
+327
+00:33:57,050 --> 00:34:02,770
+وهنا an of x y بدون اشتقاق يساوي f of x كل
+
+328
+00:34:02,770 --> 00:34:07,750
+المعاملات اللي عندنا a node of x a1 of x a2 of x
+
+329
+00:34:07,750 --> 00:34:14,330
+an-1 of x an of x f of x كلها دوال في المتغير x لا
+
+330
+00:34:14,330 --> 00:34:21,710
+تحتوي على y يبقى y للمشتقات واخر term بدون مهمبدون
+
+331
+00:34:21,710 --> 00:34:26,990
+اشتقاق تمام والي هدول الباقى كلهم دوال هدول are
+
+332
+00:34:26,990 --> 00:34:32,170
+functions of x only يبقى هذا شكل الدالة الخطيئة
+
+333
+00:34:32,170 --> 00:34:36,710
+بدي اطرح السؤال التالي ضروري كل المشتقات يكونوا
+
+334
+00:34:36,710 --> 00:34:41,600
+موجودات ولا ممكن بعضهم يكون مش موجود زي ايش مثلازي
+
+335
+00:34:41,600 --> 00:34:45,420
+بدأت انا من المشتقة العاشرة مثلا و احنا ماشيين في
+
+336
+00:34:45,420 --> 00:34:49,860
+الطريق المشتقة السادسة و الخامسة و الرابعة مش
+
+337
+00:34:49,860 --> 00:34:53,520
+موجودة لكن الباقي موجود different linear ولا لا
+
+338
+00:34:53,520 --> 00:34:58,380
+linear على طول الخط لإن المشتقة جاعدة بتنزل اتنين
+
+339
+00:34:58,380 --> 00:35:02,340
+المعاملة الدوال في X يعني ماعندنا مش مشكلة طب لو
+
+340
+00:35:02,340 --> 00:35:06,900
+كانت هذه طارت الأخيرة بضال linear و لا مهياش
+
+341
+00:35:06,900 --> 00:35:10,970
+linearLinear لان طبقا للشرط كل المعاملات دوال
+
+342
+00:35:10,970 --> 00:35:14,650
+fixed و المشتقات جاعدة بتنزل اتغيب واحدة اتغيب
+
+343
+00:35:14,650 --> 00:35:18,170
+تنتين اتغيب .. يعني بتكون احدى المشتقات ب zero هذا
+
+344
+00:35:18,170 --> 00:35:23,530
+اللي خلها تغيب يبقى لو غاب بعضهما لا دايرة في ذلك
+
+345
+00:35:23,530 --> 00:35:31,290
+تمام؟ طب لو كل هدول كانوا غايبات مرة واحدة و هاد
+
+346
+00:35:31,290 --> 00:35:38,790
+اللي موجودة كيف لأ عاد؟ليه معادلة فضولية خطية من
+
+347
+00:35:38,790 --> 00:35:43,450
+الرتب النونية كمان؟ ليش مش تقنونية موجودة و هكذا؟
+
+348
+00:35:43,450 --> 00:35:47,590
+طب الآن بدنا نعرف وقت إيش بتبطل يصير Linear يبقى
+
+349
+00:35:47,590 --> 00:35:50,530
+نعطي بعض الأمثلة if the differential equation
+
+350
+00:35:50,530 --> 00:35:54,010
+ماكنتش في الشكل الستاري يبقى بقول عنها non-linear
+
+351
+00:35:54,010 --> 00:36:01,780
+فمثلا طلع لي هنا في Y'ماعنديش، راحت، تمام؟ لكن هذه
+
+352
+00:36:01,780 --> 00:36:05,400
+دالة في X وهذا كونوسنت اللي بعتبره دالة في X وهذا
+
+353
+00:36:05,400 --> 00:36:11,560
+دالة في X وY'' يبقى هذه دالة خطية طلع هنا كلهم
+
+354
+00:36:11,560 --> 00:36:16,280
+ثوابت والثوابت بعتبره دالة في X، ليه؟ لأن تلاتة في
+
+355
+00:36:16,280 --> 00:36:21,610
+X أُس Zero هي اللي خلّاها تلاتة، تمام؟يبقى كلها
+
+356
+00:36:21,610 --> 00:36:25,850
+دوال fixed الاصص خمسة وثلاثة واحد المشتقات مش
+
+357
+00:36:25,850 --> 00:36:29,810
+الاصص المشتقات يبقى خمسة وثلاثة واحد قاعدة بتنزل
+
+358
+00:36:29,810 --> 00:36:34,270
+ها و ال Y مش موجودة المشتقة الثانية مش موجودة و Y
+
+359
+00:36:34,270 --> 00:36:37,830
+بدون اشتقاق مش موجودة و ال Y للمشتقة الرابعة مش
+
+360
+00:36:37,830 --> 00:36:41,810
+موجودة برضه معادلة خطية ماعناش مشكلة ان شاء الله
+
+361
+00:36:41,810 --> 00:36:47,270
+يغيبوا كلهم معدة واحدة واحدة من المشتقات لكن لو
+
+362
+00:36:47,270 --> 00:36:52,960
+غابوا هدول كلهموظل هذا بقول هذه معادلة تفاضلية؟ لأ
+
+363
+00:36:52,960 --> 00:36:57,140
+لأنه مافيش مشتقة يبقى أقل حاجة اللي لازم يكون عندي
+
+364
+00:36:57,140 --> 00:37:01,860
+ولو المشتقة الأولى مشان أقول عليها معادلة تفاضلية
+
+365
+00:37:01,860 --> 00:37:07,420
+فعلا طيب هذول كلهم إذا هي معادلة تفاضلية لكن
+
+366
+00:37:07,420 --> 00:37:11,540
+المعادلة التانية معادلة تفاضلية خاطية لكن المعادلة
+
+367
+00:37:11,540 --> 00:37:16,380
+التالية ليست معادلة تفاضلية خاطية ليش؟ ايه
+
+368
+00:37:16,380 --> 00:37:23,310
+المسكلونة؟دالة في X ماشي شرط الأول تحقق هذي Y' هنا
+
+369
+00:37:23,310 --> 00:37:30,170
+ماعنديش Y عندي لن Y يبقى فيها عندي لن هنا يبقى
+
+370
+00:37:30,170 --> 00:37:35,470
+ليست معدلة خاطية تمام أعطيكي مثال آخرعندما أقول لك
+
+371
+00:37:35,470 --> 00:37:40,290
+y double prime زائد y y prime زائد x y يساوي واحد
+
+372
+00:37:40,290 --> 00:37:43,990
+الواحد ده اللي في x و هذا x و هذا كل الصندوق .. بس
+
+373
+00:37:43,990 --> 00:37:49,770
+هذا إيش؟ y هو قال لي كل هدول بدهم يكونوا دوال في x
+
+374
+00:37:49,770 --> 00:37:53,450
+لقيت واحدة ماهياش ده اللي في x يبقى هذه ال non
+
+375
+00:37:53,450 --> 00:37:57,810
+linear differential equation تمام؟طيب لو جيت
+
+376
+00:37:57,810 --> 00:38:01,930
+للمعادلة التالتة y triple a prime و x تربية و كل
+
+377
+00:38:01,930 --> 00:38:05,590
+.. اه zero بقدر اعتبره ده اللي في ال zero في x و
+
+378
+00:38:05,590 --> 00:38:09,670
+ال zero يبقى هده عشان ده اللي في x هاي المعاملة
+
+379
+00:38:09,670 --> 00:38:14,170
+constant x تربية يبقى كل المعاملة الدوال في x ماشي
+
+380
+00:38:14,170 --> 00:38:18,570
+الحال المشتقة التالتة المشتقة الأولى و هده الدلة
+
+381
+00:38:18,570 --> 00:38:23,590
+بس المشتقة اللي راح حطالي الأس قال لي y prime لكل
+
+382
+00:38:23,590 --> 00:38:29,140
+تكعيبهنا من الأول للآخر هي المشتقة مشتقات مرفوعة
+
+383
+00:38:29,140 --> 00:38:35,000
+على اسم ماعنديش بالمرة نهائية إذا لا يوجد عند يبقى
+
+384
+00:38:35,000 --> 00:38:40,520
+كل نوع من مثل هذه الأنواع ليست معادلة تفاضلية
+
+385
+00:38:40,520 --> 00:38:45,860
+خاطية معادلة تفاضلية صح بس ليست خاطية ماهياش لنا
+
+386
+00:38:45,860 --> 00:38:51,360
+non-linear differential equationطيب نعطي مثال الآن
+
+387
+00:38:51,360 --> 00:38:54,780
+انتهى الجزء النظري تبع ال section اللي بدنا إياه
+
+388
+00:38:54,780 --> 00:39:03,700
+بدنا نعطي بعض الأمثلة يبقى example one هنا
+
+389
+00:39:03,700 --> 00:39:11,360
+بنات سؤال سبعة من الكتاب بقول verify اتأكد منه
+
+390
+00:39:11,360 --> 00:39:18,340
+that each of the functions that each ofthe
+
+391
+00:39:18,340 --> 00:39:29,340
+functions كل من الدوال y تساوي e أس ناقص x and y
+
+392
+00:39:29,340 --> 00:39:42,000
+تساوي e أس تلاتة x is a solution of
+
+393
+00:39:42,000 --> 00:39:50,610
+the differential equationللمعادلة التفاضلية yw'
+
+394
+00:39:51,170 --> 00:40:01,890
+ناقص اتنين y' ناقص ثلاثة y تساوي زيرو on any
+
+395
+00:40:01,890 --> 00:40:11,470
+interval على أي فترة و بعد هيك then show that then
+
+396
+00:40:11,470 --> 00:40:26,480
+show that بيّلّي انهY تساوي C1 E أُس ناقص X زائد
+
+397
+00:40:26,480 --> 00:40:39,000
+C2 E أُس تلاتة X is a solution of
+
+398
+00:40:39,000 --> 00:40:40,420
+the same equation
+
+399
+00:40:46,870 --> 00:40:58,190
+للمعادلة التفاضلية for any constants c1
+
+400
+00:40:58,190 --> 00:41:07,150
+and c2 يعني ماعنديش قيود لا على c1 ولا على c2
+
+401
+00:41:07,150 --> 00:41:08,750
+solution
+
+402
+00:41:25,650 --> 00:41:29,930
+السؤال مرة تانية مقول يتأكد لي أن y يساوي u أص
+
+403
+00:41:29,930 --> 00:41:34,190
+ناقص x و y تساوي u أص تلاتة x هي عبارة عن حل
+
+404
+00:41:34,190 --> 00:41:38,530
+المعادلة التفاضلية الأولى على أي فترة من الفترات
+
+405
+00:41:38,530 --> 00:41:46,520
+بدكيهاإتنين ثم يظهر أنه يتساوي constant في الحل
+
+406
+00:41:46,520 --> 00:41:50,200
+الأول زاد constant تاني في الحل التاني هو عبارة عن
+
+407
+00:41:50,200 --> 00:41:56,080
+حل المعادلة اللي بعدها لأي قيم لل constant C1 وC2
+
+408
+00:41:56,080 --> 00:42:00,010
+ماعنديش قيود عليهميعني مين ما يكونوا يكونوا بنقوله
+
+409
+00:42:00,010 --> 00:42:06,050
+بسيطة جدا الان بدنا ندى نتأكد ان y تساوي e أصناق
+
+410
+00:42:06,050 --> 00:42:10,610
+ال six هي عبارة عن حل للمعادلة التفاضية فانا عندي
+
+411
+00:42:10,610 --> 00:42:17,230
+y يساوي e أصناق ال six لو اشتقناها y primeبصير
+
+412
+00:42:17,230 --> 00:42:23,050
+ناقص EOS ناقص X لو جبنا المشتقة الثانية يبقى YW'
+
+413
+00:42:23,530 --> 00:42:29,370
+بصير ناقص EOS ناقص X في ناقص يبقى بصير EOS ناقص X
+
+414
+00:42:29,370 --> 00:42:33,930
+نمسك المعلومات هذه ونعوض في المعارفة ان طلع مجموهم
+
+415
+00:42:33,930 --> 00:42:39,280
+يساوي السفر بصير خلاص يبقى كلامنا صحيحيبقى بالداجل
+
+416
+00:42:39,280 --> 00:42:46,540
+الى الـ yw' ناقص اتنين y' ناقص تلاتة y يساوي الـ
+
+417
+00:42:46,540 --> 00:42:54,800
+yw' هي eos ناقص x وهي ناقص اتنين الـ y' اللي هي
+
+418
+00:42:54,800 --> 00:43:02,440
+ناقص eos ناقص x وهنا ناقص تلاتة في الـ y الـ y هي
+
+419
+00:43:02,440 --> 00:43:12,010
+eos ناقص x y ساويعندكوا هنا بنات يوس ناقص اكس تمام
+
+420
+00:43:12,010 --> 00:43:19,490
+وعندك ناقص فى ناقص بزايدى اتنين يوس ناقص اكس وعندك
+
+421
+00:43:19,490 --> 00:43:24,510
+ناقص تلاتة يوس ناقص اكس ويوس ساوى هذول قداش
+
+422
+00:43:24,510 --> 00:43:30,050
+مجموعهمتلاتة و هذه تلاتة بالسلبي بالنتيجة يساوي
+
+423
+00:43:30,050 --> 00:43:37,550
+كدهش؟ Zero يبقى بناء عليه اللي هو Y تساوي E أص
+
+424
+00:43:37,550 --> 00:43:48,890
+ناقص X is a solution of the differential equation
+
+425
+00:43:48,890 --> 00:43:53,890
+one سميلي هذه المعادلة اللي فوق رقم واحد هي
+
+426
+00:43:53,890 --> 00:43:54,930
+الأساسية
+
+427
+00:44:01,100 --> 00:44:10,880
+بنفس الطريقة عندك Y تساوي E أس تلاتة X اللي هو
+
+428
+00:44:10,880 --> 00:44:12,540
+الحل التاني اللي جايلي عليه
+
+429
+00:44:16,170 --> 00:44:24,270
+يبقى Y' يساوي تلاتة E أس تلاتة X بدي أشتق كمان مرة
+
+430
+00:44:24,270 --> 00:44:32,390
+يبقى تسعة E أس تلاتة Xبدي امسك المعلومات اللى
+
+431
+00:44:32,390 --> 00:44:36,770
+وصلتلها هذه و ايه و نجي نعوض و بفهمين في هذه
+
+432
+00:44:36,770 --> 00:44:42,410
+المعادلة يبقى لما نجي نعوض في هذه المعادلة بصير yw
+
+433
+00:44:42,410 --> 00:44:48,550
+prime ناقص اتنين y prime ناقص تلاتة y الساوي بدي
+
+434
+00:44:48,550 --> 00:44:53,730
+اشوفها بدي تساوي zero ولا بدهاش تساوي zero يبقى
+
+435
+00:44:53,730 --> 00:44:59,770
+باجي بقوله ال yw prime اللى هي تسعة اقص تلاتة x
+
+436
+00:45:00,560 --> 00:45:08,380
+ناقص اتنين الـ Y' يا بنات اللي هي تلاتة E أس تلاتة
+
+437
+00:45:08,380 --> 00:45:16,140
+X الـ Y'' أو المعادل بعدها ناقص تلاتة في E أس
+
+438
+00:45:16,140 --> 00:45:24,720
+تلاتة X يساوي يساوي تسعة E أس تلاتة X ناقص ستة E
+
+439
+00:45:24,720 --> 00:45:31,530
+أس تلاتة X ناقص E أس تلاتة X يساوي قداشرزيرو يبقى
+
+440
+00:45:31,530 --> 00:45:40,610
+بناء عليه y تساوي e أس 3x is a solution ايش ضال
+
+441
+00:45:40,610 --> 00:45:47,850
+عليه كنتوا نتأكد ان هداك هو حل يبقى تشك
+
+442
+00:45:50,130 --> 00:45:58,270
+Y يسوى C1E-X زي C2E-3X
+
+443
+00:46:06,860 --> 00:46:11,520
+طبعا عندكم محاضرة اليوم من 12 للواحدة مظبوط يلا فى
+
+444
+00:46:11,520 --> 00:46:15,100
+الوقت اللى شوفى حالك عندك فرق شيكى شوفيلى هذا حل
+
+445
+00:46:15,100 --> 00:46:20,320
+ولا لأ و اذا حد طلعته ماهوش حل بنحله احنا ان شاء
+
+446
+00:46:20,320 --> 00:46:23,180
+الله فى المحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..465c321affd590d0e152d8572d40316d2d10b869
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_postprocess.srt
@@ -0,0 +1,1636 @@
+1
+00:00:19,640 --> 00:00:25,380
+بسم الله الرحمن الرحيم بنرجع نكمل الموضوع اللى كنا
+
+2
+00:00:25,380 --> 00:00:31,040
+بنتحدث فيه قبل ساعتين طبعا اعطينا ال three
+
+3
+00:00:31,040 --> 00:00:34,800
+integrating factors ال integrating factor الاول
+
+4
+00:00:34,800 --> 00:00:39,860
+كان mu of Y بده يساوي E أُس تكامل partial N by
+
+5
+00:00:39,860 --> 00:00:41,840
+partial X ناقص partial M
+
+6
+00:00:56,840 --> 00:01:04,230
+أو مقدار ثابت درجتنا واخدنا مثال على كل منهمباقي
+
+7
+00:01:04,230 --> 00:01:08,170
+الـ integrating factor الأخير أنه لو ما حصلش لا
+
+8
+00:01:08,170 --> 00:01:12,830
+هذا ولا ذاك، شو نعمل؟ قلنا بنروح نفرض أن ال
+
+9
+00:01:12,830 --> 00:01:17,290
+integrating factor عليه الشكل M U of X و Y يسوى X
+
+10
+00:01:17,290 --> 00:01:23,570
+to the power M في Y to the power N و بنحاول نوجد
+
+11
+00:01:23,570 --> 00:01:29,090
+قيمة M و N و إذا وجدناهم بيكون جيبنا شكل ال
+
+12
+00:01:29,090 --> 00:01:33,700
+integrating factorوبالتالي بنضرب فيه وبتنحل
+
+13
+00:01:33,700 --> 00:01:37,800
+مشكلتنا تمام يبقى هذا هو ال integration factor
+
+14
+00:01:37,800 --> 00:01:43,140
+الجديد يبقى بدنا نيجي هنا ونبحث هذه المعادلة
+
+15
+00:01:43,140 --> 00:01:48,320
+الأصلية اللي هي مين اللي سمناها star يبقى بداجي
+
+16
+00:01:48,320 --> 00:01:55,580
+أخد تفاضل ال M بالنسبة إلى Y أه بس يا بنات بفضل
+
+17
+00:01:55,580 --> 00:02:01,940
+قبل ذلك أن نحاول نرتبالمعادلة اللي عندنا بشكل جديد
+
+18
+00:02:01,940 --> 00:02:05,980
+بحيث تبقى في وضعها الطبيعي يبقى هذه بدي أجيبها في
+
+19
+00:02:05,980 --> 00:02:13,860
+الأول اتنين y تكيب ناقص ثلاثة x y زائد اللي هو مين
+
+20
+00:02:13,860 --> 00:02:19,960
+اللي هو ال x تربية زائد x y تربية كله في ال y
+
+21
+00:02:19,960 --> 00:02:25,000
+prime يساوي zero هذه ال equation هي star في وضعها
+
+22
+00:02:25,000 --> 00:02:31,910
+الطبيعييبقى بتروح اخد تفاضل ال M بالنسبة الى Y
+
+23
+00:02:31,910 --> 00:02:40,250
+يبقى بنشتق الأولى بالنسبة الى Y يبقى 6Y تربيع ناقص
+
+24
+00:02:40,250 --> 00:02:47,370
+3X الان بدنا نيجي تفاضل ال N بالنسبة الى X
+
+25
+00:02:47,370 --> 00:02:54,950
+المعادلة التانية يبقى 2X زائد Y تربيع تمام التمام
+
+26
+00:02:56,390 --> 00:03:02,030
+من اللي اتنين هدول بنستنتج انه تفاضل ال M بالنسبة
+
+27
+00:03:02,030 --> 00:03:11,350
+الى Y لا يساوي تفاضل ال N بالنسبة الى X يعني معنى
+
+28
+00:03:11,350 --> 00:03:18,930
+هذا الكلام انه The differential equation A star is
+
+29
+00:03:18,930 --> 00:03:25,900
+not exactMadam not exactly بدأ أروح أدور على ال
+
+30
+00:03:25,900 --> 00:03:30,460
+two integrating factors الأساسيات الأثنين بتاعتنا
+
+31
+00:03:30,460 --> 00:03:34,700
+يبقى أنا مش عارف أبدأ .. يبقى بدي أغمض و أتوكل على
+
+32
+00:03:34,700 --> 00:03:40,480
+الله و أشوف تيجي ولا بتجيش لإن شكلهم مكلكع يعني مش
+
+33
+00:03:40,480 --> 00:03:45,990
+.. مش عند بعض ليش؟ لإن لو طرحتممكن انتهيش او
+
+34
+00:03:45,990 --> 00:03:49,990
+ماوصلش لـ function of y او function of x اذا لو
+
+35
+00:03:49,990 --> 00:03:55,430
+جيت اخد partial n by partial x ناقص partial m by
+
+36
+00:03:55,430 --> 00:04:00,710
+partial y بدي اقسم على m partial n by partial x له
+
+37
+00:04:00,710 --> 00:04:09,410
+اتنين x زائد y تربيع ناقص ستة y تربيع زائد تلاتة x
+
+38
+00:04:09,410 --> 00:04:20,220
+كله على مين؟ على mيبقى M بـ 2Y تكييب ناقص 3XY و
+
+39
+00:04:20,220 --> 00:04:27,760
+يساوي هذه لو جمعتها مع بعض بيصير 5X و عندك Y تربيع
+
+40
+00:04:27,760 --> 00:04:35,160
+و ناقص 6Y تربيع بيظل ناقص 5Y تربيع على مين على ليه
+
+41
+00:04:35,160 --> 00:04:41,520
+2Y تكييب ناقص 3XY
+
+42
+00:04:42,450 --> 00:04:48,590
+طيب في عامل مشترك فوق اللي هو فيه خمسة فقط لغير
+
+43
+00:04:48,590 --> 00:04:57,390
+بيضل x ناقص y تربية تحت في عندنا y عامل مشترك فقط
+
+44
+00:04:57,390 --> 00:05:04,490
+لغير مصبوط بيضل عندنا اتنين y تربية اتنين y تربية
+
+45
+00:05:04,490 --> 00:05:13,900
+ناقص تلاتة xهل هذه function of y في اختصارات؟
+
+46
+00:05:13,900 --> 00:05:24,060
+ماعنديش، يبقى هذه not function of y onlyما هيش
+
+47
+00:05:24,060 --> 00:05:30,660
+function في Y فقط يبقى بنفعش شو نعمل نبدل النص في
+
+48
+00:05:30,660 --> 00:05:37,200
+الثاني يبقى بدي أخد تفاضل ال M بالنسبة إلى Y نقص
+
+49
+00:05:37,200 --> 00:05:43,720
+تفاضل ال N بالنسبة إلى X كله مقسوما على Nيبقى بدنا
+
+50
+00:05:43,720 --> 00:05:52,340
+نقلب الوضع PARTIAL M BY PARTIAL Y 6Y تربية ناقص 3X
+
+51
+00:05:52,340 --> 00:05:59,300
+ناقص 2X
+
+52
+00:05:59,300 --> 00:06:07,760
+ناقص Y تربية كل هذا مقسوما على Nوين ال N هيها؟ X
+
+53
+00:06:07,760 --> 00:06:14,880
+تربيع زائد XY تربيع تمام يبقى هذه بدها تساوي
+
+54
+00:06:14,880 --> 00:06:21,140
+طلعيلي هنا ستة Y تربيع وناقص Y تربيع بيظل خمسة Y
+
+55
+00:06:21,140 --> 00:06:31,240
+تربيع ناقص خمسة X كله مقسوما على X تربيع زائد XY
+
+56
+00:06:31,240 --> 00:06:39,550
+تربيعيبقى بناء عليه أصبح عندي partial M by partial
+
+57
+00:06:39,550 --> 00:06:47,830
+Y ناقص partial N by partial X كله مقسوما على N بده
+
+58
+00:06:47,830 --> 00:06:53,510
+يساوي في عندي هنا خمسة عامل مشترك وبظل عندي Y
+
+59
+00:06:53,510 --> 00:07:02,090
+تربيع ناقص X على هنا في X عامل مشترك وبظل عندي X
+
+60
+00:07:02,090 --> 00:07:09,000
+زائدY تعرفيها في اختصارات؟ لأ لأ يبقى اختصارات
+
+61
+00:07:09,000 --> 00:07:16,800
+ماعنديش اتنين ليست function في X تمام يبقى not
+
+62
+00:07:16,800 --> 00:07:22,420
+يبقى
+
+63
+00:07:22,420 --> 00:07:31,770
+ال not a function of X onlyيبقى مانفعش لا هادي ولا
+
+64
+00:07:31,770 --> 00:07:36,150
+هادي بتجيبلي integrative factors يبقى ماضلش قدام
+
+65
+00:07:36,150 --> 00:07:39,490
+التالت
+
+66
+00:07:39,490 --> 00:07:42,270
+يبقى بالداجة اقول suppose that
+
+67
+00:07:46,510 --> 00:07:53,830
+الميو of x و y يسوي x to the power m في y to the
+
+68
+00:07:53,830 --> 00:08:01,910
+power n suppose that هذا يسوي هذا is an
+
+69
+00:08:01,910 --> 00:08:13,810
+integrating factor for the differential
+
+70
+00:08:16,920 --> 00:08:25,080
+Equation star مدام هذا هو عامل تكمل إذا هضرب
+
+71
+00:08:25,080 --> 00:08:30,840
+الطرفين في X أس M في Y أس N
+
+72
+00:08:34,700 --> 00:08:40,280
+بدي أضربها كلها من أولها إلى آخرها في الـ X أُس M
+
+73
+00:08:40,280 --> 00:08:47,680
+Y أُس N شوف أيش اللي بدي يصير ها اتنين زي ما هي X
+
+74
+00:08:47,680 --> 00:08:56,540
+أُس M ماعنديش X أُس M عندك Y أُس N زائد تلاتة
+
+75
+00:08:56,540 --> 00:09:06,350
+انتهينا منهانقص هاي تلاتة اكس اس ام زائد واحد واي
+
+76
+00:09:06,350 --> 00:09:15,270
+اس ان زائد واحد ضربناهازائد هاي قصة وعندك هنا X
+
+77
+00:09:15,270 --> 00:09:26,130
+أُس M زائدي اتنين في ال Y أُس N زائد X أُس M زائد
+
+78
+00:09:26,130 --> 00:09:35,390
+واحد Y أُس N زائدي اتنين كل هذا في ال Y prime بده
+
+79
+00:09:35,390 --> 00:09:42,910
+سوى قداش0 هو هذي اللي هي الـ main double star مدام
+
+80
+00:09:42,910 --> 00:09:48,610
+فرضنا هذي integrative و هذي إيش بدتكون exact لإنه
+
+81
+00:09:48,610 --> 00:09:55,590
+جالها integrative vector يبقى هنا we get بنحصل على
+
+82
+00:09:55,590 --> 00:09:59,030
+من ال differential هذي is exact
+
+83
+00:10:01,250 --> 00:10:06,790
+ما دام exact يبقى بدي اخد تفاضل ال M by partial Y
+
+84
+00:10:06,790 --> 00:10:13,010
+و تفاضل N بالنسبة ل X وزي أساوي اتنين بعض يبقى بدي
+
+85
+00:10:13,010 --> 00:10:22,270
+اخد هنا تفاضل هذا كلهتفاضل ال M بالنسبة إلى Y
+
+86
+00:10:22,270 --> 00:10:25,490
+تفاضل
+
+87
+00:10:25,490 --> 00:10:31,230
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+88
+00:10:31,230 --> 00:10:36,610
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+89
+00:10:36,610 --> 00:10:38,710
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+90
+00:10:38,710 --> 00:10:40,710
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+91
+00:10:40,710 --> 00:10:41,590
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+92
+00:10:41,590 --> 00:10:42,050
+ال M بالنسبة إلى Y تفاضل ال M بالنسبة إلى Y تفاضل
+
+93
+00:10:42,050 --> 00:10:45,320
+ال M بالنسبة إلى Y تفاضل ال M بالنلأنه بيفضل ال Y
+
+94
+00:10:45,320 --> 00:10:52,360
+نيجي هذه بيدفضلها كمان يبقى ناقص تلاتة في M زائد
+
+95
+00:10:52,360 --> 00:11:03,990
+واحد في X أس M زائد واحد في ال Y أس N واضحة ظنطب
+
+96
+00:11:03,990 --> 00:11:08,370
+ايش رايك؟ و بده اخد منهم عامل مشترك يبقى لو جيت
+
+97
+00:11:08,370 --> 00:11:15,170
+اخدت ال X أُس M في ال Y أُس N عامل مشترك بظل عندنا
+
+98
+00:11:15,170 --> 00:11:22,830
+مين؟ اتنين N زائد ستة هذا مالوش دعوة هذه طارت بظل
+
+99
+00:11:22,830 --> 00:11:31,870
+Y تربيع شكل عندنا هذا اللي بعدناقص وهذه ثلاثة N
+
+100
+00:11:31,870 --> 00:11:39,450
+زائد ثلاثة وهنا X والـ X أُسم طلعت والـ Y أُسم N
+
+101
+00:11:39,450 --> 00:11:47,530
+طلعت مع السلامة طيب بدالي أخد تفاضل الـ N بالنسبة
+
+102
+00:11:47,530 --> 00:11:54,570
+إلى X يبقى بضروحة فاضل هذه بالنسبة إلى Xبصير M
+
+103
+00:11:54,570 --> 00:12:01,850
+زائدي اتنين X أُس M زائد واحد ال Y أُس N مقدار
+
+104
+00:12:01,850 --> 00:12:10,810
+ثابت مالوش دعوة اللي بعده زائد M زائد واحد في ال X
+
+105
+00:12:10,810 --> 00:12:19,330
+أُس M في ال Y أُس N زائدي اتنينخلّصنا منها يساوي
+
+106
+00:12:19,330 --> 00:12:27,020
+بدي أخد X أُس M في Y أُس N عامل مشتركيبقى بيظل هنا
+
+107
+00:12:27,020 --> 00:12:34,720
+مين؟ بيظل M زائد اتنين في ال X يبقى M زائد اتنين
+
+108
+00:12:34,720 --> 00:12:40,240
+كله في ال X و ال X و السم و ال Y و السن هيبرة ليه
+
+109
+00:12:40,240 --> 00:12:47,920
+جلال اللي بعده؟ زائد M زائد واحد ال X و السم يجه Y
+
+110
+00:12:47,920 --> 00:12:53,860
+تربيع الآن يا بنات احنا عندنا هذه exactما دام
+
+111
+00:12:53,860 --> 00:13:00,340
+exact هدول لازم يساويوا بعض مظبوط يبقى sense
+
+112
+00:13:00,340 --> 00:13:09,720
+equation double star is exact
+
+113
+00:13:13,220 --> 00:13:20,340
+ان تفاضل ال M بالنسبة الى Y بيساوي تفاضل ال N
+
+114
+00:13:20,340 --> 00:13:27,940
+بالنسبة الى X هذا معناه ان هذول بيساوي بعض اظن هذا
+
+115
+00:13:27,940 --> 00:13:32,360
+لو شطبتهم بيروح ماعناش مشكلة بيظل ال term هذا
+
+116
+00:13:32,360 --> 00:13:40,430
+بيساوي ال term هذا يبقى بصير عندنا2N زائد 6 في الـ
+
+117
+00:13:40,430 --> 00:13:51,630
+Y تربيع ناقص 3N زائد 3 في الـ X بده يساوي الـ M
+
+118
+00:13:51,630 --> 00:13:59,030
+زائد 2 كله في الـ X زائد الـ M زائد 1 في الـ Y
+
+119
+00:13:59,030 --> 00:14:04,000
+تربيعهذه بدي اكتبها هنا و اكتبها هنا بيكون جسمت
+
+120
+00:14:04,000 --> 00:14:10,460
+عليهم بيظلوا بيساووا بعض اذا يا بنات معامل Y تربيع
+
+121
+00:14:10,460 --> 00:14:16,180
+هنا هو معامل Y تربيع هنا و معامل X هنا هو معامل X
+
+122
+00:14:16,180 --> 00:14:20,970
+هنا تعالوا نسوي هذه المعاملات ببعضيبقى انا عندى
+
+123
+00:14:20,970 --> 00:14:30,690
+هنا M زائد 2 تبعت ال X بدى تساوي ناقص تلاتة N ناقص
+
+124
+00:14:30,690 --> 00:14:36,190
+تلاتة ناقص بتخش على الاتنين المعادلة التانية معامل
+
+125
+00:14:36,190 --> 00:14:46,550
+Y تربية يبقى M زائد 1 بدى يساوي اتنين N زائد ستة
+
+126
+00:14:47,100 --> 00:14:53,900
+معادلتين في مجهولين بقدر أحلهم مع بعض بدون مشاكل
+
+127
+00:14:53,900 --> 00:15:01,370
+تمام باجي بقول هذا بده يعطيناأظن هذه لو كانت M
+
+128
+00:15:01,370 --> 00:15:07,070
+زائد واحد كانت انتهت مشكلتنا يبقى خلّيني أطرح واحد
+
+129
+00:15:07,070 --> 00:15:12,810
+من الطرفين يبقى لو طرحنا واحد من الطرفين بصير M
+
+130
+00:15:12,810 --> 00:15:22,920
+زائد واحد تساوي ناقص ثلاثة N ناقص أربعةو هذي بده
+
+131
+00:15:22,920 --> 00:15:30,680
+يخلّيها زي ما هي M زائد واحد يساوي اتنين N زائد
+
+132
+00:15:30,680 --> 00:15:35,440
+ستة مش الطرف الشمال هو الطرف الشمال اذا الطرف
+
+133
+00:15:35,440 --> 00:15:40,820
+اليمين بده يساوي الطرف اليمين يبقى هذا معناه ان
+
+134
+00:15:40,820 --> 00:15:48,600
+اتنين N زائد ستة بده يساوي ناقص تلاتة N ناقص
+
+135
+00:15:48,600 --> 00:15:55,330
+الاربع هذا معناهبيدخل ال N في شجة و ال constant في
+
+136
+00:15:55,330 --> 00:16:03,050
+شجة تانية يبقى هذا بيصير خمسة N يساوي ناقص عشرة
+
+137
+00:16:03,050 --> 00:16:11,170
+إذا ال N بيبقى ناقص اتنينطيب بدي أشيل ال N و أحط
+
+138
+00:16:11,170 --> 00:16:17,150
+مكانها ناقص اتنين و أشوف قداش ال M يبقى هذه
+
+139
+00:16:17,150 --> 00:16:23,790
+المعلومة الأولى هذا بدي أعطيكي ان M زائد واحد
+
+140
+00:16:23,790 --> 00:16:28,490
+يساوي اي واحدة من التنتين سبيان يبقى هذه قداش
+
+141
+00:16:28,490 --> 00:16:36,850
+بناقص اتنين يبقى اتنين في ناقص اتنين زائد ستة يعني
+
+142
+00:16:36,850 --> 00:16:43,990
+Mزائد واحد بده يساوي كده يا بنات؟ يساوي اتنين لإنه
+
+143
+00:16:43,990 --> 00:16:50,010
+ناقص اربعة وزايد ستة بيظل اتنين هذا معناه إن ال M
+
+144
+00:16:50,010 --> 00:16:56,890
+يساوي كده؟ يساوي واحد إذا أصبح شكل ال integrating
+
+145
+00:16:56,890 --> 00:17:00,910
+factor على الشكل التالي
+
+146
+00:17:08,060 --> 00:17:13,960
+يبقى الان the integrating
+
+147
+00:17:13,960 --> 00:17:25,060
+factor is
+
+148
+00:17:26,210 --> 00:17:36,290
+الميو X Y يساوي X أُس M مابجداش واحد يبجى X فقط و
+
+149
+00:17:36,290 --> 00:17:43,550
+Y أُس N مابجداش ناقص اتنينهل حين بدى اشوف هذا
+
+150
+00:17:43,550 --> 00:17:49,850
+بيحولى ال equation ال star الى exact equation ولا
+
+151
+00:17:49,850 --> 00:17:55,150
+لأ يبقى بدى اروح اضرب المعادلة star في x y اصلا
+
+152
+00:17:55,150 --> 00:17:59,610
+قصة اتنين يبقى بدى امسك كده ال integrating factor
+
+153
+00:17:59,610 --> 00:18:04,450
+و اضربه في المعادلة هذه يبقى هذه بيصير اتنين يا
+
+154
+00:18:04,450 --> 00:18:12,540
+بنات و هنا x زي ما هي و هنا y فقط لا غيروهنا ناقص
+
+155
+00:18:12,540 --> 00:18:25,740
+تلاتة X تربيع Y ناقص واحد زائدهنا يصير x تكيب y اص
+
+156
+00:18:25,740 --> 00:18:33,680
+ناقص اتنين زائد x تربيع و ال y مع السلامة y prime
+
+157
+00:18:33,680 --> 00:18:40,540
+يساوي zero وهذه المعادلة هي double star لان بدى
+
+158
+00:18:40,540 --> 00:18:47,720
+اشوف double star exact ولا لايبقى هذه كلها أصبحت
+
+159
+00:18:47,720 --> 00:18:55,760
+بـ M وهذه كلها أصبحت بالـ N يبقى بدي أخد تفاضل M
+
+160
+00:18:55,760 --> 00:19:04,210
+بالنسبة إلى Yبقدرش يا بنات هنا اتنين X وهنا زائد
+
+161
+00:19:04,210 --> 00:19:12,490
+تلاتة X تربيع Y أثناء قصي اتنين بدي اخد تفاضل ال N
+
+162
+00:19:12,490 --> 00:19:20,610
+بالنسبة إلى X تمام؟ بالنسبة إلى X وY وساوي تلاتة
+
+163
+00:19:33,840 --> 00:19:41,320
+يبقى شغلنا الأولاني كله سليم 100%يبقى من هدول
+
+164
+00:19:41,320 --> 00:19:46,660
+اتنين مع بعض بس تنتج انه partial m by partial y
+
+165
+00:19:46,660 --> 00:19:53,240
+يسوى partial n by partial x يبقى هذا بيعطيني انه
+
+166
+00:19:53,240 --> 00:20:00,700
+the differential equation double star is exact
+
+167
+00:20:00,700 --> 00:20:09,770
+مدام exact يبقى there exists a functionفاي of x و
+
+168
+00:20:09,770 --> 00:20:20,170
+y يكون سنسيوان such that بحيث ان اظن الشغل هذا كله
+
+169
+00:20:20,170 --> 00:20:25,030
+مالوش لزومة الحين حد ضايق بده اي كلمة من العمود
+
+170
+00:20:25,030 --> 00:20:31,610
+اللي هناك نصفة ثانية من الصبورة لازم طيب خلاص نمسح
+
+171
+00:20:31,610 --> 00:20:34,830
+هذا عشان نكمل حل السؤال
+
+172
+00:20:41,210 --> 00:20:49,240
+بحيث انPartial FI by partial X يساوي الـ M هذه لـ
+
+173
+00:20:49,240 --> 00:20:58,280
+2XY ناقص 3X تربيع Y أساليب واحد وتفاضل الـ FI
+
+174
+00:20:58,280 --> 00:21:06,520
+بالنسبة إلى Y يساوي الـ M لـ X تكييب Y أساليب 2
+
+175
+00:21:06,520 --> 00:21:14,220
+زائد X تربيع بالشكل اللي عندنا هناالان بدي اكمل
+
+176
+00:21:14,220 --> 00:21:19,200
+هذه بالنسبة ل X سهلة و بدي اكمل هذه او هذه بالنسبة
+
+177
+00:21:19,200 --> 00:21:24,380
+ل Y على كل الأمرين التنتين سهلات ماعناش مشكلة يبقى
+
+178
+00:21:24,380 --> 00:21:29,480
+اتنين تنتين بنفس السهولة يبقى لو جيت قلت لك في of
+
+179
+00:21:29,480 --> 00:21:35,190
+XY يساويبدي أكمل بالنسبة لـ x يبقى دي x تربيع على
+
+180
+00:21:35,190 --> 00:21:42,450
+2 بصير x تربيع y و 2 مع 2 هذه الناقص x تكيب على 3
+
+181
+00:21:42,450 --> 00:21:50,590
+مع 3 وهذه y أسالب 1 كملة بالنسبة ل x يبقى زائد f
+
+182
+00:21:50,590 --> 00:21:59,050
+of yبدي أشتق هذه الدالة بالنسبة إلى Y يساوي هنا
+
+183
+00:21:59,050 --> 00:22:09,150
+عندك X تربيع وهنا ناقص يصير زائد X تكييب Y ناقص
+
+184
+00:22:09,150 --> 00:22:16,650
+اتنين زائد F prime of Yهذه اللي هي نفس المشتقة
+
+185
+00:22:16,650 --> 00:22:21,490
+أيضًا بدي أسوأ المقدارين اللي اتنين هدول ببعض يبقى
+
+186
+00:22:21,490 --> 00:22:28,810
+هذا بدي يعطيلك انه X تربيع زائد X تكييب Y أس ناقص
+
+187
+00:22:28,810 --> 00:22:35,730
+اتنين زائد F prime of Y يسوى X تكييب Y أس ناقص
+
+188
+00:22:35,730 --> 00:22:41,870
+اتنين زائد X تربيع أظن هذه هي هذه وهذه هي هذه
+
+189
+00:22:41,870 --> 00:22:48,600
+بالضبطيبقى بناء عليه ال f prime of y بده يسوي zero
+
+190
+00:22:48,600 --> 00:22:55,560
+يبقى ال f of y بده يسوي constant c2 يبقى حل
+
+191
+00:22:55,560 --> 00:23:01,960
+المعادلة الأصلية هو يبقى باجي بقوله the solution
+
+192
+00:23:01,960 --> 00:23:13,930
+of theDifferential equation star is phi of x,y
+
+193
+00:23:13,930 --> 00:23:14,710
+يساوي
+
+194
+00:23:29,670 --> 00:23:32,790
+أه هذا بياخد واجس مش زي اللي جابله اللي جابله
+
+195
+00:23:32,790 --> 00:23:36,870
+بسيطات لأن هذا عبارة عن حل مجموعة من الأسلة مش
+
+196
+00:23:36,870 --> 00:23:40,970
+عاجزة سؤال واحد طيب وصلنا
+
+197
+00:23:43,840 --> 00:23:50,920
+إلى نهاية هذا المثال لكن بإمكاني أن أحط هذا الحل
+
+198
+00:23:50,920 --> 00:23:57,620
+بصيغة أخرى غير هذه الصيغة يعني بقدر أجيب الحل مش
+
+199
+00:23:57,620 --> 00:24:02,060
+ضمني زي هيك بقدر أجيب الحل why as a function of g
+
+200
+00:24:02,060 --> 00:24:06,210
+انت هيك خلصتيلكن يمكن واحدة يطرح عبالة أوي تروح
+
+201
+00:24:06,210 --> 00:24:10,290
+يتفتح هي الكتاب هيك طبعا السؤال في الكتاب ماتلاقيش
+
+202
+00:24:10,290 --> 00:24:14,910
+هذا الجواب تقول هيك والله حالي غلط مظبوط لأ حالي
+
+203
+00:24:14,910 --> 00:24:18,630
+غلط لأ جد حال سليم مائة بالمائة طب إيش الجواب اللي
+
+204
+00:24:18,630 --> 00:24:20,870
+ممكن ألاقيه تعالى أوريكي إيش الجواب اللي ممكن
+
+205
+00:24:20,870 --> 00:24:27,560
+أتلاقيه الحين عندنا هذه هيك بده يساوي كونستانسيأنا
+
+206
+00:24:27,560 --> 00:24:32,480
+عندي Y بالموجب وهنا Y الأس تبعها السالد بقدر أخلي
+
+207
+00:24:32,480 --> 00:24:38,420
+الأس تبعي معله موجب شو أعمل؟ أضرب الطرفين في Y إذا
+
+208
+00:24:38,420 --> 00:24:43,180
+المعادلة هذه بقدر أكتبها على الشكل التالي X تربيع
+
+209
+00:24:43,180 --> 00:24:52,310
+Y تربيع ناقص X تكعيب يساوي C في Yضربت الطرفين في Y
+
+210
+00:24:52,310 --> 00:24:58,490
+فقط لا غير ممكن أعيد ترتيبها و أقول X تربيع Y
+
+211
+00:24:58,490 --> 00:25:08,210
+تربيع ناقص Cy ناقص X تكيب يساوي Zero إيش رأيك؟ هذه
+
+212
+00:25:08,210 --> 00:25:13,750
+معادلة من الدرجة الثانية في Y، مظبوط؟ إذا منحلك
+
+213
+00:25:14,980 --> 00:25:22,960
+بالقانون تمام يبقى بناء عليه y يسوى ناقص با يعني
+
+214
+00:25:22,960 --> 00:25:29,700
+ايش صارت ناقص ناقص بصير زائد c زائد او ناقص الجذري
+
+215
+00:25:29,700 --> 00:25:35,260
+التربية اللي هي c تربية ناقص أربعة الف اللي هي x
+
+216
+00:25:35,260 --> 00:25:42,940
+تربية جيم اللي هو ناقص x تكيبكله على اتنين الف
+
+217
+00:25:42,940 --> 00:25:50,860
+يبقى اتنين اكس تربيع او ان شئتولنا فقلنا هذه C
+
+218
+00:25:50,860 --> 00:25:59,780
+زائدة او ناقص الجذر التربيعي لمن؟ لـC تربيع زائد
+
+219
+00:25:59,780 --> 00:26:08,940
+اربعة اكس أس خمسة تمام؟ كل هذا الكلام على الاتنين
+
+220
+00:26:08,940 --> 00:26:16,530
+اكس تربيعطيب هذا الكلام بده يساوي يا بنات لو طلعت
+
+221
+00:26:16,530 --> 00:26:22,410
+فوق x وقلت أسالي باتنين بنفعلها بالفعلبظل في
+
+222
+00:26:22,410 --> 00:26:29,930
+المقام اتنين يعني C على اتنين زادة أو ناقص الجذري
+
+223
+00:26:29,930 --> 00:26:34,750
+التربيعي اتنين هذه لو دخلتها تحتها بتدخل بقداش
+
+224
+00:26:34,750 --> 00:26:41,370
+اربعة يعني كانها بصير C على اتنين لكل تربية يبقى
+
+225
+00:26:41,370 --> 00:26:48,170
+هذه C على اتنين لكل تربية زاد اربعة هتروح مع
+
+226
+00:26:48,170 --> 00:26:56,980
+الاربعة فح يبقى بظل جداشX أُس خمسة تمام يبقى C على
+
+227
+00:26:56,980 --> 00:27:01,380
+اتنين زائد او ناقص الجدران لـC على اتنين لكل تربية
+
+228
+00:27:01,380 --> 00:27:06,040
+زائد X أُس خمسة لو روحت في الكتاب بلاجيش هذا
+
+229
+00:27:06,040 --> 00:27:12,170
+الجواب كمان عايش بلاجي مش هذا مقدار ثابتوهذا مقدر
+
+230
+00:27:12,170 --> 00:27:18,750
+ابدأ اسميه ثابت جديد يبقى هذا بقدر اقول Y يسوى X
+
+231
+00:27:18,750 --> 00:27:26,210
+أسالي باتنين في C مثلا و الله سميه بدل الـ C سميه
+
+232
+00:27:26,210 --> 00:27:36,230
+A زائد أو ناقص الجدري التربيعي ل A تربيع زائد X أس
+
+233
+00:27:36,230 --> 00:27:41,080
+خمسةيبقى هذا الجواب اللي بتلاقيه في الكتاب بتلاقيه
+
+234
+00:27:41,080 --> 00:27:44,400
+بالشكل هذا طبعا ليس بالضرورة ايه يمكن تلاقيه P
+
+235
+00:27:44,400 --> 00:27:49,020
+يمكن تلاقيه C يمكن يمكن اخره بس انا مشان ماخليش ال
+
+236
+00:27:49,020 --> 00:27:52,440
+C واحد و ال C اتنين اللي فوق هما هما او اروح اجالك
+
+237
+00:27:52,440 --> 00:27:56,060
+عليك C تلاتة جولتك ايه و خلاصنا يبقى هتلاقي الحل
+
+238
+00:27:56,060 --> 00:27:59,220
+على الشكل اللي عندنا على اي حال لاجي T على الشكل
+
+239
+00:27:59,220 --> 00:28:04,190
+هذا و الله لاجي T على الشكل هذا اللي عندنالإتنين
+
+240
+00:28:04,190 --> 00:28:11,830
+أرضسين كله نفس الحل طيب وصلنا إلى نهاية هذا ال
+
+241
+00:28:11,830 --> 00:28:18,970
+section و بدنا نروح ناخد المسائل التالية يبقى
+
+242
+00:28:18,970 --> 00:28:25,470
+exercises واحد أربعة exercises واحد أربعة المسائل
+
+243
+00:28:25,470 --> 00:28:35,580
+التاليةواحد و تلاتة و خمسة و سبعة و عشرة و أحداشر
+
+244
+00:28:35,580 --> 00:28:44,060
+و ستاشر و سبعتاشر و تسعتاشر و عشرين و اتنين و
+
+245
+00:28:44,060 --> 00:28:51,450
+عشرين ايوة هذه الطريقة اني عجيب انتجريتياللي جبت
+
+246
+00:28:51,450 --> 00:28:54,930
+ايه؟ اخر واحدة التالتة فأستخدمها لو كانت من هنا
+
+247
+00:28:54,930 --> 00:28:58,610
+متحققين اللي بالاول و لا لازم يعني لازم يعني انت
+
+248
+00:28:58,610 --> 00:29:02,650
+حابة توجه ع دماغك اكتر من اللازم لأ جصدي ان مثلا
+
+249
+00:29:02,650 --> 00:29:07,150
+واحد فكرها ماتصبتش بالاول و كانت انها بتصبط و راح
+
+250
+00:29:07,150 --> 00:29:11,270
+انتجها للتالت طب انا بقدر اسألك بمجرد النظر بتنفع
+
+251
+00:29:11,270 --> 00:29:16,690
+ولا بتنفعش انا بقوله بتنفعشلأن هناك اكس بولينشي
+
+252
+00:29:16,690 --> 00:29:21,230
+فانكشن وهذه دالة X مرفوعة لأس في Y مرفوعة على أس
+
+253
+00:29:21,230 --> 00:29:27,680
+فكيف ينفع في الشركةمظبوط؟ يبقى لا يمكنها نفعة ده
+
+254
+00:29:27,680 --> 00:29:31,320
+يعني إذا نفعت إذا نفعت أنا بروح أدور في اللي بعدها
+
+255
+00:29:31,320 --> 00:29:35,120
+و أنا قاعد بشتغل نفعت بقول الحمد لله و بتريح لسه
+
+256
+00:29:35,120 --> 00:29:38,560
+في مشاكل في مسائل تانية بروح أحد السؤال تاني و
+
+257
+00:29:38,560 --> 00:29:41,960
+هكذا و لا بروح أعكس ليش هو بنفع ولا بنفعش لأ جد
+
+258
+00:29:41,960 --> 00:29:45,620
+أنا بس إنه لو واحد يعني الطالب من جرد مجلة جهة
+
+259
+00:29:45,620 --> 00:29:49,280
+بتنفس السعادة بقول الحمد لله خلاص هذا ايه ماروحش
+
+260
+00:29:49,280 --> 00:29:54,260
+يدور على اللي أصعب مظبوط؟ هي اللي بيحصلطيب لحد هنا
+
+261
+00:29:54,260 --> 00:29:58,100
+انتهى هذا ال section منتقل الان الى ال section
+
+262
+00:29:58,100 --> 00:30:04,220
+اللذي يليه وهو ال first order linear differential
+
+263
+00:30:04,220 --> 00:30:10,860
+equations يبقى بدنا نيجي ال section واحد خمسة
+
+264
+00:30:10,860 --> 00:30:21,900
+first order linear differential equations
+
+265
+00:30:22,600 --> 00:30:28,320
+يبقى المعادلة التفاضلية الخطية من الرتبة الأولى
+
+266
+00:30:28,320 --> 00:30:36,400
+نمسح هذا ولا لسه نعطي
+
+267
+00:30:36,400 --> 00:30:44,420
+تعريف وبعدين بنمسح ولا يمن يبقى هذا definition the
+
+268
+00:30:44,420 --> 00:30:45,780
+first order
+
+269
+00:30:51,340 --> 00:30:57,540
+first order linear differential
+
+270
+00:30:57,540 --> 00:31:13,600
+equation is an equation in the form الشكل التاليA0
+
+271
+00:31:13,600 --> 00:31:21,020
+as a function of X في الـ Y' A1 of X في الـ Y بده
+
+272
+00:31:21,020 --> 00:31:28,540
+يساوي ال F of X هذه ممكن أحطها على الشكل التالي Y'
+
+273
+00:31:29,340 --> 00:31:35,720
+زائد P of X في ال Y بده يساوي Q of X واسميها
+
+274
+00:31:35,720 --> 00:31:44,510
+المعادلة رقم واحد whereحيث ال P of X يسوى A1 of X
+
+275
+00:31:44,510 --> 00:31:54,090
+على A node of X and ال Q of X هي عبارة عن F of X
+
+276
+00:31:54,090 --> 00:32:07,520
+على A node of X and ال P of X andالـ q of x
+
+277
+00:32:07,520 --> 00:32:15,660
+دليليتين الأتنين هدول are continuous functions
+
+278
+00:32:15,660 --> 00:32:29,580
+دوال متصلة on an open interval ده
+
+279
+00:32:29,580 --> 00:32:30,020
+يا ريم
+
+280
+00:32:51,350 --> 00:33:03,290
+المعادلة الرقم واحد is given from the formula
+
+281
+00:33:07,860 --> 00:33:15,900
+هذه هي الفورملة لـ Mu of X في الـ Y as a function
+
+282
+00:33:15,900 --> 00:33:25,860
+of X يسوى تكامل لـ Mu of X في الـ Q of X في الـ DX
+
+283
+00:33:32,800 --> 00:33:43,160
+where الـ mu of x بده يساوي E أس تكامل ال P of x
+
+284
+00:33:43,160 --> 00:33:51,760
+dx note كملاحظة بسيطة we must sure that
+
+285
+00:34:02,460 --> 00:34:08,560
+و يجب أن نتأكد أن
+
+286
+00:34:08,560 --> 00:34:16,560
+الـ coefficient .. الـ
+
+287
+00:34:16,560 --> 00:34:28,260
+coefficient of Y' هو 1 في الـ equation 1
+
+288
+00:35:52,210 --> 00:35:56,910
+يجي الى سكتشن واحد خمسة اللى بتكلم عن ال first
+
+289
+00:35:56,910 --> 00:36:03,050
+order linear differential equation اللى
+
+290
+00:36:03,050 --> 00:36:05,570
+هو ال first order linear differential equation
+
+291
+00:36:05,570 --> 00:36:12,160
+معادلة التفاضلية الخطية من الرتبة الأولىالـ First
+
+292
+00:36:12,160 --> 00:36:17,580
+Order Differential Equation بقول عنها Linear إذا
+
+293
+00:36:17,580 --> 00:36:19,280
+كانت على الشكل التالي
+
+294
+00:36:27,690 --> 00:36:33,870
+هذه المعادلة يمكن إعادة صياغتها وكتابتها على الشكل
+
+295
+00:36:33,870 --> 00:36:39,730
+التالي لو روحنا جسمنا الطرفين على a node of x يبقى
+
+296
+00:36:39,730 --> 00:36:43,490
+المعامل هنا قداش بصير واحد صحيح في ال wire prime
+
+297
+00:36:43,490 --> 00:36:48,670
+هي ال wire primeA1 of X على A node of X بدي اسميها
+
+298
+00:36:48,670 --> 00:36:55,010
+P of X F of X على A node of X بدي اسميها Q of X
+
+299
+00:36:55,010 --> 00:36:58,790
+إذا المعادلة اللي فوق هذا كتبناها بالشكل الجديد
+
+300
+00:36:58,790 --> 00:37:04,250
+لهمين الشكل واحد إذا أصبح الشكل المتعرف عليه أو
+
+301
+00:37:04,250 --> 00:37:08,010
+الدارج عندنا لل first order linear differential
+
+302
+00:37:08,010 --> 00:37:12,160
+equationهو الـ y prime زاد p of x في الـ y بيبقى
+
+303
+00:37:12,160 --> 00:37:18,000
+ساوية مان ل q of x حيث هذي حصلنا عليها عن طريق ان
+
+304
+00:37:18,000 --> 00:37:22,680
+ال p of x صار a1 of x على a node و ال q of x هي f
+
+305
+00:37:22,680 --> 00:37:28,180
+of x على a node of x و ال p و ال q كانوا دوال
+
+306
+00:37:28,180 --> 00:37:35,440
+متصلة على فترة ماطيب يبقى الآن حتى الآن أنا بس
+
+307
+00:37:35,440 --> 00:37:39,000
+اتعرفت على شكل ال first order linear differential
+
+308
+00:37:39,000 --> 00:37:42,640
+equation احنا قبل هيك اعطيناكوا شكل ال linear
+
+309
+00:37:42,640 --> 00:37:46,800
+differential equation in the general form اذا
+
+310
+00:37:46,800 --> 00:37:49,900
+كنتوا بتذكروا سواء كان من الرتبة الأولى ولا
+
+311
+00:37:49,900 --> 00:37:53,130
+التانية ولا التالتة ولا الرابعة ولا النونيةوكنا
+
+312
+00:37:53,130 --> 00:37:57,990
+بنقول لك a node of x y to the derivative n زائد a
+
+313
+00:37:57,990 --> 00:38:02,410
+one of x y to the derivative n minus one زائد زائد
+
+314
+00:38:02,410 --> 00:38:09,610
+a n minus one of x في ال y prime زائد a n of x في
+
+315
+00:38:09,610 --> 00:38:14,110
+ال y بده يساوي f of x هذا ال general form إذا لو
+
+316
+00:38:14,110 --> 00:38:17,330
+أنا أخدت ال first order كل اللي جابله هذا بالغيوب
+
+317
+00:38:17,330 --> 00:38:20,550
+تصبح المعادل عالمينعلى الشكل اللي عندنا هذا اللي
+
+318
+00:38:20,550 --> 00:38:25,470
+روحت حطيتها في الشكل اللي عندنا هذا الان بدنا نبحث
+
+319
+00:38:25,470 --> 00:38:29,350
+عن الحل طبعا الكتب اللي ان الطلاب اللي بدرسوا
+
+320
+00:38:29,350 --> 00:38:34,310
+differential equation فقط بروح نثبت لهم كيف يكون
+
+321
+00:38:34,310 --> 00:38:38,320
+شكل الحل اللي احنا بنتكلم عليه هناإنتوا هندسة بني
+
+322
+00:38:38,320 --> 00:38:41,660
+أعطيكوا الحل على طول القرن يبقى النظرية بيقول ال
+
+323
+00:38:41,660 --> 00:38:45,360
+solution تبع ال differential equation هذي هو ال mu
+
+324
+00:38:45,360 --> 00:38:50,800
+of x في ال y اللي هي الحل بدو يساوي تكمن ال mu of
+
+325
+00:38:50,800 --> 00:38:57,920
+x في ال q of x اللي عندنا هذا dx طب مين هي ال mu؟
+
+326
+00:38:58,050 --> 00:39:05,230
+ميو اف اكس يا ايه استكامل P of X DX اذا الميو
+
+327
+00:39:05,230 --> 00:39:11,570
+كأنها عامل التكامل جبتها من وين؟ من تكامل المعامل
+
+328
+00:39:11,570 --> 00:39:17,670
+تبع ال Y والطرف اليمين حاصل ضرب الميو اللي طلعت
+
+329
+00:39:17,670 --> 00:39:22,470
+عندي في ال Q بكمل اتنين مبعض وبالتالي بجيب شكل
+
+330
+00:39:22,470 --> 00:39:28,630
+الحل تبع هذه المعادلة التفاضليةإذا لما بدي أجيب
+
+331
+00:39:28,630 --> 00:39:33,550
+هذا الحل اللي عندى مشان يجيب كلامي الصحيح لازم
+
+332
+00:39:33,550 --> 00:39:40,750
+أخلي المعامل تبع y' هو واحد صحيح ديري بالك كتبتلك
+
+333
+00:39:40,750 --> 00:39:45,490
+ملاحظة مشان ماتنسهاش we must sure that لازم أتأكد
+
+334
+00:39:45,490 --> 00:39:51,190
+أنه المعامل تبع y' هو واحد صحيح في ال equation one
+
+335
+00:39:51,190 --> 00:39:56,240
+حد فيكم بتحب تسأل أي سؤال هناخلصنا النظرية بدنا
+
+336
+00:39:56,240 --> 00:40:00,240
+ندخل في الأعمل يعني ندخل أمثلة على ال first order
+
+337
+00:40:00,240 --> 00:40:03,980
+linear differential equation حد بتحب تسأل أي سؤال
+
+338
+00:40:03,980 --> 00:40:10,120
+طيب نبدأ في الأمثلة بنأخد أول مثال يبقى example
+
+339
+00:40:10,120 --> 00:40:18,240
+one بيقول
+
+340
+00:40:18,240 --> 00:40:23,780
+solve the initial value problem solve the initial
+
+341
+00:40:24,310 --> 00:40:29,310
+Value Problem XY'
+
+342
+00:40:31,970 --> 00:40:35,270
+-3Y
+
+343
+00:40:35,270 --> 00:40:38,550
+X تكيب
+
+344
+00:40:51,130 --> 00:40:56,310
+هذه المثلة محفوظة على الشكل الأصلي لإنها تمام لكن
+
+345
+00:40:56,310 --> 00:41:00,390
+إحنا لإيش تفرضه ده بدنا نخلي المعامل تبع واي فاي
+
+346
+00:41:00,390 --> 00:41:06,470
+هو جدرس وإلا بدنا نضطر X في الطرفين على الـP على X
+
+347
+00:41:06,470 --> 00:41:12,390
+للجابان يبقى جمال أصلاً للإنسانالمعادلة هذي بحطها
+
+348
+00:41:12,390 --> 00:41:18,770
+بالشكل التام و أي prime نقص ثلاثة على XP1 يساوي
+
+349
+00:41:18,770 --> 00:41:24,630
+كده؟ يساوي X ترمية يساوية على X الاشياء ال
+
+350
+00:41:24,630 --> 00:41:29,490
+condition بيظل زي ما يساوي Zero وهذه المعادلة
+
+351
+00:41:29,490 --> 00:41:34,770
+بتسميها Minimum معادلة واحدة زي ما انت شايف هذه
+
+352
+00:41:34,770 --> 00:41:40,150
+First Father Minimum
+
+353
+00:41:47,490 --> 00:41:52,210
+ماذا بصراحة كده بتروح أدور على ال integrating
+
+354
+00:41:52,210 --> 00:42:02,050
+factor يبدأ ال U of X هو E of Z تكامل، تكامل مين؟
+
+355
+00:42:02,050 --> 00:42:07,250
+بأخدها بإشارة، مش هتروح أصيب الإشارة إلى موجة بقى،
+
+356
+00:42:07,250 --> 00:42:11,810
+مش هتروح تقرأ ال E ده السنة، بأخدها بإشارتهايبقى
+
+357
+00:42:11,810 --> 00:42:19,230
+اناقس ثلاثة على X بالديكس يبقى E أس ناقس ثلاثة من
+
+358
+00:42:19,230 --> 00:42:28,070
+X يبقى E من X أس ناقس ثلاثة يبقى X أس ناقس ثلاثة
+
+359
+00:42:28,070 --> 00:42:33,170
+يبقى هذا ال integrating factor يبقى بعدين بقوله ذا
+
+360
+00:42:33,170 --> 00:42:46,360
+solution of equation one isGiven from الميو
+
+361
+00:42:46,360 --> 00:42:55,300
+of X في ال Y as a function of X تكمن الميو of X في
+
+362
+00:42:55,300 --> 00:43:03,080
+ال Q of X من DX الميو of X هي X والثالث ثلاثة وهذا
+
+363
+00:43:03,080 --> 00:43:09,720
+ال Y يساوي وهي تكمن الميو X والثالث ثلاثة ال Q هذا
+
+364
+00:43:09,720 --> 00:43:18,120
+جمعناهايبقى x تربيع يبقى x تربيع وهذا مين يكون dx
+
+365
+00:43:18,120 --> 00:43:26,620
+يبقى صارع بx أساليب تلاتة يسمي تكامل x أساليب واحد
+
+366
+00:43:26,620 --> 00:43:38,200
+dx يعني مين يعني تكامل واحد على x dxشكل انا تمام؟
+
+367
+00:43:38,200 --> 00:43:47,820
+طيب هذا ما هو عبارة عن ان ال X ذات المنصة C طب ليش
+
+368
+00:43:47,820 --> 00:43:51,900
+انا ماكنتش اشتغل أبسل و زجل X؟
+
+369
+00:44:07,160 --> 00:44:15,120
+بعد ان اقول Y يستخدم اكس تكعيد
+
+370
+00:44:20,070 --> 00:44:24,850
+زا قد سي X تقريبا الان انا بروح لل condition
+
+371
+00:44:24,850 --> 00:44:32,690
+conditions but ولكن عندك ال Y عند ال واحد يسوي
+
+372
+00:44:32,690 --> 00:44:43,670
+زيرو it implies Y بالزيرو ولن الواحد جدرس زيرو زا
+
+373
+00:44:43,670 --> 00:44:51,250
+قد سي في الواحد تقريبا يبقى سي جدرس تشغلان0 يبقى
+
+374
+00:44:51,250 --> 00:44:59,010
+بالإنها ليه أصبح الحل هو Y يسوى X تقريب من X فقط
+
+375
+00:44:59,010 --> 00:45:14,470
+هذا is the solution of the initial value of Y أخد
+
+376
+00:45:14,470 --> 00:45:16,330
+كمان مثلها بسيطة زي ذلك
+
+377
+00:45:28,690 --> 00:45:38,170
+يبقى example two provenance
+
+378
+00:45:38,170 --> 00:45:47,470
+of the differential equation المعادلة التفاغرية
+
+379
+00:45:47,470 --> 00:45:59,330
+الـ y' سنة و ثانية x في الواقع جسم تلاتةصين ال X
+
+380
+00:45:59,330 --> 00:46:07,470
+فيكو صين ال X وال X هذه موجودة في الفقرة المفتوحة
+
+381
+00:46:07,470 --> 00:46:20,810
+من Zero لوا يطول فطول
+
+382
+00:46:20,810 --> 00:46:26,090
+ال question انا منك اظن المعادلة جاهزة؟لا بدأ أقسم
+
+383
+00:46:26,090 --> 00:46:30,130
+ولا أقرأ، المعاملة تبع واي القرآن هي واحد صحيح،
+
+384
+00:46:30,130 --> 00:46:36,430
+كذا بدأ أروح أجيب له الـ Mu of X مباشرة، يبقى E
+
+385
+00:46:36,430 --> 00:46:42,970
+أُس تكامل الـP of X DX يبقى E أُس تكامل P of X
+
+386
+00:46:42,970 --> 00:46:50,290
+اللي هو كتان الـX بالنسبة إلى DX، يبقى E أس، كدهش
+
+387
+00:46:50,290 --> 00:46:58,760
+الكتانتكمل .. لن لل sign .. لن لل sign مظبوط يعني
+
+388
+00:46:58,760 --> 00:47:03,360
+ال cosine على ال science على البسطى فاض مقام يبقى
+
+389
+00:47:03,360 --> 00:47:11,840
+لن للمقام يبقى لن لصين ال X ولا داعي نفسي نفرق من
+
+390
+00:47:11,840 --> 00:47:16,360
+الصين خلال الفترة هذه دايما أو أبدا و جمال من صفر
+
+391
+00:47:16,360 --> 00:47:23,260
+لغاية 180 يمكن أن تجمع مدار صين ال Xيبقى هذه
+
+392
+00:47:23,260 --> 00:47:28,020
+المعالجة لو راح تسميتها معالجة رقم واحد فأنا راح
+
+393
+00:47:28,020 --> 00:47:37,120
+بقول لها solution of the differential equation
+
+394
+00:47:37,120 --> 00:47:45,600
+when this الـ mu of x هو sin of x dy يسوى تكامل
+
+395
+00:47:45,600 --> 00:47:50,720
+الـ mu of x هو sin of x في الـ q of x اللي هي
+
+396
+00:47:50,720 --> 00:47:51,800
+تلاتة
+
+397
+00:48:08,450 --> 00:48:18,170
+مش تقت ال sign ولا لا صح يبقى بقدر اقول دي لصين ال
+
+398
+00:48:18,170 --> 00:48:26,310
+Xيبقى هذه التلاتة اللي برا وهذه تكاملها بالـSin
+
+399
+00:48:26,310 --> 00:48:33,490
+تكييب X على ثلاثة زائد كنصان لأن هذه كانت تكامل
+
+400
+00:48:33,490 --> 00:48:37,290
+اللي همين زي التربية دي زي دي وزي التكييب على
+
+401
+00:48:37,290 --> 00:48:45,980
+تلاتة يبقى صارت Sin تكييب Xزائد constant c لو
+
+402
+00:48:45,980 --> 00:48:53,140
+جسمنا كله على sign بصير الحل يساوي sign تربيع ال x
+
+403
+00:48:53,140 --> 00:49:01,680
+زائد c على sign ال x او الحل بديش اخلي فيه كسور
+
+404
+00:49:01,680 --> 00:49:09,160
+ماعناش مشكلة يبقى y تساوي sign تربيع ال x زائد c
+
+405
+00:49:09,160 --> 00:49:17,890
+واحد على sign المقلوب منمقلب الصين مين؟ ال
+
+406
+00:49:17,890 --> 00:49:24,990
+cosecant x يبقى ال C في cosecant X يبقى هذا حل
+
+407
+00:49:24,990 --> 00:49:31,070
+المعادلة التفاضلية لا يزال عندنا المزيد من الأمثلة
+
+408
+00:49:31,070 --> 00:49:36,850
+للمحاضرة القادمة ان شاء الله تبارك وتعالى يعطيكم
+
+409
+00:49:36,850 --> 00:49:37,510
+العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..bc3c8baa0958b7140cc2b1214c8520c1cfba5395
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/dXKI0vChjEQ_raw.json
@@ -0,0 +1 @@
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8032, 995, 16254, 39894, 7435, 1829, 3555, 20292, 3572, 1166, 6771, 7251, 3555, 4587, 7578, 3714, 46958, 1211, 8592, 12174, 3215, 10943, 16712, 6027, 2655, 7251, 3555, 4587, 7578, 20666, 3215, 26108, 3660, 1975, 39648, 7297, 300], "avg_logprob": -0.2471454321191861, "compression_ratio": 1.3700787401574803, "no_speech_prob": 0.0, "words": [{"start": 449.09, "end": 449.95, "word": "يبقى", "probability": 0.8206787109375}, {"start": 449.95, "end": 450.87, "word": " مانفعش", "probability": 0.710986328125}, {"start": 450.87, "end": 451.09, "word": " لا", "probability": 0.51953125}, {"start": 451.09, "end": 451.53, "word": " هادي", "probability": 0.6937662760416666}, {"start": 451.53, "end": 451.77, "word": " ولا", "probability": 0.87646484375}, {"start": 451.77, "end": 452.25, "word": " هادي", "probability": 0.9098307291666666}, {"start": 452.25, "end": 452.85, "word": " بتجيبلي", "probability": 0.91689453125}, {"start": 452.85, "end": 453.87, "word": " integrative", "probability": 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that هذا يسوي هذا is an integrating factor for the differential", "tokens": [45340, 1829, 2407, 295, 2031, 4032, 288, 7251, 3794, 45865, 2031, 281, 264, 1347, 275, 8978, 288, 281, 264, 1347, 297, 7297, 300, 23758, 7251, 3794, 45865, 23758, 307, 364, 26889, 5952, 337, 264, 15756], "avg_logprob": -0.3294270899560716, "compression_ratio": 1.2820512820512822, "no_speech_prob": 0.0, "words": [{"start": 466.51, "end": 467.55, "word": "الميو", "probability": 0.6297200520833334}, {"start": 467.55, "end": 468.19, "word": " of", "probability": 0.128173828125}, {"start": 468.19, "end": 468.65, "word": " x", "probability": 0.52734375}, {"start": 468.65, "end": 468.91, "word": " و", "probability": 0.744140625}, {"start": 468.91, "end": 469.25, "word": " y", "probability": 0.69970703125}, {"start": 469.25, "end": 470.35, "word": " يسوي", "probability": 0.6507975260416666}, {"start": 470.35, "end": 470.87, "word": " x", "probability": 0.89794921875}, {"start": 470.87, "end": 471.13, "word": " to", 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الأولى نمسح هذا ولا لسه نعطي تعريف وبعدين بنمسح ولا يمن يبقى هذا definition the first order", "tokens": [1829, 3555, 4587, 7578, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 33962, 9566, 10632, 9154, 34892, 2655, 49401, 16247, 12610, 7578, 8717, 2304, 3794, 5016, 23758, 49429, 5296, 3794, 3224, 8717, 3615, 9566, 1829, 37279, 16572, 5172, 46599, 22488, 9957, 44945, 2304, 3794, 5016, 49429, 7251, 27842, 7251, 3555, 4587, 7578, 23758, 7123, 264, 700, 1668], "avg_logprob": -0.18829448495881032, "compression_ratio": 1.4697986577181208, "no_speech_prob": 0.0, "words": [{"start": 1822.6, "end": 1823.12, "word": "يبقى", "probability": 0.8812255859375}, {"start": 1823.12, "end": 1823.86, "word": " المعادلة", "probability": 0.96044921875}, {"start": 1823.86, "end": 1824.96, "word": " التفاضلية", "probability": 0.86708984375}, {"start": 1824.96, "end": 1825.76, "word": " الخطية", "probability": 0.8982747395833334}, {"start": 1825.76, "end": 1826.04, "word": " من", "probability": 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"probability": 0.719482421875}, {"start": 2904.49, "end": 2905.49, "word": " تكاملها", "probability": 0.95263671875}, {"start": 2905.49, "end": 2906.31, "word": " بالـSin", "probability": 0.521026611328125}, {"start": 2906.31, "end": 2907.35, "word": " تكييب", "probability": 0.84833984375}, {"start": 2907.35, "end": 2908.45, "word": " X", "probability": 0.466796875}, {"start": 2908.45, "end": 2909.25, "word": " على", "probability": 0.6357421875}, {"start": 2909.25, "end": 2910.49, "word": " ثلاثة", "probability": 0.832958984375}, {"start": 2910.49, "end": 2911.21, "word": " زائد", "probability": 0.8087565104166666}, {"start": 2911.21, "end": 2911.73, "word": " كنصان", "probability": 0.6632080078125}, {"start": 2911.73, "end": 2911.97, "word": " لأن", "probability": 0.593017578125}, {"start": 2911.97, "end": 2912.21, "word": " هذه", "probability": 0.382080078125}, {"start": 2912.21, "end": 2912.67, "word": " كانت", "probability": 0.890869140625}, {"start": 2912.67, "end": 2913.49, "word": " تكامل", "probability": 0.9862060546875}, {"start": 2913.49, "end": 2914.09, "word": " اللي", "probability": 0.586669921875}, {"start": 2914.09, "end": 2914.49, "word": " همين", "probability": 0.7646484375}, {"start": 2914.49, "end": 2914.99, "word": " زي", "probability": 0.4013671875}, {"start": 2914.99, "end": 2915.73, "word": " التربية", "probability": 0.7528483072916666}, {"start": 2915.73, "end": 2916.01, "word": " دي", "probability": 0.77978515625}, {"start": 2916.01, "end": 2916.23, "word": " زي", "probability": 0.64208984375}, {"start": 2916.23, "end": 2916.35, "word": " دي", "probability": 0.86328125}, {"start": 2916.35, "end": 2916.59, "word": " وزي", "probability": 0.7007649739583334}, {"start": 2916.59, "end": 2917.13, "word": " التكييب", "probability": 0.96015625}, {"start": 2917.13, "end": 2917.29, "word": " على", "probability": 0.84912109375}, {"start": 2917.29, "end": 2917.91, "word": " تلاتة", "probability": 0.909423828125}, {"start": 2917.91, "end": 2919.67, "word": " يبقى", "probability": 0.84588623046875}, {"start": 2919.67, "end": 2920.35, "word": " صارت", "probability": 0.8548177083333334}, {"start": 2920.35, "end": 2921.05, "word": " Sin", "probability": 0.32763671875}, {"start": 2921.05, "end": 2922.43, "word": " تكييب", "probability": 0.98525390625}, {"start": 2922.43, "end": 2923.03, "word": " X", "probability": 0.98974609375}], "temperature": 1.0}, {"id": 119, "seek": 295246, "start": 2923.44, "end": 2952.46, "text": "زائد constant c لو جسمنا كله على sign بصير الحل يساوي sign تربيع ال x زائد c على sign ال x او الحل بديش اخلي فيه كسور ماعناش مشكلة يبقى y تساوي sign تربيع ال x زائد c واحد على sign المقلوب من", "tokens": [11622, 16373, 3215, 416, 372, 394, 269, 45164, 10874, 38251, 8315, 28242, 3224, 15844, 1465, 4724, 9381, 13546, 21542, 1211, 7251, 3794, 995, 45865, 1465, 6055, 2288, 21292, 3615, 2423, 2031, 30767, 16373, 3215, 269, 15844, 1465, 2423, 2031, 1975, 2407, 21542, 1211, 4724, 16254, 8592, 1975, 9778, 20292, 8978, 3224, 9122, 3794, 13063, 19446, 3615, 1863, 33599, 37893, 28820, 3660, 7251, 3555, 4587, 7578, 288, 6055, 3794, 995, 45865, 1465, 6055, 2288, 21292, 3615, 2423, 2031, 30767, 16373, 3215, 269, 36764, 24401, 15844, 1465, 9673, 4587, 1211, 37746, 9154], "avg_logprob": -0.2860576798627665, "compression_ratio": 1.7836257309941521, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 2923.44, "end": 2924.16, "word": "زائد", "probability": 0.640869140625}, {"start": 2924.16, "end": 2925.04, "word": " constant", "probability": 0.545684814453125}, {"start": 2925.04, "end": 2925.36, "word": " c", "probability": 0.429931640625}, {"start": 2925.36, "end": 2925.98, "word": " لو", "probability": 0.7080078125}, {"start": 2925.98, "end": 2926.72, "word": " جسمنا", "probability": 0.9049479166666666}, {"start": 2926.72, "end": 2927.4, "word": " كله", "probability": 0.921142578125}, {"start": 2927.4, "end": 2927.78, "word": " على", "probability": 0.90576171875}, {"start": 2927.78, "end": 2928.5, "word": " sign", "probability": 0.66259765625}, {"start": 2928.5, "end": 2929.52, "word": " بصير", "probability": 0.69140625}, {"start": 2929.52, "end": 2930.3, "word": " الحل", "probability": 0.980712890625}, {"start": 2930.3, "end": 2931.38, "word": " يساوي", "probability": 0.7960205078125}, {"start": 2931.38, "end": 2931.96, "word": " sign", "probability": 0.4697265625}, {"start": 2931.96, "end": 2932.68, "word": " تربيع", "probability": 0.8310546875}, {"start": 2932.68, "end": 2932.84, "word": " ال", "probability": 0.787109375}, {"start": 2932.84, "end": 2933.14, "word": " x", "probability": 0.277587890625}, {"start": 2933.14, "end": 2934.68, "word": " زائد", "probability": 0.9532877604166666}, {"start": 2934.68, "end": 2935.74, "word": " c", "probability": 0.88623046875}, {"start": 2935.74, "end": 2936.76, "word": " على", "probability": 0.81591796875}, {"start": 2936.76, "end": 2937.84, "word": " sign", "probability": 0.89404296875}, {"start": 2937.84, "end": 2938.08, "word": " ال", "probability": 0.79345703125}, {"start": 2938.08, "end": 2938.48, "word": " x", "probability": 0.91943359375}, {"start": 2938.48, "end": 2939.18, "word": " او", "probability": 0.69189453125}, {"start": 2939.18, "end": 2939.84, "word": " الحل", "probability": 0.962646484375}, {"start": 2939.84, "end": 2940.58, "word": " بديش", "probability": 0.5768636067708334}, {"start": 2940.58, "end": 2940.98, "word": " اخلي", "probability": 0.7420247395833334}, {"start": 2940.98, "end": 2941.28, "word": " فيه", "probability": 0.86962890625}, {"start": 2941.28, "end": 2941.68, "word": " كسور", "probability": 0.7027994791666666}, {"start": 2941.68, "end": 2942.18, "word": " ماعناش", "probability": 0.757568359375}, {"start": 2942.18, "end": 2942.84, "word": " مشكلة", "probability": 0.9788411458333334}, {"start": 2942.84, "end": 2943.8, "word": " يبقى", "probability": 0.9688720703125}, {"start": 2943.8, "end": 2944.22, "word": " y", "probability": 0.83935546875}, {"start": 2944.22, "end": 2945.16, "word": " تساوي", "probability": 0.9329833984375}, {"start": 2945.16, "end": 2946.08, "word": " sign", "probability": 0.87744140625}, {"start": 2946.08, "end": 2946.98, "word": " تربيع", "probability": 0.9683837890625}, {"start": 2946.98, "end": 2947.14, "word": " ال", "probability": 0.96240234375}, {"start": 2947.14, "end": 2947.52, "word": " x", "probability": 0.94384765625}, {"start": 2947.52, "end": 2948.8, "word": " زائد", "probability": 0.97314453125}, {"start": 2948.8, "end": 2949.16, "word": " c", "probability": 0.9609375}, {"start": 2949.16, "end": 2949.66, "word": " واحد", "probability": 0.7548828125}, {"start": 2949.66, "end": 2949.96, "word": " على", "probability": 0.884765625}, {"start": 2949.96, "end": 2950.96, "word": " sign", "probability": 0.83837890625}, {"start": 2950.96, "end": 2952.24, "word": " المقلوب", "probability": 0.688507080078125}, {"start": 2952.24, "end": 2952.46, "word": " من", "probability": 0.5673828125}], "temperature": 1.0}, {"id": 120, "seek": 297751, "start": 2953.85, "end": 2977.51, "text": "مقلب الصين مين؟ ال cosecant x يبقى ال C في cosecant X يبقى هذا حل المعادلة التفاضلية لا يزال عندنا المزيد من الأمثلة للمحاضرة القادمة ان شاء الله تبارك وتعالى يعطيكم العافية", "tokens": [2304, 4587, 46152, 31767, 9957, 3714, 9957, 22807, 2423, 30261, 66, 394, 2031, 7251, 3555, 4587, 7578, 2423, 383, 8978, 30261, 66, 394, 1783, 7251, 3555, 4587, 7578, 23758, 11331, 1211, 9673, 3615, 18513, 37977, 16712, 5172, 46958, 1211, 10632, 20193, 7251, 11622, 6027, 43242, 8315, 9673, 11622, 25708, 9154, 16247, 2304, 12984, 37977, 5296, 19528, 5016, 46958, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 6055, 3555, 9640, 4117, 34683, 3615, 6027, 7578, 37495, 9566, 1829, 24793, 18863, 31845, 10632], "avg_logprob": -0.18578505879495202, "compression_ratio": 1.6174863387978142, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 2953.85, "end": 2954.27, "word": "مقلب", "probability": 0.6014811197916666}, {"start": 2954.27, "end": 2955.05, "word": " الصين", "probability": 0.5670166015625}, {"start": 2955.05, "end": 2957.21, "word": " مين؟", "probability": 0.5090738932291666}, {"start": 2957.21, "end": 2957.89, "word": " ال", "probability": 0.67919921875}, {"start": 2957.89, "end": 2958.67, "word": " cosecant", "probability": 0.6091715494791666}, {"start": 2958.67, "end": 2959.17, "word": " x", "probability": 0.474365234375}, {"start": 2959.17, "end": 2960.13, "word": " يبقى", "probability": 0.936279296875}, {"start": 2960.13, "end": 2960.35, "word": " ال", "probability": 0.473388671875}, {"start": 2960.35, "end": 2960.75, "word": " C", "probability": 0.45263671875}, {"start": 2960.75, "end": 2961.19, "word": " في", "probability": 0.9248046875}, {"start": 2961.19, "end": 2962.53, "word": " cosecant", "probability": 0.9646809895833334}, {"start": 2962.53, "end": 2963.27, "word": " X", "probability": 0.484375}, {"start": 2963.27, "end": 2964.11, "word": " يبقى", "probability": 0.9534912109375}, {"start": 2964.11, "end": 2964.47, "word": " هذا", "probability": 0.91845703125}, {"start": 2964.47, "end": 2964.99, "word": " حل", "probability": 0.97607421875}, {"start": 2964.99, "end": 2965.91, "word": " المعادلة", "probability": 0.9918212890625}, {"start": 2965.91, "end": 2967.59, "word": " التفاضلية", "probability": 0.92861328125}, {"start": 2967.59, "end": 2968.15, "word": " لا", "probability": 0.51708984375}, {"start": 2968.15, "end": 2968.73, "word": " يزال", "probability": 0.9806315104166666}, {"start": 2968.73, "end": 2969.15, "word": " عندنا", "probability": 0.98583984375}, {"start": 2969.15, "end": 2969.85, "word": " المزيد", "probability": 0.9698893229166666}, {"start": 2969.85, "end": 2970.17, "word": " من", "probability": 0.98876953125}, {"start": 2970.17, "end": 2971.07, "word": " الأمثلة", "probability": 0.9732666015625}, {"start": 2971.07, "end": 2972.45, "word": " للمحاضرة", "probability": 0.921875}, {"start": 2972.45, "end": 2973.21, "word": " القادمة", "probability": 0.99365234375}, {"start": 2973.21, "end": 2973.53, "word": " ان", "probability": 0.7216796875}, {"start": 2973.53, "end": 2973.89, "word": " شاء", "probability": 0.978271484375}, {"start": 2973.89, "end": 2974.19, "word": " الله", "probability": 0.94482421875}, {"start": 2974.19, "end": 2974.85, "word": " تبارك", "probability": 0.891357421875}, {"start": 2974.85, "end": 2975.77, "word": " وتعالى", "probability": 0.9652099609375}, {"start": 2975.77, "end": 2976.85, "word": " يعطيكم", "probability": 0.9290771484375}, {"start": 2976.85, "end": 2977.51, "word": " العافية", "probability": 0.97412109375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2978.28425, "duration_after_vad": 2790.782499999993}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/eSiXtXR8S5g.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/eSiXtXR8S5g.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8d4faef635f25f9ee2a84ea2710effa0fc0cfa58
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/eSiXtXR8S5g.srt
@@ -0,0 +1,1042 @@
+1
+00:00:21,010 --> 00:00:25,750
+بسم الله الرحمن الرحيم انتهينا في المرة الماضية من
+
+2
+00:00:25,750 --> 00:00:31,490
+chapter 4 الذي كان يتحدث عن diagonalization والآن
+
+3
+00:00:31,490 --> 00:00:35,870
+ننتقل من موضوع الجبر الخطي لموضوع المعادلات
+
+4
+00:00:35,870 --> 00:00:40,250
+التفاضلية وهو أول chapter ابتدأنا به هذا المقرر 
+
+5
+00:00:40,250 --> 00:00:43,750
+أخذنا أول chapter في المعادلة التفاضلية وبعدين
+
+6
+00:00:43,750 --> 00:00:48,480
+three chapters كلها كان في الجبر الخطي الآن نعود
+
+7
+00:00:48,480 --> 00:00:52,740
+للمعادلات التفاضلية لكن سنربطها زي ما أنتم شايفين
+
+8
+00:00:52,740 --> 00:00:57,600
+من خلال ما هو أمامنا بموضوع الجبر الخطي إلى حد ما
+
+9
+00:00:57,600 --> 00:01:02,200
+الـ section الذي بين أيدينا يقول linear
+
+10
+00:01:02,200 --> 00:01:06,800
+differential equations يبقى المعادلات التفاضلية
+
+11
+00:01:06,800 --> 00:01:11,160
+الخطية طبعاً  أشرنا قبل ذلك لمعادلة تفاضلية 
+
+12
+00:01:11,160 --> 00:01:16,340
+الخطية لكن كانت من الرتبة الأولى فقط الآن ننتقل من 
+
+13
+00:01:16,340 --> 00:01:22,520
+الرتبة الأولى إلى الرتبة النونية فبقول a linear
+
+14
+00:01:22,520 --> 00:01:26,020
+differential equation of order n المعادلة
+
+15
+00:01:26,020 --> 00:01:30,820
+التفاضلية الخطية من الرتبة n أو من الرتبة النونية
+
+16
+00:01:30,820 --> 00:01:35,240
+هي معادلة على الشكل التالي a<sub>0</sub>(x)y<sup>(n)</sup> +
+
+17
+00:01:35,240 --> 00:01:41,290
+a<sub>1</sub>(x)y<sup>(n-1)</sup> +
+
+18
+00:01:41,290 --> 00:01:48,150
++ a<sub>n-1</sub>(x)y' + a<sub>n</sub>(x)y =
+
+19
+00:01:48,150 --> 00:01:53,190
+F(x) لاحظوا أن المشتقة بدأت من عند الـ n و
+
+20
+00:01:53,190 --> 00:01:57,310
+بدأت تنزل n - 1، n - 2، لغاية ما وصلنا
+
+21
+00:01:57,310 --> 00:02:02,010
+للمشتقة الأولى و y بدون اشتقاق = F
+
+22
+00:02:02,010 --> 00:02:07,860
+(x) وسميناها المعادلة (*) الآن المعاملات التي
+
+23
+00:02:07,860 --> 00:02:12,000
+قبل الـ Y's  اللي هي A<sub>0</sub> و A<sub>1</sub> و A<sub>2</sub> و A<sub>3</sub> و A<sub>4</sub> و A<sub>5</sub> و
+
+24
+00:02:12,000 --> 00:02:12,560
+A<sub>6</sub> و A<sub>7</sub> و A<sub>8</sub> و A<sub>9</sub> و A<sub>10</sub> و A<sub>11</sub> و A<sub>12</sub> و A<sub>12</sub> و A<sub>13</sub> و
+
+25
+00:02:12,560 --> 00:02:16,920
+A<sub>13</sub> و A<sub>14</sub> و A<sub>14</sub> و A<sub>15</sub> و A<sub>16</sub> و A<sub>17</sub> و A<sub>18</sub> و A<sub>19</sub> و
+
+26
+00:02:16,920 --> 00:02:20,360
+A<sub>20</sub> و A<sub>21</sub> و A<sub>22</sub> و A<sub>22</sub> و A<sub>22</sub> و A<sub>22</sub> و A<sub>22</sub> و A<sub>21</sub> و
+
+27
+00:02:20,360 --> 00:02:20,840
+A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و
+
+28
+00:02:20,840 --> 00:02:22,240
+A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و
+
+29
+00:02:22,240 --> 00:02:22,500
+A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و
+
+30
+00:02:22,500 --> 00:02:24,420
+A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub> و A<sub>21</sub>  ونعطي تعريف آخر 
+
+31
+00:02:24,420 --> 00:02:29,660
+لو كانت الـ F(x) هذه تساوي Zero يعني شلنا الـ F
+
+32
+00:02:29,660 --> 00:02:33,120
+(x) وعطينا مكانها الصفر، الـ differential equation
+
+33
+00:02:33,120 --> 00:02:37,500
+of the (*) is called homogeneous يبقى ما نسميها
+
+34
+00:02:37,500 --> 00:02:41,240
+معادلة متجانسة دي لبالك مش الـ homogeneous طبع الـ
+
+35
+00:02:41,240 --> 00:02:46,100
+first order هناك لأ بقى هنا نقول إذا بنقدر نحط على
+
+36
+00:02:46,100 --> 00:02:51,060
+صيغة Y على X أو X على Y بقول عنها homogeneous بس
+
+37
+00:02:51,060 --> 00:02:55,020
+هنا لأ لو كانت المعادلة كلها تساوي 0 بقى بقول هذه
+
+38
+00:02:55,020 --> 00:02:59,520
+homogeneous differential equation لكن إذا كان الـ F
+
+39
+00:02:59,520 --> 00:03:04,760
+(x) لا يساوي 0 يعني أعطتني أي دالة في X بسميها
+
+40
+00:03:04,760 --> 00:03:08,180
+non homogeneous differential equation معادلة
+
+41
+00:03:08,180 --> 00:03:13,800
+تفاضلية غير متجانسة ولا تشبيه زي ما كنا نقول
+
+42
+00:03:13,800 --> 00:03:19,580
+homogeneous system مجموعة من المعادلات الخطية
+
+43
+00:03:19,580 --> 00:03:21,060
+نهائتهم Zero
+
+44
+00:03:23,900 --> 00:03:28,860
+معادلة خطية مجموعة لكن النتائج تبع الطرف اليمين
+
+45
+00:03:28,860 --> 00:03:33,140
+التي لا تساوي 0 قد تساوي بعضها 0 لكن على الأقل بدي
+
+46
+00:03:33,140 --> 00:03:37,560
+معادلة واحدة لا تساوي 0 عشان أقول عنها non
+
+47
+00:03:37,560 --> 00:03:42,540
+homogeneous يبقى إذا كان الطرف اليمين Zero بسميها
+
+48
+00:03:42,540 --> 00:03:46,280
+homogeneous differential equation إذا non Zero أي
+
+49
+00:03:46,280 --> 00:03:50,120
+دالة في x تبقى بسميها non homogeneous differential
+
+50
+00:03:50,120 --> 00:03:53,720
+equation في عندنا بعض الملاحظات الـ homogeneous
+
+51
+00:03:53,720 --> 00:03:57,520
+differential equation التي عندنا هذه التي هي تساوي
+
+52
+00:03:57,520 --> 00:04:03,000
+Zero مالها؟ بقدر أكتبها على الشكل التالي L(y)
+
+53
+00:04:03,000 --> 00:04:07,420
+تساوي Zero اختصاراً بدل الشكل هذا الذي هو يمين هو
+
+54
+00:04:07,420 --> 00:04:13,380
+الـ L الـ L بسميه مؤثر تفاضلي يعني هو المشتقة الأولى
+
+55
+00:04:13,380 --> 00:04:17,240
+والتانية والثالثة والرابعة والنونية كلها مع بعض
+
+56
+00:04:17,240 --> 00:04:22,000
+مجموعات بسميهم main الذي هو L يبقى اختصاراً هكتب
+
+57
+00:04:22,000 --> 00:04:26,200
+بالشكل هذا وزي ما تافياً قالت لك الـ L is a linear
+
+58
+00:04:26,200 --> 00:04:33,310
+differential operator يبقى هو مؤثر تفاضلي خطي هذا
+
+59
+00:04:33,310 --> 00:04:36,630
+الملاحظة الأولى الملاحظة الثانية لو أخذت element
+
+60
+00:04:36,630 --> 00:04:42,950
+موجود في الـ vector space طبعاً قبل ذلك قلنا الـ vector
+
+61
+00:04:42,950 --> 00:04:50,410
+space كل الـ function التي لها مشتقات نونية تمام is
+
+62
+00:04:50,410 --> 00:04:55,830
+a solution of الـ L(y) = Zero إذا كان الـ F
+
+63
+00:04:55,830 --> 00:05:03,190
+التي أخذتها هذه حققت المعادلة هذه يبقى المعادلة
+
+64
+00:05:03,190 --> 00:05:08,070
+التفاضلية التي بشكل خطب المؤثر هذا ههه التي
+
+65
+00:05:08,070 --> 00:05:13,750
+عندنا هذه مالها؟ المعادلة هذه لو أخذت element موجود
+
+66
+00:05:13,750 --> 00:05:16,770
+في الـ vector space الذي عندنا والذي جئته هو
+
+67
+00:05:16,770 --> 00:05:22,150
+solution الـ element الذي أخذته لهذا الـ system يبقى
+
+68
+00:05:22,150 --> 00:05:28,240
+بقدر أكتب أن الـ L(f) يساوي من؟ يساوي Zero تمام
+
+69
+00:05:28,240 --> 00:05:33,100
+يعني كل الـ F التي تحقق الـ homogeneous system بقدر
+
+70
+00:05:33,100 --> 00:05:37,600
+اكتبها بالشكل الذي عندنا هذا 3 the set of all
+
+71
+00:05:37,600 --> 00:05:42,660
+solutions of الـ L(y) = Zero is the kernel
+
+72
+00:05:42,660 --> 00:05:48,060
+of L يبقى لو اعتبرت أن الـ L هي Linear
+
+73
+00:05:48,060 --> 00:05:53,280
+Transformation أو Function أو شيء من هذا القبيل 
+
+74
+00:05:53,280 --> 00:05:59,180
+معناته إلها Kernel مين هو الـ Kernel؟ كل الـ functions
+
+75
+00:05:59,180 --> 00:06:04,160
+التي تحقق من الـ homogeneous linear differential
+
+76
+00:06:04,160 --> 00:06:08,450
+equations يبقى هو الـ Kernel تبع الـ L and hence these
+
+77
+00:06:08,450 --> 00:06:14,070
+solutions is a subspace of الـ F<sup>n</sup> ليش قال عنها 
+
+78
+00:06:14,070 --> 00:06:19,490
+subspace؟ لأنه أثبتنا في chapter 3 أن الـ Kernel
+
+79
+00:06:19,490 --> 00:06:25,310
+لأي Linear transformation هو subspace ممتاز جداً 
+
+80
+00:06:25,310 --> 00:06:30,350
+يبقى الـ Kernel لهذا الـ operator عبارة عن مين؟ عبارة عن
+
+81
+00:06:30,350 --> 00:06:36,170
+subspace من الـ set of all continuous functions
+
+82
+00:06:36,170 --> 00:06:41,290
+التي المشتقات النونية تبعها كل ما لا كلها exist
+
+83
+00:06:41,290 --> 00:06:46,950
+ما علينا مجرد تسميات زي ما أنتم شايفينها ومجرد ربط
+
+84
+00:06:46,950 --> 00:06:51,330
+لـ linear differential equations بمين؟ بالـ linear
+
+85
+00:06:51,330 --> 00:06:55,850
+algebra  نأخذ بعض الخواص للـ homogeneous
+
+86
+00:06:55,850 --> 00:07:00,530
+differential equation التي مكتوبة بشكل الـ operator
+
+87
+00:07:00,530 --> 00:07:07,910
+L(y) اختصاراً تساوي Zero الخاصية الأولى بقول لو
+
+88
+00:07:07,910 --> 00:07:12,710
+أخذت element موجود في set of real number وأخذت
+
+89
+00:07:12,710 --> 00:07:16,770
+element هذا الـ element هذا حقق المعادلة التي فوق
+
+90
+00:07:16,770 --> 00:07:23,090
+يبقى هذا الـ element صار solution للمعادلة يبقى cf
+
+91
+00:07:23,090 --> 00:07:27,610
+is a solution ايش يعني؟ يعني لو كان عندي حل
+
+92
+00:07:27,610 --> 00:07:32,490
+للمعادلة التفاضلية وضربتها في constant النتيجة كذلك
+
+93
+00:07:32,490 --> 00:07:37,820
+حل وهذا كنا برضه نستخدمه يعني في الـ chapter الأول
+
+94
+00:07:37,820 --> 00:07:41,540
+يبقى ما ينطبق على الـ chapter الأول ينطبق هنا عالمياً
+
+95
+00:07:41,540 --> 00:07:45,060
+على هذا الـ chapter لو كان عندي function والـ function
+
+96
+00:07:45,060 --> 00:07:49,320
+هذه solution لهذه المعادلة يبقى ضرب هذه المعادلة
+
+97
+00:07:49,320 --> 00:07:55,740
+للحل في constant بيجيب لي حل آخر لمين؟ للمعادلة
+
+98
+00:07:55,740 --> 00:07:59,700
+التفاضلية التي عملناها النقطة الثانية لو كان عندي
+
+99
+00:07:59,700 --> 00:08:03,740
+حلّين للمعادلة التفاضلية الـ homogeneous يبقى
+
+100
+00:08:03,740 --> 00:08:10,000
+مجموعهما كذلك عبارة عن حل الحالة الثالثة هي تعميم
+
+101
+00:08:10,000 --> 00:08:13,680
+للحالة الثانية بدل ما هما اثنين بداخليهم ثلاثة
+
+102
+00:08:13,680 --> 00:08:17,280
+أربعة خمسة عشر عشرين قد ما يكونوا أن هما يكونوا
+
+103
+00:08:17,280 --> 00:08:23,250
+finite عدد محدود يبقى لو كان f<sub>1</sub> و f<sub>2</sub> و لغاية f<sub>n</sub>
+
+104
+00:08:23,250 --> 00:08:28,250
+solutions لهذه المعادلة وعندي scalars موجودة في R
+
+105
+00:08:28,250 --> 00:08:34,710
+يبقى c<sub>1</sub>f<sub>1</sub> c<sub>2</sub>f<sub>2</sub> زي زي c كذلك هو عبارة عن حل مين؟
+
+106
+00:08:34,710 --> 00:08:40,030
+للمعادلة التفاضلية يبقى لو عندي حلّين  بنقينا نقول الـ
+
+107
+00:08:40,030 --> 00:08:44,010
+general solution constant في الأول زائد constant
+
+108
+00:08:44,010 --> 00:08:48,650
+في الثاني ويمثل من الحل العام صحيح ولا لأ؟ طيب لو
+
+109
+00:08:48,650 --> 00:08:51,630
+كانوا ثلاثة أربعة يبقى constant في الأول constant
+
+110
+00:08:51,630 --> 00:08:54,550
+في الثاني constant في الثالث constant في الرابع 
+
+111
+00:08:54,550 --> 00:09:00,750
+constant في رقم n وأجمعهم بيعطيني كذلك حل جديد
+
+112
+00:09:00,750 --> 00:09:04,810
+لمن؟ لو بيعطيني الـ general solution لمن؟ للـ
+
+113
+00:09:04,810 --> 00:09:12,380
+homogeneous system هذه الخواص محققة دائماً وأبداً للـ 
+
+114
+00:09:12,380 --> 00:09:17,280
+linear differential equations لكن الـ non linear
+
+115
+00:09:17,280 --> 00:09:22,380
+هذا الكلام لا يحققه يعني هذا الكلام صحيح الخواص
+
+116
+00:09:22,380 --> 00:09:26,980
+الثلاثة صحيحة على الـ linear differential equations
+
+117
+00:09:26,980 --> 00:09:30,940
+لكن على الـ non linear هذا الكلام ما هو صحيح
+
+118
+00:09:30,940 --> 00:09:37,840
+نعطيكِ شغلة بسيطة لو عندي Non-linear differential
+
+119
+00:09:37,840 --> 00:09:44,740
+equation يعني زي ايش؟ زي ما نقول مثلاً دالة في X في 
+
+120
+00:09:44,740 --> 00:09:51,960
+Y'' زائد دالة في X في Y' كل تربيع
+
+121
+00:09:53,900 --> 00:09:58,580
+يبقى زائد دالة في X في Y تساوي Zero هل هذه linear؟
+
+122
+00:09:58,580 --> 00:10:02,520
+لأ لأن الـ Y' روحنا تقولنا تربيع يعني معرفة على
+
+123
+00:10:02,520 --> 00:10:07,720
+الأس 2 يبقى هذه Non linear وبالتالي constant
+
+124
+00:10:07,720 --> 00:10:10,880
+في الأول وconstant في الثاني وconstant في كده لا
+
+125
+00:10:10,880 --> 00:10:16,140
+يكون حل لمثل هذه المعادلة نجي للنظرية التي عندنا
+
+126
+00:10:16,140 --> 00:10:21,140
+بقول لي المعاملات تبعات المعادلة الأصلية إلى (*)
+
+127
+00:10:21,140 --> 00:10:26,920
+لـ a<sub>0</sub>(x) و a<sub>1</sub>(x) و لغاية a<sub>n</sub>(x) are continuous
+
+128
+00:10:26,920 --> 00:10:34,060
+with الذي هو a<sub>0</sub>(x) لا يساوي 0 طب استنى شوية ليش
+
+129
+00:10:34,060 --> 00:10:41,340
+قال لي أن الـ a<sub>0</sub>(x) لا تساوي 0؟ ليش اشترطت أن هذه
+
+130
+00:10:41,340 --> 00:10:48,310
+لا تساوي 0؟ طلع في المقام بتعرف إلى حالك، لو كانت
+
+131
+00:10:48,310 --> 00:10:53,370
+هذه بالـ Zero ايش بدي يحصل؟ تنزل الرتبة من النونية
+
+132
+00:10:53,370 --> 00:10:56,990
+أقل شوية لأ أنا بدي احافظ على الرتبة النونية لو
+
+133
+00:10:56,990 --> 00:11:00,930
+التي بعدها كلها كانت اصفار ما عنديش مشكلة ليش أنا
+
+134
+00:11:00,930 --> 00:11:06,490
+بضلها من الرتبة النونية تمام؟ إذا هو لما اشترط أن 
+
+135
+00:11:06,490 --> 00:11:10,490
+هذه لا تساوي Zero الهدف من ذلك أن تبقى المعادلة من 
+
+136
+00:11:10,490 --> 00:11:14,670
+الرتبة النونية لكن لو أي term من التي بعدها طار
+
+137
+00:11:14,670 --> 00:11:18,720
+اثنين ثلاثة إن شاء الله يطيروا كلهم تبقى كذلك من
+
+138
+00:11:18,720 --> 00:11:23,500
+الرتبة النونية يبقى بقول الـ homogeneous
+
+139
+00:11:23,500 --> 00:11:27,020
+differential الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+140
+00:11:27,020 --> 00:11:27,180
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ 
+
+141
+00:11:27,180 --> 00:11:27,200
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+142
+00:11:27,200 --> 00:11:28,140
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+143
+00:11:28,140 --> 00:11:28,360
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+144
+00:11:28,360 --> 00:11:28,760
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+145
+00:11:28,760 --> 00:11:29,260
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+146
+00:11:29,260 --> 00:11:29,440
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+147
+00:11:29,440 --> 00:11:29,700
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+148
+00:11:29,700 --> 00:11:30,020
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ
+
+149
+00:11:30,020 --> 00:11:30,540
+.. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. الـ ..
+
+150
+00:11:30,540 --> 00:11:35,500
+الـ .. الـ .. الـ .. الـ .. الـ .. الـ .. 
+
+151
+00:11:35,500 --> 00:11:42,240
+الـ .. الـ
+
+152
+00:11:43,720 --> 00:11:48,600
+Linear operator L هو عبارة عن vector space of
+
+153
+00:11:48,600 --> 00:11:54,260
+dimension N يبقى مجموعة كل الحلول لهذه المعادلة هو
+
+154
+00:11:54,260 --> 00:11:58,780
+vector space of dimension L يساوي N خليني أسألكم
+
+155
+00:11:58,780 --> 00:12:07,470
+السؤال التالي لو هذه كانت تساوي Zero هذا الـ term يبقى
+
+156
+00:12:07,470 --> 00:12:13,910
+عطّل يبقى صلة المعادلة بالشكل هذه هل هذه ممكنة الـ
+
+157
+00:12:13,910 --> 00:12:19,990
+dimension هيكون N لا يمكن أن يكون أكثر ما يمكن أن
+
+158
+00:12:19,990 --> 00:12:24,810
+يكون n-1 تمام إذا لما حطّ الشرط هذا هو يقصده
+
+159
+00:12:24,810 --> 00:12:29,850
+بعينه أن هذه بدأت تبقى موجودة وبالتالي مجموعة
+
+160
+00:12:29,850 --> 00:12:35,750
+الحلول للمعادلة التفاضلية التي هي الـ kernel للـ
+
+161
+00:12:35,750 --> 00:12:41,870
+operator الـ dimension L يساوي N ايش يعني؟ يعني في
+
+162
+00:12:41,870 --> 00:12:48,530
+عندي N من الحلول المستقلة ولا واحد فيهم يعتمد على
+
+163
+00:12:48,530 --> 00:12:54,310
+الثاني مش الـ vector space هذا والـ dimension له نتج عن 
+
+164
+00:12:54,310 --> 00:12:58,870
+basis والـ basis شروطها أن يكونوا كل العناصر التي 
+
+165
+00:12:58,870 --> 00:13:02,490
+في الـ basis are linearly independent يبقى هذه 
+
+166
+00:13:02,490 --> 00:13:08,930
+المعادلة لها N من الحلول وكل هذه الحلول are
+
+167
+00:13:08,930 --> 00:13:15,930
+linearly independent وعددها يساوي N طيب قبل أن
+
+168
+00:13:15,930 --> 00:13:21,370
+نبدأ الأمثلة في أحد بتسأل أي سؤال هنا قبل أن نمسح 
+
+169
+00:13:23,200 --> 
+
+201
+00:18:31,390 --> 00:18:35,930
+قدامنا يعني طبعا بنذكرها قبل ما نبدأ قولنا لو
+
+202
+00:18:35,930 --> 00:18:40,930
+المعاملة الدواء المتاصل أو أي node of x لا يساوي
+
+203
+00:18:40,930 --> 00:18:47,530
+zero يبقى ال kernel لمين؟ ال linear operator يمثل 
+
+204
+00:18:47,530 --> 00:18:52,630
+vector space ال dimension له يساوي n الـ remark
+
+205
+00:18:52,630 --> 00:18:56,850
+بتقول من النظرية اللي عندنا لو كان عندي مجموعة من
+
+206
+00:18:56,850 --> 00:19:01,830
+الحلول وهذه المجموعة are linearly independent
+
+207
+00:19:01,830 --> 00:19:06,490
+solutions للمعادلة اللي قدامنا هذه يبقى هذه
+
+208
+00:19:06,490 --> 00:19:08,530
+المجموعة من الحلول
+
+209
+00:19:12,530 --> 00:19:18,550
+مجموعة الحلول اللينيارلي independent بتكوّن أساس
+
+210
+00:19:18,550 --> 00:19:30,540
+لكل حلول المعادلة L of Y يساوي 0 بالتالي أي حل يكون
+
+211
+00:19:30,540 --> 00:19:36,980
+مبني على هذه المجموعة من الحلول يعني بدي يكون أي
+
+212
+00:19:36,980 --> 00:19:41,840
+حل هو linear combination من هذه الحلول إنهم دول
+
+213
+00:19:41,840 --> 00:19:48,370
+basis يبقى أي حل سيكون على الصورة c1y1 زائد c2y2 زائد 
+
+214
+00:19:48,370 --> 00:19:55,130
+cnyn هذا الحل بسميه الحل العام للمعادلة main اللي 
+
+215
+00:19:55,130 --> 00:20:02,140
+عندنا الذي يشتمل على أي حل آخر نبدأ ناخد أمثلة قال
+
+216
+00:20:02,140 --> 00:20:07,480
+لي طبعا هذا نمر إيه؟ هذا السؤال اثنين من الكتاب
+
+217
+00:20:07,480 --> 00:20:14,140
+رقم إيه؟ وهذا السؤال ثلاثة من الكتاب رقم إيه كذلك؟
+
+218
+00:20:15,840 --> 00:20:19,300
+السؤال الثاني الرقم إيه؟ بيقول لي بيقول لي أن 
+
+219
+00:20:19,300 --> 00:20:25,980
+الدالتين الاثنين هدول بيكونوا basis لمام للـ space
+
+220
+00:20:25,980 --> 00:20:29,900
+تبع الـ solutions تبع الـ differential equation اللي
+
+221
+00:20:29,900 --> 00:20:33,340
+عندنا يبقى مشان أثبت له أن هدول بيكونوا basis
+
+222
+00:20:33,340 --> 00:20:41,150
+أولا بدي أثبت إنهم حلّين بعد ما أثبت إنهم حلّين بدأ
+
+223
+00:20:41,150 --> 00:20:45,570
+أثبت إنهم linearly independent بعد ذلك لما أصبحوا
+
+224
+00:20:45,570 --> 00:20:48,890
+linearly independent يبقى أي حل بيكون هو linear
+
+225
+00:20:48,890 --> 00:20:52,810
+combination أو الـ general solution هو linear
+
+226
+00:20:52,810 --> 00:20:58,060
+combination من الحلّين الاثنين بالتالي هدول كوّنوا
+
+227
+00:20:58,060 --> 00:21:05,700
+لإيه؟ Basis لمن؟ للـ kernel أو لمجموعة الحلول تبع هذه
+
+228
+00:21:05,700 --> 00:21:10,580
+المعادلة بعد ما خلص بروح للنمر بيه قال لي هاتلي الـ
+
+229
+00:21:10,580 --> 00:21:14,220
+solution لـ الـ initial problem هذه طبعا هي نفس
+
+230
+00:21:14,220 --> 00:21:18,420
+المعادلة اللي فوق بس روحنا أضفنا عليها مين؟ الشروط
+
+231
+00:21:18,420 --> 00:21:23,480
+بنشوف كيف بدنا نعمل فيها يبقى باجي بقوله solution
+
+232
+00:21:25,720 --> 00:21:30,600
+أول شيء بدي أثبت أن الـ cos x و sin x هي عبارة عن
+
+233
+00:21:30,600 --> 00:21:41,350
+مين؟ الحل يبقى f1 of x يساوي cos x هنا بلزمنا
+
+234
+00:21:41,350 --> 00:21:48,250
+المشتقة الثانية إذا هذا بده يخليني أجيب المشتقة 
+
+235
+00:21:48,250 --> 00:21:55,350
+الأولى f1 prime of x تفاضل cosine مقدارها سالب sin
+
+236
+00:21:55,350 --> 00:22:00,730
+x هذا بده يخليني أجيب المشتقة الثانية as a
+
+237
+00:22:00,730 --> 00:22:08,020
+function of x يبقى سالب cosine x الآن بدأت ياخد الـ
+
+238
+00:22:08,020 --> 00:22:15,860
+y w prime زائد y يساوي zero implies إن كان هذا حل 
+
+239
+00:22:15,860 --> 00:22:21,200
+يبقى هذا بده يحققها وإذا مش حل ليه؟ يمكن أن يحققها
+
+240
+00:22:21,390 --> 00:22:29,410
+يبقى y w' مرتب قيمة الإمام سالب cosine x يبقى سالب
+
+241
+00:22:29,410 --> 00:22:36,930
+cosine x و y هي عبارة عن الحل الذي زائد cosine x كم
+
+242
+00:22:36,930 --> 00:22:49,190
+جمعهم يبقى هذا معناه أن f1 of x سواء cosine x is a
+
+243
+00:22:49,190 --> 00:22:50,790
+solution
+
+244
+00:23:02,730 --> 00:23:09,770
+بنفس الطريقة لو جيت للـ sin نفس النتيجة similar بنفس
+
+245
+00:23:09,770 --> 00:23:20,520
+الطريقة Similarly, f2 تساوي sin الـ x is a solution
+
+246
+00:23:20,520 --> 00:23:28,550
+of equation star يبقى صاروا هدول عبارة عن إيش؟ 
+
+247
+00:23:28,550 --> 00:23:33,730
+عبارة عن حلّين جاي يبين لي أن الاثنين هدول بيكونوا 
+
+248
+00:23:33,730 --> 00:23:39,570
+basis للـ vector space و هدول اللي هو الـ vector
+
+249
+00:23:39,570 --> 00:23:44,170
+space يساوي مجموعة الحلول بناء عليه بدي أشوف هل
+
+250
+00:23:44,170 --> 00:23:52,950
+الحلّين linearly dependent ولا linearly من هنا
+
+251
+00:23:52,950 --> 00:23:59,790
+بدأ المطلوب الأول نمر إيه؟ بدأ يأخذ الـ Wronskian as a
+
+252
+00:23:59,790 --> 00:24:06,430
+function of x الحل الأول cos x الحل الثاني sin x
+
+253
+00:24:06,430 --> 00:24:15,410
+مشتقته سالب sin x مشتقته cos x نفك المحدد يبقى
+
+254
+00:24:15,410 --> 00:24:20,110
+cosine تربيع الـ x زائد sin تربيع الـ x اللي يبقى
+
+255
+00:24:20,110 --> 00:24:25,970
+الواحد ماله لا يساوي zero مدام الـ Wronskian
+
+256
+00:24:25,970 --> 00:24:28,610
+لا يساوي zero يبقى الاثنين هدول 
+
+257
+00:24:31,250 --> 00:24:42,570
+يبقى هذا يعني أن الحل الأول cos x و الحل الثاني
+
+258
+00:24:42,570 --> 00:24:47,830
+sin x هم مستقلّين
+
+259
+00:24:49,550 --> 00:24:55,190
+طيب هالي في الـ remark إيش بتقول؟ بتقول لو كانوا
+
+260
+00:24:55,190 --> 00:25:00,390
+هدول linearly independent solutions للمعادلة يبقى 
+
+261
+00:25:00,390 --> 00:25:06,810
+هذه المعادلة تكون basis لمن؟ للـ kernel يعني لمجموعة 
+
+262
+00:25:06,810 --> 00:25:17,090
+الحلول يبقى هنا {cos الـ x and sin الـ x} و 
+
+263
+00:25:17,090 --> 00:25:25,470
+لنضعهم على شكل set the set {cos الـ x
+
+264
+00:25:25,470 --> 00:25:35,810
+وكذلك sin الـ x} form a basis for
+
+265
+00:25:35,810 --> 00:25:46,070
+the vector space of solutions
+
+266
+00:25:46,070 --> 00:25:48,810
+of
+
+267
+00:25:49,440 --> 00:25:57,860
+the equation star ما دول هدول بيضلوا يبقى أي حل
+
+268
+00:25:57,860 --> 00:26:04,920
+بقدر أكسبه بدلالته يبقى هنا هذا بده يعطيني there
+
+269
+00:26:04,920 --> 00:26:13,300
+exist constant c1 و c2 موجودات في الأرض such that
+
+270
+00:26:13,300 --> 00:26:26,320
+بحيث أن any solution of equation star is in the
+
+271
+00:26:26,320 --> 00:26:35,980
+form y يساوي c1 cos x زائد c2 sin x
+
+272
+00:26:46,550 --> 00:26:49,950
+لحد هنا انتهينا من مين؟ انتهينا من المطلوب الأول
+
+273
+00:26:49,950 --> 00:26:53,850
+قال لي بيبين لي أن الناس بيكونوا basis للـ
+
+274
+00:26:53,850 --> 00:26:57,130
+solutions بيبيّن له أنه بيبيّن له solutions وجبنا 
+
+275
+00:26:57,130 --> 00:27:01,390
+الشكل الحل العام المطلوب الثاني قال لي حل الـ
+
+276
+00:27:01,390 --> 00:27:07,650
+initial value problem مش الحل هو هذا صح ولا لأ؟
+
+277
+00:27:07,650 --> 00:27:11,090
+يبقى مش إن أجيب لي الـ solutions بدي أروح أجيب لي
+
+278
+00:27:11,090 --> 00:27:18,350
+المشتقة الأولى والمشتقة الثانية وأروح أعوّض فيهم في 
+
+279
+00:27:18,350 --> 00:27:22,970
+المعادلة اللي عندنا أنا يبقى احنا هنا عندنا مين؟
+
+280
+00:27:22,970 --> 00:27:34,710
+عندنا نمرة بيه عندك y تساوي c1 cos x زائد c2 sin x
+
+281
+00:27:34,710 --> 00:27:47,110
+لو اشتقيت هالشكل بتعطيني y' سالب c1 sin x زائد c2 في
+
+282
+00:27:47,110 --> 00:27:53,550
+cos x الـ condition الأولاني المعطى اللي هو بيقول 
+
+283
+00:27:53,550 --> 00:28:01,430
+لي مين؟ y عند الـ pi تساوي قداش؟ تساوي zero implies y
+
+284
+00:28:01,430 --> 00:28:09,520
+يساوي صفر وسالب واحد يبقى سالب c1 sin 
+
+285
+00:28:09,520 --> 00:28:17,280
+180 يبقى زائد zero هذا معناه أن c1 يساوي
+
+286
+00:28:17,280 --> 00:28:27,700
+zero y' تساوي كده؟ سالب اثنين يساوي sin 180 بـ zero
+
+287
+00:28:27,700 --> 00:28:36,000
+و sin 180 بسالب واحد يبقى سالب c2 يبقى c2 يساوي
+
+288
+00:28:36,000 --> 00:28:41,940
+اثنين و c1 يساوي واحد يبقى بروح بقوله هنا the
+
+289
+00:28:41,940 --> 00:28:42,860
+solution
+
+290
+00:28:45,370 --> 00:28:55,590
+solution of the initial value problem is y تساوي 
+
+291
+00:29:10,750 --> 00:29:15,730
+لازلنا في نفس الـ section ولما ننتهي بعد للمرة 
+
+292
+00:29:15,730 --> 00:29:17,630
+القادمة إن شاء الله
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5e7422962361ba1cdc0fa5e67e8e5517d3811a1f
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw.srt
@@ -0,0 +1,1445 @@
+1
+00:00:19,590 --> 00:00:23,010
+بسم الله الرحمن الرحيم اللي هنكم اللي ما بدأنا
+
+2
+00:00:23,010 --> 00:00:26,650
+بيه في المرة الماضية كنا متحدثين في المرة الماضية عن
+
+3
+00:00:26,650 --> 00:00:33,670
+الـ subspaces الفضاءات الجزئية لفضاء اتجاهي و أخذنا
+
+4
+00:00:33,670 --> 00:00:38,470
+أمثلة كثيرة جدا و بعدين أخذنا نظرية قلنا لو عندي
+
+5
+00:00:38,470 --> 00:00:43,950
+set و الـ set تولدت بمجموعة من الـ vectors أو كل
+
+6
+00:00:43,950 --> 00:00:47,270
+element فيها كتبناه على صيغة linear combination من
+
+7
+00:00:47,270 --> 00:00:51,450
+مجموعة من الـ vectors يبقى هذا الـ set عبارة عن sub
+
+8
+00:00:51,450 --> 00:00:56,070
+space و ابتدأنا أن نأخذ على ذلك أمثلة و أخذنا بدل
+
+9
+00:00:56,070 --> 00:01:01,400
+المثال اثنين و هذا هو المثال رقم ثلاثة بقول في هذا
+
+10
+00:01:01,400 --> 00:01:07,580
+المثال افترض أن U عبارة عن subspace من R3 that is
+
+11
+00:01:07,580 --> 00:01:11,940
+spanned by the vectors يبقى الـ U هذا ولد بواسطة
+
+12
+00:01:11,940 --> 00:01:18,620
+three vectors V1 و V2 و V3 بقول هل الـ vector V2 و
+
+13
+00:01:18,620 --> 00:01:24,310
+V1 و V5 موجود في الـ set U ولا لأ ممتاز يبقى أنا في
+
+14
+00:01:24,310 --> 00:01:28,910
+عندي vector space اللي هو R3 اللي هو عبارة عن كل
+
+15
+00:01:28,910 --> 00:01:34,670
+العناصر المتكونة من 3 تيوبل تمام روحت على الـ
+
+16
+00:01:34,670 --> 00:01:38,610
+vector space هذا أخذت منه مجموعة جزئية المجموعة
+
+17
+00:01:38,610 --> 00:01:44,150
+الجزئية سميتها U مين هي الـ U؟ قال لي هي الـ U هي
+
+18
+00:01:44,150 --> 00:01:49,830
+المجموعة التي ولدت بواسطة الـ three vectors V1 و V2
+
+19
+00:01:49,830 --> 00:01:56,850
+و V3 يعني الثلاث عناصر دول ولدوا لي جميع عناصر الـ U
+
+20
+00:01:56,850 --> 00:02:02,990
+بلا ستة يعني جميع عناصر الـ subspace U بسأل هل الـ
+
+21
+00:02:02,990 --> 00:02:09,270
+vector 2 و 1 و 5 موجود في الـ set U أم لا بقوله
+
+22
+00:02:09,270 --> 00:02:14,600
+والله إذا كان الـ vector 2 و 1 و 5 قدرنا نكتبه على
+
+23
+00:02:14,600 --> 00:02:19,980
+صيغة linear combination من V1 و V2 و V3 إذا بيكون
+
+24
+00:02:19,980 --> 00:02:25,600
+موجود في الـ U صحيح ولا لأ يبقى هنا مرة ثانية بقول
+
+25
+00:02:25,600 --> 00:02:31,200
+مشان أثبت أن الـ vector 2 و 1 و 5 موجود في الـ
+
+26
+00:02:31,200 --> 00:02:37,960
+subspace U بدي أحاول أثبت أن 2 و 1 و 5 هو linear
+
+27
+00:02:37,960 --> 00:02:45,350
+combination من V1 و V2 و V3 إن تحقق ذلك يبقى هذا
+
+28
+00:02:45,350 --> 00:02:50,250
+العنصر موجود فيه إن لم يتحقق ذلك يبقى هذا العنصر
+
+29
+00:02:50,250 --> 00:02:55,850
+غير موجود في الـ sub space U على الإطلاق واضح الشيء
+
+30
+00:02:55,850 --> 00:03:01,340
+اللي بدنا نعمله؟ يبقى مشان أثبت أنه 2 و 5 .. 2 و 1
+
+31
+00:03:01,340 --> 00:03:06,040
+و 5 موجود فيه و بدي أحاول أثبت أنه 2 و 1 و 5 هذا
+
+32
+00:03:06,040 --> 00:03:10,580
+يساوي Constant في V1 زائد Constant في V2 زائد
+
+33
+00:03:10,580 --> 00:03:15,680
+Constant في V3 يعني على صيغة Linear Combination من
+
+34
+00:03:15,680 --> 00:03:21,680
+الـ three vectors ماجي العالم يبقى هنا باجي بقول
+
+35
+00:03:21,680 --> 00:03:23,640
+assume
+
+36
+00:03:24,950 --> 00:03:37,130
+الذات افترض أن الـ V اللي بده يساوي 2 1 2 1 و 5 بده
+
+37
+00:03:37,130 --> 00:03:48,090
+يساوي C1 V1 C2 V2 C3 V3 إن حدث ذلك بمعنى آخر اللي
+
+38
+00:03:48,090 --> 00:03:53,830
+جاءت حل هذه المعادلة بمعنى آخر اللي جاءت قيم لـ C1
+
+39
+00:03:53,830 --> 00:03:59,550
+و C2 و C3 بكلام نصي ما وجدت يبقى لا يمكن أن يكون
+
+40
+00:03:59,550 --> 00:04:04,470
+هذا الـ vector موجود في الـ Set U فبعدين بقوله كويس
+
+41
+00:04:04,470 --> 00:04:16,730
+يبقى أصبح النميم C1 في V1 و 2 و 1 زائد c2 في v2 اللي
+
+42
+00:04:16,730 --> 00:04:24,030
+هو واحد و زيرو و اثنين زائد c3 في v3 اللي هو واحد
+
+43
+00:04:24,030 --> 00:04:28,550
+و واحد و زيرو بده يساوي 2 1 5
+
+44
+00:04:31,010 --> 00:04:37,190
+بدأ أجمع هذه العناصر يبقى بدأ أدخل الـ C1 و C2 و C3
+
+45
+00:04:37,190 --> 00:04:43,250
+داخل الأقواس التهدي و ابدأ أجمع يبقى بدأت الخطوتين
+
+46
+00:04:43,250 --> 00:04:52,090
+بخطوة واحدة يبقى هذه C1 زائد C2 زائد C3 المركبة
+
+47
+00:04:52,090 --> 00:05:00,530
+الثانية 2C1 زيرو طار مع السلامة زائد C3 المركبة
+
+48
+00:05:00,530 --> 00:05:07,530
+الثالثة C1 زائد 2 C2 و المركبة الثالثة ما لها مع
+
+49
+00:05:07,530 --> 00:05:15,880
+السلامة يبقى يساوي 2 1 5 هذا ليس ما حصل لدي، لدي
+
+50
+00:05:15,880 --> 00:05:21,680
+الآن ثلاثة تيوبل يساوي ثلاثة تيوبل فكل عنصر سيساوي
+
+51
+00:05:21,680 --> 00:05:27,940
+ثلاثة نظيره هذا سيعطيني ثلاث معادلات المعادلة
+
+52
+00:05:27,940 --> 00:05:36,030
+الأولى C1 زائد C2 زائد C3 يساوي 2 المعادلة الثانية
+
+53
+00:05:36,030 --> 00:05:45,030
+2C1 و هنا زائد C3 يساوي 1 المعادلة الثالثة C1
+
+54
+00:05:45,030 --> 00:05:54,720
+زائد 2 C2 بده يساوي كده؟ خمسة يبقى احنا انتقلنا
+
+55
+00:05:54,720 --> 00:05:59,860
+إلى الـ System of Linear Equations مظبوط ولا لأ؟
+
+56
+00:05:59,860 --> 00:06:06,180
+يبقى صار عندي ثلاث معادلات في ثلاثة مجاهيل إذا
+
+57
+00:06:06,180 --> 00:06:10,100
+بدنا نحاول حل المعادلات الثلاث مش هنأتي قيم
+
+58
+00:06:10,100 --> 00:06:17,630
+المجاهيل C1 و C2 و C3 إن أمكن ذلك طبعا قدامي أكثر من
+
+59
+00:06:17,630 --> 00:06:20,830
+طريقة يا إما الـ Echelon Form على الـ Augmented
+
+60
+00:06:20,830 --> 00:06:26,270
+Matrix يا إما الـ Gaussian Method طريقة الجاوس يا
+
+61
+00:06:26,270 --> 00:06:30,890
+إما نشتغل عادي اللي بنقدر عليه يعني بأي وسيلة من
+
+62
+00:06:30,890 --> 00:06:35,550
+الوسائل اللي تعلمناها قبل ذلك بنحاول نحل هذه
+
+63
+00:06:35,550 --> 00:06:40,550
+المعادلات لكن هذه المعادلات الثلاث بسيطة لن نحتاج
+
+64
+00:06:40,550 --> 00:06:46,420
+Echelon ولا Gaussian ولا غيره كيف؟ باجي بقول لو
+
+65
+00:06:46,420 --> 00:06:52,500
+ضربت المعادلة الثانية هذه في سالب واحد و جمعت بكون
+
+66
+00:06:52,500 --> 00:06:59,580
+ضعت main اللي هو C1 و C3 و لم يبقى عندي إلا main
+
+67
+00:06:59,580 --> 00:07:05,820
+C2 و بالتالي نحل الـ system بسهولة بدون ما يلجأ ل
+
+68
+00:07:05,820 --> 00:07:10,910
+لإيشيلون ولا ليجوسيان ولا لغيره يبقى هذا الـ system
+
+69
+00:07:10,910 --> 00:07:18,710
+بدي أعيد صورته كالتالي يبقى C1 زائد C2 زائد C3 يساوي
+
+70
+00:07:18,710 --> 00:07:28,830
+2 سالب 2 C1 و هنا سالب C3 بده يساوي سالب 1 و هنا C1
+
+71
+00:07:28,830 --> 00:07:36,310
+زائد 2 C2 بده يساوي كده؟ بده يساوي 5 و بدنا نجي نجمع
+
+72
+00:07:37,610 --> 00:07:42,890
+لو جينا لنجمع أظن أن هدول مع السلامة و هدول زيهم
+
+73
+00:07:42,890 --> 00:07:47,810
+مع السلامة يبقى الموضوع اللي عندي C2 و 2C2 يبقى
+
+74
+00:07:47,810 --> 00:07:54,550
+3C2 يبقى هذا بده يعطينا الـ system ما يأتي اللي هو
+
+75
+00:07:54,550 --> 00:08:00,370
+3C2 بده يساوي سبعة بده أشيل منهم واحد بده يساوي
+
+76
+00:08:00,370 --> 00:08:09,210
+قداش ستة و منه C2 يساوي قداش اثنين طيب لما C2 يساوي 2
+
+77
+00:08:09,210 --> 00:08:17,070
+بقدر أجيب له مين؟ C1 يبقى هذا جبنا C2 هذا بده
+
+78
+00:08:17,070 --> 00:08:24,320
+يعطينا مين؟ بتعوض في المعادلة الثالثة يبقى C1 زيدي
+
+79
+00:08:24,320 --> 00:08:30,740
+2 في 2 بده يساوي 5 هذا بيعطينا أن C1 بده يساوي
+
+80
+00:08:30,740 --> 00:08:36,620
+كده؟ 2 في 2 أبقى 4 بجيب الشجة الثانية سالب 4 بيظل
+
+81
+00:08:36,620 --> 00:08:43,320
+عندي كده C1 يساوي 1 أصبح C1 معروف و C2 معروف بيظل
+
+82
+00:08:43,320 --> 00:08:47,470
+المجهول من عندنا C3 يبقى يا ما بعوض في المعادلة
+
+83
+00:08:47,470 --> 00:08:53,330
+الأولى يا بعوض في المعادلة الثانية في أي منهم إذا
+
+84
+00:08:53,330 --> 00:09:00,530
+لو جيت عوض في المعادلة الأولى C1 ب 1 و C2 ب 2 و C3
+
+85
+00:09:00,530 --> 00:09:09,230
+الله أعلم يساوي 2 يبقى C3 يساوي كم؟ سالب واحد يبقى
+
+86
+00:09:09,230 --> 00:09:15,740
+لجيت قيم لـ C1 و C2 و C3 معناته أن الـ vector اللي عندي
+
+87
+00:09:15,740 --> 00:09:21,020
+2 و 1 و 5 بقدر أكتبه على صيغة linear combination
+
+88
+00:09:21,020 --> 00:09:27,920
+من من؟ من الـ three vectors كيف؟ كالتالي شوف إيش
+
+89
+00:09:27,920 --> 00:09:33,740
+اللي بدي يصير الآن عندنا الـ V اللي هو 2 و 1 و 5
+
+90
+00:09:34,050 --> 00:09:39,850
+بقدر أكتبه على الشكل التالي C1 ب 1 يبقى هاي واحد في
+
+91
+00:09:39,850 --> 00:09:46,030
+الـ vector الأول اللي هو واحد و اثنين و واحد زائد
+
+92
+00:09:46,030 --> 00:09:53,530
+C2 ب 2 في الـ vector الثاني اللي هو واحد و زيرو و
+
+93
+00:09:53,530 --> 00:09:59,750
+اثنين اللي ثالث سالب واحد في الـ vector الثالث اللي
+
+94
+00:09:59,750 --> 00:10:03,860
+هو عبارة عن one واحد واحد واحد واحد واحد واحد واحد
+
+95
+00:10:03,860 --> 00:10:04,000
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+96
+00:10:04,000 --> 00:10:04,720
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+97
+00:10:04,720 --> 00:10:09,800
+واحد واحد واحد واحد واحد
+
+98
+00:10:09,800 --> 00:10:13,660
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+99
+00:10:13,660 --> 00:10:16,300
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+100
+00:10:16,300 --> 00:10:21,620
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+101
+00:10:21,620 --> 00:10:28,380
+واحد واحد واحد واحد واحد واحد واحد واحد
+
+102
+00:10:28,380 --> 00:10:39,400
+واحد و V1 و V2 و V3 يبقى هنا ساعة الاثنين و واحد
+
+103
+00:10:39,400 --> 00:10:46,360
+و خمسة موجود في الـ subspace U انتهينا من المسألة
+
+104
+00:10:46,360 --> 00:10:49,680
+طيب
+
+105
+00:10:49,680 --> 00:10:54,010
+يمكن واحدة تقول طيب أنا كل سؤال زي هيك لمساني هل الـ
+
+106
+00:10:54,010 --> 00:10:59,350
+vector موجود هنا بسوي نفس الطريقة ماشي الآن طلعت
+
+107
+00:10:59,350 --> 00:11:06,150
+قيم لـ C1 و C2 و C3 كيف بده يش يطلع قيم يعني كيف بده يش
+
+108
+00:11:06,150 --> 00:11:10,930
+يكون هذا مش موجود فبنقولك مشان بيبينك الشغل هذه
+
+109
+00:11:10,930 --> 00:11:16,070
+إليك المثال الرابع يبقى example four
+
+110
+00:11:24,740 --> 00:11:33,320
+بقول أن الـ V واحد بده يساوي واحد و اثنين و سالب
+
+111
+00:11:33,320 --> 00:11:41,240
+واحد و الـ V اثنين بده يساوي ستة أربعة اثنين كل هذا
+
+112
+00:11:41,240 --> 00:11:49,460
+موجود في أعلى ثلاثة show that the vector show that
+
+113
+00:11:49,460 --> 00:11:52,760
+that
+
+114
+00:11:57,210 --> 00:12:06,650
+V يساوي أربعة و سالب واحد و ثمانية does not belong
+
+115
+00:12:06,650 --> 00:12:11,830
+للسبين of V واحد و V اثنين
+
+116
+00:12:29,860 --> 00:12:34,500
+طلب لي في صيغة السؤال هنا أعطاني مجموعة من الـ
+
+117
+00:12:34,500 --> 00:12:37,780
+vectors و قال لي اثبت لي أن الـ vector هذا موجود في
+
+118
+00:12:37,780 --> 00:12:41,400
+الـ linear combination لمين؟ لهذا الـ أو موجود في الـ
+
+119
+00:12:41,400 --> 00:12:46,780
+span تبع هذه الـ vector هنا برضه أعطاني two vectors
+
+120
+00:12:46,780 --> 00:12:51,080
+و قال لي بيلي أن الـ vector اللي عندنا مش موجود في
+
+121
+00:12:51,080 --> 00:12:56,980
+الـ span هذا تمام أنا كان بإمكاني أعيد صياغة السؤال
+
+122
+00:12:56,980 --> 00:13:02,290
+بطريقة أخرى أي من الاثنين أي واحد منهم و أقول خذي
+
+123
+00:13:02,290 --> 00:13:08,890
+لي V1 و V2 و V3 مثلا موجودة في R3 و خذي لي الـ U
+
+124
+00:13:08,890 --> 00:13:13,770
+هو الـ Spain تبع هذا الـ Vector و أقول Approve or
+
+125
+00:13:13,770 --> 00:13:17,210
+Disapprove ذات أن الـ Vector هذا موجود في الـ
+
+126
+00:13:17,210 --> 00:13:21,680
+Spain هذا يبقى هذا صياغة ثالثة للسؤال و بالتالي
+
+127
+00:13:21,680 --> 00:13:26,540
+حيارتك لا قلت لك موجود ولا قلت لك مش موجود تمام؟
+
+128
+00:13:26,540 --> 00:13:30,380
+و بالتالي أنت لحالك بدك تمشي نفس الـ tactic اللي
+
+129
+00:13:30,380 --> 00:13:33,940
+مشينا فيه في حل السؤال هذا و اللي هنمشي فيه حل
+
+130
+00:13:33,940 --> 00:13:39,620
+السؤال الثاني حتى نصل إلى النتيجة يجي أنا بدي أبدأ
+
+131
+00:13:39,620 --> 00:13:44,760
+حل مثل ما حلت هذا هو قال لي اثبت أنه هذا هذا أنه مش
+
+132
+00:13:44,760 --> 00:13:50,720
+موجود في الاسبان بدي أروح أفرض أنه موجود طيب لما
+
+133
+00:13:50,720 --> 00:13:57,680
+أفرض أنه موجود هوصل إلى نتيجة خاطئة يبقى إذا وصلت
+
+134
+00:13:57,680 --> 00:14:02,500
+إلى نتيجة خاطئة معناته الفرضي صح ولا غلط؟ غلط و عكسه
+
+135
+00:14:02,500 --> 00:14:07,280
+صح هو الصحيح تمام يبقى تمام يبقى بدي أبدأ زي هذا
+
+136
+00:14:07,280 --> 00:14:15,860
+بالضبط تماما يبقى بدي أقول له solution assume
+
+137
+00:14:15,860 --> 00:14:16,500
+that
+
+138
+00:14:19,950 --> 00:14:27,050
+أن الـ V بيساوي أربعة و سالب واحد و ثمانية موجود
+
+139
+00:14:27,050 --> 00:14:34,350
+في الاسبان تبع الـ V واحد و V اثنين هذا معناته أن
+
+140
+00:14:34,350 --> 00:14:40,750
+هناك C واحد و C اثنين موجودة في الـ set of real
+
+141
+00:14:40,750 --> 00:14:53,400
+numbers such that بحيث أن C1 V1 زائد C2 V2 يبقى
+
+142
+00:14:53,400 --> 00:15:03,880
+C1 في V1 V1 يعني واحد اثنين سالب واحد C2 في ستة
+
+143
+00:15:03,880 --> 00:15:14,040
+أربعة اثنين يبقى V أربعة سالب واحد و ثمانية حتى الآن هل
+
+144
+00:15:14,040 --> 00:15:19,260
+اختلفت الفكرة؟ لا يبقى باجي أفك القوس و أجمعهم
+
+145
+00:15:19,260 --> 00:15:24,320
+اثنين مع بعض بقوس واحد أو بثري تيوبل الواحد يبقى
+
+146
+00:15:24,320 --> 00:15:32,360
+بقدر أقوله هنا ما يأتي هذه c1 زائد 6 c2 اثنين C
+
+147
+00:15:32,360 --> 00:15:40,060
+واحد زائد أربعة C اثنين اللي بعده سالب C واحد زائد
+
+148
+00:15:40,060 --> 00:15:45,080
+اثنين C اثنين كله بده يساوي أربعة و سالب واحد
+
+149
+00:15:45,080 --> 00:15:49,820
+و ثمانية بالشكل اللي عندنا هذا صار عندي هنا three
+
+150
+00:15:49,820 --> 00:15:55,000
+tuple بيساوي three tuple من الناحية الأخرى إذا بدي
+
+151
+00:15:55,000 --> 00:16:01,740
+أقارن كل مركبة بنظيرتها معناته حصل إيش؟ يبقى بيصير
+
+152
+00:16:01,740 --> 00:16:13,560
+C1 زائد 6 C2 بده يساوي 4 اللي بعدها 2C1 زائد 2C2
+
+153
+00:16:13,560 --> 00:16:21,140
+بده يساوي سالب 1 يبقى 2C واحد زائد 4C
+
+154
+00:16:21,140 --> 00:16:27,400
+اثنين بده يساوي سالب واحد اللي بعده سالب C واحد
+
+155
+00:16:27,400 --> 00:16:34,340
+زائد 2C اثنين بده يساوي قداش؟ ثمانية يبقى the
+
+156
+00:16:34,340 --> 00:16:39,760
+system of linear equations ثلاثة ثلاث معادلات في
+
+157
+00:16:39,760 --> 00:16:45,540
+مجهولين أظن أن هذا سهل بسبب المعادلات التي وضعت
+
+158
+00:16:45,540 --> 00:16:52,660
+الله عليها البركة و المجاهيل. لكن بمجرد النظر، لو
+
+159
+00:16:52,660 --> 00:16:58,680
+كانت هذه الشرط سالب و جمعت بضيع أحد المجاهيل و بنوجد
+
+160
+00:16:58,680 --> 00:17:03,410
+من المجهول الثاني مباشرة من دول لا إيشيلون ولا
+
+161
+00:17:03,410 --> 00:17:08,530
+جاوسيان ولا غيره إذا بقدر أقول هذا الـ system لحله
+
+162
+00:17:08,530 --> 00:17:13,110
+بقول ما يأتي بدي أضرب الأول في سالب واحد يبقى سالب
+
+163
+00:17:13,110 --> 00:17:25,230
+C1 سالب ستة C2 سالب أربعة 2C1 زائد 4C2
+
+164
+00:17:25,230 --> 00:17:33,880
+سالب واحد سالب C1 زي دي 2C2 بده يساوي كده؟ بده
+
+165
+00:17:33,880 --> 00:17:40,660
+يساوي الثمانية تعالوا نجمع يبقى لو جمعنا هدول مع
+
+166
+00:17:40,660 --> 00:17:47,160
+السلامة تمام؟ و هدول مع السلامة مش هيك؟ يبقى صار
+
+167
+00:17:47,160 --> 00:17:52,160
+طرف الشمال يساوي كده يا بنات؟ بده طرف اليمين سالب
+
+168
+00:17:52,160 --> 00:17:57,000
+خمسة و ثمانية ثلاثة يبقى Zero تساوي ثلاثة إيش
+
+169
+00:17:57,000 --> 00:18:03,240
+رأيكم؟ مفقود؟ في حاجة اسمها real number Zero تساوي
+
+170
+00:18:03,240 --> 00:18
+
+201
+00:23:03,890 --> 00:23:09,290
+أخدت منه two subspaces الأول أنا سميته U والثاني
+
+202
+00:23:09,290 --> 00:23:15,670
+سميته V كل واحد منهم subspace من الـ R<sup>n</sup>
+
+203
+00:23:15,670 --> 00:23:19,010
+the set of all inner tuples under the usual
+
+204
+00:23:19,010 --> 00:23:23,490
+addition and usual multiplication طيب الـ subspaces
+
+205
+00:23:23,490 --> 00:23:30,410
+هذول spanned الأول ولد بالـ vectors U<sub>1</sub> و U<sub>2</sub> و لغاية 
+
+206
+00:23:30,410 --> 00:23:38,630
+U<sub>r</sub> الـ V ولد بالعناصر V<sub>1</sub> و V<sub>2</sub> لغاية V<sub>s</sub> تمام؟ يبقى
+
+207
+00:23:38,630 --> 00:23:43,910
+الـ vectors للـ subspace اللي هو U و الـ vectors للـ
+
+208
+00:23:43,910 --> 00:23:49,350
+subspace الثاني اللي هو V نجي لنظرية النظرية بتقول
+
+209
+00:23:49,350 --> 00:23:54,550
+إذا كان كل واحد من الـ vectors هدول Linear
+
+210
+00:23:54,550 --> 00:23:59,450
+Combination من الـ V's اللي عندنا هدول يبقى الـ U
+
+211
+00:23:59,450 --> 00:24:04,590
+هو عبارة عن Subspace من الـ Subspace V مش كل واحد
+
+212
+00:24:04,590 --> 00:24:10,270
+فيهم Subspace من R<sup>n</sup> إن حدث أن Subspace الأول يعني
+
+213
+00:24:10,270 --> 00:24:16,200
+أي Vector V اللي هو U لقيته linear combination من
+
+214
+00:24:16,200 --> 00:24:20,700
+الـ V<sub>1</sub> و الـ V<sub>2</sub> و الـ V<sub>s</sub> يبقى على طول الـ U بدي يكون
+
+215
+00:24:20,700 --> 00:24:27,940
+subspace من الـ V النقطة الثانية لو كان كل U هو
+
+216
+00:24:27,940 --> 00:24:33,440
+linear combination من الـ V و كل V هي linear
+
+217
+00:24:33,440 --> 00:24:37,660
+combination من الـ U يعني العملية العكسية يبقى
+
+218
+00:24:37,660 --> 00:24:42,860
+automatically الـ U و الـ V are equal يبقى ال U يساوي ال V
+
+219
+00:24:42,860 --> 00:24:48,040
+مرة ثانية بتفترض المثل اللي قلتها ثانية كلهم ال
+
+220
+00:24:48,040 --> 00:24:54,080
+vector space R<sup>n</sup> روحت أخدت مجموعة هذه مجموعة وهذه
+
+221
+00:24:54,080 --> 00:24:59,760
+مجموعة ثانية لو جيت كل واحد هنا بقدر اكتبه كـ linear
+
+222
+00:24:59,760 --> 00:25:05,400
+combination من اللي هنا إن حدث ذلك يبقى بالضرورة ال
+
+223
+00:25:05,400 --> 00:25:10,160
+vector space ده هو ال subspace من المجموعة الثانية
+
+224
+00:25:10,160 --> 00:25:14,860
+العملية العكسية لو جيت كل vector هنا هو linear
+
+225
+00:25:14,860 --> 00:25:18,740
+combination من اللي هنا و كل vector هناك هو linear
+
+226
+00:25:18,740 --> 00:25:23,340
+combination من اللي هنا معناته الاثنين are equal
+
+227
+00:25:23,340 --> 00:25:29,220
+يبقى الاثنين ينطبقان على بعضهما تماما الانطلاق واضح
+
+228
+00:25:29,220 --> 00:25:34,720
+طيب بدنا نروح نثبت صحة هذا الكلام مشان نثبت صحة
+
+229
+00:25:34,720 --> 00:25:40,210
+هذا الكلام بقول لو كان كل U هو linear combination
+
+230
+00:25:40,210 --> 00:25:47,670
+يبقى U هو subspace من V تمام subspace احنا
+
+231
+00:25:47,670 --> 00:25:53,880
+بجينا نروح نثبت الثلاث شروط الـ zero و constant فيه
+
+232
+00:25:53,880 --> 00:26:00,280
+vector في نفس ال subset هذا و حاصل جمع two
+
+233
+00:26:00,280 --> 00:26:04,200
+vectors من ال set هذه بيكون موجود إن كان ذلك بقول
+
+234
+00:26:04,200 --> 00:26:09,380
+subspace صح؟ لكن بعد ذلك تطوّرنا شوية و أخذنا نظرية
+
+235
+00:26:09,380 --> 00:26:14,110
+بتقول لو كان الـ vector اللي عندنا أو ال subset
+
+236
+00:26:14,110 --> 00:26:17,990
+هذه اللي أخذنا كل vector فيها على صيغة linear
+
+237
+00:26:17,990 --> 00:26:22,990
+combination يبقى ال set اللي تولد بالمجموعة ال
+
+238
+00:26:22,990 --> 00:26:26,330
+vectors اللي عندنا span هذه الـ vectors بتبقى ال
+
+239
+00:26:26,330 --> 00:26:31,730
+subspace صحيح ولا لأ؟ طيب يبقى احنا بدنا نيجي ناخد
+
+240
+00:26:31,730 --> 00:26:38,570
+بدي أفترض ال X مثلا هو أي واحد من هدول يبقى هنا
+
+241
+00:26:38,570 --> 00:26:49,210
+let الـ X بـ any vector
+
+242
+00:26:49,210 --> 00:27:01,890
+of المجموعة U<sub>1</sub> و U<sub>2</sub> و لغاية U<sub>r</sub> بدي أفترض أن ال X هو
+
+243
+00:27:01,890 --> 00:27:08,830
+أي واحد من هدول طب ايش بيقول ليه؟ إذا كان ال U هو
+
+244
+00:27:08,830 --> 00:27:13,290
+linear combination من الـ V يبقى معناته ال X هي
+
+245
+00:27:13,290 --> 00:27:20,290
+linear combination من من؟ من الـ V's يبقى هنا سا ال
+
+246
+00:27:20,290 --> 00:27:26,470
+X is a linear combination
+
+247
+00:27:28,840 --> 00:27:41,240
+of الـ V's that is أي أن ال X هنا بقدر اكتبه A<sub>1</sub> V<sub>1</sub>
+
+248
+00:27:41,240 --> 00:27:47,000
+زي A<sub>2</sub> V<sub>2</sub> زي A<sub>s</sub> V<sub>s</sub>
+
+249
+00:27:54,330 --> 00:27:59,930
+الـ X أخذته واحد معين و الله أي واحد من المجموعة
+
+250
+00:27:59,930 --> 00:28:04,730
+هذه يعني هذا الكلام اللي أنا بقوله ينطبق على أي
+
+251
+00:28:04,730 --> 00:28:10,910
+vector من ال U<sub>1</sub> لغاية ال U<sub>r</sub> بمعنى آخر كل vector من
+
+252
+00:28:10,910 --> 00:28:15,970
+الـ U هات هدول هو عبارة عن linear combination من ال
+
+253
+00:28:15,970 --> 00:28:21,710
+V هات من V<sub>1</sub> V<sub>2</sub> لغاية V<sub>s</sub> صحيح ولا لأ؟ معناته أن هذا
+
+254
+00:28:21,710 --> 00:28:27,490
+يولد به صحيح ولا لأ؟ يبقى هنا مدام ال X كتبته على
+
+255
+00:28:27,490 --> 00:28:34,070
+صيغة linear combination من ال V<sub>1</sub> و V<sub>2</sub> و V<sub>3</sub> هذا
+
+256
+00:28:34,070 --> 00:28:40,030
+معناه الحين احنا قلنا هذا ال subspace يولد بهذه
+
+257
+00:28:40,030 --> 00:28:46,250
+العناصر يبقى معناته ال X وين موجودة؟ وين موجودة؟
+
+258
+00:28:46,250 --> 00:28:52,070
+في ال V صحيح ولا لأ؟ يبقى هذا معناه أن ال X هذا
+
+259
+00:28:52,070 --> 00:29:02,920
+موجودة في ال V هذا معناه أن ال U هو subset من V
+
+260
+00:29:02,920 --> 00:29:06,800
+خلصت؟
+
+261
+00:29:06,800 --> 00:29:13,820
+لا ما خلصت ما خلصت ايش؟ جالي جالي و اثبت أن الـ U
+
+262
+00:29:13,820 --> 00:29:18,880
+subspace وليس ال subset مظبوط؟ هو جالي اثبت أنه
+
+263
+00:29:18,880 --> 00:29:22,560
+subspace مش أنا حتى لا أثبت أنها subset يبقى باقي 
+
+264
+00:29:22,560 --> 00:29:29,930
+أثبت أنها subspace مظبوط؟ بقول والله كويس الآن كل
+
+265
+00:29:29,930 --> 00:29:37,650
+element في U هو linear combination من الـ V يعني
+
+266
+00:29:37,650 --> 00:29:43,550
+الـ U بده يساوي span تبع V<sub>1</sub> و V<sub>2</sub> و لغاية V<sub>s</sub> يبقى
+
+267
+00:29:43,550 --> 00:29:55,690
+هذا معناه أن every element of
+
+268
+00:29:56,610 --> 00:30:13,350
+U is an element of V هذا معناه subset ولكن لـ
+
+269
+00:30:13,350 --> 00:30:27,840
+span of V<sub>1</sub> و V<sub>2</sub> و V<sub>s</sub> و V<sub>s</sub> بده يساوي الـ U لأن كل
+
+270
+00:30:27,840 --> 00:30:30,320
+element من U باقي بقى على صيغة linear combination
+
+271
+00:30:30,320 --> 00:30:40,560
+من V هذا معناه أن ال U is a subspace of V
+
+272
+00:30:44,320 --> 00:30:48,880
+أخذنا نظرية طبعا سابقا قلنا span تبع مجموعة في ال
+
+273
+00:30:48,880 --> 00:30:54,320
+vectors هو subspace مظبوط ولا لا؟ هنا أثبتنا أن كل
+
+274
+00:30:54,320 --> 00:31:02,550
+element في U هو موجود في V بقال U subset من V الآن
+
+275
+00:31:02,550 --> 00:31:06,570
+كل element في U بقدر اكتبه على صيغة linear
+
+276
+00:31:06,570 --> 00:31:12,330
+combination من من؟ من الـ V يبقى ال U بده يساوي ال
+
+277
+00:31:12,330 --> 00:31:17,470
+span تبع الـ V هات هدول، مظبوط ولا لأ؟ طيب ليه span
+
+278
+00:31:17,470 --> 00:31:21,830
+أثبتناه سابقا من نظرية أنه عبارة عن subspace؟ يبقى
+
+279
+00:31:21,830 --> 00:31:26,450
+بالتالي صار ال U هو ال subspace من V وهو المطلوب
+
+280
+00:31:26,450 --> 00:31:37,350
+الأول الآن نأتي للمطلوب الثاني المطلوب الثاني بقول
+
+281
+00:31:37,350 --> 00:31:42,800
+لو كان كل U هي linear combination من V اللي هو main
+
+282
+00:31:42,800 --> 00:31:48,180
+اللي عندنا يبقى U subspace من V وكان في نفس الوقت
+
+283
+00:31:48,180 --> 00:31:53,780
+كل V هو linear combination من اللي هو U يبقى هذا
+
+284
+00:31:53,780 --> 00:31:58,280
+مجموعة يبقى صار ال U subset من V و ال V subset من
+
+285
+00:31:58,280 --> 00:32:01,860
+U حسب خواص المجموعة يبقى ال U بده يساوي V وهو
+
+286
+00:32:01,860 --> 00:32:13,080
+المطلوب مظبوط يبقى باجي بقول هنا from part I أن الـ
+
+287
+00:32:13,080 --> 00:32:17,920
+U هو subset من V Similarly
+
+288
+00:32:19,970 --> 00:32:28,690
+بنفس الطريقة ال V هو subset من من؟ من ال U لأن
+
+289
+00:32:28,690 --> 00:32:35,590
+النص هذا هو النص اللي فوق وهذا نفس النص بس قلبنا
+
+290
+00:32:35,590 --> 00:32:42,850
+يبقى هذا يؤدي إلى نفس النتيجة يبقى هكذا ال U
+
+291
+00:32:42,850 --> 00:32:47,830
+بده يساوي مين؟ بده يساوي V وأنت هنا من المثل
+
+292
+00:32:49,650 --> 00:32:55,190
+يبقى يا بنات إذا عندي مجموعتين أثبت أن الأولى كل
+
+293
+00:32:55,190 --> 00:32:59,550
+عنصر هنا هو linear combination من جميع العناصر
+
+294
+00:32:59,550 --> 00:33:03,530
+اللي هنا وعكس أثبت أن كل عنصر هنا هو linear
+
+295
+00:33:03,530 --> 00:33:07,170
+combination من جميع العناصر اللي هنا يبقى ال two
+
+296
+00:33:07,170 --> 00:33:12,270
+sets are equal أو ال two subspaces are equal الاثنين
+
+297
+00:33:12,270 --> 00:33:17,190
+نفس الشيء بالضبط تماما نأخذ مثال عملي توضيحي على
+
+298
+00:33:17,190 --> 00:33:18,450
+ذلك example
+
+299
+00:33:27,310 --> 00:33:40,110
+بقول لـ let U be the subspace of
+
+300
+00:33:40,110 --> 00:33:47,650
+R<sup>3</sup> spanned by
+
+301
+00:33:49,100 --> 00:33:53,940
+يبقى هذا الـ subspace ولد بالعناصر U<sub>1</sub> يساوي
+
+302
+00:33:53,940 --> 00:34:07,720
+(1, 2, 3) and U<sub>2</sub> يساوي (2, 4, 2)
+
+303
+00:34:07,720 --> 00:34:18,550
+و U<sub>3</sub> يساوي (-1, 0, 2) الـ V 
+
+304
+00:34:18,550 --> 00:34:33,650
+Be the subspace Be the subspace Of R<sup>3</sup> Of R<sup>3</sup>
+
+305
+00:34:33,650 --> 00:34:40,070
+Spanned by Spanned by
+
+306
+00:34:40,070 --> 00:34:51,580
+V<sub>1</sub> بده يساوي (1, 2, 3) و V<sub>2</sub> بده يساوي (2, 4, 6)
+
+307
+00:34:51,580 --> 00:35:04,960
+المطلوب الأول بيقول is اللي هو ال V ال
+
+308
+00:35:04,960 --> 00:35:13,800
+subspace of U أم لا؟ ده السؤال الأول السؤال
+
+309
+00:35:13,800 --> 00:35:14,480
+الثاني
+
+310
+00:35:19,280 --> 00:35:29,920
+المطلوب الثاني بيقول are ال U و ال V the same
+
+311
+00:35:29,920 --> 00:35:33,840
+هذا
+
+312
+00:35:33,840 --> 00:35:35,780
+المطلوب الثاني
+
+313
+00:35:48,680 --> 00:35:53,940
+نرجع لسؤالنا مرة ثانية بقول افترض عندي ال sub
+
+314
+00:35:53,940 --> 00:36:01,680
+space U من R<sup>3</sup> ولد بالـ vectors U<sub>1</sub> و U<sub>2</sub> و افترض عندي 
+
+315
+00:36:01,680 --> 00:36:07,560
+sub space ثاني V ولد بالعناصر V<sub>1</sub> و V<sub>2</sub> بالشكل اللي 
+
+316
+00:36:07,560 --> 00:36:13,590
+عندنا بسأل هل ال V subspace من U ولا لأ؟ هل ال V
+
+317
+00:36:13,590 --> 00:36:18,470
+هو subspace منه ولا لأ؟ بنقول والله تمام إذا كان
+
+318
+00:36:18,470 --> 00:36:23,190
+كل عنصر من الـ vectors الأول كتبناه على صيغة linear
+
+319
+00:36:23,190 --> 00:36:27,370
+combination من الـ vectors الثاني بكون خلصنا من
+
+320
+00:36:27,370 --> 00:36:32,990
+الموضوع صحيح ولا لأ؟ يعني أنا عندي هذا solution
+
+321
+00:36:35,890 --> 00:36:41,510
+هو بدي أبدأ بالنقطة الأولى احنا عندنا يا بنات ال U
+
+322
+00:36:41,510 --> 00:36:53,930
+تساوي span تبع مين U<sub>1</sub> و U<sub>2</sub> and ال V اللي 
+
+323
+00:36:53,930 --> 00:36:58,710
+هو بده يساوي span تبع ال V<sub>1</sub> و V<sub>2</sub>
+
+324
+00:37:02,700 --> 00:37:08,860
+بسأل هل ال V subset من كأنه جلب نص النظرية؟ جلب ما
+
+325
+00:37:08,860 --> 00:37:14,080
+جلب مش مشكلة عندنا يبقى أنا ههه لو قدرت أثبت له
+
+326
+00:37:14,080 --> 00:37:18,640
+أنه كل element هنا هو linear combination من
+
+327
+00:37:18,640 --> 00:37:23,440
+الاثنين هدول بصير V subset من من؟ subset من صحيح
+
+328
+00:37:23,440 --> 00:37:28,280
+ولا لأ؟ يبقى باجي بقوله لو جيت أخذت العنصر الأول
+
+329
+00:37:28,280 --> 00:37:33,760
+بدي آجي آخذ V<sub>1</sub> في V<sub>1</sub> عند مين يا بنات اللي هو
+
+330
+00:37:33,760 --> 00:37:40,680
+(1, 2, 3) السؤال هو هل بقدر أكتبه على صيغة
+
+331
+00:37:40,680 --> 00:37:45,340
+linear combination من الاثنين هدول أم لا هذا
+
+332
+00:37:45,340 --> 00:37:51,540
+السؤال بنجيب و بنقول بنقدر يعني بقدر أكتب هذا
+
+333
+00:37:51,540 --> 00:37:58,990
+constant هنا زائد constant هنا 1 و 0 ممتاز جدا يبقى
+
+334
+00:37:58,990 --> 00:38:08,270
+بقدر أقول هذا 1 × (1, 2, 3) زائد 0 × (2, -1, 0) 
+
+335
+00:38:08,270 --> 00:38:17,930
+يعني هذا كأن 1 × U<sub>1</sub> زائد 0 × U<sub>2</sub> يبقى 
+
+336
+00:38:17,930 --> 00:38:24,440
+V<sub>1</sub> هو linear combination من مين؟ من U<sub>1</sub> و U<sub>2</sub> صحيح
+
+337
+00:38:24,440 --> 00:38:31,960
+ولا لا يبقى بنفس الطريقة لو جيت لل V<sub>2</sub> ال V<sub>2</sub> اللي
+
+338
+00:38:31,960 --> 00:38:38,060
+هو عبارة عن (2, 4, 6) بدي أشوف هل بقدر أكتب
+
+339
+00:38:38,060 --> 00:38:43,600
+هذا على صيغة linear combination من ال U<sub>1</sub> و U<sub>2</sub> أم
+
+340
+00:38:43,600 --> 00:38:48,580
+لا قول تمام في هنا 2 عامل مشترك أظن يا بنات
+
+341
+00:38:52,830 --> 00:38:57,950
+الذي بقدر أو أكتبه عليه الشكل التالي 2 × (1, 2, 3) 
+
+342
+00:38:57,950 --> 00:39:04,850
+زائد 0 × (2, -1, 0) مظبوط
+
+343
+00:39:04,850 --> 00:39:10,070
+يبقى معناته أن الـ V<sub>1</sub> و الـ V<sub>2</sub> كتبته على صيغة
+
+344
+00:39:10,070 --> 00:39:15,710
+linear combination من من من الآخرين يبقى بناء عليه
+
+345
+00:39:15,710 --> 00:39:21,970
+الـ V هو subspace منه تبقى للنقطة الأولى من من من
+
+346
+00:39:21,970 --> 00:39:26,130
+نص النظرية جليلا كينيديو هو linear combination من 
+
+347
+00:39:26,130 --> 00:39:38,610
+هذا يبقى باجي يقول له so V<sub>1</sub> and V<sub>2</sub> is a linear
+
+348
+00:39:38,610 --> 00:39:45,870
+combination of
+
+349
+00:39:45,870 --> 00:40:01,270
+U<sub>1</sub> and U<sub>2</sub> يبقى بناء عليه by the above theorem part
+
+350
+00:40:01,270 --> 00:40:13,030
+I اللي هو النقطة الأولى الـ V is a subspace of U
+
+351
+00:40:13,030 --> 00:40:20,750
+وهو المطلوب خلصنا المطلوب الأول بدنا نروح للمطلوب
+
+352
+00:40:20,750 --> 00:40:25,830
+الثاني المطلوب الثاني بيقول لي هل ال U و ال V هدول
+
+353
+00:40:25,830 --> 00:40:30,690
+بيساووا بعض أم لا يعني هل الـ vectors U هو نفس ال
+
+354
+00:40:30,690 --> 00:40:35,050
+vectors V ولا لأ؟ يعني اللي أثبتته هنا بنات أنه مين
+
+355
+00:40:35,050 --> 00:40:40,970
+أن ال V هو sub space من U يعني V subset من U يبقى
+
+356
+00:40:40,970 --> 00:40:45,850
+هذا معناه أن
+
+357
+00:40:45,850 --> 00:40:48,550
+ال V subset من U
+
+358
+00:40:51,600 --> 00:41:00,420
+لو قدرت أثبت أن الـ U subset من V بتتم المطلوب،
+
+359
+00:41:00,420 --> 00:41:08,960
+يعني إذا قدرت أثبت أن أي vector في U هو linear
+
+360
+00:41:08,960 --> 00:41:14,830
+combination من الاثنين هؤلاء بتتم المطلوب أظن الأولاني
+
+361
+00:41:14,830 --> 00:41:19,150
+بسيط ما فيش فيه مشكلة المشكلة في الثاني طيب تعالي
+
+362
+00:41:19,150 --> 00:41:27,310
+مشان هيك باجي بقول له let مثلا a<sub>1</sub> و a<sub>2</sub> موجودة في
+
+363
+00:41:27,310 --> 00:41:33,270
+set of real numbers such that اللي هو من؟ اللي هو
+
+364
+00:41:33,270 --> 00:41:41,460
+(2, -1, 0) بده يساوي a<sub>1</sub> × (1, 2, 3) + a<sub>2</sub> × (2, 4, 6)
+
+365
+00:41:41,460 --> 00:41:54,540
+a<sub>1</sub> × V<sub>1</sub> زائد a<sub>2</sub> × V<sub>2</sub> ثم بدي آخذ a<sub>1</sub> × V<sub>1</sub> زائد
+
+366
+00:41:54,540 --> 00:42:00,580
+a<sub>2</sub> × V<sub>2</sub> بده يساوي بدي أدخل على طول الخط وين V<sub>1</sub> و V<sub>2</sub>
+
+367
+00:42:00,580 --> 00:42:14,540
+هاي هم هناك يبقى ايش بده يصير يبقى a<sub>1</sub> , 2a<sub>1</sub> , 3a<sub>1</sub> + 2a<sub>2</sub>, 4a<sub>2</sub>
+
+368
+00:42:14,540 --> 00:42:21,680
+, 6a<sub>2</sub>
+
+369
+00:42:23,480 --> 00:42:30,400
+كل هذا الكلام سيكون (2, -1, 0)
+
+370
+00:42:30,400 --> 00:42:37,420
+تعالوا نجمع يبقى يصير عندي هنا a<sub>1</sub> + 2a<sub>2</sub>
+
+371
+00:42:37,420 --> 00:42:48,
+
+401
+00:45:26,590 --> 00:45:35,730
+V1 و V2 هذا الـ vector موجود في الـ U يبقى هنا
+
+402
+00:45:35,730 --> 00:45:46,190
+Therefore, ولهذا الـ U ليس مجموعة من V هذا معناه 
+
+403
+00:45:46,190 --> 00:45:50,890
+أن الـ U لا يمكن أن تساوي الـ V
+
+404
+00:45:55,920 --> 00:45:59,400
+في مبادئ الرياضيات البنات مشان أثبت أن الـ two sets
+
+405
+00:45:59,400 --> 00:46:03,500
+are equal بداية أثبت أن أي element في ال set
+
+406
+00:46:03,500 --> 00:46:07,080
+الأولى هو موجود في ال set الثانية والعكس أن أي
+
+407
+00:46:07,080 --> 00:46:10,040
+element في ال set الثانية هو موجود في ال set
+
+408
+00:46:10,040 --> 00:46:15,020
+الأولى إن حدث ذلك بيحدث التساوي لم يحدث ولو عنصر 
+
+409
+00:46:15,020 --> 00:46:19,840
+واحد يبقى  معناته ما عنديش تساوي في هذه الحالة وهذا ما
+
+410
+00:46:19,840 --> 00:46:22,980
+أثبتناه هنا أخدنا vector و أثبتنا إنه هذا ال
+
+411
+00:46:22,980 --> 00:46:27,360
+vector غير موجود يبقى معناته هدول ما لهم غير 
+
+412
+00:46:27,360 --> 00:46:33,260
+متساوين بنجي لآخر حاجة في هذا ال section وهي
+
+413
+00:46:33,260 --> 00:46:39,860
+exercises تلاتة اتنين المسائل واحد واتنين وتلاتة
+
+414
+00:46:39,860 --> 00:46:44,880
+وخمسة وستة وسبعة وتسعة
+
+415
+00:46:47,390 --> 00:46:54,850
+وتلتاشر واربعتاشر بدنا ياكى تتدربى عليهم حد فيكوا
+
+416
+00:46:54,850 --> 00:46:59,910
+لايه تساول هنا المرة القادمة إن شاء الله يوم السبت
+
+417
+00:46:59,910 --> 00:47:06,310
+بنضلنا طيبين وبصحة جيدة والجامعة كانت فاتحة طبعا
+
+418
+00:47:06,310 --> 00:47:10,650
+بنيجي ونبدأ ال section اللى بعده وهو تلاتة تلاتة
+
+419
+00:47:11,320 --> 00:47:14,620
+الثلاثة ثلاثة إرادة مرّيلي عليه جيب النتيجة وهو
+
+420
+00:47:14,620 --> 00:47:19,600
+Linear Dependence و Linear Independent Vector
+
+421
+00:47:19,600 --> 00:47:26,160
+المتجهات المستقلة والمعتمدة على بعضها خطيا 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..54fa961ca890ca2485e1bb3a7b1bf19e12f1a4de
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3679, "start": 19.59, "end": 36.79, "text": "بسم الله الرحمن الرحيم اللي هانكم اللي مابتدأنا بيه في المرة الماضية كنا متحدث في المرة الماضية عن ال subspaces الفضاءات الجزئية لفضاء اتجاهي و أخدنا أمثلة كثيرة جدا و بعدين أخدنا نظرية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 13672, 1829, 8032, 7649, 24793, 13672, 1829, 3714, 16758, 2655, 3215, 10721, 8315, 4724, 1829, 3224, 8978, 9673, 25720, 9673, 46958, 10632, 9122, 8315, 44650, 24401, 12984, 8978, 9673, 25720, 9673, 46958, 10632, 18871, 2423, 2090, 79, 2116, 27188, 11242, 16606, 9307, 25724, 11622, 19986, 10632, 5296, 5172, 11242, 16606, 1975, 2655, 7435, 40294, 1829, 4032, 5551, 9778, 3215, 8315, 5551, 2304, 12984, 37977, 9122, 12984, 48923, 10874, 28259, 4032, 39182, 9957, 5551, 9778, 3215, 8315, 8717, 19913, 2288, 10632], "avg_logprob": -0.15486111839612324, "compression_ratio": 1.8908045977011494, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 19.59, "end": 19.87, "word": "بسم", "probability": 0.893310546875}, {"start": 19.87, "end": 20.07, "word": " الله", "probability": 0.96240234375}, {"start": 20.07, "end": 20.49, "word": " الرحمن", "probability": 0.9622395833333334}, {"start": 20.49, "end": 21.03, "word": " الرحيم", "probability": 0.98974609375}, {"start": 21.03, "end": 21.87, "word": " اللي", "probability": 0.57470703125}, {"start": 21.87, "end": 22.33, "word": " هانكم", "probability": 0.5406901041666666}, {"start": 22.33, "end": 22.47, "word": " اللي", "probability": 0.94873046875}, {"start": 22.47, "end": 23.01, "word": " مابتدأنا", "probability": 0.8168131510416666}, {"start": 23.01, "end": 23.29, "word": " بيه", "probability": 0.7942708333333334}, {"start": 23.29, "end": 23.39, "word": " في", "probability": 0.80126953125}, {"start": 23.39, "end": 23.75, "word": " المرة", "probability": 0.989501953125}, {"start": 23.75, "end": 24.23, "word": " الماضية", "probability": 0.9939778645833334}, {"start": 24.23, "end": 24.49, "word": " كنا", "probability": 0.650634765625}, {"start": 24.49, "end": 24.97, "word": " متحدث", "probability": 0.8502604166666666}, {"start": 24.97, "end": 25.07, "word": " في", "probability": 0.50439453125}, {"start": 25.07, "end": 25.35, "word": " المرة", "probability": 0.991943359375}, {"start": 25.35, "end": 26.01, "word": " الماضية", "probability": 0.9952799479166666}, {"start": 26.01, "end": 26.65, "word": " عن", "probability": 0.9931640625}, {"start": 26.65, "end": 26.85, "word": " ال", "probability": 0.83642578125}, {"start": 26.85, "end": 27.89, "word": " subspaces", "probability": 0.755126953125}, {"start": 27.89, "end": 29.19, "word": " الفضاءات", "probability": 0.9561767578125}, {"start": 29.19, "end": 30.03, "word": " الجزئية", "probability": 0.8787841796875}, {"start": 30.03, "end": 30.71, "word": " لفضاء", "probability": 0.9537353515625}, {"start": 30.71, "end": 31.79, "word": " اتجاهي", "probability": 0.95}, {"start": 31.79, "end": 32.55, "word": " و", "probability": 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المثال افترض ان U عبارة عن subspace من R3 that is spanned by the vectors يبقى ال U هذا ولد بواسطة three vectors V1 و V2 و V3 بقول هل ال vector V2 و V1 و V5 موجود في set U ولا لأ ممتازة", "tokens": [3555, 39648, 8978, 23758, 9673, 12984, 6027, 1975, 5172, 2655, 43042, 16472, 624, 6225, 3555, 9640, 3660, 18871, 2090, 17940, 9154, 497, 18, 300, 307, 637, 5943, 538, 264, 18875, 7251, 3555, 4587, 7578, 2423, 624, 23758, 35525, 3215, 4724, 14407, 3794, 9566, 3660, 1045, 18875, 691, 16, 4032, 691, 17, 4032, 691, 18, 4724, 39648, 8032, 1211, 2423, 8062, 691, 17, 4032, 691, 16, 4032, 691, 20, 3714, 29245, 23328, 8978, 992, 624, 49429, 5296, 10721, 3714, 2304, 2655, 31377, 3660], "avg_logprob": -0.24774096313729344, "compression_ratio": 1.4473684210526316, "no_speech_prob": 0.0, "words": [{"start": 60.46, "end": 60.94, "word": "بقول", "probability": 0.489990234375}, {"start": 60.94, "end": 61.12, "word": " في", "probability": 0.6728515625}, {"start": 61.12, "end": 61.4, "word": " هذا", 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سميتها", "probability": 0.781494140625}, {"start": 99.81, "end": 100.09, "word": " U", "probability": 0.75927734375}, {"start": 100.09, "end": 100.75, "word": " مين", "probability": 0.822021484375}, {"start": 100.75, "end": 101.03, "word": " هي", "probability": 0.935546875}, {"start": 101.03, "end": 101.29, "word": " ال", "probability": 0.95166015625}, {"start": 101.29, "end": 101.93, "word": " U؟", "probability": 0.734619140625}], "temperature": 1.0}, {"id": 5, "seek": 12981, "start": 101.97, "end": 129.81, "text": "قال لي هي الـ U هي المجموعة التي ولدت بواسطة ال three vectors V1 و V2 و V3 يعني التلت عناصر دول ولدولي جميع عناصر ال U بلا ستة يعني جميع عناصر ال subspace U بسأل هل ال vector 2 و 1 و 5 موجود في ال set U أم لا بقوله والله", "tokens": [4587, 6027, 32239, 39896, 2423, 39184, 624, 39896, 9673, 7435, 2304, 2407, 27884, 38392, 35525, 3215, 2655, 4724, 14407, 3794, 9566, 3660, 2423, 1045, 18875, 691, 16, 4032, 691, 17, 4032, 691, 18, 37495, 22653, 16712, 1211, 2655, 18871, 33546, 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"word": " 5", "probability": 0.876953125}, {"start": 125.15, "end": 126.23, "word": " موجود", "probability": 0.9734700520833334}, {"start": 126.23, "end": 126.41, "word": " في", "probability": 0.9609375}, {"start": 126.41, "end": 126.61, "word": " ال", "probability": 0.74267578125}, {"start": 126.61, "end": 126.93, "word": " set", "probability": 0.765625}, {"start": 126.93, "end": 127.43, "word": " U", "probability": 0.9365234375}, {"start": 127.43, "end": 127.93, "word": " أم", "probability": 0.84033203125}, {"start": 127.93, "end": 128.37, "word": " لا", "probability": 0.779296875}, {"start": 128.37, "end": 129.27, "word": " بقوله", "probability": 0.560546875}, {"start": 129.27, "end": 129.81, "word": " والله", "probability": 0.8505859375}], "temperature": 1.0}, {"id": 6, "seek": 15888, "start": 130.2, "end": 158.88, "text": "إذا كان الـ vector 2 و 1 و 5 كدرنا نكتبه على صيغة linear combination من V1 و V2 و V3 إذا بيكون موجود في الـ U صحيح ولا لأ يبقى هنا مرة تانية بقول مشان أثبت أن ال vector 2 و 1 و 5 موجود في ال subspace U بدي أحاول أثبت أن 2 و 1 و 5 هو linear combination", "tokens": [28814, 15730, 25961, 2423, 39184, 8062, 568, 4032, 502, 4032, 1025, 9122, 3215, 2288, 8315, 8717, 4117, 2655, 3555, 3224, 15844, 20328, 1829, 17082, 3660, 8213, 6562, 9154, 691, 16, 4032, 691, 17, 4032, 691, 18, 11933, 15730, 4724, 1829, 30544, 3714, 29245, 23328, 8978, 2423, 39184, 624, 20328, 5016, 1829, 5016, 49429, 5296, 10721, 7251, 3555, 4587, 7578, 34105, 3714, 25720, 6055, 7649, 10632, 4724, 39648, 37893, 7649, 5551, 12984, 3555, 2655, 14739, 2423, 8062, 568, 4032, 502, 4032, 1025, 3714, 29245, 23328, 8978, 2423, 2090, 17940, 624, 4724, 16254, 5551, 5016, 995, 12610, 5551, 12984, 3555, 2655, 14739, 568, 4032, 502, 4032, 1025, 31439, 8213, 6562], "avg_logprob": -0.18807340051056048, "compression_ratio": 1.712962962962963, "no_speech_prob": 0.0, "words": [{"start": 130.2, "end": 130.68, "word": "إذا", "probability": 0.813232421875}, {"start": 130.68, "end": 130.94, "word": " 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U", "probability": 0.50341796875}, {"start": 142.08, "end": 142.64, "word": " صحيح", "probability": 0.85870361328125}, {"start": 142.64, "end": 142.8, "word": " ولا", "probability": 0.91259765625}, {"start": 142.8, "end": 143.14, "word": " لأ", "probability": 0.73046875}, {"start": 143.14, "end": 144.06, "word": " يبقى", "probability": 0.8472900390625}, {"start": 144.06, "end": 144.34, "word": " هنا", "probability": 0.91650390625}, {"start": 144.34, "end": 144.68, "word": " مرة", "probability": 0.967041015625}, {"start": 144.68, "end": 145.02, "word": " تانية", "probability": 0.9871419270833334}, {"start": 145.02, "end": 145.6, "word": " بقول", "probability": 0.9599609375}, {"start": 145.6, "end": 146.4, "word": " مشان", "probability": 0.633056640625}, {"start": 146.4, "end": 147.12, "word": " أثبت", "probability": 0.98828125}, {"start": 147.12, "end": 147.52, "word": " أن", "probability": 0.4658203125}, {"start": 147.52, "end": 147.74, "word": " ال", "probability": 0.880859375}, {"start": 147.74, "end": 148.12, "word": " vector", "probability": 0.81298828125}, {"start": 148.12, "end": 148.52, "word": " 2", "probability": 0.95849609375}, {"start": 148.52, "end": 148.76, "word": " و", "probability": 0.98193359375}, {"start": 148.76, "end": 149.0, "word": " 1", "probability": 0.89111328125}, {"start": 149.0, "end": 149.18, "word": " و", "probability": 0.99560546875}, {"start": 149.18, "end": 149.54, "word": " 5", "probability": 0.93701171875}, {"start": 149.54, "end": 150.52, "word": " موجود", "probability": 0.98583984375}, {"start": 150.52, "end": 150.98, "word": " في", "probability": 0.9716796875}, {"start": 150.98, "end": 151.2, "word": " ال", "probability": 0.8505859375}, {"start": 151.2, "end": 152.04, "word": " subspace", "probability": 0.692138671875}, {"start": 152.04, "end": 152.52, "word": " U", "probability": 0.95654296875}, {"start": 152.52, "end": 153.36, "word": " بدي", "probability": 0.831787109375}, {"start": 153.36, "end": 153.9, "word": " أحاول", "probability": 0.9775390625}, {"start": 153.9, "end": 154.6, "word": " أثبت", "probability": 0.9888916015625}, {"start": 154.6, "end": 155.02, "word": " أن", "probability": 0.80517578125}, {"start": 155.02, "end": 155.96, "word": " 2", "probability": 0.6611328125}, {"start": 155.96, "end": 156.14, "word": " و", "probability": 0.98388671875}, {"start": 156.14, "end": 156.42, "word": " 1", "probability": 0.91552734375}, {"start": 156.42, "end": 156.64, "word": " و", "probability": 0.99462890625}, {"start": 156.64, "end": 157.06, "word": " 5", "probability": 0.94580078125}, {"start": 157.06, "end": 157.5, "word": " هو", "probability": 0.63916015625}, {"start": 157.5, "end": 157.96, "word": " linear", "probability": 0.9501953125}, {"start": 157.96, "end": 158.88, "word": " combination", "probability": 0.9599609375}], "temperature": 1.0}, {"id": 7, "seek": 17665, "start": 159.33, "end": 176.65, "text": "من V1 و V2 و V3 إن تحقق ذلك يبقى هذا العنصر موجود فيه إن لم يتحقق ذلك يبقى هذا العنصر غير موجود في ال sub space U على الإطلاق واضح الشي اللي بدنا نعمله؟", "tokens": [27842, 691, 16, 4032, 691, 17, 4032, 691, 18, 36145, 6055, 5016, 4587, 4587, 29910, 23275, 7251, 3555, 4587, 7578, 23758, 18863, 1863, 9381, 2288, 3714, 29245, 23328, 8978, 3224, 36145, 32767, 7251, 2655, 5016, 4587, 4587, 29910, 23275, 7251, 3555, 4587, 7578, 23758, 18863, 1863, 9381, 2288, 32771, 13546, 3714, 29245, 23328, 8978, 2423, 1422, 1901, 624, 15844, 33688, 9566, 15040, 4587, 4032, 46958, 5016, 25124, 1829, 13672, 1829, 47525, 8315, 8717, 25957, 43761, 22807], "avg_logprob": -0.16822240801600666, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 159.33, "end": 159.67, "word": "من", "probability": 0.373291015625}, {"start": 159.67, "end": 160.29, "word": " V1", "probability": 0.793212890625}, {"start": 160.29, "end": 160.49, "word": " و", "probability": 0.927734375}, {"start": 160.49, "end": 161.19, "word": " V2", "probability": 0.866943359375}, {"start": 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"word": " يتحقق", "probability": 0.994140625}, {"start": 168.47, "end": 168.95, "word": " ذلك", "probability": 0.986083984375}, {"start": 168.95, "end": 169.55, "word": " يبقى", "probability": 0.9427490234375}, {"start": 169.55, "end": 169.75, "word": " هذا", "probability": 0.96923828125}, {"start": 169.75, "end": 170.25, "word": " العنصر", "probability": 0.996337890625}, {"start": 170.25, "end": 170.67, "word": " غير", "probability": 0.987060546875}, {"start": 170.67, "end": 171.37, "word": " موجود", "probability": 0.9910481770833334}, {"start": 171.37, "end": 171.85, "word": " في", "probability": 0.978515625}, {"start": 171.85, "end": 172.11, "word": " ال", "probability": 0.65478515625}, {"start": 172.11, "end": 172.31, "word": " sub", "probability": 0.2418212890625}, {"start": 172.31, "end": 172.99, "word": " space", "probability": 0.51611328125}, {"start": 172.99, "end": 173.39, "word": " U", "probability": 0.810546875}, {"start": 173.39, "end": 174.09, "word": " على", 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"word": " واحد", "probability": 0.927490234375}, {"start": 621.62, "end": 621.62, "word": " واحد", "probability": 0.926513671875}, {"start": 621.62, "end": 621.64, "word": " واحد", "probability": 0.92529296875}, {"start": 621.64, "end": 621.64, "word": " واحد", "probability": 0.92236328125}, {"start": 621.64, "end": 621.64, "word": " واحد", "probability": 0.9208984375}, {"start": 621.64, "end": 621.64, "word": " واحد", "probability": 0.91796875}, {"start": 621.64, "end": 621.64, "word": " واحد", "probability": 0.914306640625}, {"start": 621.64, "end": 628.38, "word": " واحد", "probability": 0.907470703125}, {"start": 628.38, "end": 628.56, "word": " واحد", "probability": 0.909423828125}, {"start": 628.56, "end": 629.7, "word": " وا", "probability": 0.84423828125}], "temperature": 1.0}, {"id": 27, "seek": 65072, "start": 629.96, "end": 650.72, "text": "V1 وV2 وV3 يبقى هنا ساعة الواتنين وواحد وخمسة موجود في ال subspace U انتهينا من المسألة طيب يمكن واحدة تقول", "tokens": [53, 16, 4032, 53, 17, 4032, 53, 18, 7251, 3555, 4587, 7578, 34105, 8608, 995, 27884, 2423, 14407, 2655, 1863, 9957, 4032, 14407, 24401, 4032, 9778, 2304, 3794, 3660, 3714, 29245, 23328, 8978, 2423, 2090, 17940, 624, 16472, 47395, 1829, 8315, 9154, 9673, 3794, 10721, 37977, 23032, 1829, 3555, 7251, 43020, 36764, 24401, 3660, 6055, 39648], "avg_logprob": -0.25315241646348385, "compression_ratio": 1.3065693430656935, "no_speech_prob": 0.0, "words": [{"start": 629.96, "end": 631.08, "word": "V1", "probability": 0.562744140625}, {"start": 631.08, "end": 632.86, "word": " وV2", "probability": 0.7122395833333334}, {"start": 632.86, "end": 634.56, "word": " وV3", "probability": 0.9617513020833334}, {"start": 634.56, "end": 635.88, "word": " يبقى", "probability": 0.9163818359375}, {"start": 635.88, "end": 636.26, "word": " هنا", "probability": 0.88525390625}, {"start": 636.26, "end": 637.16, "word": " ساعة", "probability": 0.6075032552083334}, {"start": 637.16, "end": 638.44, "word": " الواتنين", "probability": 0.537255859375}, {"start": 638.44, "end": 639.4, "word": " وواحد", "probability": 0.9158528645833334}, {"start": 639.4, "end": 641.08, "word": " وخمسة", "probability": 0.96572265625}, {"start": 641.08, "end": 642.12, "word": " موجود", "probability": 0.9698893229166666}, {"start": 642.12, "end": 642.92, "word": " في", "probability": 0.89794921875}, {"start": 642.92, "end": 643.28, "word": " ال", "probability": 0.728515625}, {"start": 643.28, "end": 643.78, "word": " subspace", "probability": 0.5955810546875}, {"start": 643.78, "end": 644.32, "word": " U", "probability": 0.70458984375}, {"start": 644.32, "end": 644.98, "word": " انتهينا", "probability": 0.7470703125}, {"start": 644.98, "end": 645.32, "word": " من", "probability": 0.97119140625}, {"start": 645.32, "end": 646.36, "word": " المسألة", "probability": 0.9266357421875}, {"start": 646.36, "end": 649.68, "word": " طيب", "probability": 0.92578125}, {"start": 649.68, "end": 649.94, "word": " يمكن", "probability": 0.902099609375}, {"start": 649.94, "end": 650.34, "word": " واحدة", "probability": 0.9143880208333334}, {"start": 650.34, "end": 650.72, "word": " تقول", "probability": 0.994384765625}], "temperature": 1.0}, {"id": 28, "seek": 67607, "start": 651.51, "end": 676.07, "text": "طب انا كل سؤال زي هيك لمساني هل ال vector موجود هنا بسوي نفس الطريقة ماشي الأن طلعت قيم ل C1 و C2 و C3 كيف بدهش يطلع قيم يعني كيف بدهش يكون هذا مش موجود فبنقولك مشان بيبينك الشغل هذه إليك المثال الرابع يبقى example four", "tokens": [9566, 3555, 1975, 8315, 28242, 8608, 33604, 6027, 30767, 1829, 39896, 4117, 32767, 3794, 7649, 1829, 8032, 1211, 2423, 8062, 3714, 29245, 23328, 34105, 4724, 3794, 45865, 8717, 36178, 41950, 16572, 28671, 3714, 33599, 1829, 16247, 1863, 23032, 1211, 34268, 12174, 32640, 5296, 383, 16, 4032, 383, 17, 4032, 383, 18, 9122, 33911, 47525, 3224, 8592, 7251, 9566, 1211, 3615, 12174, 32640, 37495, 22653, 9122, 33911, 47525, 3224, 8592, 7251, 30544, 23758, 37893, 3714, 29245, 23328, 6156, 3555, 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example", "probability": 0.93408203125}, {"start": 675.37, "end": 676.07, "word": " four", "probability": 0.396484375}], "temperature": 1.0}, {"id": 29, "seek": 71276, "start": 684.74, "end": 712.76, "text": "بقول الات ال V واحد بده يساوي واحد و اتنين و سالب واحد وال V اتنين بده يساوي ستة اربعة اتنين كل هذا موجود في اعلى ثلاثة show that the vector show that that", "tokens": [3555, 39648, 2423, 9307, 2423, 691, 36764, 24401, 47525, 3224, 7251, 3794, 995, 45865, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 4032, 8608, 6027, 3555, 36764, 24401, 16070, 691, 1975, 2655, 1863, 9957, 47525, 3224, 7251, 3794, 995, 45865, 8608, 2655, 3660, 1975, 25513, 27884, 1975, 2655, 1863, 9957, 28242, 23758, 3714, 29245, 23328, 8978, 1975, 3615, 23942, 38637, 1211, 5718, 104, 3660, 855, 300, 264, 8062, 855, 300, 300], "avg_logprob": -0.2984155063897791, "compression_ratio": 1.6734693877551021, "no_speech_prob": 0.0, "words": [{"start": 684.74, "end": 685.24, "word": "بقول", "probability": 0.512451171875}, {"start": 685.24, "end": 685.78, "word": " الات", "probability": 0.3114013671875}, {"start": 685.78, "end": 688.12, "word": " ال", "probability": 0.7265625}, {"start": 688.12, "end": 688.34, "word": " V", "probability": 0.6484375}, {"start": 688.34, "end": 688.88, "word": " واحد", "probability": 0.6331787109375}, {"start": 688.88, "end": 689.32, "word": " بده", "probability": 0.456787109375}, {"start": 689.32, "end": 689.94, "word": " يساوي", "probability": 0.8634033203125}, {"start": 689.94, "end": 691.78, "word": " واحد", "probability": 0.6376953125}, {"start": 691.78, "end": 692.0, "word": " و", "probability": 0.919921875}, {"start": 692.0, "end": 692.58, "word": " اتنين", "probability": 0.783905029296875}, {"start": 692.58, "end": 692.82, "word": " و", "probability": 0.65869140625}, {"start": 692.82, "end": 693.32, "word": " سالب", "probability": 0.8644205729166666}, {"start": 693.32, "end": 693.76, "word": " واحد", "probability": 0.977783203125}, {"start": 693.76, "end": 694.66, "word": " وال", "probability": 0.54638671875}, {"start": 694.66, "end": 694.94, "word": " V", "probability": 0.9189453125}, {"start": 694.94, "end": 695.74, "word": " اتنين", "probability": 0.8797607421875}, {"start": 695.74, "end": 696.82, "word": " بده", "probability": 0.880126953125}, {"start": 696.82, "end": 697.32, "word": " يساوي", "probability": 0.98779296875}, {"start": 697.32, "end": 698.38, "word": " ستة", "probability": 0.9210611979166666}, {"start": 698.38, "end": 699.16, "word": " اربعة", "probability": 0.83203125}, {"start": 699.16, "end": 699.94, "word": " اتنين", "probability": 0.977294921875}, {"start": 699.94, "end": 700.68, "word": " كل", "probability": 0.755859375}, {"start": 700.68, "end": 701.24, "word": " هذا", "probability": 0.8681640625}, {"start": 701.24, "end": 702.16, "word": " موجود", "probability": 0.9720052083333334}, {"start": 702.16, "end": 702.5, "word": " في", "probability": 0.951171875}, {"start": 702.5, "end": 703.1, "word": " اعلى", "probability": 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295, 691, 36764, 24401, 4032, 691, 1975, 2655, 1863, 9957], "avg_logprob": -0.39020269303708466, "compression_ratio": 1.202020202020202, "no_speech_prob": 0.0, "words": [{"start": 717.21, "end": 718.59, "word": "V", "probability": 0.18994140625}, {"start": 718.59, "end": 719.97, "word": " يساوي", "probability": 0.6982269287109375}, {"start": 719.97, "end": 721.37, "word": " أربعة", "probability": 0.7020670572916666}, {"start": 721.37, "end": 721.93, "word": " و", "probability": 0.35791015625}, {"start": 721.93, "end": 722.47, "word": " سالب", "probability": 0.8175455729166666}, {"start": 722.47, "end": 722.99, "word": " واحد", "probability": 0.959228515625}, {"start": 722.99, "end": 723.39, "word": " و", "probability": 0.61181640625}, {"start": 723.39, "end": 724.29, "word": " تمانية", "probability": 0.953125}, {"start": 724.29, "end": 725.11, "word": " does", "probability": 0.0810546875}, {"start": 725.11, "end": 725.69, "word": " not", "probability": 0.97021484375}, {"start": 725.69, "end": 726.65, "word": " belong", "probability": 0.90771484375}, {"start": 726.65, "end": 728.53, "word": " للثبين", "probability": 0.507080078125}, {"start": 728.53, "end": 729.49, "word": " of", "probability": 0.83740234375}, {"start": 729.49, "end": 730.07, "word": " V", "probability": 0.86474609375}, {"start": 730.07, "end": 730.87, "word": " واحد", "probability": 0.9384765625}, {"start": 730.87, "end": 731.25, "word": " و", "probability": 0.9482421875}, {"start": 731.25, "end": 731.47, "word": " V", "probability": 0.8583984375}, {"start": 731.47, "end": 731.83, "word": " اتنين", "probability": 0.906494140625}], "temperature": 1.0}, {"id": 31, "seek": 75144, "start": 749.86, "end": 751.44, "text": "طلّايلي في صيغة السؤالين", "tokens": [9566, 1211, 11703, 47302, 20292, 8978, 20328, 1829, 17082, 3660, 21136, 33604, 6027, 9957], "avg_logprob": -0.28020832141240437, "compression_ratio": 0.9375, "no_speech_prob": 0.0, "words": [{"start": 749.86, "end": 750.38, "word": "طلّايلي", 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يبقى إذا وصلت إلى نتيجة خاطئة معناته الفرضي صح ولا غلط غلط وعكسه صح هو الصحيح تمام يبقى تمام يبقى بدي أبدأ زي هذا بالضبط تماما يبقى بدي أقول له solution assume that", "tokens": [9566, 3555, 5296, 15042, 5551, 5172, 43042, 14739, 3224, 3714, 29245, 23328, 8032, 2407, 36520, 30731, 8717, 31371, 7435, 3660, 16490, 41193, 19986, 3660, 7251, 3555, 4587, 7578, 11933, 15730, 4032, 36520, 2655, 30731, 8717, 31371, 7435, 3660, 16490, 41193, 19986, 3660, 20449, 8315, 47395, 27188, 43042, 1829, 20328, 5016, 49429, 32771, 1211, 9566, 32771, 1211, 9566, 4032, 3615, 4117, 3794, 3224, 20328, 5016, 31439, 31767, 5016, 1829, 5016, 46811, 10943, 7251, 3555, 4587, 7578, 46811, 10943, 7251, 3555, 4587, 7578, 4724, 16254, 5551, 44510, 10721, 30767, 1829, 23758, 20666, 11242, 3555, 9566, 46811, 10943, 995, 7251, 3555, 4587, 7578, 4724, 16254, 5551, 39648, 46740, 3827, 6552, 300], "avg_logprob": -0.18764334151504236, "compression_ratio": 1.792929292929293, "no_speech_prob": 0.0, "words": [{"start": 829.62, "end": 830.0, "word": "طب", "probability": 0.7255859375}, {"start": 830.0, "end": 830.72, "word": " لما", "probability": 0.8095703125}, {"start": 830.72, "end": 831.18, "word": " أفرض", "probability": 0.8712565104166666}, {"start": 831.18, "end": 831.44, "word": " أنه", "probability": 0.6505126953125}, {"start": 831.44, "end": 832.04, "word": " موجود", "probability": 0.9842122395833334}, {"start": 832.04, "end": 833.08, "word": " هوصل", "probability": 0.86767578125}, {"start": 833.08, "end": 833.52, "word": " إلى", "probability": 0.8173828125}, {"start": 833.52, "end": 834.38, "word": " نتيجة", "probability": 0.99658203125}, {"start": 834.38, "end": 835.62, "word": " خاطئة", "probability": 0.9842529296875}, {"start": 835.62, "end": 837.02, "word": " يبقى", "probability": 0.7414703369140625}, {"start": 837.02, "end": 837.22, "word": " إذا", "probability": 0.82568359375}, {"start": 837.22, "end": 837.68, "word": " وصلت", "probability": 0.95263671875}, {"start": 837.68, "end": 837.78, "word": " إلى", "probability": 0.43408203125}, {"start": 837.78, "end": 838.2, "word": " نتيجة", "probability": 0.995361328125}, {"start": 838.2, "end": 838.66, "word": " خاطئة", "probability": 0.9910888671875}, {"start": 838.66, "end": 839.12, "word": " معناته", "probability": 0.8570963541666666}, {"start": 839.12, "end": 839.76, "word": " الفرضي", "probability": 0.7838541666666666}, {"start": 839.76, "end": 839.98, "word": " صح", "probability": 0.9892578125}, {"start": 839.98, "end": 840.22, "word": " ولا", "probability": 0.71484375}, {"start": 840.22, "end": 840.62, "word": " غلط", "probability": 0.9944661458333334}, {"start": 840.62, "end": 841.5, "word": " غلط", "probability": 0.7776692708333334}, {"start": 841.5, "end": 842.5, "word": " وعكسه", "probability": 0.87021484375}, {"start": 842.5, "end": 842.84, "word": " صح", "probability": 0.771240234375}, {"start": 842.84, "end": 843.14, "word": " هو", "probability": 0.480224609375}, {"start": 843.14, "end": 843.9, "word": " الصحيح", "probability": 0.95947265625}, {"start": 843.9, "end": 844.5, "word": " تمام", "probability": 0.65185546875}, {"start": 844.5, "end": 845.28, "word": " يبقى", "probability": 0.89404296875}, {"start": 845.28, "end": 845.58, "word": " تمام", "probability": 0.8671875}, {"start": 845.58, "end": 845.78, "word": " يبقى", "probability": 0.9385986328125}, {"start": 845.78, "end": 846.1, "word": " بدي", "probability": 0.768310546875}, {"start": 846.1, "end": 846.62, "word": " أبدأ", "probability": 0.9541015625}, {"start": 846.62, "end": 846.96, "word": " زي", "probability": 0.930419921875}, {"start": 846.96, "end": 847.28, "word": " هذا", "probability": 0.96240234375}, {"start": 847.28, "end": 847.96, "word": " بالضبط", "probability": 0.9044189453125}, {"start": 847.96, "end": 848.94, "word": " تماما", "probability": 0.9811197916666666}, {"start": 848.94, "end": 850.42, "word": " يبقى", "probability": 0.8355712890625}, {"start": 850.42, "end": 850.72, "word": " بدي", "probability": 0.446044921875}, {"start": 850.72, "end": 851.24, "word": " أقول", "probability": 0.648193359375}, {"start": 851.24, "end": 851.44, "word": " له", "probability": 0.59375}, {"start": 851.44, "end": 852.36, "word": " solution", "probability": 0.978515625}, {"start": 852.36, "end": 855.86, "word": " assume", "probability": 0.83837890625}, {"start": 855.86, "end": 856.5, "word": " that", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 37, "seek": 88295, "start": 859.95, "end": 882.95, "text": "إن الـ V بيساوي أربعة و سالب واحد و تمانية موجود في الاسبان تبع ال V واحد و V اتنين هذا معناته ان هناك C واحد و C اتنين موجودة في ال set of real numbers such that", "tokens": [28814, 1863, 2423, 39184, 691, 4724, 1829, 3794, 995, 45865, 5551, 25513, 27884, 4032, 8608, 6027, 3555, 36764, 24401, 4032, 46811, 7649, 10632, 3714, 29245, 23328, 8978, 2423, 32277, 3555, 7649, 6055, 3555, 3615, 2423, 691, 36764, 24401, 4032, 691, 1975, 2655, 1863, 9957, 23758, 20449, 8315, 47395, 16472, 34105, 4117, 383, 36764, 24401, 4032, 383, 1975, 2655, 1863, 9957, 3714, 29245, 23328, 3660, 8978, 2423, 992, 295, 957, 3547, 1270, 300], "avg_logprob": -0.30757706459254436, "compression_ratio": 1.5636363636363637, "no_speech_prob": 0.0, "words": [{"start": 859.95, "end": 860.37, "word": "إن", "probability": 0.531707763671875}, {"start": 860.37, "end": 860.73, "word": " الـ", "probability": 0.5162353515625}, {"start": 860.73, "end": 861.03, "word": " V", "probability": 0.6328125}, {"start": 861.03, "end": 862.71, "word": " بيساوي", "probability": 0.497607421875}, {"start": 862.71, "end": 863.31, "word": " أربعة", "probability": 0.7489420572916666}, {"start": 863.31, "end": 863.59, "word": " و", "probability": 0.55859375}, {"start": 863.59, "end": 864.03, "word": " سالب", "probability": 0.8151041666666666}, {"start": 864.03, "end": 864.53, "word": " واحد", "probability": 0.90576171875}, {"start": 864.53, "end": 864.73, "word": " و", "probability": 0.494384765625}, {"start": 864.73, "end": 865.57, "word": " تمانية", "probability": 0.95654296875}, {"start": 865.57, "end": 867.05, "word": " موجود", "probability": 0.9493815104166666}, {"start": 867.05, "end": 867.37, "word": " في", "probability": 0.86376953125}, {"start": 867.37, "end": 868.29, "word": " الاسبان", "probability": 0.6666259765625}, {"start": 868.29, "end": 869.09, "word": " تبع", "probability": 0.8938802083333334}, {"start": 869.09, "end": 869.31, "word": " ال", "probability": 0.92919921875}, {"start": 869.31, "end": 869.51, "word": " V", "probability": 0.82568359375}, {"start": 869.51, "end": 870.07, "word": " واحد", "probability": 0.877685546875}, {"start": 870.07, "end": 870.29, "word": " و", "probability": 0.66357421875}, {"start": 870.29, "end": 870.59, "word": " V", "probability": 0.55078125}, {"start": 870.59, "end": 871.07, "word": " اتنين", "probability": 0.9053955078125}, {"start": 871.07, "end": 872.57, "word": " هذا", "probability": 0.7783203125}, {"start": 872.57, "end": 873.45, "word": " معناته", "probability": 0.97265625}, {"start": 873.45, "end": 874.35, "word": " ان", "probability": 0.4287109375}, {"start": 874.35, "end": 875.75, "word": " هناك", "probability": 0.820556640625}, {"start": 875.75, "end": 876.57, "word": " C", "probability": 0.501953125}, {"start": 876.57, "end": 877.19, "word": " واحد", "probability": 0.94921875}, {"start": 877.19, "end": 877.57, "word": " و", "probability": 0.9501953125}, {"start": 877.57, "end": 877.85, "word": " C", "probability": 0.8037109375}, {"start": 877.85, "end": 878.77, "word": " اتنين", "probability": 0.9627685546875}, {"start": 878.77, "end": 879.67, "word": " موجودة", "probability": 0.8951416015625}, {"start": 879.67, "end": 879.81, "word": " في", "probability": 0.953125}, {"start": 879.81, "end": 879.93, "word": " ال", "probability": 0.374755859375}, {"start": 879.93, "end": 880.17, "word": " set", "probability": 0.43994140625}, {"start": 880.17, "end": 880.45, "word": " of", "probability": 0.9501953125}, {"start": 880.45, "end": 880.75, "word": " real", "probability": 0.9619140625}, {"start": 880.75, "end": 881.43, "word": " numbers", "probability": 0.82373046875}, {"start": 881.43, "end": 882.25, "word": " such", "probability": 0.84912109375}, {"start": 882.25, "end": 882.95, "word": " that", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 38, "seek": 91148, "start": 884.28, "end": 911.48, "text": "بحيث ان C1 V1 زاد C2 V2 يبقى C1 في V1 V1 يعني واحد اتنين سالب واحد C2 في ستة اربعة اتنين يبقى V4 سالب واحد و تمانية", "tokens": [3555, 5016, 1829, 12984, 16472, 383, 16, 691, 16, 30767, 18513, 383, 17, 691, 17, 7251, 3555, 4587, 7578, 383, 16, 8978, 691, 16, 691, 16, 37495, 22653, 36764, 24401, 1975, 2655, 1863, 9957, 8608, 6027, 3555, 36764, 24401, 383, 17, 8978, 8608, 2655, 3660, 1975, 25513, 27884, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 691, 19, 8608, 6027, 3555, 36764, 24401, 4032, 46811, 7649, 10632], "avg_logprob": -0.3200827122611158, "compression_ratio": 1.5163934426229508, "no_speech_prob": 0.0, "words": [{"start": 884.28, "end": 885.04, "word": "بحيث", "probability": 0.84197998046875}, {"start": 885.04, "end": 885.5, "word": " ان", "probability": 0.76708984375}, {"start": 885.5, "end": 886.84, "word": " C1", "probability": 0.5733642578125}, {"start": 886.84, "end": 887.86, "word": " V1", "probability": 0.65869140625}, {"start": 887.86, "end": 888.54, "word": " زاد", "probability": 0.4334259033203125}, {"start": 888.54, "end": 889.44, "word": " C2", "probability": 0.976806640625}, {"start": 889.44, "end": 890.34, "word": " V2", "probability": 0.96435546875}, {"start": 890.34, "end": 893.4, "word": " يبقى", "probability": 0.651885986328125}, {"start": 893.4, "end": 894.16, "word": " C1", "probability": 0.5792236328125}, {"start": 894.16, "end": 894.42, "word": " في", "probability": 0.27685546875}, {"start": 894.42, "end": 895.44, "word": " V1", "probability": 0.969482421875}, {"start": 895.44, "end": 896.56, "word": " V1", "probability": 0.89013671875}, {"start": 896.56, "end": 896.92, "word": " يعني", "probability": 0.5029830932617188}, {"start": 896.92, "end": 897.6, "word": " واحد", "probability": 0.8134765625}, {"start": 897.6, "end": 899.22, "word": " اتنين", "probability": 0.8453369140625}, {"start": 899.22, "end": 899.76, "word": " سالب", "probability": 0.9326171875}, {"start": 899.76, "end": 900.22, "word": " واحد", "probability": 0.98388671875}, {"start": 900.22, "end": 901.76, "word": " C2", "probability": 0.81201171875}, {"start": 901.76, "end": 902.66, "word": " في", "probability": 0.89794921875}, {"start": 902.66, "end": 903.88, "word": " ستة", "probability": 0.8507486979166666}, {"start": 903.88, "end": 904.9, "word": " اربعة", "probability": 0.82470703125}, {"start": 904.9, "end": 905.94, "word": " اتنين", "probability": 0.978515625}, {"start": 905.94, "end": 906.74, "word": " يبقى", "probability": 0.66497802734375}, {"start": 906.74, "end": 908.84, "word": " V4", "probability": 0.807861328125}, {"start": 908.84, "end": 910.06, "word": " سالب", "probability": 0.6706949869791666}, {"start": 910.06, "end": 910.62, "word": " واحد", "probability": 0.964111328125}, {"start": 910.62, "end": 910.96, "word": " و", "probability": 0.47705078125}, {"start": 910.96, "end": 911.48, "word": " تمانية", "probability": 0.7467447916666666}], "temperature": 1.0}, {"id": 39, "seek": 93042, "start": 913.16, "end": 930.42, "text": "حتى الآن هل اختلفت الفكرة؟ لأ يبقى بداجي افك القوس و اجمعهم اتنين مع بعض بقوس واحد او بثري تيوب الواحد يبقى بقدر اقوله هنا ما يأتي هذه c1 زائد 6 c2", "tokens": [33753, 7578, 6024, 48506, 8032, 1211, 1975, 46456, 46538, 2655, 27188, 4117, 25720, 22807, 5296, 10721, 7251, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 5172, 4117, 25062, 41779, 4032, 1975, 7435, 2304, 3615, 16095, 1975, 2655, 1863, 9957, 20449, 45030, 11242, 4724, 4587, 41779, 36764, 24401, 1975, 2407, 4724, 12984, 16572, 6055, 1829, 37746, 2423, 14407, 24401, 7251, 3555, 4587, 7578, 4724, 28543, 2288, 1975, 39648, 3224, 34105, 19446, 7251, 10721, 31371, 29538, 269, 16, 30767, 16373, 3215, 1386, 269, 17], "avg_logprob": -0.24542683017690006, "compression_ratio": 1.5828220858895705, "no_speech_prob": 0.0, "words": [{"start": 913.16, "end": 913.62, "word": "حتى", "probability": 0.73046875}, {"start": 913.62, "end": 913.82, "word": " الآن", "probability": 0.7265625}, {"start": 913.82, "end": 914.04, "word": " هل", "probability": 0.800537109375}, {"start": 914.04, "end": 914.58, "word": " اختلفت", "probability": 0.9354248046875}, {"start": 914.58, "end": 915.34, "word": " الفكرة؟", "probability": 0.8551025390625}, {"start": 915.34, "end": 916.12, "word": " لأ", "probability": 0.73583984375}, {"start": 916.12, "end": 916.8, "word": " يبقى", "probability": 0.864990234375}, {"start": 916.8, "end": 917.52, "word": " بداجي", "probability": 0.6368408203125}, {"start": 917.52, "end": 917.98, "word": " افك", "probability": 0.8780924479166666}, {"start": 917.98, "end": 918.58, 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"probability": 0.963623046875}, {"start": 924.32, "end": 924.68, "word": " بقدر", "probability": 0.92919921875}, {"start": 924.68, "end": 925.08, "word": " اقوله", "probability": 0.8138020833333334}, {"start": 925.08, "end": 925.42, "word": " هنا", "probability": 0.89453125}, {"start": 925.42, "end": 925.64, "word": " ما", "probability": 0.81298828125}, {"start": 925.64, "end": 926.2, "word": " يأتي", "probability": 0.90625}, {"start": 926.2, "end": 926.86, "word": " هذه", "probability": 0.328125}, {"start": 926.86, "end": 928.14, "word": " c1", "probability": 0.5911865234375}, {"start": 928.14, "end": 929.06, "word": " زائد", "probability": 0.7477213541666666}, {"start": 929.06, "end": 929.58, "word": " 6", "probability": 0.9384765625}, {"start": 929.58, "end": 930.42, "word": " c2", "probability": 0.718505859375}], "temperature": 1.0}, {"id": 40, "seek": 94780, "start": 931.18, "end": 947.8, "text": "أتنين C واحد زائد أربعة C اتنين اللي بعده سالب C واحد زائد اتنين C اتنين كله بده 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"probability": 0.38714599609375}, {"start": 1200.98, "end": 1206.64, "word": " Spanned", "probability": 0.91064453125}], "temperature": 1.0}, {"id": 50, "seek": 123648, "start": 1208.38, "end": 1236.48, "text": "by u1 و u2 و ur and v1 و v2 و vs respectively respectively يعني على الترتيب النقطة الأولى", "tokens": [2322, 344, 16, 4032, 344, 17, 4032, 4038, 293, 371, 16, 4032, 371, 17, 4032, 12041, 25009, 25009, 37495, 22653, 15844, 16712, 43500, 1829, 3555, 28239, 47432, 3660, 16247, 12610, 7578], "avg_logprob": -0.24682617466896772, "compression_ratio": 1.2526315789473683, "no_speech_prob": 0.0, "words": [{"start": 1208.38, "end": 1209.16, "word": "by", "probability": 0.199951171875}, {"start": 1209.16, "end": 1212.48, "word": " u1", "probability": 0.49957275390625}, {"start": 1212.48, "end": 1213.22, "word": " و", "probability": 0.8046875}, {"start": 1213.22, "end": 1214.02, "word": " u2", "probability": 0.953857421875}, {"start": 1214.02, "end": 1214.98, "word": " و", "probability": 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1234.22, "end": 1236.04, "word": " النقطة", "probability": 0.9446614583333334}, {"start": 1236.04, "end": 1236.48, "word": " الأولى", "probability": 0.9723307291666666}], "temperature": 1.0}, {"id": 51, "seek": 126415, "start": 1236.87, "end": 1264.15, "text": "من هذه النظرية بتقول if every u if every u is a linear combination is a linear combination of the the vs then", "tokens": [27842, 29538, 28239, 19913, 2288, 10632, 39894, 39648, 498, 633, 344, 498, 633, 344, 307, 257, 8213, 6562, 307, 257, 8213, 6562, 295, 264, 264, 12041, 550], "avg_logprob": -0.27092634035008295, "compression_ratio": 1.3125, "no_speech_prob": 0.0, "words": [{"start": 1236.87, "end": 1237.17, "word": "من", "probability": 0.56396484375}, {"start": 1237.17, "end": 1237.47, "word": " هذه", "probability": 0.9130859375}, {"start": 1237.47, "end": 1238.01, "word": " النظرية", "probability": 0.975341796875}, {"start": 1238.01, "end": 1238.49, "word": " بتقول", "probability": 0.6875}, {"start": 1238.49, "end": 1239.03, 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"probability": 0.91943359375}, {"start": 1256.05, "end": 1257.21, "word": " combination", "probability": 0.96533203125}, {"start": 1257.21, "end": 1257.99, "word": " of", "probability": 0.97705078125}, {"start": 1257.99, "end": 1259.83, "word": " the", "probability": 0.9052734375}, {"start": 1259.83, "end": 1260.43, "word": " the", "probability": 0.497314453125}, {"start": 1260.43, "end": 1261.81, "word": " vs", "probability": 0.525390625}, {"start": 1261.81, "end": 1264.15, "word": " then", "probability": 0.81884765625}], "temperature": 1.0}, {"id": 52, "seek": 129215, "start": 1268.07, "end": 1292.15, "text": "الـ U is a subspace of V نقطة ثانية بيقول ف every U is a linear combination", "tokens": [6027, 39184, 624, 307, 257, 2090, 17940, 295, 691, 8717, 47432, 3660, 38637, 7649, 10632, 4724, 1829, 39648, 6156, 633, 624, 307, 257, 8213, 6562], "avg_logprob": -0.314002398114938, "compression_ratio": 0.9893617021276596, "no_speech_prob": 0.0, "words": [{"start": 1268.07, "end": 1268.49, "word": "الـ", "probability": 0.6441650390625}, {"start": 1268.49, "end": 1268.85, "word": " U", "probability": 0.6806640625}, {"start": 1268.85, "end": 1270.85, "word": " is", "probability": 0.291259765625}, {"start": 1270.85, "end": 1272.39, "word": " a", "probability": 0.96240234375}, {"start": 1272.39, "end": 1273.75, "word": " subspace", "probability": 0.895751953125}, {"start": 1273.75, "end": 1275.49, "word": " of", "probability": 0.97607421875}, {"start": 1275.49, "end": 1276.91, "word": " V", "probability": 0.9638671875}, {"start": 1276.91, "end": 1278.79, "word": " نقطة", "probability": 0.8046875}, {"start": 1278.79, "end": 1279.69, "word": " ثانية", "probability": 0.9837239583333334}, {"start": 1279.69, "end": 1282.57, "word": " بيقول", "probability": 0.6146647135416666}, {"start": 1282.57, "end": 1283.13, "word": " ف", "probability": 0.1298828125}, {"start": 1283.13, "end": 1285.45, "word": " every", "probability": 0.603515625}, {"start": 1285.45, "end": 1286.87, "word": " U", "probability": 0.94775390625}, {"start": 1286.87, "end": 1288.23, "word": " is", "probability": 0.9619140625}, {"start": 1288.23, "end": 1289.17, "word": " a", "probability": 0.9638671875}, {"start": 1289.17, "end": 1289.85, "word": " linear", "probability": 0.9482421875}, {"start": 1289.85, "end": 1292.15, "word": " combination", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 53, "seek": 132628, "start": 1297.38, "end": 1326.28, "text": "of the v's of the v's and every and every v is a linear combination linear combination of the", "tokens": [2670, 264, 371, 311, 295, 264, 371, 311, 293, 633, 293, 633, 371, 307, 257, 8213, 6562, 8213, 6562, 295, 264], "avg_logprob": -0.1990411877632141, "compression_ratio": 1.55, "no_speech_prob": 0.0, "words": [{"start": 1297.38, "end": 1298.0, "word": "of", "probability": 0.5595703125}, {"start": 1298.0, "end": 1299.9, "word": " the", "probability": 0.896484375}, {"start": 1299.9, "end": 1301.74, "word": " v's", "probability": 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{"start": 1320.6, "end": 1322.52, "word": " linear", "probability": 0.869140625}, {"start": 1322.52, "end": 1323.52, "word": " combination", "probability": 0.96337890625}, {"start": 1323.52, "end": 1324.5, "word": " of", "probability": 0.984375}, {"start": 1324.5, "end": 1326.28, "word": " the", "probability": 0.9208984375}], "temperature": 1.0}, {"id": 54, "seek": 134077, "start": 1327.81, "end": 1340.77, "text": "U تساوي V", "tokens": [52, 6055, 3794, 995, 45865, 691], "avg_logprob": -0.5080915178571429, "compression_ratio": 0.6086956521739131, "no_speech_prob": 0.0, "words": [{"start": 1327.81, "end": 1328.25, "word": "U", "probability": 0.1566162109375}, {"start": 1328.25, "end": 1339.81, "word": " تساوي", "probability": 0.75732421875}, {"start": 1339.81, "end": 1340.77, "word": " V", "probability": 0.73046875}], "temperature": 1.0}, {"id": 55, "seek": 137963, "start": 1378.27, "end": 1379.63, "text": "النظرية مرة تانية", "tokens": [6027, 1863, 19913, 2288, 10632, 3714, 25720, 6055, 7649, 10632], "avg_logprob": -0.08172052827748386, "compression_ratio": 0.8205128205128205, "no_speech_prob": 0.0, "words": [{"start": 1378.27, "end": 1378.99, "word": "النظرية", "probability": 0.94833984375}, {"start": 1378.99, "end": 1379.27, "word": " مرة", "probability": 0.893310546875}, {"start": 1379.27, "end": 1379.63, "word": " تانية", "probability": 0.9065755208333334}], "temperature": 1.0}, {"id": 56, "seek": 140575, "start": 1381.01, "end": 1405.75, "text": "أنا جيت على الـ vector space R3 أخدت منه two subspaces الأول انا سميته U والثاني سميته V كابتن كل واحد منهم subspace من الـ R into the set of all inner tuples under the usual addition and usual multiplication طيب ال subspaces هذول spanned الأول", "tokens": [10721, 8315, 10874, 36081, 15844, 2423, 39184, 8062, 1901, 497, 18, 5551, 9778, 3215, 2655, 9154, 3224, 732, 2090, 79, 2116, 2423, 10721, 12610, 1975, 8315, 8608, 2304, 36081, 3224, 624, 16070, 12984, 7649, 1829, 8608, 2304, 36081, 3224, 691, 9122, 16758, 2655, 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0.9921875}, {"start": 1474.78, "end": 1475.14, "word": " الـU", "probability": 0.9322916666666666}, {"start": 1475.14, "end": 1475.38, "word": " يعني", "probability": 0.8984375}, {"start": 1475.38, "end": 1475.98, "word": " العملية", "probability": 0.9677734375}, {"start": 1475.98, "end": 1476.8, "word": " العكسية", "probability": 0.9964599609375}, {"start": 1476.8, "end": 1477.66, "word": " يبقى", "probability": 0.9725341796875}, {"start": 1477.66, "end": 1478.16, "word": " automatic", "probability": 0.630859375}, {"start": 1478.16, "end": 1478.74, "word": " الـU", "probability": 0.9576822916666666}, {"start": 1478.74, "end": 1479.3, "word": " والـV", "probability": 0.8199869791666666}, {"start": 1479.3, "end": 1479.8, "word": " are", "probability": 0.2479248046875}, {"start": 1479.8, "end": 1480.26, "word": " equal", "probability": 0.884765625}], "temperature": 1.0}, {"id": 60, "seek": 149512, "start": 1480.8, "end": 1495.12, "text": "يبقى ال U يسوى ال V مرة تانية بتفترض المثل اللي قلتها تانية كلهم ال vector space RN روحت أخدت مجموعة هذه مجموعة وهذه مجموعة تانية", "tokens": [1829, 3555, 4587, 7578, 2423, 624, 7251, 3794, 2407, 7578, 2423, 691, 3714, 25720, 6055, 7649, 10632, 39894, 5172, 2655, 43042, 9673, 12984, 1211, 13672, 1829, 12174, 1211, 2655, 11296, 6055, 7649, 10632, 28242, 16095, 2423, 8062, 1901, 45702, 12602, 2407, 33753, 5551, 9778, 3215, 2655, 3714, 7435, 2304, 2407, 27884, 29538, 3714, 7435, 2304, 2407, 27884, 37037, 24192, 3714, 7435, 2304, 2407, 27884, 6055, 7649, 10632], "avg_logprob": -0.3028492725947324, "compression_ratio": 1.5683453237410072, "no_speech_prob": 0.0, "words": [{"start": 1480.8, "end": 1481.52, "word": "يبقى", "probability": 0.85986328125}, {"start": 1481.52, "end": 1481.58, "word": " ال", "probability": 0.74560546875}, {"start": 1481.58, "end": 1481.76, "word": " U", "probability": 0.2208251953125}, {"start": 1481.76, "end": 1482.52, "word": " يسوى", "probability": 0.429351806640625}, {"start": 1482.52, "end": 1482.64, "word": " ال", "probability": 0.78173828125}, {"start": 1482.64, "end": 1482.86, "word": " V", "probability": 0.978515625}, {"start": 1482.86, "end": 1483.4, "word": " مرة", "probability": 0.80908203125}, {"start": 1483.4, "end": 1483.98, "word": " تانية", "probability": 0.8544921875}, {"start": 1483.98, "end": 1486.04, "word": " بتفترض", "probability": 0.68792724609375}, {"start": 1486.04, "end": 1486.44, "word": " المثل", "probability": 0.7439778645833334}, {"start": 1486.44, "end": 1486.56, "word": " اللي", "probability": 0.79833984375}, {"start": 1486.56, "end": 1486.86, "word": " قلتها", "probability": 0.67108154296875}, {"start": 1486.86, "end": 1487.08, "word": " تانية", "probability": 0.790771484375}, {"start": 1487.08, "end": 1487.8, "word": " كلهم", "probability": 0.7071533203125}, {"start": 1487.8, "end": 1488.04, "word": " ال", "probability": 0.91552734375}, {"start": 1488.04, "end": 1488.34, "word": " vector", "probability": 0.81494140625}, {"start": 1488.34, "end": 1488.88, "word": " space", "probability": 0.796875}, {"start": 1488.88, "end": 1489.64, "word": " RN", "probability": 0.17431640625}, {"start": 1489.64, "end": 1491.04, "word": " روحت", "probability": 0.8107096354166666}, {"start": 1491.04, "end": 1491.86, "word": " أخدت", "probability": 0.847412109375}, {"start": 1491.86, "end": 1492.56, "word": " مجموعة", "probability": 0.9005859375}, {"start": 1492.56, "end": 1493.04, "word": " هذه", "probability": 0.53271484375}, {"start": 1493.04, "end": 1493.68, "word": " مجموعة", "probability": 0.93486328125}, {"start": 1493.68, "end": 1494.08, "word": " وهذه", "probability": 0.74951171875}, {"start": 1494.08, "end": 1494.64, "word": " مجموعة", "probability": 0.95810546875}, {"start": 1494.64, "end": 1495.12, "word": " تانية", "probability": 0.9850260416666666}], "temperature": 1.0}, {"id": 61, "seek": 151620, "start": 1495.36, "end": 1516.2, "text": "لو جيت كل واحد هنا بقدر اكتبه كlinear combination من اللي هنا ان حدث ذلك يبقى بالصير ال vector space ده هو ال subspace من المجموعة الثانية العملية العكسية لو جيت كل vector هنا هو linear combination من اللي هنا", "tokens": [1211, 2407, 10874, 36081, 28242, 36764, 24401, 34105, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 3224, 9122, 28263, 6562, 9154, 13672, 1829, 34105, 16472, 11331, 3215, 12984, 29910, 23275, 7251, 3555, 4587, 7578, 20666, 9381, 13546, 2423, 8062, 1901, 11778, 3224, 31439, 2423, 2090, 17940, 9154, 9673, 7435, 2304, 2407, 27884, 6024, 104, 7649, 10632, 18863, 42213, 10632, 18863, 4117, 3794, 10632, 45164, 10874, 36081, 28242, 8062, 34105, 31439, 8213, 6562, 9154, 13672, 1829, 34105], "avg_logprob": -0.19366776962813578, "compression_ratio": 1.807909604519774, "no_speech_prob": 0.0, "words": [{"start": 1495.36, "end": 1496.74, "word": "لو", "probability": 0.6258544921875}, {"start": 1496.74, "end": 1497.0, "word": " جيت", "probability": 0.45062255859375}, {"start": 1497.0, "end": 1497.4, "word": " كل", "probability": 0.86669921875}, {"start": 1497.4, "end": 1497.92, "word": 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العملية", "probability": 0.9591471354166666}, {"start": 1511.22, "end": 1511.98, "word": " العكسية", "probability": 0.9940185546875}, {"start": 1511.98, "end": 1512.46, "word": " لو", "probability": 0.65869140625}, {"start": 1512.46, "end": 1512.8, "word": " جيت", "probability": 0.7470703125}, {"start": 1512.8, "end": 1513.56, "word": " كل", "probability": 0.80615234375}, {"start": 1513.56, "end": 1513.98, "word": " vector", "probability": 0.91650390625}, {"start": 1513.98, "end": 1514.34, "word": " هنا", "probability": 0.947265625}, {"start": 1514.34, "end": 1514.56, "word": " هو", "probability": 0.77392578125}, {"start": 1514.56, "end": 1514.86, "word": " linear", "probability": 0.9033203125}, {"start": 1514.86, "end": 1515.56, "word": " combination", "probability": 0.95068359375}, {"start": 1515.56, "end": 1515.88, "word": " من", "probability": 0.96533203125}, {"start": 1515.88, "end": 1516.02, "word": " اللي", "probability": 0.98486328125}, {"start": 1516.02, "end": 1516.2, "word": " هنا", "probability": 0.99072265625}], "temperature": 1.0}, {"id": 62, "seek": 153566, "start": 1516.72, "end": 1535.66, "text": "وكل vector هناك هو linear combination من اللي هنا معناته اتنين are equal يبقى اتنين ينطبقان على بعضهما تمام الانطلاق واضح طيب بدنا نروح نثبت صحة هذا الكلام مشان نثبت صحة هذا الكلام", "tokens": [2407, 28820, 8062, 34105, 4117, 31439, 8213, 6562, 9154, 13672, 1829, 34105, 20449, 8315, 47395, 1975, 2655, 1863, 9957, 366, 2681, 7251, 3555, 4587, 7578, 1975, 2655, 1863, 9957, 7251, 1863, 9566, 3555, 4587, 7649, 15844, 45030, 11242, 3224, 15042, 46811, 10943, 2423, 7649, 9566, 15040, 4587, 4032, 46958, 5016, 23032, 1829, 3555, 47525, 8315, 8717, 32887, 5016, 8717, 12984, 3555, 2655, 20328, 5016, 3660, 23758, 2423, 28820, 10943, 37893, 7649, 8717, 12984, 3555, 2655, 20328, 5016, 3660, 23758, 2423, 28820, 10943], "avg_logprob": -0.17385166380778852, "compression_ratio": 1.6592178770949721, "no_speech_prob": 0.0, "words": [{"start": 1516.72, "end": 1517.46, "word": "وكل", "probability": 0.72265625}, {"start": 1517.46, "end": 1517.92, "word": " vector", "probability": 0.544921875}, {"start": 1517.92, "end": 1518.4, "word": " هناك", "probability": 0.91357421875}, {"start": 1518.4, "end": 1518.46, "word": " هو", "probability": 0.53662109375}, {"start": 1518.46, "end": 1518.74, "word": " linear", "probability": 0.8525390625}, {"start": 1518.74, "end": 1519.62, "word": " combination", "probability": 0.953125}, {"start": 1519.62, "end": 1519.94, "word": " من", "probability": 0.8212890625}, {"start": 1519.94, "end": 1520.16, "word": " اللي", "probability": 0.764404296875}, {"start": 1520.16, "end": 1520.38, "word": " هنا", "probability": 0.9521484375}, {"start": 1520.38, "end": 1520.94, "word": " معناته", "probability": 0.8899739583333334}, {"start": 1520.94, "end": 1521.72, "word": " اتنين", "probability": 0.82470703125}, {"start": 1521.72, "end": 1522.34, "word": " are", "probability": 0.313720703125}, {"start": 1522.34, "end": 1523.34, "word": " equal", "probability": 0.9111328125}, {"start": 1523.34, "end": 1524.1, "word": " يبقى", "probability": 0.9183349609375}, {"start": 1524.1, "end": 1524.56, "word": " اتنين", "probability": 0.9617919921875}, {"start": 1524.56, "end": 1525.44, "word": " ينطبقان", "probability": 0.9256184895833334}, {"start": 1525.44, "end": 1525.74, "word": " على", "probability": 0.6552734375}, {"start": 1525.74, "end": 1526.58, "word": " بعضهما", "probability": 0.9078369140625}, {"start": 1526.58, "end": 1527.28, "word": " تمام", "probability": 0.989013671875}, {"start": 1527.28, "end": 1528.56, "word": " الانطلاق", "probability": 0.7412109375}, {"start": 1528.56, "end": 1529.22, "word": " واضح", "probability": 0.7545572916666666}, {"start": 1529.22, "end": 1530.1, "word": " طيب", "probability": 0.82080078125}, {"start": 1530.1, "end": 1530.44, "word": " بدنا", "probability": 0.79345703125}, {"start": 1530.44, "end": 1530.7, "word": " نروح", "probability": 0.9812825520833334}, {"start": 1530.7, "end": 1531.36, "word": " نثبت", "probability": 0.962646484375}, {"start": 1531.36, "end": 1531.94, "word": " صحة", "probability": 0.9765625}, {"start": 1531.94, "end": 1532.34, "word": " هذا", "probability": 0.96875}, {"start": 1532.34, "end": 1532.88, "word": " الكلام", "probability": 0.95068359375}, {"start": 1532.88, "end": 1533.84, "word": " مشان", "probability": 0.6409912109375}, {"start": 1533.84, "end": 1534.28, "word": " نثبت", "probability": 0.9713134765625}, {"start": 1534.28, "end": 1534.72, "word": " صحة", "probability": 0.9860026041666666}, {"start": 1534.72, "end": 1535.02, "word": " هذا", "probability": 0.97900390625}, {"start": 1535.02, "end": 1535.66, "word": " الكلام", "probability": 0.9674479166666666}], "temperature": 1.0}, {"id": 63, "seek": 155093, "start": 1536.03, "end": 1550.93, "text": "بقول لو كان كل U هو linear combination يبقى U هو subspace من من V تمام subspace احنا بجينا نروح نثبت الثلاث شروط", "tokens": [3555, 39648, 45164, 25961, 28242, 624, 31439, 8213, 6562, 7251, 3555, 4587, 7578, 624, 31439, 2090, 17940, 9154, 9154, 691, 6055, 15042, 2304, 2090, 17940, 1975, 5016, 8315, 4724, 7435, 1829, 8315, 8717, 32887, 5016, 8717, 12984, 3555, 2655, 6024, 104, 1211, 5718, 104, 13412, 32887, 9566], "avg_logprob": -0.28401692149539787, "compression_ratio": 1.2868217054263567, "no_speech_prob": 0.0, "words": [{"start": 1536.03, "end": 1536.59, "word": "بقول", "probability": 0.4285888671875}, {"start": 1536.59, "end": 1537.29, "word": " لو", "probability": 0.50341796875}, {"start": 1537.29, "end": 1537.91, "word": " كان", "probability": 0.86083984375}, {"start": 1537.91, "end": 1538.39, "word": " كل", "probability": 0.89111328125}, {"start": 1538.39, "end": 1538.63, "word": " U", "probability": 0.60498046875}, {"start": 1538.63, "end": 1538.85, "word": " هو", "probability": 0.76611328125}, {"start": 1538.85, "end": 1539.19, "word": " linear", "probability": 0.68701171875}, {"start": 1539.19, "end": 1540.21, "word": " combination", "probability": 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" V", "probability": 0.916015625}, {"start": 1831.26, "end": 1832.88, "word": " هذا", "probability": 0.74609375}, {"start": 1832.88, "end": 1833.84, "word": " معناه", "probability": 0.79296875}, {"start": 1833.84, "end": 1834.3, "word": " ان", "probability": 0.295166015625}, {"start": 1834.3, "end": 1834.56, "word": " ال", "probability": 0.62890625}, {"start": 1834.56, "end": 1834.92, "word": " U", "probability": 0.6630859375}, {"start": 1834.92, "end": 1835.74, "word": " is", "probability": 0.375}, {"start": 1835.74, "end": 1836.6, "word": " a", "probability": 0.91943359375}, {"start": 1836.6, "end": 1837.86, "word": " subspace", "probability": 0.898681640625}, {"start": 1837.86, "end": 1839.54, "word": " of", "probability": 0.95703125}, {"start": 1839.54, "end": 1840.56, "word": " V", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 77, "seek": 186130, "start": 1844.32, "end": 1861.3, "text": "أخدنا نظرية طبعا سابقا قلنا نسبين تبع مجموعة في ال vectors هو subspace مظبوط ولا لا؟ هنا أثبتنا أن كل element في U هو موجود في V بقال U subset من V", "tokens": [10721, 9778, 3215, 8315, 8717, 19913, 2288, 10632, 23032, 3555, 3615, 995, 8608, 16758, 4587, 995, 12174, 1211, 8315, 8717, 35457, 9957, 6055, 3555, 3615, 3714, 7435, 2304, 2407, 27884, 8978, 2423, 18875, 31439, 2090, 17940, 3714, 19913, 3555, 2407, 9566, 49429, 20193, 22807, 34105, 5551, 12984, 3555, 2655, 8315, 14739, 28242, 4478, 8978, 624, 31439, 3714, 29245, 23328, 8978, 691, 4724, 4587, 6027, 624, 2090, 302, 9154, 691], "avg_logprob": -0.2595982074737549, "compression_ratio": 1.4085365853658536, "no_speech_prob": 0.0, "words": [{"start": 1844.32, "end": 1844.8, "word": "أخدنا", "probability": 0.7813720703125}, {"start": 1844.8, "end": 1845.24, "word": " نظرية", "probability": 0.9725341796875}, {"start": 1845.24, "end": 1845.56, "word": " طبعا", "probability": 0.82940673828125}, {"start": 1845.56, "end": 1846.34, "word": " سابقا", "probability": 0.9725341796875}, {"start": 1846.34, "end": 1847.32, 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هو main اللي عندنا يبقى u subspace من v وكان في نفس الوقت كل v هو linear combination من اللي هو v يبقى هذا مجموعة يبقى صار ال u subset من v و ال v subset من u حسب خواصة المجموعة يبقى ال u بده يساوي v وهو المطلوب مظبوط يبقى باجي بقول هنا from part I", "tokens": [6027, 20292, 31439, 2135, 13672, 1829, 43242, 8315, 7251, 3555, 4587, 7578, 344, 2090, 17940, 9154, 371, 4032, 41361, 8978, 8717, 36178, 2423, 30543, 2655, 28242, 371, 31439, 8213, 6562, 9154, 13672, 1829, 31439, 371, 7251, 3555, 4587, 7578, 23758, 3714, 7435, 2304, 45367, 3660, 7251, 3555, 4587, 7578, 20328, 9640, 2423, 344, 25993, 9154, 371, 4032, 2423, 371, 25993, 9154, 344, 11331, 35457, 16490, 2407, 33546, 3660, 9673, 7435, 2304, 2407, 27884, 7251, 3555, 4587, 7578, 2423, 344, 47525, 3224, 7251, 3794, 995, 45865, 371, 37037, 2407, 9673, 9566, 1211, 37746, 3714, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 34105, 490, 644, 286], "avg_logprob": -0.20199888058610865, "compression_ratio": 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مين؟ بده يساوي V وانت هنا من المثل", "tokens": [3555, 1863, 36178, 41950, 16572, 28671, 2423, 691, 31439, 25993, 9154, 9154, 22807, 9154, 2423, 624, 5296, 33456, 28239, 9381, 23758, 31439, 28239, 9381, 13672, 1829, 6156, 30543, 37037, 15730, 8717, 36178, 28239, 9381, 4724, 3794, 12174, 46152, 8315, 7251, 3555, 4587, 7578, 23758, 7251, 33604, 16254, 30731, 8717, 36178, 28239, 31371, 7435, 3660, 7251, 3555, 4587, 7578, 11778, 9381, 37037, 4117, 15730, 2423, 624, 47525, 3224, 7251, 3794, 995, 45865, 3714, 9957, 22807, 47525, 3224, 7251, 3794, 995, 45865, 691, 4032, 7649, 2655, 34105, 9154, 9673, 12984, 1211], "avg_logprob": -0.20381944742467667, "compression_ratio": 1.8465909090909092, "no_speech_prob": 0.0, "words": [{"start": 1939.97, "end": 1940.77, "word": "بنفس", "probability": 0.9752604166666666}, {"start": 1940.77, "end": 1941.85, "word": " الطريقة", "probability": 0.9912109375}, {"start": 1941.85, "end": 1942.85, "word": " ال", "probability": 0.76318359375}, {"start": 1942.85, 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213578, "start": 2119.28, "end": 2135.78, "text": "المطلوب الثاني بيقول are ال U and ال V the same هذا المطلوب الثاني", "tokens": [45340, 9566, 1211, 37746, 6024, 104, 7649, 1829, 4724, 1829, 39648, 366, 2423, 624, 293, 2423, 691, 264, 912, 23758, 9673, 9566, 1211, 37746, 6024, 104, 7649, 1829], "avg_logprob": -0.2667025903175617, "compression_ratio": 1.3164556962025316, "no_speech_prob": 0.0, "words": [{"start": 2119.2799999999997, "end": 2120.68, "word": "المطلوب", "probability": 0.79217529296875}, {"start": 2120.68, "end": 2121.38, "word": " الثاني", "probability": 0.906005859375}, {"start": 2121.38, "end": 2122.36, "word": " بيقول", "probability": 0.8359375}, {"start": 2122.36, "end": 2123.22, "word": " are", "probability": 0.11065673828125}, {"start": 2123.22, "end": 2124.88, "word": " ال", "probability": 0.6904296875}, {"start": 2124.88, "end": 2125.3, "word": " U", "probability": 0.6298828125}, {"start": 2125.3, "end": 2126.5, "word": " and", "probability": 0.82421875}, {"start": 2126.5, "end": 2127.86, "word": " ال", "probability": 0.814453125}, {"start": 2127.86, "end": 2128.34, "word": " V", "probability": 0.98486328125}, {"start": 2128.34, "end": 2129.28, "word": " the", "probability": 0.8857421875}, {"start": 2129.28, "end": 2129.92, "word": " same", "probability": 0.90576171875}, {"start": 2129.92, "end": 2133.84, "word": " هذا", "probability": 0.41845703125}, {"start": 2133.84, "end": 2134.66, "word": " المطلوب", "probability": 0.9854736328125}, {"start": 2134.66, "end": 2135.78, "word": " الثاني", "probability": 0.9100341796875}], "temperature": 1.0}, {"id": 89, "seek": 217192, "start": 2148.68, "end": 2171.92, "text": "بنرجع لسؤالنا مرة تانية بقول افترض عندي ال sub space U من R3 ولد بال vector U1 و U2 و افترض عندي sub space ثاني V ولد بالعناصر V1 و V2 بالشكل اللي عندنا بسأل هل ال V sub space من U ولا لأ؟", "tokens": [3555, 1863, 47341, 3615, 5296, 3794, 33604, 6027, 8315, 3714, 25720, 6055, 7649, 10632, 4724, 39648, 1975, 5172, 2655, 43042, 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{"start": 2165.96, "end": 2166.88, "word": " V2", "probability": 0.917236328125}, {"start": 2166.88, "end": 2167.42, "word": " بالشكل", "probability": 0.9378255208333334}, {"start": 2167.42, "end": 2167.56, "word": " اللي", "probability": 0.920654296875}, {"start": 2167.56, "end": 2167.94, "word": " عندنا", "probability": 0.813720703125}, {"start": 2167.94, "end": 2168.92, "word": " بسأل", "probability": 0.868408203125}, {"start": 2168.92, "end": 2169.26, "word": " هل", "probability": 0.96533203125}, {"start": 2169.26, "end": 2169.42, "word": " ال", "probability": 0.86083984375}, {"start": 2169.42, "end": 2169.6, "word": " V", "probability": 0.939453125}, {"start": 2169.6, "end": 2169.98, "word": " sub", "probability": 0.68408203125}, {"start": 2169.98, "end": 2170.58, "word": " space", "probability": 0.94140625}, {"start": 2170.58, "end": 2170.92, "word": " من", "probability": 0.9853515625}, {"start": 2170.92, "end": 2171.18, "word": " U", "probability": 0.974609375}, {"start": 2171.18, "end": 2171.4, "word": " ولا", "probability": 0.796875}, {"start": 2171.4, "end": 2171.92, "word": " لأ؟", "probability": 0.8284505208333334}], "temperature": 1.0}, {"id": 90, "seek": 219298, "start": 2172.25, "end": 2192.99, "text": "هل ال V هو subspace منه ولا لأ؟ بنقول والله تمام إذا كان كل عنصر من ال vector الأول كتبناه على صيغة linear combination من ال vector الثاني بكون خلصنا من الموضوع صحيح ولا لأ؟ يعني أنا عندش هذا solution", "tokens": [3224, 1211, 2423, 691, 31439, 2090, 17940, 9154, 3224, 49429, 5296, 10721, 22807, 4724, 1863, 39648, 16070, 43761, 46811, 10943, 11933, 15730, 25961, 28242, 18871, 9381, 2288, 9154, 2423, 8062, 16247, 12610, 9122, 2655, 3555, 8315, 3224, 15844, 20328, 1829, 17082, 3660, 8213, 6562, 9154, 2423, 8062, 6024, 104, 7649, 1829, 4724, 30544, 16490, 1211, 9381, 8315, 9154, 9673, 2407, 11242, 45367, 20328, 5016, 1829, 5016, 49429, 5296, 10721, 22807, 37495, 22653, 41850, 43242, 8592, 23758, 3827], "avg_logprob": -0.2299679500552324, 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{"start": 2177.57, "end": 2178.01, "word": " إذا", "probability": 0.7410888671875}, {"start": 2178.01, "end": 2178.47, "word": " كان", "probability": 0.96923828125}, {"start": 2178.47, "end": 2178.91, "word": " كل", "probability": 0.9560546875}, {"start": 2178.91, "end": 2179.79, "word": " عنصر", "probability": 0.93994140625}, {"start": 2179.79, "end": 2180.35, "word": " من", "probability": 0.97314453125}, {"start": 2180.35, "end": 2180.53, "word": " ال", "probability": 0.9482421875}, {"start": 2180.53, "end": 2180.91, "word": " vector", "probability": 0.9111328125}, {"start": 2180.91, "end": 2181.33, "word": " الأول", "probability": 0.89892578125}, {"start": 2181.33, "end": 2182.13, "word": " كتبناه", "probability": 0.96630859375}, {"start": 2182.13, "end": 2182.31, "word": " على", "probability": 0.88330078125}, {"start": 2182.31, "end": 2182.81, "word": " صيغة", "probability": 0.9512939453125}, {"start": 2182.81, "end": 2183.19, "word": " linear", "probability": 0.71435546875}, {"start": 2183.19, "end": 2184.31, "word": " combination", "probability": 0.9267578125}, {"start": 2184.31, "end": 2185.15, "word": " من", "probability": 0.966796875}, {"start": 2185.15, "end": 2185.39, "word": " ال", "probability": 0.95751953125}, {"start": 2185.39, "end": 2185.73, "word": " vector", "probability": 0.9892578125}, {"start": 2185.73, "end": 2186.39, "word": " الثاني", "probability": 0.9599609375}, {"start": 2186.39, "end": 2186.75, "word": " بكون", "probability": 0.724853515625}, {"start": 2186.75, "end": 2187.25, "word": " خلصنا", "probability": 0.94482421875}, {"start": 2187.25, "end": 2187.37, "word": " من", "probability": 0.96240234375}, {"start": 2187.37, "end": 2187.91, "word": " الموضوع", "probability": 0.998046875}, {"start": 2187.91, "end": 2188.63, "word": " صحيح", "probability": 0.89306640625}, {"start": 2188.63, "end": 2188.79, "word": " ولا", "probability": 0.92236328125}, {"start": 2188.79, "end": 2189.65, "word": " لأ؟", "probability": 0.791015625}, 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{"start": 2433.89, "end": 2434.11, "word": " هنا", "probability": 0.91552734375}, {"start": 2434.11, "end": 2434.53, "word": " بنات", "probability": 0.64892578125}, {"start": 2434.53, "end": 2434.81, "word": " انه", "probability": 0.4432373046875}, {"start": 2434.81, "end": 2435.05, "word": " مين", "probability": 0.699462890625}, {"start": 2435.05, "end": 2435.51, "word": " ان", "probability": 0.318359375}, {"start": 2435.51, "end": 2435.79, "word": " ال", "probability": 0.61181640625}, {"start": 2435.79, "end": 2435.95, "word": " V", "probability": 0.96142578125}, {"start": 2435.95, "end": 2436.25, "word": " هو", "probability": 0.98291015625}, {"start": 2436.25, "end": 2436.57, "word": " sub", "probability": 0.4365234375}, {"start": 2436.57, "end": 2437.03, "word": " space", "probability": 0.62158203125}, {"start": 2437.03, "end": 2437.35, "word": " من", "probability": 0.9765625}, {"start": 2437.35, "end": 2437.45, "word": " U", "probability": 0.9833984375}, {"start": 2437.45, "end": 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2423, 691, 16, 30767, 16373, 3215, 257, 17, 8978, 2423, 691, 17, 38637, 2304, 4724, 16254, 1975, 9778, 3215, 257, 16, 691, 16, 30767, 16373, 3215, 257, 17, 691, 17, 7251, 44510, 2407, 7251, 3794, 995, 45865, 4724, 16254, 1975, 3215, 9778, 1211, 15844, 23032, 12610, 33962, 9566, 4032, 9957, 691, 16, 4032, 691, 17, 8032, 47302, 8032, 2304, 34105, 4117, 7251, 3555, 4587, 7578, 1975, 1829, 8592, 47525, 3224, 7251, 9381, 13546, 7251, 3555, 4587, 7578, 257, 16], "avg_logprob": -0.28888887895478144, "compression_ratio": 1.7391304347826086, "no_speech_prob": 0.0, "words": [{"start": 2500.62, "end": 2501.0, "word": "يبدو", "probability": 0.2142333984375}, {"start": 2501.0, "end": 2501.46, "word": " يساوي", "probability": 0.5914306640625}, {"start": 2501.46, "end": 2502.14, "word": " a1", "probability": 0.730224609375}, {"start": 2502.14, "end": 2502.52, "word": " في", "probability": 0.369140625}, {"start": 2502.52, "end": 2502.78, "word": " ال", "probability": 0.63720703125}, {"start": 2502.78, 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"Vector V1 V2 V3 V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V12 V13 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12", "tokens": [53, 20814, 691, 16, 691, 17, 691, 18, 691, 19, 691, 20, 691, 21, 691, 22, 691, 23, 691, 24, 691, 3279, 691, 5348, 691, 4762, 691, 7668, 691, 4762, 691, 7668, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762, 691, 4762], "avg_logprob": -0.3025793698098924, "compression_ratio": 2.0892857142857144, "no_speech_prob": 0.0, "words": [{"start": 2699.68, "end": 2701.08, "word": "Vector", "probability": 0.526947021484375}, {"start": 2701.08, "end": 2702.48, "word": " V1", "probability": 0.290374755859375}, {"start": 2702.48, "end": 2703.24, "word": " V2", "probability": 0.6998291015625}, {"start": 2703.24, "end": 2707.98, "word": " V3", "probability": 0.60986328125}, {"start": 2707.98, "end": 2707.98, "word": " V4", "probability": 0.92529296875}, {"start": 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2822.59, "end": 2824.09, "word": " جيدة", "probability": 0.9265950520833334}, {"start": 2824.09, "end": 2824.35, "word": " و", "probability": 0.447021484375}, {"start": 2824.35, "end": 2824.87, "word": " الجامعة", "probability": 0.9474283854166666}, {"start": 2824.87, "end": 2825.31, "word": " كانت", "probability": 0.982421875}, {"start": 2825.31, "end": 2825.81, "word": " فاتحة", "probability": 0.9827880859375}, {"start": 2825.81, "end": 2826.31, "word": " طبعا", "probability": 0.9833984375}, {"start": 2826.31, "end": 2827.03, "word": " بنيجي", "probability": 0.74853515625}, {"start": 2827.03, "end": 2827.55, "word": " ونبدأ", "probability": 0.816650390625}, {"start": 2827.55, "end": 2827.67, "word": " ال", "probability": 0.74072265625}, {"start": 2827.67, "end": 2827.99, "word": " section", "probability": 0.84130859375}, {"start": 2827.99, "end": 2828.23, "word": " اللى", "probability": 0.796875}, {"start": 2828.23, "end": 2828.59, "word": " بعده", "probability": 0.822021484375}, {"start": 2828.59, "end": 2828.95, "word": " وهو", "probability": 0.8201497395833334}, {"start": 2828.95, "end": 2829.91, "word": " تلاتة", "probability": 0.9453125}, {"start": 2829.91, "end": 2830.65, "word": " تلاتة", "probability": 0.9705810546875}], "temperature": 1.0}, {"id": 116, "seek": 284616, "start": 2831.32, "end": 2846.16, "text": "الثلاثة ثلاثة إرادة مرّيلي عليه جيب النتيجة وهو Linear Dependence و Linear Independent Vector المتجهات المستقلة والمعتمدة على بعضها خطيا", "tokens": [6027, 12984, 1211, 5718, 104, 3660, 38637, 1211, 5718, 104, 3660, 11933, 2288, 18513, 3660, 3714, 2288, 11703, 1829, 20292, 47356, 10874, 1829, 3555, 2423, 29399, 1829, 7435, 3660, 37037, 2407, 14670, 289, 4056, 521, 655, 4032, 14670, 289, 40310, 691, 20814, 9673, 2655, 7435, 3224, 9307, 9673, 14851, 4587, 37977, 16070, 2304, 34268, 2304, 41891, 15844, 45030, 11242, 11296, 16490, 9566, 25528], "avg_logprob": -0.3395996047183871, "compression_ratio": 1.3986928104575163, "no_speech_prob": 0.0, "words": [{"start": 2831.32, "end": 2832.0, "word": "الثلاثة", "probability": 0.6986897786458334}, {"start": 2832.0, "end": 2832.4, "word": " ثلاثة", "probability": 0.9416015625}, {"start": 2832.4, "end": 2832.76, "word": " إرادة", "probability": 0.62640380859375}, {"start": 2832.76, "end": 2833.22, "word": " مرّيلي", "probability": 0.489111328125}, {"start": 2833.22, "end": 2833.44, "word": " عليه", "probability": 0.810546875}, {"start": 2833.44, "end": 2833.72, "word": " جيب", "probability": 0.6394856770833334}, {"start": 2833.72, "end": 2834.28, "word": " النتيجة", "probability": 0.741162109375}, {"start": 2834.28, "end": 2834.62, "word": " وهو", "probability": 0.769775390625}, {"start": 2834.62, "end": 2835.3, "word": " Linear", "probability": 0.7181396484375}, {"start": 2835.3, "end": 2836.46, "word": " Dependence", "probability": 0.7478841145833334}, {"start": 2836.46, "end": 2836.8, "word": " و", "probability": 0.6962890625}, {"start": 2836.8, "end": 2837.58, "word": " Linear", "probability": 0.834228515625}, {"start": 2837.58, "end": 2838.76, "word": " Independent", "probability": 0.484619140625}, {"start": 2838.76, "end": 2839.6, "word": " Vector", "probability": 0.853515625}, {"start": 2839.6, "end": 2841.28, "word": " المتجهات", "probability": 0.812109375}, {"start": 2841.28, "end": 2842.04, "word": " المستقلة", "probability": 0.98095703125}, {"start": 2842.04, "end": 2843.82, "word": " والمعتمدة", "probability": 0.88857421875}, {"start": 2843.82, "end": 2844.14, "word": " على", "probability": 0.59716796875}, {"start": 2844.14, "end": 2844.9, "word": " بعضها", "probability": 0.9982096354166666}, {"start": 2844.9, "end": 2846.16, "word": " خطيا", "probability": 0.89501953125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2848.80975, "duration_after_vad": 2666.631249999993}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..959a3b1c86e10c922f9684205ae57eea05172b04
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/fBV8nr4A0Dw_raw.srt
@@ -0,0 +1,1704 @@
+1
+00:00:19,590 --> 00:00:23,010
+بسم الله الرحمن الرحيم اللي هانكم اللي مابتدأنا
+
+2
+00:00:23,010 --> 00:00:26,650
+بيه في المرة الماضية كنا متحدث في المرة الماضية عن
+
+3
+00:00:26,650 --> 00:00:33,670
+ال subspaces الفضاءات الجزئية لفضاء اتجاهي و أخدنا
+
+4
+00:00:33,670 --> 00:00:38,470
+أمثلة كثيرة جدا و بعدين أخدنا نظريةقلنا لو كعندي
+
+5
+00:00:38,470 --> 00:00:43,950
+set و ال set تولدت بمجموعة من ال vectors أو كل
+
+6
+00:00:43,950 --> 00:00:47,270
+element فيها كتبناه على صيغة linear combination من
+
+7
+00:00:47,270 --> 00:00:51,450
+مجموعة من ال vectors يبجي هذا ال set عبارة عن sub
+
+8
+00:00:51,450 --> 00:00:56,070
+space و ابتدأنا أن أخد على ذلك أمثلة و أخدنا بدل
+
+9
+00:00:56,070 --> 00:01:01,400
+المثال اتنين و هذا هو المثال رقم ثلاثةبقول في هذا
+
+10
+00:01:01,400 --> 00:01:07,580
+المثال افترض ان U عبارة عن subspace من R3 that is
+
+11
+00:01:07,580 --> 00:01:11,940
+spanned by the vectors يبقى ال U هذا ولد بواسطة
+
+12
+00:01:11,940 --> 00:01:18,620
+three vectors V1 و V2 و V3 بقول هل ال vector V2 و
+
+13
+00:01:18,620 --> 00:01:24,310
+V1 و V5 موجود في set U ولا لأ ممتازةيبقى انا في
+
+14
+00:01:24,310 --> 00:01:28,910
+عندى vector space اللي هو R3 اللي هو عبارة عن كل
+
+15
+00:01:28,910 --> 00:01:34,670
+العناصر المتكونة من 3 تيوبل تمام روحت على ال
+
+16
+00:01:34,670 --> 00:01:38,610
+vector space هذا خدت منه مجموعة جزئية المجموعة
+
+17
+00:01:38,610 --> 00:01:44,150
+الجزئية سميتها U مين هي ال U؟قال لي هي الـ U هي
+
+18
+00:01:44,150 --> 00:01:49,830
+المجموعة التي ولدت بواسطة ال three vectors V1 و V2
+
+19
+00:01:49,830 --> 00:01:56,850
+و V3 يعني التلت عناصر دول ولدولي جميع عناصر ال U
+
+20
+00:01:56,850 --> 00:02:02,990
+بلا ستة يعني جميع عناصر ال subspace U بسأل هل ال
+
+21
+00:02:02,990 --> 00:02:09,270
+vector 2 و 1 و 5 موجود في ال set U أم لا بقوله
+
+22
+00:02:09,270 --> 00:02:14,600
+واللهإذا كان الـ vector 2 و 1 و 5 كدرنا نكتبه على
+
+23
+00:02:14,600 --> 00:02:19,980
+صيغة linear combination من V1 و V2 و V3 إذا بيكون
+
+24
+00:02:19,980 --> 00:02:25,600
+موجود في الـ U صحيح ولا لأ يبقى هنا مرة تانية بقول
+
+25
+00:02:25,600 --> 00:02:31,200
+مشان أثبت أن ال vector 2 و 1 و 5 موجود في ال
+
+26
+00:02:31,200 --> 00:02:37,960
+subspace U بدي أحاول أثبت أن 2 و 1 و 5 هو linear
+
+27
+00:02:37,960 --> 00:02:45,350
+combinationمن V1 و V2 و V3 إن تحقق ذلك يبقى هذا
+
+28
+00:02:45,350 --> 00:02:50,250
+العنصر موجود فيه إن لم يتحقق ذلك يبقى هذا العنصر
+
+29
+00:02:50,250 --> 00:02:55,850
+غير موجود في ال sub space U على الإطلاق واضح الشي
+
+30
+00:02:55,850 --> 00:03:01,340
+اللي بدنا نعمله؟يبقى مشان أثبت أنه 2 و 5 .. 2 و 1
+
+31
+00:03:01,340 --> 00:03:06,040
+و 5 موجود فيه و بدي أحاول أثبت أنه 2 و 1 و 5 هذا
+
+32
+00:03:06,040 --> 00:03:10,580
+يساوي Constant في V1 زائد Constant في V2 زائد
+
+33
+00:03:10,580 --> 00:03:15,680
+Constant في V3 يعني على صيغة Linear Combination من
+
+34
+00:03:15,680 --> 00:03:21,680
+الـ three vectors ماجي العالم يبقى هنا باجي بقول
+
+35
+00:03:21,680 --> 00:03:23,640
+assume
+
+36
+00:03:24,950 --> 00:03:37,130
+الذات افترض ان ال V اللي بده يساوي 2 1 2 1 و 5 بده
+
+37
+00:03:37,130 --> 00:03:48,090
+يساوي C1 V1 C2 V2 C3 V3إن حدث ذلك بمعنى آخر اللي
+
+38
+00:03:48,090 --> 00:03:53,830
+جاءت حل هذه المعادلة بمعنى آخر اللي جاءت قيم لـC1
+
+39
+00:03:53,830 --> 00:03:59,550
+وC2 وC3 بكلام نصائي ما وجدت يبقى لا يمكن أن يكون
+
+40
+00:03:59,550 --> 00:04:04,470
+هذا الـvector موجود في الـSet U فبعدين بقوله كويس
+
+41
+00:04:04,470 --> 00:04:16,730
+يبقى أصبح النميم C1 في V1و2 و1 زائد c2 في v2 اللي
+
+42
+00:04:16,730 --> 00:04:24,030
+هو واحد وزيرو واثنين زائد c3 في v3 اللي هو واحد
+
+43
+00:04:24,030 --> 00:04:28,550
+وواحد وزيرو بده يساوي 2 1 5
+
+44
+00:04:31,010 --> 00:04:37,190
+بدا أجمع هذه العناصر يبقى بدأ ادخل الـC1 وC2 وC3
+
+45
+00:04:37,190 --> 00:04:43,250
+داخل الأقواص التهدي وابدأ أجمع يبقى بداشت الخطوطين
+
+46
+00:04:43,250 --> 00:04:52,090
+بخطوة واحدة يبقى هذه C1 زائد C2 زائد C3 المركبة
+
+47
+00:04:52,090 --> 00:05:00,530
+الثانية 2C1زيرو طار مع السلامة زائد C3 المركبة
+
+48
+00:05:00,530 --> 00:05:07,530
+التالتة C1 زائد 2 C2 والمركبة التالتة ما لها مع
+
+49
+00:05:07,530 --> 00:05:15,880
+السلامة يبقى يساوي 2 1 5هذا ليس ما حصل لدي ، لدي
+
+50
+00:05:15,880 --> 00:05:21,680
+الآن ثلاثة يوبل يسوى ثلاثة يوبل فكل عنصر سيسوى
+
+51
+00:05:21,680 --> 00:05:27,940
+ثلاثة نظيره هذا سيعطيني ثلاث معادلات المعادلة
+
+52
+00:05:27,940 --> 00:05:36,030
+الأولىC1 زائد C2 زائد C3 يساوي 2 المعادلة A ثانية
+
+53
+00:05:36,030 --> 00:05:45,030
+اتنين C1 وهنا زائد C3 يساوي 1 المعادلة التالتة C1
+
+54
+00:05:45,030 --> 00:05:54,720
+زائد اتنين C2 بده يساوي كده؟ خمسةيبقى احنا انتقلنا
+
+55
+00:05:54,720 --> 00:05:59,860
+إلى الـ System of Linear Equations مظبوط ولا لأ؟
+
+56
+00:05:59,860 --> 00:06:06,180
+يبقى صار عندى ثلاث معادلات في ثلاثة مجاهيل إذا
+
+57
+00:06:06,180 --> 00:06:10,100
+بدنا نحاول الحل المعادلات التلاتة مش هنجيب قيم
+
+58
+00:06:10,100 --> 00:06:17,630
+المجاهيل C1 وC2 وC3 إن أمكن ذلكطبعا قدامي أكتر من
+
+59
+00:06:17,630 --> 00:06:20,830
+طريق يا إما الـ Echelon Form على الـ Augmented
+
+60
+00:06:20,830 --> 00:06:26,270
+Matrix يا إما الـ Gaussian Method طريقة الجوز يا
+
+61
+00:06:26,270 --> 00:06:30,890
+إما نشتغل عادي اللي بنقدر عليه يعني بأي وسيلة من
+
+62
+00:06:30,890 --> 00:06:35,550
+الوسائل اللي تعلمناها قبل ذلك بنحاول نحل هذه
+
+63
+00:06:35,550 --> 00:06:40,550
+المعادلات لكن هذه المعادلات التلاتة بسيطة لن محتاج
+
+64
+00:06:40,550 --> 00:06:46,420
+Echelon ولا Gaussian ولا غيره كيف؟باجي بقول لو
+
+65
+00:06:46,420 --> 00:06:52,500
+ضربت المعادلة التانية هذه في سالب واحد و جمعت بكون
+
+66
+00:06:52,500 --> 00:06:59,580
+ضيعت main اللي هو C1 و C3 ولم يبقى عندي إلا main
+
+67
+00:06:59,580 --> 00:07:05,820
+C2 وبالتالي نحل ال system بسهولة بدون من يلجأ لا
+
+68
+00:07:05,820 --> 00:07:10,910
+ليشيلون ولا ليجاوسيان ولا لغيرهيبقى هذا ال system
+
+69
+00:07:10,910 --> 00:07:18,710
+بدي أعيد صورته كتالة يبقى C1 زائد C2 زائد C3 يسوى
+
+70
+00:07:18,710 --> 00:07:28,830
+2 سالب 2 C1 وهنا سالب C3 بده يسوى سالب 1 وهنا C1
+
+71
+00:07:28,830 --> 00:07:36,310
+زائد 2 C2 بده يسوى كده؟ بده يسوى 5 وبدنا نيجي نجمع
+
+72
+00:07:37,610 --> 00:07:42,890
+لو جينا لنجمع اظن ان هدول مع السلامة و هدول زيهم
+
+73
+00:07:42,890 --> 00:07:47,810
+مع السلامة يبقى الموضوع اللي عندى C2 و 2C2 يبقى
+
+74
+00:07:47,810 --> 00:07:54,550
+3C2 يبقى هذا بده يعطينا ال system ما يأتي اللي هو
+
+75
+00:07:54,550 --> 00:08:00,370
+3C2 بده يساوي سبعة بده اشيل منهم واحد بده يساوي
+
+76
+00:08:00,370 --> 00:08:09,210
+قداش ستة ومنه C2 يساوي قداش اتنينطب لما C2 يساوي 2
+
+77
+00:08:09,210 --> 00:08:17,070
+بقدر اجيب له مين؟ C1 يبقى هذا جيبنا C2 هذا بده
+
+78
+00:08:17,070 --> 00:08:24,320
+يعطينا مين؟بتعود في المعادلة التالتة يبقى C1 زيدي
+
+79
+00:08:24,320 --> 00:08:30,740
+2 في 2 بده يساوي 5 هذا بيعطينا ان C1 بده يساوي
+
+80
+00:08:30,740 --> 00:08:36,620
+كده؟ 2 في 2 أبقى 4 بجيب الشجة التانية سالب 4 بيظل
+
+81
+00:08:36,620 --> 00:08:43,320
+عندى كده C1 يساوي 1 أصبح C1 معروف و C2 معروف بيظل
+
+82
+00:08:43,320 --> 00:08:47,470
+المجهول من عندناC3 يبقى يا ما بعوض في المعادلة
+
+83
+00:08:47,470 --> 00:08:53,330
+الأولى يا بعوض في المعادلة الثانية في أي منهم إذا
+
+84
+00:08:53,330 --> 00:09:00,530
+لو جيت عوض في المعادلة الأولى C1 ب1 وC2 ب2 وC3
+
+85
+00:09:00,530 --> 00:09:09,230
+الله أعلم يساوي 2 يبقى C3 يساوي كم؟ سالب واحد يبقى
+
+86
+00:09:09,230 --> 00:09:15,740
+لجيت قيم لـC1 وC2 وC3معناته ان ال vector اللي عندى
+
+87
+00:09:15,740 --> 00:09:21,020
+2 و 1 و 5 بقدر اكتبه على صيغة linear combination
+
+88
+00:09:21,020 --> 00:09:27,920
+من من؟ من ال three vectors كيف؟ كالتالي شوف ايش
+
+89
+00:09:27,920 --> 00:09:33,740
+اللي بدي يصير الان عندنا ال V اللي هو 2 و 1 و 5
+
+90
+00:09:34,050 --> 00:09:39,850
+بقدر اكتبه على الشكل التالي C1 ب1 يبقى هاي واحد في
+
+91
+00:09:39,850 --> 00:09:46,030
+ال vector الأول اللي هو واحد و اتنين و واحد زائد
+
+92
+00:09:46,030 --> 00:09:53,530
+C2 ب2 في ال vector الثاني اللي هو واحد و زيرو و
+
+93
+00:09:53,530 --> 00:09:59,750
+اتنين اللي تالت سالب واحد في ال vector التالت اللي
+
+94
+00:09:59,750 --> 00:10:03,860
+هو عبارة عنone واحد واحد واحد واحد واحد واحد واحد
+
+95
+00:10:03,860 --> 00:10:04,000
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+96
+00:10:04,000 --> 00:10:04,720
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+97
+00:10:04,720 --> 00:10:09,800
+واحد واحد واحد واحد واحد
+
+98
+00:10:09,800 --> 00:10:13,660
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+99
+00:10:13,660 --> 00:10:13,660
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+100
+00:10:13,660 --> 00:10:13,660
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+101
+00:10:13,660 --> 00:10:13,660
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+102
+00:10:13,660 --> 00:10:16,300
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+103
+00:10:16,300 --> 00:10:21,620
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+104
+00:10:21,620 --> 00:10:21,620
+واحد واحد واحد واحد واحد واحد واحد واحد واحد واحد
+
+105
+00:10:21,620 --> 00:10:28,380
+واحد واحد واحد واحد واحد واحد واحد واحد
+
+106
+00:10:28,380 --> 00:10:39,400
+واحد واV1 وV2 وV3 يبقى هنا ساعة الواتنين وواحد
+
+107
+00:10:39,400 --> 00:10:46,360
+وخمسة موجود في ال subspace U انتهينا من المسألة
+
+108
+00:10:46,360 --> 00:10:49,680
+طيب
+
+109
+00:10:49,680 --> 00:10:54,010
+يمكن واحدة تقولطب انا كل سؤال زي هيك لمساني هل ال
+
+110
+00:10:54,010 --> 00:10:59,350
+vector موجود هنا بسوي نفس الطريقة ماشي الأن طلعت
+
+111
+00:10:59,350 --> 00:11:06,150
+قيم ل C1 و C2 و C3 كيف بدهش يطلع قيم يعني كيف بدهش
+
+112
+00:11:06,150 --> 00:11:10,930
+يكون هذا مش موجود فبنقولك مشان بيبينك الشغل هذه
+
+113
+00:11:10,930 --> 00:11:16,070
+إليك المثال الرابع يبقى example four
+
+114
+00:11:24,740 --> 00:11:33,320
+بقول الات ال V واحد بده يساوي واحد و اتنين و سالب
+
+115
+00:11:33,320 --> 00:11:41,240
+واحد وال V اتنين بده يساوي ستة اربعة اتنين كل هذا
+
+116
+00:11:41,240 --> 00:11:49,460
+موجود في اعلى ثلاثة show that the vector show that
+
+117
+00:11:49,460 --> 00:11:52,760
+that
+
+118
+00:11:57,210 --> 00:12:06,650
+V يساوي أربعة و سالب واحد و تمانية does not belong
+
+119
+00:12:06,650 --> 00:12:11,830
+للثبين of V واحد و V اتنين
+
+120
+00:12:29,860 --> 00:12:34,500
+طلّايلي في صيغة السؤالينهنا اعطاني مجموعة من ال
+
+121
+00:12:34,500 --> 00:12:37,780
+vectors وقال لي اثبتلي ان ال vector هذا موجود في
+
+122
+00:12:37,780 --> 00:12:41,400
+ال linear combination لمين لهذا ال او موجود في ال
+
+123
+00:12:41,400 --> 00:12:46,780
+span تبع هذه ال vector هنا برضه اعطاني two vectors
+
+124
+00:12:46,780 --> 00:12:51,080
+وقال لي بيلي ان ال vector اللي عندنا مش موجود في
+
+125
+00:12:51,080 --> 00:12:56,980
+ال span هذا تمام انا كان بإمكاني اعيد صياغة السؤال
+
+126
+00:12:56,980 --> 00:13:02,290
+بطريقة اخرى اي من الاتنين اي واحد منهموأقول خُذي
+
+127
+00:13:02,290 --> 00:13:08,890
+لي V1 و V2 و V3 مثلا موجودة في R3 وخُذي لي الـ U
+
+128
+00:13:08,890 --> 00:13:13,770
+هو الـ Spain تبع هذا الـ Vector و أقول Approve or
+
+129
+00:13:13,770 --> 00:13:17,210
+Disapprove ذات ان الـ Vector هذا موجود في الـ
+
+130
+00:13:17,210 --> 00:13:21,680
+Spain هذايبقى هذا صياغة تالتة للسؤال وبالتالي
+
+131
+00:13:21,680 --> 00:13:26,540
+حيارتك لا قلتلك موجود ولا قلتلك مش موجود تمام؟
+
+132
+00:13:26,540 --> 00:13:30,380
+وبالتالي انت لحالك بدك تمشي نفس ال tactic اللي
+
+133
+00:13:30,380 --> 00:13:33,940
+مشينا فيه في حل السؤال هذا و اللي هنمشي فيه حل
+
+134
+00:13:33,940 --> 00:13:39,620
+السؤال الثاني حتى نصل إلى النتيجةيجى انا بدى ابدأ
+
+135
+00:13:39,620 --> 00:13:44,760
+حل مثل ما حلت هذا هو قاللي اثبت انه هذا هذا انه مش
+
+136
+00:13:44,760 --> 00:13:50,720
+موجود فى الاسبان بدي اروح افرض انه موجودطب لما
+
+137
+00:13:50,720 --> 00:13:57,680
+أفرض أنه موجود هوصل إلى نتيجة خاطئة يبقى إذا وصلت
+
+138
+00:13:57,680 --> 00:14:02,500
+إلى نتيجة خاطئة معناته الفرضي صح ولا غلط غلط وعكسه
+
+139
+00:14:02,500 --> 00:14:07,280
+صح هو الصحيح تمام يبقى تمام يبقى بدي أبدأ زي هذا
+
+140
+00:14:07,280 --> 00:14:15,860
+بالضبط تماما يبقى بدي أقول له solution assume
+
+141
+00:14:15,860 --> 00:14:16,500
+that
+
+142
+00:14:19,950 --> 00:14:27,050
+إن الـ V بيساوي أربعة و سالب واحد و تمانية موجود
+
+143
+00:14:27,050 --> 00:14:34,350
+في الاسبان تبع ال V واحد و V اتنين هذا معناته ان
+
+144
+00:14:34,350 --> 00:14:40,750
+هناك C واحد و C اتنين موجودة في ال set of real
+
+145
+00:14:40,750 --> 00:14:53,400
+numbers such thatبحيث ان C1 V1 زاد C2 V2 يبقى
+
+146
+00:14:53,400 --> 00:15:03,880
+C1 في V1 V1 يعني واحد اتنين سالب واحد C2 في ستة
+
+147
+00:15:03,880 --> 00:15:14,040
+اربعة اتنين يبقى V4 سالب واحد و تمانيةحتى الآن هل
+
+148
+00:15:14,040 --> 00:15:19,260
+اختلفت الفكرة؟ لأ يبقى بداجي افك القوس و اجمعهم
+
+149
+00:15:19,260 --> 00:15:24,320
+اتنين مع بعض بقوس واحد او بثري تيوب الواحد يبقى
+
+150
+00:15:24,320 --> 00:15:32,360
+بقدر اقوله هنا ما يأتي هذه c1 زائد 6 c2أتنين C
+
+151
+00:15:32,360 --> 00:15:40,060
+واحد زائد أربعة C اتنين اللي بعده سالب C واحد زائد
+
+152
+00:15:40,060 --> 00:15:45,080
+اتنين C اتنين كله بده يسوى أربعة وسالب واحد
+
+153
+00:15:45,080 --> 00:15:49,820
+كتمانية بالشكل اللي عندنا هذاصار عندى هنا three
+
+154
+00:15:49,820 --> 00:15:55,000
+tuple بيساوي three tuple من الناحية الأخرى إذا بدي
+
+155
+00:15:55,000 --> 00:16:01,740
+أقارن كل مركبة بنظيرتها معناته حصل إيش يبقى بيصير
+
+156
+00:16:01,740 --> 00:16:13,560
+C1 زائد 6 C2 بده يساوي 4 اللي بعدها 2C1 زائد 2C2
+
+157
+00:16:13,560 --> 00:16:21,140
+بده يساوي سالب 1يبقى اتنين C واحد زائد اربعة C
+
+158
+00:16:21,140 --> 00:16:27,400
+اتنين بدر يساوي سالب واحد اللي بعده سالب C واحد
+
+159
+00:16:27,400 --> 00:16:34,340
+زائد اتنين C اتنين بدر يساوي جداش تمانية يبقى the
+
+160
+00:16:34,340 --> 00:16:39,760
+system of linear equations ثلاثة ثلاث معادلات في
+
+161
+00:16:39,760 --> 00:16:45,540
+مجهولينأظن أن هذا سهل بسبب المعادلات التي وضعت
+
+162
+00:16:45,540 --> 00:16:52,660
+الله عليها البرك والمجاهيل. لكن بمجرد النظر، لو
+
+163
+00:16:52,660 --> 00:16:58,680
+كانت هذه الشرط سالب وجمعت بضيء أحد المجاهيل وبنوجد
+
+164
+00:16:58,680 --> 00:17:03,410
+من المجهول الثاني مباشرةمن دول لا إشيلون ولا
+
+165
+00:17:03,410 --> 00:17:08,530
+جاوسيان ولا غيره إذا بقدر أقول هذا ال system لحله
+
+166
+00:17:08,530 --> 00:17:13,110
+بقول ما ياتي بدي أضرب الأول في سالب واحد يبقى سالب
+
+167
+00:17:13,110 --> 00:17:25,230
+C1 سالب ستة C2 سالب أربعة اتنين C1 زائد أربعة C2
+
+168
+00:17:25,230 --> 00:17:33,880
+سالب واحد سالب C1زي دي اتنين C2 بده يساوي كده؟ بده
+
+169
+00:17:33,880 --> 00:17:40,660
+يساوي التمانية تعالوا نجمع يبقى لو جمعنا هدول مع
+
+170
+00:17:40,660 --> 00:17:47,160
+السلامة تمام؟ و هدول مع السلامة مش هيك؟ يبقى صارة
+
+171
+00:17:47,160 --> 00:17:52,160
+طرف الشمال يساوي كده يا بنات؟ بده طرف اليمين سالب
+
+172
+00:17:52,160 --> 00:17:57,000
+خمسة وتمانية تلاتة يبقى Zero تساوي تلاتة ايش
+
+173
+00:17:57,000 --> 00:18:03,240
+رأيكم؟ مفقود؟في حاجة اسمها real number zero تساوي
+
+174
+00:18:03,240 --> 00:18:08,780
+تلاتة يبقى this is impossible غير ممكن يبقى فرض
+
+175
+00:18:08,780 --> 00:18:13,820
+اللي انا فرضته صح ولا غلط غلط يبقى صح انه لا يمكن
+
+176
+00:18:13,820 --> 00:18:19,400
+ان يكون هذا ال vector موجود في اليوم يبقى هنا بقول
+
+177
+00:18:19,400 --> 00:18:25,580
+zero تساوي تلاتة this is impossible
+
+178
+00:18:27,130 --> 00:18:34,150
+هذا الكلام غير ممكن على الإطلاق فرضي
+
+179
+00:18:34,150 --> 00:18:41,270
+غلط اللي أنا فرضته يبقى ال V يساوي أربعة و سالب
+
+180
+00:18:41,270 --> 00:18:46,570
+واحد و تمانية لمن
+
+181
+00:18:46,570 --> 00:18:54,090
+لا لسبين تبع من تبع ال V واحد و ال V اتنين الشكل
+
+182
+00:18:54,090 --> 00:18:54,650
+اللي عندنا
+
+183
+00:19:04,440 --> 00:19:09,300
+يبقى هاي مثالين شرحنا فيهم كيف بتأثبت ان هذا ال
+
+184
+00:19:09,300 --> 00:19:14,120
+vector موجود في ال spill مجموعة من ال vectors ام
+
+185
+00:19:14,120 --> 00:19:29,840
+لا ويمكن ان نقيس عليهم ما شئنا نجي
+
+186
+00:19:29,840 --> 00:19:31,280
+لنظرية theorem
+
+187
+00:19:37,300 --> 00:19:47,060
+نظرية بتقول ما ياتي ال let ال U and ال V بيه
+
+188
+00:19:47,060 --> 00:19:53,820
+subspaces بيه subspaces
+
+189
+00:19:53,820 --> 00:20:00,980
+of R N Spanned
+
+190
+00:20:00,980 --> 00:20:06,640
+Spanned
+
+191
+00:20:08,380 --> 00:20:12,480
+by u1
+
+192
+00:20:12,480 --> 00:20:26,960
+و u2 و ur and v1 و v2 و vs respectively
+
+193
+00:20:26,960 --> 00:20:32,720
+respectively
+
+194
+00:20:32,720 --> 00:20:38,490
+يعني على الترتيب النقطة الأولىمن هذه النظرية بتقول
+
+195
+00:20:38,490 --> 00:20:55,310
+if every u if every u is a linear combination is
+
+196
+00:20:55,310 --> 00:21:04,150
+a linear combination of the the vs then
+
+197
+00:21:08,070 --> 00:21:25,450
+الـ U is a subspace of V نقطة ثانية بيقول ف every
+
+198
+00:21:25,450 --> 00:21:32,150
+U is a linear combination
+
+199
+00:21:37,380 --> 00:21:52,580
+of the v's of the v's and every and
+
+200
+00:21:52,580 --> 00:22:00,600
+every v is a linear combination
+
+201
+00:22:00,600 --> 00:22:06,280
+linear combination of the
+
+202
+00:22:07,810 --> 00:22:19,810
+U تساوي
+
+203
+00:22:19,810 --> 00:22:20,770
+V
+
+204
+00:22:58,270 --> 00:23:03,890
+النظرية مرة تانيةأنا جيت على الـ vector space R3
+
+205
+00:23:03,890 --> 00:23:09,290
+أخدت منه two subspaces الأول انا سميته U والثاني
+
+206
+00:23:09,290 --> 00:23:15,670
+سميته V كابتن كل واحد منهم subspace من الـ R into
+
+207
+00:23:15,670 --> 00:23:19,010
+the set of all inner tuples under the usual
+
+208
+00:23:19,010 --> 00:23:23,490
+addition and usual multiplication طيب ال subspaces
+
+209
+00:23:23,490 --> 00:23:30,410
+هذول spanned الأولولد بالـ vectors U1 و U2 و لغاية
+
+210
+00:23:30,410 --> 00:23:38,630
+UR الـ V ولد بالعناصر V1 و V2 لغاية VS تمام؟ يبقى
+
+211
+00:23:38,630 --> 00:23:43,910
+اليهات للـ subspace اللي هو U و الفيهات للـ
+
+212
+00:23:43,910 --> 00:23:49,350
+subspace التاني اللي هو V نجي لنظرية النظرية بتقول
+
+213
+00:23:49,350 --> 00:23:54,550
+إذا كان كل واحد من اليهات هدولهو Linear
+
+214
+00:23:54,550 --> 00:23:59,450
+Combination من الـ Vات اللي عندنا هدول يبقى الـ U
+
+215
+00:23:59,450 --> 00:24:04,590
+هو عبارة عن Subspace من الـ Subspace V مش كل واحد
+
+216
+00:24:04,590 --> 00:24:10,270
+فيهم Subspace من R N إن حدث أن Subspace الأول يعني
+
+217
+00:24:10,270 --> 00:24:16,200
+أي Vector V اللي هو Uلقيته linear combination من
+
+218
+00:24:16,200 --> 00:24:20,700
+الـV1 والـV2 والـVS يبقى على طول الـU بدي يكون
+
+219
+00:24:20,700 --> 00:24:27,940
+subspace من من الـV النقطة التانية لو كان كل U هو
+
+220
+00:24:27,940 --> 00:24:33,440
+linear combination من الـV وكل V هي linear
+
+221
+00:24:33,440 --> 00:24:37,660
+combination من الـU يعني العملية العكسية يبقى
+
+222
+00:24:37,660 --> 00:24:42,860
+automatic الـU والـV are equalيبقى ال U يسوى ال V
+
+223
+00:24:42,860 --> 00:24:48,040
+مرة تانية بتفترض المثل اللي قلتها تانية كلهم ال
+
+224
+00:24:48,040 --> 00:24:54,080
+vector space RN روحت أخدت مجموعة هذه مجموعة وهذه
+
+225
+00:24:54,080 --> 00:24:59,760
+مجموعة تانيةلو جيت كل واحد هنا بقدر اكتبه كlinear
+
+226
+00:24:59,760 --> 00:25:05,400
+combination من اللي هنا ان حدث ذلك يبقى بالصير ال
+
+227
+00:25:05,400 --> 00:25:10,160
+vector space ده هو ال subspace من المجموعة الثانية
+
+228
+00:25:10,160 --> 00:25:14,860
+العملية العكسية لو جيت كل vector هنا هو linear
+
+229
+00:25:14,860 --> 00:25:18,740
+combination من اللي هناوكل vector هناك هو linear
+
+230
+00:25:18,740 --> 00:25:23,340
+combination من اللي هنا معناته اتنين are equal
+
+231
+00:25:23,340 --> 00:25:29,220
+يبقى اتنين ينطبقان على بعضهما تمام الانطلاق واضح
+
+232
+00:25:29,220 --> 00:25:34,720
+طيب بدنا نروح نثبت صحة هذا الكلام مشان نثبت صحة
+
+233
+00:25:34,720 --> 00:25:40,210
+هذا الكلامبقول لو كان كل U هو linear combination
+
+234
+00:25:40,210 --> 00:25:47,670
+يبقى U هو subspace من من V تمام subspace احنا
+
+235
+00:25:47,670 --> 00:25:53,880
+بجينا نروح نثبت الثلاث شروطالـ zero و constant فيه
+
+236
+00:25:53,880 --> 00:26:00,280
+vector في نفس ال subset هذا وحاصل جامعة two
+
+237
+00:26:00,280 --> 00:26:04,200
+vectors من ال set هذه بيكون موجود انها ذلك بقول
+
+238
+00:26:04,200 --> 00:26:09,380
+subspace صح؟ لكن بعد ذلك اتطورنا شوية واخدنا نظرية
+
+239
+00:26:09,380 --> 00:26:14,110
+بتقوليلو كان الـ vector اللي عندنا أو ال subset
+
+240
+00:26:14,110 --> 00:26:17,990
+هذه اللي أخدنا كل vector فيها على صيغة linear
+
+241
+00:26:17,990 --> 00:26:22,990
+combination يبقى ال set اللي تولد بالمجموعة ال
+
+242
+00:26:22,990 --> 00:26:26,330
+vectors اللي عندنا span هذه ال vector بتبقى ال
+
+243
+00:26:26,330 --> 00:26:31,730
+subspace صحيح ولا لأ طيب يبقى احنا بدنا نيجي ناخد
+
+244
+00:26:31,730 --> 00:26:38,570
+بدي افترض ال X مثلا هو أي واحد من هدول يبقى هنا
+
+245
+00:26:38,570 --> 00:26:49,210
+letالـ X بـ any vector
+
+246
+00:26:49,210 --> 00:27:01,890
+of المجموعة U1 و U2 و لغاية URبدي افترض ان ال X هو
+
+247
+00:27:01,890 --> 00:27:08,830
+اي واحد من هدول طب ايش بيقول ليه؟ اذا كان ال U هو
+
+248
+00:27:08,830 --> 00:27:13,290
+linear combination من ال V يبقى معناته ال X هي
+
+249
+00:27:13,290 --> 00:27:20,290
+linear combination من من؟ من ال V's يبقى هنا سا ال
+
+250
+00:27:20,290 --> 00:27:26,470
+X is a linear combination
+
+251
+00:27:28,840 --> 00:27:41,240
+of الـ vs that is أي أن ال X هنا بقدر اكتبه A1 V1
+
+252
+00:27:41,240 --> 00:27:47,000
+زي A2 V2 زي AS VS
+
+253
+00:27:54,330 --> 00:27:59,930
+الـ X خدته واحد معين و الله اي واحد من المجموعة
+
+254
+00:27:59,930 --> 00:28:04,730
+هذهيعني هذا الكلام اللي أنا بقوله ينطبق على أي
+
+255
+00:28:04,730 --> 00:28:10,910
+vector من ال U1 لغاية ال UR بمعنى آخر كل vector من
+
+256
+00:28:10,910 --> 00:28:15,970
+ال U هات هدول هو عبارة عن linear combination من ال
+
+257
+00:28:15,970 --> 00:28:21,710
+V هات من V1 V2 لغاية VS صحيح ولا لأ؟ معناته أن هذا
+
+258
+00:28:21,710 --> 00:28:27,490
+يولد به صحيح ولا لأ؟يبقى هنا مدام ال X كتبته على
+
+259
+00:28:27,490 --> 00:28:34,070
+صيغة linear combination من ال V1 و V2 و V3 هذا
+
+260
+00:28:34,070 --> 00:28:40,030
+معناه الحين احنا قلنا هذا ال subspace يولد بهذه
+
+261
+00:28:40,030 --> 00:28:46,250
+العناصر يبقى معناته ال X وين موجودة؟ وين موجودة؟
+
+262
+00:28:46,250 --> 00:28:52,070
+في ال V صحيح ولا لأ؟ يبقى هذا معناه ان ال X هذا
+
+263
+00:28:52,070 --> 00:29:02,920
+موجودة في ال Vهذا معناه ان ال U هو subset من V
+
+264
+00:29:02,920 --> 00:29:06,800
+خلصت؟
+
+265
+00:29:06,800 --> 00:29:13,820
+لا ماخلصتشمخلص ايش؟ جالي جالي و اثبت ان الـ U
+
+266
+00:29:13,820 --> 00:29:18,880
+subspace و ليس ال subset مظبوط؟ هو جالي اثبت انه
+
+267
+00:29:18,880 --> 00:29:22,560
+subspace مش انا حتى لا اثبت انها subset يبغى ضايل
+
+268
+00:29:22,560 --> 00:29:29,930
+اثبت انها subspace مظبوط؟ بقول والله كويس الانكل
+
+269
+00:29:29,930 --> 00:29:37,650
+element في U هو linear combination من الـV يعني
+
+270
+00:29:37,650 --> 00:29:43,550
+الـU بده يساوي لسبين تبع V1 و V2 و لغاية Vs يبقى
+
+271
+00:29:43,550 --> 00:29:55,690
+هذا معناه ان every element of
+
+272
+00:29:56,610 --> 00:30:13,350
+U is an element of V هذا معناه subset but ولكن لـ
+
+273
+00:30:13,350 --> 00:30:27,840
+Spain of V1 و V2 و Vs و Vs بده يساوي الـ Uلأن كل
+
+274
+00:30:27,840 --> 00:30:30,320
+element من U باقت بقى على صيغة لينا ال combination
+
+275
+00:30:30,320 --> 00:30:40,560
+من V هذا معناه ان ال U is a subspace of V
+
+276
+00:30:44,320 --> 00:30:48,880
+أخدنا نظرية طبعا سابقا قلنا نسبين تبع مجموعة في ال
+
+277
+00:30:48,880 --> 00:30:54,320
+vectors هو subspace مظبوط ولا لا؟ هنا أثبتنا أن كل
+
+278
+00:30:54,320 --> 00:31:02,550
+element في U هو موجود في V بقال U subset من Vالان
+
+279
+00:31:02,550 --> 00:31:06,570
+كل element في U بقدر اكتبه على صيغة linear
+
+280
+00:31:06,570 --> 00:31:12,330
+combination من من؟ من ال V يبقى ال U بده يساوي ال
+
+281
+00:31:12,330 --> 00:31:17,470
+span تبع ال V هات هدول، مظبوط ولا لأ؟ طيب ليه span
+
+282
+00:31:17,470 --> 00:31:21,830
+أثبتناه سابقا من نظرية انه عبارة عن subspace؟ يبقى
+
+283
+00:31:21,830 --> 00:31:26,450
+بالتالي صار ال U هو ال subspace من V وهو المطلوب
+
+284
+00:31:26,450 --> 00:31:37,350
+الأولالان نأتي للمطلوب الثاني المطلوب الثاني بقول
+
+285
+00:31:37,350 --> 00:31:42,800
+لو كان كل U هي linear combination من Vاللي هو main
+
+286
+00:31:42,800 --> 00:31:48,180
+اللي عندنا يبقى u subspace من v وكان في نفس الوقت
+
+287
+00:31:48,180 --> 00:31:53,780
+كل v هو linear combination من اللي هو v يبقى هذا
+
+288
+00:31:53,780 --> 00:31:58,280
+مجموعة يبقى صار ال u subset من v و ال v subset من
+
+289
+00:31:58,280 --> 00:32:01,860
+u حسب خواصة المجموعة يبقى ال u بده يساوي v وهو
+
+290
+00:32:01,860 --> 00:32:13,080
+المطلوب مظبوط يبقى باجي بقول هنا from part Iأن الـ
+
+291
+00:32:13,080 --> 00:32:17,920
+U هو subset من V Similarly
+
+292
+00:32:19,970 --> 00:32:28,690
+بنفس الطريقة ال V هو subset من من؟ من ال U لأن
+
+293
+00:32:28,690 --> 00:32:35,590
+النص هذا هو النص اللي فوق وهذا نفس النص بس قلبنا
+
+294
+00:32:35,590 --> 00:32:42,850
+يبقى هذا يؤدي إلى نفس النتيجة يبقى دص وهكذا ال U
+
+295
+00:32:42,850 --> 00:32:47,830
+بده يساوي مين؟ بده يساوي V وانت هنا من المثل
+
+296
+00:32:49,650 --> 00:32:55,190
+يبقى يا بنات إذا عندي مجموعتين أثبت أن الأولى كل
+
+297
+00:32:55,190 --> 00:32:59,550
+عنصر هنا هو linear combination من جميع العناصر
+
+298
+00:32:59,550 --> 00:33:03,530
+اللي هنا وعكس أثبت أن كل عنصر هنا هو linear
+
+299
+00:33:03,530 --> 00:33:07,170
+combination من جميع العناصر اللي هنا يبقى ال two
+
+300
+00:33:07,170 --> 00:33:12,270
+sets are equal أو ال two subspaces are equal اتنين
+
+301
+00:33:12,270 --> 00:33:17,190
+نفس الشيء بالضبط تماما ناخد مثال عملي توضيحي على
+
+302
+00:33:17,190 --> 00:33:18,450
+ذلك example
+
+303
+00:33:27,310 --> 00:33:40,110
+بقول لـ let u be the subspace of
+
+304
+00:33:40,110 --> 00:33:47,650
+R3 spanned by
+
+305
+00:33:49,100 --> 00:33:53,940
+يبقى هذا الـ subspace ولد بالعناصر يواحد يساوي
+
+306
+00:33:53,940 --> 00:34:07,720
+واحد واتنين وتلاتة and يتنين يتنين يساوي اتنين
+
+307
+00:34:07,720 --> 00:34:18,550
+اربعة اتنين اتنين و سالب واحد وزيرو little vالـ V
+
+308
+00:34:18,550 --> 00:34:33,650
+Be the subspace Be the subspace Of R3 Of R3
+
+309
+00:34:33,650 --> 00:34:40,070
+Spanned by Spanned by
+
+310
+00:34:40,070 --> 00:34:51,580
+V1 بده يساوي واحد اتنين تلاتةو V2 بده يساوي اتنين
+
+311
+00:34:51,580 --> 00:35:04,960
+اربعة ستة المطلوب الاول بيقول is اللي هو ال V ال
+
+312
+00:35:04,960 --> 00:35:13,800
+subspace of you ام لا ده السؤال الاول السؤال
+
+313
+00:35:13,800 --> 00:35:14,480
+الثاني
+
+314
+00:35:19,280 --> 00:35:29,920
+المطلوب الثاني بيقول are ال U and ال V the same
+
+315
+00:35:29,920 --> 00:35:33,840
+هذا
+
+316
+00:35:33,840 --> 00:35:35,780
+المطلوب الثاني
+
+317
+00:35:48,680 --> 00:35:53,940
+بنرجع لسؤالنا مرة تانية بقول افترض عندي ال sub
+
+318
+00:35:53,940 --> 00:36:01,680
+space U من R3 ولد بال vector U1 و U2 و افترض عندي
+
+319
+00:36:01,680 --> 00:36:07,560
+sub space ثاني V ولد بالعناصر V1 و V2 بالشكل اللي
+
+320
+00:36:07,560 --> 00:36:13,590
+عندنا بسأل هل ال V sub space من U ولا لأ؟هل ال V
+
+321
+00:36:13,590 --> 00:36:18,470
+هو subspace منه ولا لأ؟ بنقول والله تمام إذا كان
+
+322
+00:36:18,470 --> 00:36:23,190
+كل عنصر من ال vector الأول كتبناه على صيغة linear
+
+323
+00:36:23,190 --> 00:36:27,370
+combination من ال vector الثاني بكون خلصنا من
+
+324
+00:36:27,370 --> 00:36:32,990
+الموضوع صحيح ولا لأ؟ يعني أنا عندش هذا solution
+
+325
+00:36:35,890 --> 00:36:41,510
+هو بدي ابدا بالنقطة الأولى احنا عندنا يا بنات ال U
+
+326
+00:36:41,510 --> 00:36:53,930
+تساوي لسبين تبع مين U واحد و U اتنين and ال V اللي
+
+327
+00:36:53,930 --> 00:36:58,710
+هو بده تساوي لسبين تبع ال V واحد و V اتنين
+
+328
+00:37:02,700 --> 00:37:08,860
+بسأل هل ال V subset من كانه جلب نص النظرية؟ جلب ما
+
+329
+00:37:08,860 --> 00:37:14,080
+جلب مش مشكلة عندنا يبقى أنا ههه لو قدرت أثبت له
+
+330
+00:37:14,080 --> 00:37:18,640
+أنه كل element هنا هو linear combination من
+
+331
+00:37:18,640 --> 00:37:23,440
+الاتنين هذول بصير V subset من من؟ subset من صحيح
+
+332
+00:37:23,440 --> 00:37:28,280
+ولا لأ؟ يبقى باجي بقوله لو جيت أخدت العنصر الأول
+
+333
+00:37:28,280 --> 00:37:33,760
+بدي أجي أخد V واحدفي واحد عند مين يا بنات اللي هو
+
+334
+00:37:33,760 --> 00:37:40,680
+واحد واتنين وتلاتة السؤال هو هل بقدر اكتب على صيغة
+
+335
+00:37:40,680 --> 00:37:45,340
+linear combination من الاتنين هدول ام لا هذا
+
+336
+00:37:45,340 --> 00:37:51,540
+السؤال بنجيب و بنقول بنقدر يعني بقدر اكتب هذا
+
+337
+00:37:51,540 --> 00:37:58,990
+constant هنا زائد constant هنا1 و 0 ممتاز جدا يبقى
+
+338
+00:37:58,990 --> 00:38:08,270
+بقدر اقول هذا 1 في 1 و 2 و 3 زائد 0 في 2 و سالب 1
+
+339
+00:38:08,270 --> 00:38:17,930
+و 0 يعني هذا كأن 1 في ال U 1 زائد 0 في ال U 2 يبقى
+
+340
+00:38:17,930 --> 00:38:24,440
+V1 هو linear combination من مين؟من U1 و U2 صحيح
+
+341
+00:38:24,440 --> 00:38:31,960
+ولا لا يبقى بنفس الطريقة لو جيت لل V2 ال V2 اللي
+
+342
+00:38:31,960 --> 00:38:38,060
+هو عبارة عن اتنين اربعة ستة بدي اشوف هل بقدر اكتب
+
+343
+00:38:38,060 --> 00:38:43,600
+هذا على صيغة linear combination من ال U1 و U2 ام
+
+344
+00:38:43,600 --> 00:38:48,580
+لا قول تمام في هنا اتنين عامل مشترك اظن يا بنات
+
+345
+00:38:52,830 --> 00:38:57,950
+الذي بقدر او كتبه عليه الشكل التالي اتنين واحد
+
+346
+00:38:57,950 --> 00:39:04,850
+اتنين تلاتة زائد زير و اتنين سالب واحد وزيرمظبوط
+
+347
+00:39:04,850 --> 00:39:10,070
+يبقى معناته ان الـ V1 و الـ V2 كتبته على صيغة
+
+348
+00:39:10,070 --> 00:39:15,710
+linear combination من من من الأخرين يبقى بناء عليه
+
+349
+00:39:15,710 --> 00:39:21,970
+الـ V هو subspace منه تبقى للنقطة الأولى من من من
+
+350
+00:39:21,970 --> 00:39:26,130
+نص النظرية جليلا كينيديو هو linear combination من
+
+351
+00:39:26,130 --> 00:39:38,610
+هذا يبقى باجي يقول له س H V1 andV2 is a linear
+
+352
+00:39:38,610 --> 00:39:45,870
+combination of
+
+353
+00:39:45,870 --> 00:40:01,270
+U1 and U2 يبقى بناء عليه by the above theorem part
+
+354
+00:40:01,270 --> 00:40:13,030
+Iاللي هو النقطة الأولى الـ V is a subspace of U
+
+355
+00:40:13,030 --> 00:40:20,750
+وهو المطلوب خلصنا المطلوب الأول بدنا نروح للمطلوب
+
+356
+00:40:20,750 --> 00:40:25,830
+التانيالمطلوب التاني بيقولّي هل ال U و ال V هدول
+
+357
+00:40:25,830 --> 00:40:30,690
+بيسووا بعض أم لا يعني هل ال vector U هو نفس ال
+
+358
+00:40:30,690 --> 00:40:35,050
+vector V ولا لأ يعني اللي أثبتته هنا بنات انه مين
+
+359
+00:40:35,050 --> 00:40:40,970
+ان ال V هو sub space من U يعني V subset من U يبقى
+
+360
+00:40:40,970 --> 00:40:45,850
+هذا معناه ان
+
+361
+00:40:45,850 --> 00:40:48,550
+ال V subset من U
+
+362
+00:40:51,600 --> 00:41:00,420
+لو قدرت أثبت أن الـ U subset من U بتم المطلوب،
+
+363
+00:41:00,420 --> 00:41:08,960
+يعني إذا قدرت أثبت أن أي فيكتور في U هو linear
+
+364
+00:41:08,960 --> 00:41:14,830
+combination من إتنين هؤلاء بتم المطلوبأظن الأولاني
+
+365
+00:41:14,830 --> 00:41:19,150
+بسيط مافيش فيه مشكلة المشكلة في التاني طيب تعالي
+
+366
+00:41:19,150 --> 00:41:27,310
+مشان هيك بداجي أقوله let مثلا a1 و a2 موجودة في
+
+367
+00:41:27,310 --> 00:41:33,270
+set of real numbers such that اللي هو من؟ اللي هو
+
+368
+00:41:33,270 --> 00:41:41,460
+الاتنين و سالب واحد و zero بده يسوى a1يبدو يساوي
+
+369
+00:41:41,460 --> 00:41:54,540
+a1 في ال V1 زائد a2 في ال V2 ثم بدي اخد a1 V1 زائد
+
+370
+00:41:54,540 --> 00:42:00,580
+a2 V2 يبدو يساوي بدي ادخل على طول الخط وين V1 و V2
+
+371
+00:42:00,580 --> 00:42:14,540
+هاي هم هناك يبقى ايش بده يصير يبقى a12A1 3A1 A2 B2
+
+372
+00:42:14,540 --> 00:42:21,680
+2A2 4A2 6A2
+
+373
+00:42:23,480 --> 00:42:30,400
+6A2 كل هذا الكلام سيكون اتنين سالب واحد و Zero
+
+374
+00:42:30,400 --> 00:42:37,420
+تعالوا نجمع يبقاش بيصير عندي هنا A1 زائد اتنين A2
+
+375
+00:42:37,420 --> 00:42:48,080
+اتنين A1 زائد اربعة A2 تلاتة A1 زائد ستة A2 كله
+
+376
+00:42:48,080 --> 00:42:54,770
+سيكون اتنين سالب واحدوزير صار عندى three tuple
+
+377
+00:42:54,770 --> 00:43:02,070
+بساوي three tuple اذا بدنا نكون ال system المناظر
+
+378
+00:43:02,070 --> 00:43:11,230
+لهما يبقى
+
+379
+00:43:11,230 --> 00:43:16,790
+ال system المناظر لهما ا واحد زائد اتنين ا اتنين
+
+380
+00:43:16,790 --> 00:43:19,550
+بده يسوى قداش اتنين
+
+381
+00:43:23,490 --> 00:43:30,230
+2A1 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2
+
+382
+00:43:30,230 --> 00:43:30,870
+زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد
+
+383
+00:43:30,870 --> 00:43:31,630
+4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2
+
+384
+00:43:31,630 --> 00:43:31,690
+زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد
+
+385
+00:43:31,690 --> 00:43:31,690
+4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2
+
+386
+00:43:31,690 --> 00:43:32,830
+زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد
+
+387
+00:43:32,830 --> 00:43:41,750
+4A2 زائد 4A2 زائد 4A2 زائد 4A2 زائد 4A
+
+388
+00:43:42,420 --> 00:43:49,140
+بنحل هذه المعادلة اظن لو ضربنا تالتة في سالب واحد
+
+389
+00:43:49,140 --> 00:43:54,540
+و جماعنا بيكون ايه؟ حلنا النظام اللي عندنا هذا
+
+390
+00:43:54,540 --> 00:44:01,210
+يبقى ا واحد زيدي اتنين اتنين يساوي اتنينأتنين ا
+
+391
+00:44:01,210 --> 00:44:08,530
+واحد زائد أربعة اتنين يساوي ناقص واحد تلاتة ا واحد
+
+392
+00:44:08,530 --> 00:44:16,330
+زائد او ناقص و هنا ناقص ستة اتنين يساوي مين؟ زيرو
+
+393
+00:44:16,330 --> 00:44:21,570
+ايجي معاه يبقى هدول مع السلامة و ده يلحقهم مع
+
+394
+00:44:21,570 --> 00:44:27,370
+السلامة هذا معناته ان زيرو يساوي كده؟ يساوي واحد
+
+395
+00:44:27,370 --> 00:44:31,930
+ايش رأيكم موافقين؟يبقى هذا الكلام مش صحيح يبقى
+
+396
+00:44:31,930 --> 00:44:37,610
+impossible إيش يعني impossible يعني لا يمكن كتابة
+
+397
+00:44:37,610 --> 00:44:41,090
+ال vector اللي عندنا على صيغة linear combination
+
+398
+00:44:41,090 --> 00:44:46,610
+من ال two vectors معناته هذا subset منه لأ يبقى
+
+399
+00:44:46,610 --> 00:44:56,530
+هنا هذا this is impossible هذا الكلام غير ممكن so
+
+400
+00:44:56,530 --> 00:44:56,810
+that
+
+401
+00:44:59,680 --> 00:45:07,980
+Vector V1 V2 V3
+
+402
+00:45:07,980 --> 00:45:10,540
+V4 V5 V6 V7 V8 V9 V10 V11 V12 V13 V12 V13 V12 V12
+
+403
+00:45:10,540 --> 00:45:18,080
+V12 V12 V12 V12 V12 V12 V12 V12 V12 V12 V12
+
+404
+00:45:18,080 --> 00:45:23,000
+V12
+
+405
+00:45:23,000 --> 00:45:26,060
+V12
+
+406
+00:45:26,590 --> 00:45:35,730
+V1 و V2 هذا الـ vector موجود في الـ U يبقى هنا
+
+407
+00:45:35,730 --> 00:45:46,190
+Therefore و لهذا الـ U ليس مجموعة من V هذا معناه
+
+408
+00:45:46,190 --> 00:45:50,890
+أن الـ U لا يمكن أن تساوي الـ V
+
+409
+00:45:55,920 --> 00:45:59,400
+في مبادئ رياضات البنات مشان أثبت أن الـ two sets
+
+410
+00:45:59,400 --> 00:46:03,500
+are equal بداية أثبت أن أي element في ال set
+
+411
+00:46:03,500 --> 00:46:07,080
+الأولى هو موجود في ال set الثانية و العكس أن أي
+
+412
+00:46:07,080 --> 00:46:10,040
+element في ال set الثانية هو موجود في ال set
+
+413
+00:46:10,040 --> 00:46:15,020
+الأولى إن حدث ذلك بيحدث التساوي لم يحدث و لو عنصر
+
+414
+00:46:15,020 --> 00:46:19,840
+واحد يبقى مصير ماعنديش تساوي في هذه الحالةوهذا ما
+
+415
+00:46:19,840 --> 00:46:22,980
+أثبتناه هنا أخدنا vector و أثبتنا إنه هذا ال
+
+416
+00:46:22,980 --> 00:46:27,360
+vector غير موجود يبقى معناته هدول ما لهم غير
+
+417
+00:46:27,360 --> 00:46:33,260
+متساوين بنجي لآخر حاجة في هذا ال section وهي
+
+418
+00:46:33,260 --> 00:46:39,860
+exercises تلاتة اتنين المسائل واحد واتنين وتلاتة
+
+419
+00:46:39,860 --> 00:46:44,880
+وخمسة وستة وسبعة وتسعة
+
+420
+00:46:47,390 --> 00:46:54,850
+وتلتاشر واربعتاشر بدنا ياكى تتدربى عليهم حد فيكوا
+
+421
+00:46:54,850 --> 00:46:59,910
+لايه تساول هنا المرة القادمة ان شاء الله يوم السبت
+
+422
+00:46:59,910 --> 00:47:06,310
+بنضلنا طيبين وبصحة جيدة و الجامعة كانت فاتحة طبعا
+
+423
+00:47:06,310 --> 00:47:10,650
+بنيجي ونبدأ ال section اللى بعده وهو تلاتة تلاتة
+
+424
+00:47:11,320 --> 00:47:14,620
+الثلاثة ثلاثة إرادة مرّيلي عليه جيب النتيجة وهو
+
+425
+00:47:14,620 --> 00:47:19,600
+Linear Dependence و Linear Independent Vector
+
+426
+00:47:19,600 --> 00:47:26,160
+المتجهات المستقلة والمعتمدة على بعضها خطيا
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/gL3eIuaC1P8_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/gL3eIuaC1P8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d16f0b84cccd01aebdbd62ff8ce365f896fc8d36
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/gL3eIuaC1P8_raw.srt
@@ -0,0 +1,1424 @@
+1
+00:00:20,750 --> 00:00:25,830
+بسم الله الرحمن الرحيم لان بنجي لهذا ال section
+
+2
+00:00:25,830 --> 00:00:30,810
+طبعا section 2-6 ابن الغيمة اللي مش داخل المقارة
+
+3
+00:00:30,810 --> 00:00:35,330
+بنجي ل section 2-7 اللي هو some special matrices
+
+4
+00:00:35,330 --> 00:00:41,860
+بعض المصوفات الخاصةنبدأ في أول مصوفة هي المصوفة
+
+5
+00:00:41,860 --> 00:00:46,260
+الصفرية ثم مصوفة الواحدة وبعد ذلك ننتقل إلى
+
+6
+00:00:46,260 --> 00:00:51,640
+المصوفات الأخرى يبقى the M في N matrix whose
+
+7
+00:00:51,640 --> 00:00:55,120
+elements are all zero is called the zero matrix of
+
+8
+00:00:55,120 --> 00:01:00,850
+size M في NAnd denoted by zero M N يعني بنكتب الـ
+
+9
+00:01:00,850 --> 00:01:05,470
+Zero لم طاول هذا شوية على شكل بيضاوي وبنحط تحته M
+
+10
+00:01:05,470 --> 00:01:09,890
+في N دليل على أنه نظامها أو ال size M في M يبقى
+
+11
+00:01:09,890 --> 00:01:13,650
+المصوفة الصفرية لو كانت مصوفة مربعة والله مصوفة
+
+12
+00:01:13,650 --> 00:01:19,860
+مستطيلة المهم جميع أنصرها بيكونوا أصفراًThe
+
+13
+00:01:19,860 --> 00:01:26,000
+Identity Matrix المصفوفة الوحدة المصفوفة الوحدة
+
+14
+00:01:26,000 --> 00:01:31,980
+هاديها الرمز IN وهي مصفوفة مربعة عدد الصفوف يساوي
+
+15
+00:01:31,980 --> 00:01:39,080
+فيها عدد الأعمدة square matrix هاديها الرمز IN وهي
+
+16
+00:01:39,080 --> 00:01:48,680
+100110 كل 001جميع عناصرها أصفرًا ما عدا عناصر
+
+17
+00:01:48,680 --> 00:01:53,780
+القطر الرئيسي كل واحد واحد واحد تمام؟ يبقى في
+
+18
+00:01:53,780 --> 00:01:57,160
+عندنا مناطق اسم القطر الرئيسي في القطر الثانوي
+
+19
+00:01:57,160 --> 00:02:01,260
+القطر اللي جاي من الشمال لليمين بسميه الرئيسي
+
+20
+00:02:01,260 --> 00:02:05,040
+واللي جاي من اليمين للشمال بسميه الثانوي ثانوي
+
+21
+00:02:05,040 --> 00:02:10,120
+بلزمنيش بلزمنا الرئيسي يبقى ال mean diagonal القطر
+
+22
+00:02:10,120 --> 00:02:13,750
+الرئيسي هو اللي جاي من الشمال لليمينجميع العناصر
+
+23
+00:02:13,750 --> 00:02:19,230
+كل واحد صحيح وباقي العناصر أصفرا ممكن أدّيها رمز
+
+24
+00:02:19,230 --> 00:02:25,950
+آخر غير رمز IN ممكن أقول عليها Delta IJ بحيث Delta
+
+25
+00:02:25,950 --> 00:02:31,170
+IJ يبدأ تساوي Zero يبدأ تساوي واحد تساوي Zero كم؟
+
+26
+00:02:31,170 --> 00:02:37,090
+إذا I لا تساوي الـJ إذا I سوى الـJ تساوي كم؟ واحد
+
+27
+00:02:37,090 --> 00:02:40,980
+صحيح فمثلاعندما أقول العنصر اللي عندي هذا واحد
+
+28
+00:02:40,980 --> 00:02:45,920
+يبقى جاي في الصف الأول والعمود الأول يبقى دلتا
+
+29
+00:02:45,920 --> 00:02:52,980
+واحد واحد I تساوي J هذا العنصر جاي في الصف الثاني
+
+30
+00:02:52,980 --> 00:02:58,500
+والعمود الثاني يبقى دلتا اتنين اتنين I تساوي J
+
+31
+00:02:58,500 --> 00:03:03,360
+اللي بعده هنا كمان واحد يبقى دلتا تلاتة تلاتة دلتا
+
+32
+00:03:03,360 --> 00:03:09,790
+اربعة اربعة دلتا خمسة خمسةDelta N N يبقى هنا مقداش
+
+33
+00:03:09,790 --> 00:03:15,270
+بواحد صين ما خلال ذلك لو جيت لهذا يبقى هذا Delta
+
+34
+00:03:15,270 --> 00:03:20,250
+واحد تلاتة الواحد لا تساوي تلاتة يبقى القيمة تساوي
+
+35
+00:03:20,250 --> 00:03:25,920
+قداش تساوي Zeroيبقى سواء رمزنا بالرمز هذا أو الرمز
+
+36
+00:03:25,920 --> 00:03:31,580
+هذا لإتنية الرمز لمصوفية الوحدة راح جلد delta ig
+
+37
+00:03:31,580 --> 00:03:37,200
+دي sample يعني الرمز delta ig بسميه chronicle
+
+38
+00:03:37,200 --> 00:03:37,900
+delta
+
+39
+00:03:40,980 --> 00:03:45,280
+من حد ما تشوف المصوفة هذه بديك تعرف إن هذه مصوفة
+
+40
+00:03:45,280 --> 00:03:49,280
+لوحدها سواء بالصيغة هذه أو بالصيغة هذه وما بتهمنيش
+
+41
+00:03:49,280 --> 00:03:53,500
+التسميات كرونيكار ماكرونيكار والزمني بالزمني تعرف
+
+42
+00:03:53,500 --> 00:03:58,340
+الإسم الدارج وهو مصوفة الواحدة هذه اللي هو very
+
+43
+00:03:58,340 --> 00:04:03,860
+important لأنه ولا كتاب هايت في الجبر الخطي إلا
+
+44
+00:04:03,860 --> 00:04:16,160
+وفي هذه التسمية اللي هي مصوفة الواحدةبنشوف بعض
+
+45
+00:04:16,160 --> 00:04:20,940
+الخواص بالنسبة لهم الخاصية الأولى لو جيت جامعة
+
+46
+00:04:20,940 --> 00:04:27,640
+المصوفة N لنظام N في N إلى من المصوفة الصفرية لكي
+
+47
+00:04:27,640 --> 00:04:33,110
+أقدر أجمعها لازم تبقى المصوفة الصفرية نظامهامفي ان
+
+48
+00:04:33,110 --> 00:04:38,090
+لذلك ماخلتكي اشتريها و روحت كتب تحت مفي ان دليل
+
+49
+00:04:38,090 --> 00:04:42,630
+على ان الصفوف هنا زي الصفوف هنا و الأعمد هنا زي
+
+50
+00:04:42,630 --> 00:04:46,390
+الصفوف زي الأعمد هنا طبعا في الجامعة كل عنصر مع
+
+51
+00:04:46,390 --> 00:04:50,650
+نظيرة لما اضيف الصفر لأي عنصر بيظل نفس الانصر
+
+52
+00:04:50,650 --> 00:04:56,420
+وبالتالي هتطلع ان المصوفة ايه الأصليةطيب لو جمعت A
+
+53
+00:04:56,420 --> 00:05:00,440
+و سالب واحد في ايه؟ سالب واحد بيضرب في جميع
+
+54
+00:05:00,440 --> 00:05:04,840
+العناصر بلا استثناء لما نقضره في جميع العنصر يبقى
+
+55
+00:05:04,840 --> 00:05:08,920
+الموجب بيصير سالب وسالب بيصير الموجب إذا لما أجمع
+
+56
+00:05:08,920 --> 00:05:12,780
+كل عنصر مع نظيره النتج بيديهي أعطيني مين؟ Zero
+
+57
+00:05:12,780 --> 00:05:18,730
+بالتالة بتطلع المصحوفة الصفرية اللي هو Zero MMيعني
+
+58
+00:05:18,730 --> 00:05:23,010
+بالبلد هيك إذا أضافت المصوفة الصفرية للمصوفة بيطلع
+
+59
+00:05:23,010 --> 00:05:27,090
+نفس المصوفة إذا أضافت المصوفة لسالب المصوفة النتج
+
+60
+00:05:27,090 --> 00:05:30,950
+هو المصوفة الصفرية ومن نفس النظام على كل الأمرين
+
+61
+00:05:30,950 --> 00:05:34,970
+النقطة التالتة المرة اللي فاتة خدنا ال matrix
+
+62
+00:05:34,970 --> 00:05:40,510
+multiplication ضرب المصوفات الآن أنا عندي مصوفة
+
+63
+00:05:40,510 --> 00:05:45,830
+نظامها M في N بدي أضربها في Zero in P بتتم عملية
+
+64
+00:05:45,830 --> 00:05:50,780
+الضرببتتم لأن عدد الأعمدة في المصوفة الأولى يساوي
+
+65
+00:05:50,780 --> 00:05:55,240
+عدد الصفوف في المصوفة الثانية والناتج مصوفة نظامها
+
+66
+00:05:55,240 --> 00:06:01,760
+M في P يبقى Zero M في P يبقى هذه المصوفة الصفرية
+
+67
+00:06:01,760 --> 00:06:07,910
+يبقى لو ضربمصوفة A و 0 و 2 و 2 مش من نفس النظام
+
+68
+00:06:07,910 --> 00:06:12,370
+لكن فيهم شرط عدد أعمدة المصوفة الأولى يسوى عدد
+
+69
+00:06:12,370 --> 00:06:17,950
+صفوف المصوفة الثانية فالنتج هو مصوفة صفرية عددها
+
+70
+00:06:17,950 --> 00:06:21,730
+صفوفة هو عدد صفوف المصوفة الأولى وعدد أعمدتها هو
+
+71
+00:06:21,730 --> 00:06:29,780
+عدد أعمدت المصوفة الثانية0 المصوفة الصفرية نظامها
+
+72
+00:06:29,780 --> 00:06:36,600
+Q M ده ضربها في A M هي M في N إذاً عدد الأعمدة في
+
+73
+00:06:36,600 --> 00:06:41,060
+المصوفة الصفرية يساوي عدد الصفوف في المصوفة A إذا
+
+74
+00:06:41,060 --> 00:06:46,420
+يمكن أن تتم عملية الضرب والناتج مصوفة نظامها Q في
+
+75
+00:06:46,420 --> 00:06:52,580
+M يبقى Zero Q في N إذاً هل هذه المصوفة هي المصوفة
+
+76
+00:06:52,580 --> 00:06:57,910
+هذه؟لأ هذه صفرية صحية و هذه صفرية بس عدد الصفوف
+
+77
+00:06:57,910 --> 00:07:00,610
+اللي أعمدها في الأولى ليست كعدد الصفوف اللي أعمدها
+
+78
+00:07:00,610 --> 00:07:04,730
+في الثانية وبالتالي هما صحيح مصففين صفريات لكن هما
+
+79
+00:07:04,730 --> 00:07:12,230
+ليست متساويةنجي للنقطة الرابعة، لو ضربت المصوفة
+
+80
+00:07:12,230 --> 00:07:15,030
+ايه في مصوفة الوحدة؟ احنا قولنا ان مصوفة الوحدة
+
+81
+00:07:15,030 --> 00:07:21,530
+مصوفة مربعة يبقى لما اقول in المقصود في in في in
+
+82
+00:07:21,530 --> 00:07:26,330
+بس اختصارا بقول in وبسكتيبقى مصروفتي الواحدة هي
+
+83
+00:07:26,330 --> 00:07:31,210
+مصروف ومربع يبقى لأ ده لأن اقول N في N فاختصارا
+
+84
+00:07:31,210 --> 00:07:36,550
+بقول IM يبقى لما نقدر المصروفة ايه لنظامها M في N
+
+85
+00:07:36,550 --> 00:07:42,270
+N في N بدي يطلع اللي هو من المصروفة الاصلية
+
+86
+00:07:42,270 --> 00:07:47,770
+لنظامها M في M لأن هذه M في N وهذه N في N بيظل M
+
+87
+00:07:47,770 --> 00:07:52,630
+في N اللي هي المصروفة الاصلية بنفس الطريقةلو روحت
+
+88
+00:07:52,630 --> 00:07:57,970
+ضربت من الشمال في مصفوفة الوحدة I M هذه الوحدة غير
+
+89
+00:07:57,970 --> 00:08:02,810
+الوحدة هذه صحيح؟ لأن هذه فيها N من الصفوف و N من
+
+90
+00:08:02,810 --> 00:08:08,990
+الأعمدة هذه فيها M من الصفوف و M من الأعمدة إذا
+
+91
+00:08:08,990 --> 00:08:13,850
+هاتان المصففات مختلفتان وإن كانتكل واحدة فيهم هي
+
+92
+00:08:13,850 --> 00:08:17,990
+مصوفة الواحدة يبقى كل واحدة حسب ال size تبعها أو
+
+93
+00:08:17,990 --> 00:08:22,030
+النظام تبعها بتضربها من جهة الشمال في ال A طبعا
+
+94
+00:08:22,030 --> 00:08:27,830
+ممكن لأن هذه M في M وهذه M في N يبقى ناتج نفس
+
+95
+00:08:27,830 --> 00:08:33,320
+المصوفة اللي نظامها M في Nلحظة ان هدول اتنتين ضرب
+
+96
+00:08:33,320 --> 00:08:38,920
+من اليمين و هنا ضرب من الشمال و اعطاني نفس النتيجة
+
+97
+00:08:38,920 --> 00:08:43,960
+رغم ان المصففات اللي اتنين هدول ما لهم غير
+
+98
+00:08:43,960 --> 00:08:50,560
+متساويتينطيب نجي تعريف جديد لو أخدنا المصوفة
+
+99
+00:08:50,560 --> 00:08:56,920
+المربعة اللي عندنا طالع a11 لغاية a1n ضالية نزل
+
+100
+00:08:56,920 --> 00:09:03,200
+لغاية a n1 و هنا a nn يبجى هذه مصوفة مربعة فيها n
+
+101
+00:09:03,200 --> 00:09:08,480
+من الصفوف و n من الأعمدة يبجى هي ال n بال n matrix
+
+102
+00:09:08,480 --> 00:09:12,300
+ان ان كانت هذه المصوفة هيك يبجى فيها عندنا بعض
+
+103
+00:09:12,300 --> 00:09:16,360
+الشغلات بدنا نشير لهاالنقطة الأولى جالي the
+
+104
+00:09:16,360 --> 00:09:22,500
+elements بسميهم
+
+105
+00:09:22,500 --> 00:09:29,020
+العناصر القطرية في المصفوفة يمكن بسميهم اياش ال
+
+106
+00:09:29,020 --> 00:09:33,320
+elements are called the diagonal elements of A
+
+107
+00:09:33,320 --> 00:09:38,760
+العناصر القطرية للمصفوفة A هذه النقطة الأولى
+
+108
+00:09:38,760 --> 00:09:39,660
+النقطة الثانية
+
+109
+00:09:48,190 --> 00:09:55,910
+إذا كان كل عنصر خارج هذا القطر الرئيسي هو 0
+
+110
+00:10:00,460 --> 00:10:05,200
+يبقى لو جيت على المصوفة المربعة و جيت على القطر
+
+111
+00:10:05,200 --> 00:10:11,100
+الرئيسي في هذه المصوفة و لجيت كل العناصر خارج
+
+112
+00:10:11,100 --> 00:10:16,400
+القطر الرئيسي بأصفار ما عدا عناصر القطر الرئيسي
+
+113
+00:10:16,400 --> 00:10:21,870
+يبقى بقول هذه ما لهاdiagonal matrix طب بنفعش يكون
+
+114
+00:10:21,870 --> 00:10:26,630
+أحد العناصر أسفرا في القطرة الرئيسية؟ بنفع ان شاء
+
+115
+00:10:26,630 --> 00:10:31,510
+الله يكونوا كلهم أسفرا و لو بس أنصر واحد مايكون
+
+116
+00:10:31,510 --> 00:10:36,290
+صفر عشان أميزها عن المصموفة الصفرية صحيح ولا لأ؟
+
+117
+00:10:36,420 --> 00:10:42,680
+إذا الـ diagonal matrix هي مصفوفة جميع عناصرها
+
+118
+00:10:42,680 --> 00:10:47,880
+أسفارا عدا عناصر القطرة الرئيسية ويمكن أن تكون بعض
+
+119
+00:10:47,880 --> 00:10:54,200
+عناصر القطرة الرئيسية أسفارا المهم لو حطيت إيدي
+
+120
+00:10:54,200 --> 00:10:58,780
+على القطرة الرئيسية يبقى خارج هذا القطرة الرئيسية
+
+121
+00:10:58,780 --> 00:11:04,160
+جميع العناصر أسفارا بلا إستثناءإن حدث ذلك يبقى هذه
+
+122
+00:11:04,160 --> 00:11:08,540
+المصفوفة بسميها الـ diagonal matrix المصفوفة
+
+123
+00:11:08,540 --> 00:11:14,140
+القطرية بديها الرمز capital D وهو الحرف الأول من
+
+124
+00:11:14,140 --> 00:11:18,980
+كلمة diagonal واختصارا بقول diagonal اختصرت
+
+125
+00:11:18,980 --> 00:11:25,280
+diagonal وكتب D1 وD2 وDN مين هم الدهات هدول هم
+
+126
+00:11:25,280 --> 00:11:32,660
+عناصر القطر الرئيسييبقى الـD1 والـD2 ولغاية DN هي
+
+127
+00:11:32,660 --> 00:11:41,260
+الـdiagonal elements ورد DI بذات ساوي AII يعني D1
+
+128
+00:11:41,260 --> 00:11:49,050
+هذه اللي عندنا هي A11 اللي عندناD2 هي A22 D3 هي
+
+129
+00:11:49,050 --> 00:11:55,570
+A33 يقول I من 1 إلى N يبقى هي من اين هي عناصر
+
+130
+00:11:55,570 --> 00:12:01,950
+القطر الرئيسي مثلا لو اتلك D هي الدياجونال 3 2
+
+131
+00:12:01,950 --> 00:12:07,570
+سالب 1 مثلا يبقى معنى هذا الكلام ان هذه المصفوفة
+
+132
+00:12:07,570 --> 00:12:13,270
+مصفوفة نظامها تلاتة في تلاتةهذه العناصر القطر
+
+133
+00:12:13,270 --> 00:12:18,330
+الرئيسي وباقي العناصر أسفرها طلع هنا هذه عناصر
+
+134
+00:12:18,330 --> 00:12:21,970
+القطر الرئيسي تلاتة اتنين سالب واحد وباقي العناصر
+
+135
+00:12:21,970 --> 00:12:25,730
+اللي فوق و اللي تحت كلهم مالهم كلهم أسفار زي ما
+
+136
+00:12:25,730 --> 00:12:30,250
+انت شايفهانجي للنقطة التالتة بدنا حاجة اسمة scalar
+
+137
+00:12:30,250 --> 00:12:35,090
+matrix يعني يا بنات كأنه احنا حتى هذه اللحظة بناخد
+
+138
+00:12:35,090 --> 00:12:40,110
+حالات خاصة من المصوفة الصفرية ومن اللي هو مصوفة
+
+139
+00:12:40,110 --> 00:12:44,910
+الوحدة او قياسا على مصوفة الوحدة بطلع منها شغلات
+
+140
+00:12:44,910 --> 00:12:50,010
+جديدةيبقى اخدنا الان الـ diagonal matrix هي زي
+
+141
+00:12:50,010 --> 00:12:53,150
+مصفوفة الواحدة بس العناصر مش كل واحد واحد واحد
+
+142
+00:12:53,150 --> 00:12:57,870
+ارقام مختلفة طيب بعد ذلك بنتاجي الى ال scalar
+
+143
+00:12:57,870 --> 00:13:05,830
+matrix المصفوفة القياسية هي مصفوفة قطرية يعني جميع
+
+144
+00:13:05,830 --> 00:13:10,230
+عناصرها أصفرًا ما عدا عناصر قطر رئيسي بس عناصر قطر
+
+145
+00:13:10,230 --> 00:13:14,720
+رئيسي كلها أرقام متساويةواحد واحد واحد .. اتنين
+
+146
+00:13:14,720 --> 00:13:18,320
+اتنين اتنين .. تلاتة تلاتة تلاتة .. عشرة عشرة عشرة
+
+147
+00:13:18,320 --> 00:13:21,840
+.. ناقص خمسة ناقص خمسة ناقص خمسة .. عناصر القطة
+
+148
+00:13:21,840 --> 00:13:27,910
+الرئيسية كلها متساوية .. شلتكون كلها أصفاراصح ولا
+
+149
+00:13:27,910 --> 00:13:30,930
+لأ؟ يبقى ان شاء الله نكون عايش بقول ان الـ scalar
+
+150
+00:13:30,930 --> 00:13:36,330
+matrix is a diagonal matrix هي مصفوفة قطرية such
+
+151
+00:13:36,330 --> 00:13:40,950
+that the diagonal elements are equal كل عناصر
+
+152
+00:13:40,950 --> 00:13:45,830
+القطر الرئيسي كلها متساوية بناء عليه بدي أسألكوا
+
+153
+00:13:45,830 --> 00:13:52,070
+السؤال التالي هل المصفوفة الصفرية scalar matrix؟
+
+154
+00:13:52,070 --> 00:13:57,170
+نعمهل مصفوفة الوحدة scalar matrix؟ أه لأن عناصر
+
+155
+00:13:57,170 --> 00:14:01,550
+القطر الرئيسي أصفة أرقام متزاوية والباقية ليست
+
+156
+00:14:01,550 --> 00:14:05,550
+علاقة بها أنا أريد عناصر القطر الرئيسي يبقى
+
+157
+00:14:05,550 --> 00:14:11,860
+المصفوفة القياسية هي مصفوفة قطريةيعني جميع عناصرها
+
+158
+00:14:11,860 --> 00:14:15,700
+أصفرًا عادة عناصر القطر الرئيسي زيادة على ذلك
+
+159
+00:14:15,700 --> 00:14:21,400
+عناصر القطر الرئيسي كلها أرقام متساوية يبقى هذه
+
+160
+00:14:21,400 --> 00:14:25,580
+اللي هي ال scalar matrix for example لو بدأتي أخد
+
+161
+00:14:25,580 --> 00:14:31,210
+ال scalar matrix و أديتها الرمز دييبقى دي دي دي دي
+
+162
+00:14:31,210 --> 00:14:36,030
+مصوفة مربعة وباقي العناصر أصفرًا اللي ممكن أكتبها
+
+163
+00:14:36,030 --> 00:14:41,410
+ممكن أخد الدي برا عامل مشترك لأن الدي الرقم لو
+
+164
+00:14:41,410 --> 00:14:46,110
+ضربته في المصوفة بضربه في جميع عناصر المصوفة فدي
+
+165
+00:14:46,110 --> 00:14:51,530
+في zero ب zero دي في واحدبـ D و هكذا يبقى يا
+
+166
+00:14:51,530 --> 00:14:54,990
+بكتبها على الشكل هذه يا بكتبها على الشكل اللي أنا
+
+167
+00:14:54,990 --> 00:15:00,990
+كاينه هنا خاتة D عامل مشترك من جميع أناصر المصورة
+
+168
+00:15:00,990 --> 00:15:05,710
+طيب اللي بين جسين هذه المصورة دي من مصوفة الوحدة
+
+169
+00:15:05,710 --> 00:15:11,130
+إذا بقدر أقول دي لحاله رقم مضروبا في مصوفة الوحدة
+
+170
+00:15:11,130 --> 00:15:17,150
+I N يبقى هذه بسميها what scalar matrixالان يا بنات
+
+171
+00:15:17,150 --> 00:15:22,170
+بدنا نيجي لحاجة اسمة المصوفة المثلثة العليا او
+
+172
+00:15:22,170 --> 00:15:27,310
+المصوفة المثلثة السفلاء طيب ال upper triangle
+
+173
+00:15:27,310 --> 00:15:31,310
+matrix او ال lower triangle matrix المصوفة المثلثة
+
+174
+00:15:31,310 --> 00:15:35,850
+العليا او المثلثة السفلاء المصوفة المثلثة العليا
+
+175
+00:15:35,850 --> 00:15:42,450
+هي المصوفة اللي جمع عنصرها اسفل القطرة رئيسي أصفرا
+
+176
+00:15:43,280 --> 00:15:47,300
+المصوفة المثلثة السفلية هي المصوفة اللى جميع
+
+177
+00:15:47,300 --> 00:15:52,600
+عناصرها أعلى القطر الرئيسى بيكونوا أسفارة الكلام
+
+178
+00:15:52,600 --> 00:15:57,900
+اللى قلته بدنا نروح نكتبه هنا مشان نعتمده بعدها
+
+179
+00:15:57,900 --> 00:15:58,700
+جدر الشغل
+
+180
+00:16:13,580 --> 00:16:18,380
+يبقى بدأجي الآن للمصوفة المثلثة العليا والمصوفة
+
+181
+00:16:18,380 --> 00:16:27,160
+المثلثة السفلاء يبقى اضع رقم أربعة The Upper أو
+
+182
+00:16:27,160 --> 00:16:33,500
+Lower بين قسين Triangle Matrix
+
+183
+00:16:43,080 --> 00:16:54,680
+is a square matrix is a square matrix a
+
+184
+00:16:54,680 --> 00:17:08,300
+that has all elements that has all elements under
+
+185
+00:17:08,300 --> 00:17:19,470
+being seen overThe diagonal elements are
+
+186
+00:17:19,470 --> 00:17:35,870
+zero
+
+187
+00:17:43,070 --> 00:17:49,710
+for example الـ
+
+188
+00:17:49,710 --> 00:18:02,530
+A تساوي تلاتة واحد ناقص اتنين Zero Zero اتنين Zero
+
+189
+00:18:02,530 --> 00:18:11,210
+Zero سالب واحد is another triangle matrix is an
+
+190
+00:18:12,890 --> 00:18:25,950
+upper is an upper triangle matrix
+
+191
+00:18:25,950 --> 00:18:29,810
+but
+
+192
+00:18:29,810 --> 00:18:33,250
+ولكن
+
+193
+00:18:33,250 --> 00:18:35,430
+بيتساوي
+
+194
+00:18:36,580 --> 00:18:48,720
+1,0,0,2,1,0,1,3,2 is a lower triangle matrix
+
+195
+00:19:25,030 --> 00:19:29,690
+مرة أخرى يبقى بالداجل المصفوفة المثلثة العليا
+
+196
+00:19:29,690 --> 00:19:34,230
+والمصفوفة المثلثة السفلة يبقى upper triangle
+
+197
+00:19:34,230 --> 00:19:39,010
+matrix مصفوفة مثلثة عليا lower triangle matrix
+
+198
+00:19:39,010 --> 00:19:40,870
+مصفوفة مثلثة سفلة
+
+199
+00:19:43,630 --> 00:19:49,030
+هي عبارة عن المصفوفة المربعة a that has all
+
+200
+00:19:49,030 --> 00:19:54,430
+elements under يبقى كل العناصر تحت ال diagonal
+
+201
+00:19:54,430 --> 00:19:59,950
+elements تحت العناصر القطرية كلها أصفرا يبقى بداجي
+
+202
+00:19:59,950 --> 00:20:05,310
+على ال main diagonal بدي اللي تحته تكون كلها أصفر
+
+203
+00:20:05,310 --> 00:20:08,970
+و اللي فوق تكون أرقام طيب ال diagonal matrix نفسه
+
+204
+00:20:09,600 --> 00:20:12,860
+بهمنيش يكون أعداد ولا يكون أسفار ماعنديش ماعنديش
+
+205
+00:20:12,860 --> 00:20:16,880
+أي شرط على ال diagonal matrix اللي شرط فقط على
+
+206
+00:20:16,880 --> 00:20:21,060
+العناصر اللي منه فوق أو العناصر اللي منه أسفار طيب
+
+207
+00:20:21,060 --> 00:20:24,060
+ال lower triangle matrix هو عبارة عن المصوفة
+
+208
+00:20:24,060 --> 00:20:28,500
+المربعة إيه اللي كل عناصرها أعلى ال diagonal
+
+209
+00:20:28,500 --> 00:20:32,820
+elements كلها أسفار فلو جيتنا المصوفة إيه طلعيلي
+
+210
+00:20:32,820 --> 00:20:37,290
+هذا ال mean diagonalأيوة تلاتة و Zero سالب واحد
+
+211
+00:20:37,290 --> 00:20:42,110
+اللي منه تحت كلها أصفر يبقى هذه upper triangle
+
+212
+00:20:42,110 --> 00:20:47,390
+matrix نجي للمصوفة هذه هذا هو القط طبعا لحظة هنا
+
+213
+00:20:47,390 --> 00:20:51,770
+في Zero حتى لو كان كل مصفر ماعنديش مشكلة طيب هذا
+
+214
+00:20:51,770 --> 00:20:55,670
+القط رئيسي كل اللي منه فوق أصفر و اللي تحت أرقام
+
+215
+00:20:55,670 --> 00:20:59,390
+طب ممكن يكون هنا في رقم يعني هذا ليس بضرورة انه
+
+216
+00:20:59,390 --> 00:21:04,270
+ممكن يكون Zero كمانأنا بيهمني اللي فوق أصفر تمام
+
+217
+00:21:04,270 --> 00:21:09,330
+يبقى اللي تحت ماعنديش عليهم أي شرط يبقى كمان هذه
+
+218
+00:21:09,330 --> 00:21:14,290
+بسميها ال lower triangle matrix خليني أسفل السؤال
+
+219
+00:21:14,290 --> 00:21:19,440
+التالي هل ال zero matrix Upper Triangle Matrix
+
+220
+00:21:19,440 --> 00:21:23,240
+Upper
+
+221
+00:21:23,240 --> 00:21:31,220
+Triangle Matrix Lower Triangle Matrix Identity
+
+222
+00:21:31,220 --> 00:21:36,920
+Matrixبرضه Upper and Lower Matrix على كلا الأمرين
+
+223
+00:21:36,920 --> 00:21:42,840
+الـ Scalar Matrix المصوف القياسي برضه بتنفع Upper
+
+224
+00:21:42,840 --> 00:21:47,200
+and Lower على كلا الأمرين يبقى معنا مشكلة في هذه
+
+225
+00:21:47,200 --> 00:21:52,320
+الحل يبقى نكتب الملاحظة هذه اللي بنقولها يبقى Not
+
+226
+00:21:52,320 --> 00:21:58,280
+الملاحظة رقم واحد The Identity Matrix
+
+227
+00:22:04,550 --> 00:22:11,390
+مصفوفة الوحدة IN and
+
+228
+00:22:11,390 --> 00:22:21,430
+the n by n matrix zero and the n by n zero matrix
+
+229
+00:22:21,430 --> 00:22:31,010
+والمصفوفة الصفرية لنظامها N في N هذول are examples
+
+230
+00:22:33,660 --> 00:22:43,320
+of scalar matrices number
+
+231
+00:22:43,320 --> 00:22:48,000
+اتنين
+
+232
+00:22:48,000 --> 00:22:57,160
+the diagonal matrix
+
+233
+00:22:57,160 --> 00:23:01,040
+is
+
+234
+00:23:01,040 --> 00:23:13,590
+anUpper and Lower and
+
+235
+00:23:13,590 --> 00:23:30,250
+Lower Triangle Matrix نجي
+
+236
+00:23:30,250 --> 00:23:31,630
+لنظرية theorem
+
+237
+00:23:34,900 --> 00:23:37,240
+طبعا الكلام اللي قلناه هو واضح مظبوط اللي قلناه
+
+238
+00:23:37,240 --> 00:23:42,500
+شفو بس بعدها كتبناه عشان نثبت هذه المعلومات F
+
+239
+00:23:42,500 --> 00:23:59,680
+المصوف A تساوي ال A A11 A12 A1N A21 A22 A2N
+
+240
+00:24:01,950 --> 00:24:11,590
+وضلنا مشيين لغاية AM1 AM2 AMN الشكل اللي عندنا هذا
+
+241
+00:24:11,590 --> 00:24:16,830
+هو المصحوفة
+
+242
+00:24:16,830 --> 00:24:20,390
+C والمصحوفة
+
+243
+00:24:20,390 --> 00:24:31,860
+capital Cبدها تساوي الـ diagonal اللي هو C1 و C2 و
+
+244
+00:24:31,860 --> 00:24:33,320
+لغاية CM
+
+245
+00:24:35,720 --> 00:24:51,240
+اللي هي main بدها تساوي C10000C200000CM
+
+246
+00:24:51,240 --> 00:24:57,220
+بالشكل اللي عندنا هنا جالي
+
+247
+00:24:57,220 --> 00:25:09,040
+zeroوهذه ستبقى نزلة وهذه نزلة بشكل انه CM and ال
+
+248
+00:25:09,040 --> 00:25:19,460
+D بدها تساوي ال diagonal دي واحد و دي اتنين و
+
+249
+00:25:19,460 --> 00:25:24,280
+لغاية DN و اللي هي بدها تساوي
+
+250
+00:25:33,440 --> 00:25:39,760
+D1 D2 D3
+
+251
+00:25:39,760 --> 00:25:40,200
+D4 D5 D6 D7 D8 D9 D10 D11 D12 D13 D14 D15 D16 D17
+
+252
+00:25:40,200 --> 00:25:42,960
+D18 D19 D20 D21 D22 D23 D22 D23 D23 D23 D23 D23
+
+253
+00:25:42,960 --> 00:25:46,260
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23
+
+254
+00:25:46,260 --> 00:25:47,280
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23
+
+255
+00:25:47,280 --> 00:25:47,280
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23
+
+256
+00:25:47,280 --> 00:25:47,280
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23
+
+257
+00:25:47,280 --> 00:25:47,280
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 D23
+
+258
+00:25:47,280 --> 00:25:47,960
+D23 D23 D23 D23 D23 D23 D23 D23 D23 D23 Dert Dert
+
+259
+00:25:47,960 --> 00:25:57,900
+Dert Dert Dert Dert Dert Dert Dertالـ C في A الـ C
+
+260
+00:25:57,900 --> 00:26:04,180
+في A يبدو يساوي C1A11
+
+261
+00:26:04,180 --> 00:26:09,240
+C1A12
+
+262
+00:26:09,240 --> 00:26:14,460
+C1A1N
+
+263
+00:26:15,870 --> 00:26:25,250
+C to A to 1 C to A to 2 C to A to N هنظل نزلين
+
+264
+00:26:25,250 --> 00:26:42,370
+لغاية CM AM1 CM AM2 هنظل نزلين لغاية CM AM1
+
+265
+00:26:42,370 --> 00:26:50,940
+CM AM2شكلها انها ده and
+
+266
+00:26:50,940 --> 00:26:54,340
+ال
+
+267
+00:26:54,340 --> 00:27:03,180
+a دي بدها تساوي ال
+
+268
+00:27:03,180 --> 00:27:12,070
+d one a one one دي two a one twoوانضل ماشيين لغاية
+
+269
+00:27:12,070 --> 00:27:27,310
+D N A N او هنا D 1 A 2 1 D 1 A 2 1 D 2 A 2 2 او
+
+270
+00:27:27,310 --> 00:27:42,560
+هنا D N A 2 M وانضل ماشيين يبقى D 1 A M 1D to A M
+
+271
+00:27:42,560 --> 00:27:59,020
+to D N A M N كروه
+
+272
+00:27:59,020 --> 00:27:59,380
+لري
+
+273
+00:28:06,180 --> 00:28:24,560
+Let الـ A بي M by N Matrix and capital C بدو يساوي
+
+274
+00:28:24,560 --> 00:28:33,620
+C000C000
+
+275
+00:28:36,000 --> 00:28:43,720
+ونظل ماشيين لغاية Zero Zero Zero Zero Zero Zero
+
+276
+00:28:43,720 --> 00:28:46,320
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+277
+00:28:46,320 --> 00:28:46,420
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+278
+00:28:46,420 --> 00:28:48,720
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+279
+00:28:48,720 --> 00:28:48,720
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+280
+00:28:48,720 --> 00:28:50,960
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+281
+00:28:50,960 --> 00:28:51,020
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+282
+00:28:51,020 --> 00:28:51,720
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+283
+00:28:51,720 --> 00:28:51,720
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+284
+00:28:51,720 --> 00:28:51,800
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+285
+00:28:51,800 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+286
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+287
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+288
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+289
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+290
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+291
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+292
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+293
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+294
+00:28:54,700 --> 00:28:54,700
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+295
+00:28:54,700 --> 00:28:54,720
+Zero Zero Zero Zero Zero Zero Zero Zero Zero Zero
+
+296
+00:28:54,720 --> 00:29:01,480
+Zero Zero Zero Zero
+
+297
+00:29:01,480 --> 00:29:03,160
+Zero Zero Zero
+
+298
+00:29:06,290 --> 00:29:26,770
+D Zero Zero Zero D Zero Zero Zero Zero Zero D In
+
+299
+00:29:26,770 --> 00:29:34,070
+By In Scalar Matrix
+
+300
+00:29:36,400 --> 00:29:43,640
+ماتريكس ثم C
+
+301
+00:29:43,640 --> 00:29:54,820
+في A بيساوي C في A و A
+
+302
+00:29:54,820 --> 00:30:00,980
+في D بيساوي D في A
+
+303
+00:30:21,260 --> 00:30:23,000
+عشان احنا بقى باستخدام البرنامج اللي بيعمله
+
+304
+00:30:23,000 --> 00:30:23,000
+البرنامج
+
+305
+00:31:00,970 --> 00:31:06,650
+نرجع لكلام اللي كتبناه هذا بيقول
+
+306
+00:31:06,650 --> 00:31:14,990
+لو عند المصوفة A نظامها M في N الـ A زي ما تشايف M
+
+307
+00:31:14,990 --> 00:31:20,270
+من الصفوف و N من الأعمدةوكان عندى الـ diagonal
+
+308
+00:31:20,270 --> 00:31:29,510
+matrix سميتها C والـ C نظامها M في M لإن الـ C1 C2
+
+309
+00:31:29,510 --> 00:31:35,910
+لغاية مين لغاية CM يبقى مصفوفة مربع نظامها M في M
+
+310
+00:31:35,910 --> 00:31:43,990
+الأولانية M في N والتانية دي M في Mوهي كتبت عليك
+
+311
+00:31:43,990 --> 00:31:47,890
+على الشكل اللي عندنا هذا اتنين عندي كمان ده يقول
+
+312
+00:31:47,890 --> 00:31:53,430
+ال matrix اعطيتها الرمز اللي هو capital D بس عدد
+
+313
+00:31:53,430 --> 00:31:59,590
+عناصرها او نظامها N في Nيبقى هذه دياجونة بتختلف عن
+
+314
+00:31:59,590 --> 00:32:03,570
+مين؟ عن اللي فوق يبقى عدد الصفوف يساوي عدد الأعمدة
+
+315
+00:32:03,570 --> 00:32:06,230
+في الأولى والتاني عدد الصفوف يساوي عدد الأعمدة في
+
+316
+00:32:06,230 --> 00:32:09,730
+التاني لكن عدد الصفوف في الأولى ليس كعدد الصفوف في
+
+317
+00:32:09,730 --> 00:32:15,450
+الثانية ولا حتى مين الأعمدة then لو ضربت C في A
+
+318
+00:32:15,450 --> 00:32:19,410
+يبقى بدي أضرب المصوفة اللي عندنا هذه في A بدي أشوف
+
+319
+00:32:19,410 --> 00:32:24,760
+بنفع تم عملية الضرب ولا لأيبقى انا عندي هذا ميم
+
+320
+00:32:24,760 --> 00:32:32,560
+اللي هو ال a نظامها m في m و هذه نظامها m في m
+
+321
+00:32:32,560 --> 00:32:38,300
+فبقول لي ca بدي اضرب ال c في a و بدي اضرب الصف
+
+322
+00:32:38,300 --> 00:32:44,480
+الأول في العمود الأول طلعيل الصف الأول في العمود
+
+323
+00:32:44,480 --> 00:32:54,060
+الأوليبقى a11 في c11 بأصفر
+
+324
+00:32:54,060 --> 00:33:00,840
+c1 a11 الصف الأول في العمودي الثاني صف الأول في
+
+325
+00:33:00,840 --> 00:33:06,380
+العمودي الثاني يبقى الأولاني ب0 وهذا يصبح c1 a11
+
+326
+00:33:07,910 --> 00:33:13,990
+يبقى هنا a الصف الأول في العمودي الثاني a11 في
+
+327
+00:33:13,990 --> 00:33:18,750
+zero بتروح a12
+
+328
+00:33:18,750 --> 00:33:25,090
+في c2 بصير a12 في a12
+
+329
+00:33:27,630 --> 00:33:32,230
+خلّي بالك هنا تاني تاني تاني يبقى انا انا بدي اضرب
+
+330
+00:33:32,230 --> 00:33:37,870
+C في A مش ال A في ال C يبقى انا بدي اضرب C في A و
+
+331
+00:33:37,870 --> 00:33:41,710
+ليس A في C يبقى باجي بقول الصف الأول في العملي
+
+332
+00:33:41,710 --> 00:33:48,490
+بصير C1 A11 هايوالصف الأول في العمود الثاني يبقى
+
+333
+00:33:48,490 --> 00:33:55,250
+C1A12 يبقى C1 يبقى المقصود في هذه الحالة أن العنصر
+
+334
+00:33:55,250 --> 00:34:01,050
+C1 بدي أضرب في جميع عناصر الصف الأول C1 C1 C1
+
+335
+00:34:01,050 --> 00:34:07,170
+والباقي العناصر كما هي C2 بضربه في الصف C3 في الصف
+
+336
+00:34:07,170 --> 00:34:15,560
+CM في الصفبالمثل لو جيت لمن لل A في D اللحظة ان ال
+
+337
+00:34:15,560 --> 00:34:20,620
+diagonal ضربت من جهة الشمال في A هنا ال diagonal
+
+338
+00:34:20,620 --> 00:34:26,160
+ضربت من جهة اليمين في A ايش الفرق ما بين الاتنين
+
+339
+00:34:26,160 --> 00:34:32,440
+الفرق في الحالة لقول ان C1 ضربت في الصفهنا D1 ضربت
+
+340
+00:34:32,440 --> 00:34:36,280
+في من؟ في العمود يبقى هذا الفرق ما بين الأتنين
+
+341
+00:34:36,280 --> 00:34:40,340
+والباقي كما هو تمام يبقى هذا الفرق ما بين الأتنين
+
+342
+00:34:40,340 --> 00:34:44,360
+ناخد كرولر كرولر يعني نتيجة على مين على هذه
+
+343
+00:34:44,360 --> 00:34:48,840
+النظرية بقول افترض ال A اللي هي M by N matrix اللي
+
+344
+00:34:48,840 --> 00:34:54,640
+فوق and ال C ال diagonal matrix نظامها M في M يعني
+
+345
+00:34:54,640 --> 00:34:59,960
+مين هي اللي فوق M في M تماماعند دي ال diagonal
+
+346
+00:34:59,960 --> 00:35:04,260
+matrix نظامها N في N اللي اللي فوق بالضبط تماما
+
+347
+00:35:04,260 --> 00:35:11,440
+then لو ضربت C في A كإني ضرب ال constant C في main
+
+348
+00:35:11,440 --> 00:35:17,920
+في المصوف A يعني بدل ما كنت أقول C1 وC2 وCM بدي
+
+349
+00:35:17,920 --> 00:35:19,400
+أخليها scalar matrix
+
+350
+00:35:22,290 --> 00:35:26,830
+متساويات تمام يبقى ايش اللي بده يصير؟ بده يصير
+
+351
+00:35:26,830 --> 00:35:34,230
+كأنه ضربت ال C لككنستان في جميع عناصر المصر فليش؟
+
+352
+00:35:34,230 --> 00:35:40,830
+لأن هذا اللي بده يصير هذي C C C C C كله C تمام؟
+
+353
+00:35:40,830 --> 00:35:45,250
+يبقى كأنه هضربها C في ايه؟بالمثل في حالة تانية
+
+354
+00:35:45,250 --> 00:35:49,850
+كأنه ضارب D في مين في المصوف A وكأنه هذه حالة خاصة
+
+355
+00:35:49,850 --> 00:35:53,930
+من مين من الحالة اللي فوق المرة الجاية بناخد أمثلة
+
+356
+00:35:53,930 --> 00:35:57,690
+على النظرية والنتائج اللي عليها ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2cefb4d7a7245d6a0736b72a64b949f121fe94a8
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i7ilzaMJ8A0_raw.json
@@ -0,0 +1 @@
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of complex numbers", "tokens": [1829, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 4117, 2655, 3555, 512, 7221, 466, 264, 3997, 3547, 7251, 3555, 4587, 7578, 47525, 26108, 1829, 1975, 39648, 34105, 512, 3875, 7221, 45030, 11242, 33962, 14407, 9381, 16247, 3794, 32277, 10632, 295, 3997, 3547], "avg_logprob": -0.19513081187425657, "compression_ratio": 1.393939393939394, "no_speech_prob": 0.0, "words": [{"start": 1580.22, "end": 1580.54, "word": "يبقى", "probability": 0.779296875}, {"start": 1580.54, "end": 1580.86, "word": " بداجي", "probability": 0.647705078125}, {"start": 1580.86, "end": 1581.18, "word": " اكتب", "probability": 0.843017578125}, {"start": 1581.18, "end": 1581.5, "word": " some", "probability": 0.72900390625}, {"start": 1581.5, "end": 1582.28, "word": " properties", "probability": 0.73388671875}, {"start": 1582.28, "end": 1583.14, "word": " about", "probability": 0.8876953125}, {"start": 1583.14, "end": 1583.7, "word": " the", "probability": 0.74658203125}, {"start": 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"word": " على", "probability": 0.81689453125}, {"start": 1644.95, "end": 1645.49, "word": " الشكل", "probability": 0.952392578125}, {"start": 1645.49, "end": 1646.27, "word": " التالي", "probability": 0.9825846354166666}, {"start": 1646.27, "end": 1647.27, "word": " z", "probability": 0.281005859375}, {"start": 1647.27, "end": 1648.49, "word": " يساوي", "probability": 0.735107421875}, {"start": 1648.49, "end": 1649.11, "word": " a", "probability": 0.8994140625}, {"start": 1649.11, "end": 1650.37, "word": " زائد", "probability": 0.7433268229166666}, {"start": 1650.37, "end": 1650.99, "word": " i", "probability": 0.4873046875}, {"start": 1650.99, "end": 1651.59, "word": " b", "probability": 0.65673828125}, {"start": 1651.59, "end": 1653.53, "word": " where", "probability": 0.93896484375}, {"start": 1653.53, "end": 1654.61, "word": " حيث", "probability": 0.900390625}, {"start": 1654.61, "end": 1655.81, "word": " ال", "probability": 0.95654296875}, {"start": 1655.81, "end": 1656.41, 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"probability": 0.58544921875}, {"start": 2255.67, "end": 2256.09, "word": " زائد", "probability": 0.9752604166666666}, {"start": 2256.09, "end": 2256.37, "word": " a", "probability": 0.95458984375}, {"start": 2256.37, "end": 2256.63, "word": " and", "probability": 0.31591796875}, {"start": 2256.63, "end": 2256.87, "word": " y", "probability": 0.779296875}, {"start": 2256.87, "end": 2257.09, "word": " يبدو", "probability": 0.7156575520833334}, {"start": 2257.09, "end": 2257.37, "word": " يساوي", "probability": 0.7789306640625}, {"start": 2257.37, "end": 2257.83, "word": " مين؟", "probability": 0.4586588541666667}, {"start": 2257.83, "end": 2258.59, "word": " يساوي", "probability": 0.894287109375}, {"start": 2258.59, "end": 2259.09, "word": " zero", "probability": 0.27734375}, {"start": 2259.09, "end": 2259.79, "word": " قلنا", "probability": 0.6749674479166666}, {"start": 2259.79, "end": 2260.03, "word": " هذه", "probability": 0.43701171875}, {"start": 2260.03, "end": 2260.71, "word": " homogeneous", "probability": 0.42236328125}, {"start": 2260.71, "end": 2261.53, "word": " differential", "probability": 0.90283203125}, {"start": 2261.53, "end": 2262.21, "word": " equation", "probability": 0.97802734375}, {"start": 2262.21, "end": 2262.95, "word": " ويمكن", "probability": 0.97021484375}, {"start": 2262.95, "end": 2263.53, "word": " اختصارها", "probability": 0.97919921875}, {"start": 2263.53, "end": 2263.75, "word": " على", "probability": 0.9384765625}, {"start": 2263.75, "end": 2264.27, "word": " صيغة", "probability": 0.9744873046875}, {"start": 2264.27, "end": 2264.57, "word": " L", "probability": 0.5986328125}, {"start": 2264.57, "end": 2264.95, "word": " of", "probability": 0.88720703125}, {"start": 2264.95, "end": 2265.17, "word": " y", "probability": 0.62841796875}, {"start": 2265.17, "end": 2265.69, "word": " يساوي", "probability": 0.9521484375}, {"start": 2265.69, "end": 2266.21, "word": " مين؟", "probability": 0.9212239583333334}, {"start": 2266.21, "end": 2267.19, "word": " يساوي", "probability": 0.9676513671875}, {"start": 2267.19, "end": 2267.75, "word": " zero", "probability": 0.7587890625}], "temperature": 1.0}, {"id": 92, "seek": 229667, "start": 2268.45, "end": 2296.67, "text": "فرضنا إن لهذه المعادلة حل هو Y تساوي E أُس R X طلعنا الـ Characteristic Equation لها نتيجة اللي فرضنا لهذا الحل فصرت المعادلة المميزة على الصينة A naught R to the power N زائد A1 R to the power N minus 1 زائد زائد A N minus 1 في R زائد A N بده ساوي مين؟ بده ساوي Zero", "tokens": [5172, 43042, 8315, 36145, 46740, 24192, 9673, 3615, 18513, 37977, 11331, 1211, 31439, 398, 6055, 3794, 995, 45865, 462, 5551, 10859, 3794, 497, 1783, 23032, 1211, 3615, 8315, 2423, 39184, 36786, 3142, 15624, 399, 5296, 11296, 8717, 31371, 7435, 3660, 13672, 1829, 6156, 43042, 8315, 46740, 15730, 21542, 1211, 6156, 9381, 43500, 9673, 3615, 18513, 37977, 9673, 2304, 1829, 11622, 3660, 15844, 31767, 9957, 3660, 316, 13138, 497, 281, 264, 1347, 426, 30767, 16373, 3215, 316, 16, 497, 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"probability": 0.9952799479166666}, {"start": 2279.33, "end": 2280.03, "word": " لهذا", "probability": 0.854248046875}, {"start": 2280.03, "end": 2280.49, "word": " الحل", "probability": 0.990234375}, {"start": 2280.49, "end": 2281.35, "word": " فصرت", "probability": 0.8907877604166666}, {"start": 2281.35, "end": 2282.07, "word": " المعادلة", "probability": 0.9935302734375}, {"start": 2282.07, "end": 2283.21, "word": " المميزة", "probability": 0.98896484375}, {"start": 2283.21, "end": 2283.77, "word": " على", "probability": 0.88916015625}, {"start": 2283.77, "end": 2284.45, "word": " الصينة", "probability": 0.682373046875}, {"start": 2284.45, "end": 2284.77, "word": " A", "probability": 0.64990234375}, {"start": 2284.77, "end": 2285.15, "word": " naught", "probability": 0.0635986328125}, {"start": 2285.15, "end": 2285.49, "word": " R", "probability": 0.87939453125}, {"start": 2285.49, "end": 2285.67, "word": " to", "probability": 0.529296875}, {"start": 2285.67, "end": 2285.81, "word": " the", "probability": 0.91162109375}, {"start": 2285.81, "end": 2286.15, "word": " power", "probability": 0.86376953125}, {"start": 2286.15, "end": 2286.45, "word": " N", "probability": 0.626953125}, {"start": 2286.45, "end": 2287.25, "word": " زائد", "probability": 0.7825520833333334}, {"start": 2287.25, "end": 2287.77, "word": " A1", "probability": 0.7880859375}, {"start": 2287.77, "end": 2288.07, "word": " R", "probability": 0.70947265625}, {"start": 2288.07, "end": 2288.25, "word": " to", "probability": 0.9638671875}, {"start": 2288.25, "end": 2288.39, "word": " the", "probability": 0.91943359375}, {"start": 2288.39, "end": 2288.63, "word": " power", "probability": 0.857421875}, {"start": 2288.63, "end": 2288.87, "word": " N", "probability": 0.81201171875}, {"start": 2288.87, "end": 2289.21, "word": " minus", "probability": 0.52490234375}, {"start": 2289.21, "end": 2289.61, "word": " 1", "probability": 0.53955078125}, {"start": 2289.61, "end": 2290.45, "word": " زائد", "probability": 0.9547526041666666}, {"start": 2290.45, "end": 2291.09, "word": " زائد", "probability": 0.9357096354166666}, {"start": 2291.09, "end": 2291.71, "word": " A", "probability": 0.65283203125}, {"start": 2291.71, "end": 2292.07, "word": " N", "probability": 0.869140625}, {"start": 2292.07, "end": 2292.47, "word": " minus", "probability": 0.978515625}, {"start": 2292.47, "end": 2292.79, "word": " 1", "probability": 0.83740234375}, {"start": 2292.79, "end": 2292.95, "word": " في", "probability": 0.69775390625}, {"start": 2292.95, "end": 2293.19, "word": " R", "probability": 0.96240234375}, {"start": 2293.19, "end": 2293.61, "word": " زائد", "probability": 0.8946940104166666}, {"start": 2293.61, "end": 2293.83, "word": " A", "probability": 0.97802734375}, {"start": 2293.83, "end": 2293.97, "word": " N", "probability": 0.962890625}, {"start": 2293.97, "end": 2294.25, "word": " بده", "probability": 0.485595703125}, {"start": 2294.25, "end": 2294.51, "word": " ساوي", "probability": 0.7893880208333334}, {"start": 2294.51, "end": 2295.09, "word": " مين؟", "probability": 0.6902669270833334}, {"start": 2295.09, "end": 2295.53, "word": " بده", "probability": 0.94287109375}, {"start": 2295.53, "end": 2296.15, "word": " ساوي", "probability": 0.9798177083333334}, {"start": 2296.15, "end": 2296.67, "word": " Zero", "probability": 0.623046875}], "temperature": 1.0}, {"id": 93, "seek": 231626, "start": 2297.36, "end": 2316.26, "text": "وقلنا المعادلة هذه إلها أحد ثلاثة احتمالات هذه معادلة من الدرجة النونية لاحتمال الأول أن تكون كل الحلول حقيقية ومختلفة لاحتمال الثاني أن تكون كل الحلول حقيقية", "tokens": [2407, 4587, 1211, 8315, 9673, 3615, 18513, 37977, 29538, 11933, 1211, 11296, 5551, 24401, 38637, 1211, 5718, 104, 3660, 1975, 33753, 2304, 6027, 9307, 29538, 20449, 18513, 37977, 9154, 32748, 47341, 3660, 28239, 11536, 10632, 20193, 33753, 2304, 6027, 16247, 12610, 14739, 6055, 30544, 28242, 21542, 1211, 12610, 11331, 38436, 4587, 10632, 4032, 2304, 46456, 46538, 3660, 20193, 33753, 2304, 6027, 6024, 104, 7649, 1829, 14739, 6055, 30544, 28242, 21542, 1211, 12610, 11331, 38436, 4587, 10632], "avg_logprob": -0.11536120245983074, "compression_ratio": 2.116788321167883, "no_speech_prob": 0.0, "words": [{"start": 2297.36, "end": 2297.8, "word": "وقلنا", "probability": 0.640106201171875}, {"start": 2297.8, "end": 2298.38, "word": " المعادلة", "probability": 0.9320068359375}, {"start": 2298.38, "end": 2298.78, "word": " هذه", "probability": 0.9140625}, {"start": 2298.78, "end": 2299.24, "word": " إلها", "probability": 0.6437174479166666}, {"start": 2299.24, "end": 2299.72, "word": " أحد", "probability": 0.876220703125}, {"start": 2299.72, "end": 2300.48, "word": " ثلاثة", "probability": 0.966015625}, {"start": 2300.48, "end": 2301.38, "word": " احتمالات", "probability": 0.9716796875}, {"start": 2301.38, "end": 2302.08, "word": " هذه", "probability": 0.70751953125}, {"start": 2302.08, "end": 2302.62, "word": " معادلة", "probability": 0.9873046875}, {"start": 2302.62, "end": 2302.78, "word": " من", "probability": 0.98974609375}, {"start": 2302.78, "end": 2303.5, "word": " الدرجة", "probability": 0.9484049479166666}, {"start": 2303.5, "end": 2304.4, "word": " النونية", "probability": 0.9651692708333334}, {"start": 2304.4, "end": 2305.46, "word": " لاحتمال", "probability": 0.80706787109375}, {"start": 2305.46, "end": 2306.0, "word": " الأول", "probability": 0.972900390625}, {"start": 2306.0, "end": 2306.32, "word": " أن", "probability": 0.80810546875}, {"start": 2306.32, "end": 2306.76, "word": " تكون", "probability": 0.98974609375}, {"start": 2306.76, "end": 2307.44, "word": " كل", "probability": 0.982421875}, {"start": 2307.44, "end": 2308.6, "word": " الحلول", "probability": 0.994140625}, {"start": 2308.6, "end": 2310.1, "word": " حقيقية", "probability": 0.9915771484375}, {"start": 2310.1, "end": 2311.3, "word": " ومختلفة", "probability": 0.9533203125}, {"start": 2311.3, "end": 2312.42, "word": " لاحتمال", "probability": 0.86639404296875}, {"start": 2312.42, "end": 2313.08, "word": " الثاني", "probability": 0.977294921875}, {"start": 2313.08, "end": 2313.42, "word": " أن", "probability": 0.8935546875}, {"start": 2313.42, "end": 2313.9, "word": " تكون", "probability": 0.99169921875}, {"start": 2313.9, "end": 2314.5, "word": " كل", "probability": 0.98876953125}, {"start": 2314.5, "end": 2315.26, "word": " الحلول", "probability": 0.99462890625}, {"start": 2315.26, "end": 2316.26, "word": " حقيقية", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 94, "seek": 233253, "start": 2316.43, "end": 2332.53, "text": "و متزاوية مكررة repeated لإحتمال الثالث والأخير كل الحلول تبجيش complex conjugate يعني كل اتنين بيكونوا complex و اتنين مرافقين لبعضهم تماما", "tokens": [2407, 44650, 11622, 995, 2407, 10632, 3714, 37983, 25720, 10477, 5296, 28814, 33753, 2304, 6027, 6024, 104, 6027, 12984, 16070, 10721, 9778, 13546, 28242, 21542, 1211, 12610, 6055, 3555, 7435, 1829, 8592, 3997, 45064, 37495, 22653, 28242, 1975, 2655, 1863, 9957, 4724, 1829, 30544, 14407, 3997, 4032, 1975, 2655, 1863, 9957, 3714, 23557, 5172, 4587, 9957, 5296, 3555, 3615, 11242, 16095, 46811, 10943, 995], "avg_logprob": -0.17463942307692307, "compression_ratio": 1.4901960784313726, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2316.43, "end": 2316.97, "word": "و", "probability": 0.404541015625}, {"start": 2316.97, "end": 2318.17, "word": " متزاوية", "probability": 0.712939453125}, {"start": 2318.17, "end": 2319.09, "word": " مكررة", "probability": 0.9334309895833334}, {"start": 2319.09, "end": 2320.09, "word": " repeated", "probability": 0.57177734375}, {"start": 2320.09, "end": 2321.43, "word": " لإحتمال", "probability": 0.716162109375}, {"start": 2321.43, "end": 2321.91, "word": " الثالث", "probability": 0.9193115234375}, {"start": 2321.91, "end": 2322.69, "word": " والأخير", "probability": 0.8204345703125}, {"start": 2322.69, "end": 2323.35, "word": " كل", "probability": 0.73828125}, {"start": 2323.35, "end": 2323.85, "word": " الحلول", "probability": 0.98681640625}, {"start": 2323.85, "end": 2324.57, "word": " تبجيش", "probability": 0.8267578125}, {"start": 2324.57, "end": 2325.15, "word": " complex", "probability": 0.80419921875}, {"start": 2325.15, "end": 2326.09, "word": " conjugate", "probability": 0.83642578125}, {"start": 2326.09, "end": 2326.79, "word": " يعني", "probability": 0.919677734375}, {"start": 2326.79, "end": 2327.19, "word": " كل", "probability": 0.9287109375}, {"start": 2327.19, "end": 2327.59, "word": " اتنين", "probability": 0.9132080078125}, {"start": 2327.59, "end": 2328.19, "word": " بيكونوا", "probability": 0.88671875}, {"start": 2328.19, "end": 2329.51, "word": " complex", "probability": 0.5986328125}, {"start": 2329.51, "end": 2329.75, "word": " و", "probability": 0.7666015625}, {"start": 2329.75, "end": 2330.27, "word": " اتنين", "probability": 0.9580078125}, {"start": 2330.27, "end": 2331.39, "word": " مرافقين", "probability": 0.97802734375}, {"start": 2331.39, "end": 2331.97, "word": " لبعضهم", "probability": 0.9314453125}, {"start": 2331.97, "end": 2332.53, "word": " تماما", "probability": 0.9954427083333334}], "temperature": 1.0}, {"id": 95, "seek": 235648, "start": 2332.73, "end": 2356.49, "text": "وقولنا معنى المرافق أنه لو كان الحل الأول أو الجدر الأول هو a زائد ib فإن الجدر التاني هو a ناقص ib هذا ما ذكرناه في محاضرة الصبح وروحنا أخدنا الحالة الأولى لو كانت الجذور حقيقية ومختلفة الآن بدنا نيجي لو كانت الجذور حقيقية", "tokens": [2407, 39648, 8315, 20449, 1863, 7578, 9673, 23557, 5172, 4587, 14739, 3224, 45164, 25961, 21542, 1211, 16247, 12610, 34051, 25724, 3215, 2288, 16247, 12610, 31439, 257, 30767, 16373, 3215, 39073, 6156, 28814, 1863, 25724, 3215, 2288, 16712, 7649, 1829, 31439, 257, 8717, 995, 4587, 9381, 39073, 23758, 19446, 29910, 37983, 8315, 3224, 8978, 3714, 5016, 46958, 25720, 31767, 49628, 4032, 32887, 5016, 8315, 5551, 9778, 3215, 8315, 21542, 6027, 3660, 16247, 12610, 7578, 45164, 25961, 2655, 25724, 8848, 13063, 11331, 38436, 4587, 10632, 4032, 2304, 46456, 46538, 3660, 6024, 48506, 47525, 8315, 8717, 1829, 7435, 1829, 45164, 25961, 2655, 25724, 8848, 13063, 11331, 38436, 4587, 10632], "avg_logprob": -0.09506425386834368, "compression_ratio": 2.015228426395939, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2332.73, "end": 2333.33, "word": "وقولنا", "probability": 0.668701171875}, {"start": 2333.33, "end": 2333.71, "word": " معنى", "probability": 0.9855143229166666}, {"start": 2333.71, "end": 2334.37, "word": " المرافق", "probability": 0.966796875}, {"start": 2334.37, "end": 2334.81, "word": " أنه", "probability": 0.62744140625}, {"start": 2334.81, "end": 2334.93, "word": " لو", "probability": 0.95947265625}, {"start": 2334.93, "end": 2335.21, "word": " كان", "probability": 0.9951171875}, {"start": 2335.21, "end": 2335.73, "word": " الحل", "probability": 0.940673828125}, {"start": 2335.73, "end": 2336.33, "word": " الأول", "probability": 0.9775390625}, {"start": 2336.33, "end": 2336.99, "word": " أو", "probability": 0.73974609375}, {"start": 2336.99, "end": 2337.51, "word": " الجدر", "probability": 0.8761393229166666}, {"start": 2337.51, "end": 2337.89, "word": " الأول", "probability": 0.973876953125}, {"start": 2337.89, "end": 2338.23, "word": " هو", "probability": 0.95361328125}, {"start": 2338.23, "end": 2338.43, "word": " a", "probability": 0.60302734375}, {"start": 2338.43, "end": 2339.01, "word": " زائد", "probability": 0.6729939778645834}, {"start": 2339.01, "end": 2339.51, "word": " ib", "probability": 0.61083984375}, {"start": 2339.51, "end": 2340.17, "word": " فإن", "probability": 0.93115234375}, {"start": 2340.17, "end": 2341.11, "word": " الجدر", "probability": 0.9892578125}, {"start": 2341.11, "end": 2341.49, "word": " التاني", "probability": 0.9098307291666666}, {"start": 2341.49, "end": 2341.79, "word": " هو", "probability": 0.9541015625}, {"start": 2341.79, "end": 2342.09, "word": " a", "probability": 0.97119140625}, {"start": 2342.09, "end": 2342.83, "word": " ناقص", "probability": 0.926513671875}, {"start": 2342.83, "end": 2343.63, "word": " ib", "probability": 0.931640625}, {"start": 2343.63, "end": 2344.47, "word": " هذا", "probability": 0.86474609375}, {"start": 2344.47, "end": 2344.71, "word": " ما", "probability": 0.79638671875}, {"start": 2344.71, "end": 2345.31, "word": " ذكرناه", "probability": 0.9892578125}, {"start": 2345.31, "end": 2345.53, "word": " في", "probability": 0.99072265625}, {"start": 2345.53, "end": 2346.17, "word": " محاضرة", "probability": 0.9522705078125}, {"start": 2346.17, "end": 2346.69, "word": " الصبح", "probability": 0.95947265625}, {"start": 2346.69, "end": 2347.63, "word": " وروحنا", "probability": 0.968017578125}, {"start": 2347.63, "end": 2348.05, "word": " أخدنا", "probability": 0.965576171875}, {"start": 2348.05, "end": 2348.57, "word": " الحالة", "probability": 0.9817708333333334}, {"start": 2348.57, "end": 2349.19, "word": " الأولى", "probability": 0.9845377604166666}, {"start": 2349.19, "end": 2349.69, "word": " لو", "probability": 0.97314453125}, {"start": 2349.69, "end": 2350.07, "word": " كانت", "probability": 0.992431640625}, {"start": 2350.07, "end": 2350.53, "word": " الجذور", "probability": 0.99267578125}, {"start": 2350.53, "end": 2351.69, "word": " حقيقية", "probability": 0.99365234375}, {"start": 2351.69, "end": 2352.67, "word": " ومختلفة", "probability": 0.96064453125}, {"start": 2352.67, "end": 2353.09, "word": " الآن", "probability": 0.6197509765625}, {"start": 2353.09, "end": 2353.39, "word": " بدنا", "probability": 0.835205078125}, {"start": 2353.39, "end": 2353.75, "word": " نيجي", "probability": 0.95849609375}, {"start": 2353.75, "end": 2354.37, "word": " لو", "probability": 0.94921875}, {"start": 2354.37, "end": 2354.85, "word": " كانت", "probability": 0.993896484375}, {"start": 2354.85, "end": 2355.41, "word": " الجذور", "probability": 0.9951171875}, {"start": 2355.41, "end": 2356.49, "word": " حقيقية", "probability": 0.9957275390625}], "temperature": 1.0}, {"id": 96, "seek": 236919, "start": 2356.73, "end": 2369.19, "text": "ومركبة إذا بدنا بعض المعلومات عن الأعداد المركبة مشان نقدر نستخدم أي من هذه المعلومات متى لازمة الأمر", "tokens": [20498, 31747, 49401, 11933, 15730, 47525, 8315, 45030, 11242, 9673, 30241, 20498, 9307, 18871, 16247, 22488, 18513, 9673, 31747, 49401, 37893, 7649, 8717, 28543, 2288, 8717, 14851, 9778, 40448, 36632, 9154, 29538, 9673, 30241, 20498, 9307, 44650, 7578, 5296, 31377, 46007, 16247, 29973], "avg_logprob": -0.14115767587314954, "compression_ratio": 1.6371681415929205, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2356.73, "end": 2358.13, "word": "ومركبة", "probability": 0.7421875}, {"start": 2358.13, "end": 2358.69, "word": " إذا", "probability": 0.56170654296875}, {"start": 2358.69, "end": 2359.17, "word": " بدنا", "probability": 0.923095703125}, {"start": 2359.17, "end": 2359.67, "word": " بعض", "probability": 0.9833984375}, {"start": 2359.67, "end": 2360.89, "word": " المعلومات", "probability": 0.9896240234375}, {"start": 2360.89, "end": 2361.39, "word": " عن", "probability": 0.99365234375}, {"start": 2361.39, "end": 2362.07, "word": " الأعداد", "probability": 0.9669596354166666}, {"start": 2362.07, "end": 2362.93, "word": " المركبة", "probability": 0.9645182291666666}, {"start": 2362.93, "end": 2363.71, "word": " مشان", "probability": 0.642333984375}, {"start": 2363.71, "end": 2364.09, "word": " نقدر", "probability": 0.8507486979166666}, {"start": 2364.09, "end": 2364.91, "word": " نستخدم", "probability": 0.994384765625}, {"start": 2364.91, "end": 2365.25, "word": " أي", "probability": 0.77001953125}, {"start": 2365.25, "end": 2365.53, "word": " من", "probability": 0.98876953125}, {"start": 2365.53, "end": 2365.97, "word": " هذه", "probability": 0.97412109375}, {"start": 2365.97, "end": 2366.89, "word": " المعلومات", "probability": 0.9931640625}, {"start": 2366.89, "end": 2367.89, "word": " متى", "probability": 0.8798828125}, {"start": 2367.89, "end": 2368.65, "word": " لازمة", "probability": 0.9176432291666666}, {"start": 2368.65, "end": 2369.19, "word": " الأمر", "probability": 0.80908203125}], "temperature": 1.0}, {"id": 97, "seek": 239421, "start": 2369.57, "end": 2394.21, "text": "فيها المعلومات اللي قدامنا اللوحة دي اللي بتلزمنا خلال دراستنا لهذا ال section بتيجي المعلوم الأولى يبقى يقولنا some basic properties of complex number بيقول لي any complex number z is written as بكتبه على شكل عددين مركبين واحد a والتاني ib يعني جزء حقيقي وجزء", "tokens": [41185, 11296, 9673, 30241, 20498, 9307, 13672, 1829, 12174, 3215, 10943, 8315, 13672, 2407, 5016, 3660, 11778, 1829, 13672, 1829, 39894, 1211, 11622, 2304, 8315, 16490, 1211, 6027, 11778, 23557, 14851, 8315, 46740, 15730, 2423, 3541, 39894, 1829, 7435, 1829, 9673, 30241, 20498, 16247, 12610, 7578, 7251, 3555, 4587, 7578, 7251, 39648, 8315, 512, 3875, 7221, 295, 3997, 1230, 4724, 1829, 39648, 32239, 604, 3997, 1230, 710, 307, 3720, 382, 4724, 4117, 2655, 3555, 3224, 15844, 13412, 28820, 6225, 3215, 3215, 9957, 3714, 31747, 3555, 9957, 36764, 24401, 257, 16070, 2655, 7649, 1829, 39073, 37495, 22653, 10874, 11622, 38207, 11331, 38436, 38436, 49610, 11622, 38207], "avg_logprob": -0.18705778386232988, "compression_ratio": 1.6584362139917694, "no_speech_prob": 0.0, "words": [{"start": 2369.57, "end": 2370.05, "word": "فيها", "probability": 0.44677734375}, {"start": 2370.05, "end": 2370.79, "word": " المعلومات", "probability": 0.8975830078125}, {"start": 2370.79, "end": 2370.91, "word": " اللي", "probability": 0.806884765625}, {"start": 2370.91, "end": 2371.41, "word": " قدامنا", "probability": 0.9464111328125}, {"start": 2371.41, "end": 2371.95, "word": " اللوحة", "probability": 0.865966796875}, {"start": 2371.95, "end": 2372.07, "word": " دي", "probability": 0.652099609375}, {"start": 2372.07, "end": 2372.17, "word": " اللي", "probability": 0.972900390625}, {"start": 2372.17, "end": 2372.85, "word": " بتلزمنا", "probability": 0.94619140625}, {"start": 2372.85, "end": 2373.19, "word": " خلال", "probability": 0.96240234375}, {"start": 2373.19, "end": 2373.95, "word": " دراستنا", "probability": 0.9190673828125}, {"start": 2373.95, "end": 2375.03, "word": " لهذا", "probability": 0.921630859375}, {"start": 2375.03, "end": 2375.27, "word": " ال", "probability": 0.3837890625}, {"start": 2375.27, "end": 2375.69, "word": " section", "probability": 0.6982421875}, {"start": 2375.69, "end": 2376.73, "word": " بتيجي", "probability": 0.81182861328125}, {"start": 2376.73, "end": 2377.19, "word": " المعلوم", "probability": 0.99072265625}, {"start": 2377.19, "end": 2377.53, "word": " الأولى", "probability": 0.7194010416666666}, {"start": 2377.53, "end": 2377.69, "word": " يبقى", "probability": 0.7437744140625}, {"start": 2377.69, "end": 2378.01, "word": " يقولنا", "probability": 0.9210611979166666}, {"start": 2378.01, "end": 2378.39, "word": " some", "probability": 0.68505859375}, {"start": 2378.39, "end": 2378.87, "word": " basic", "probability": 0.89111328125}, {"start": 2378.87, "end": 2379.49, "word": " properties", "probability": 0.75927734375}, {"start": 2379.49, "end": 2379.91, "word": " of", "probability": 0.97509765625}, {"start": 2379.91, "end": 2380.77, "word": " complex", "probability": 0.85498046875}, {"start": 2380.77, "end": 2381.33, "word": " number", "probability": 0.67041015625}, {"start": 2381.33, "end": 2381.85, "word": " بيقول", "probability": 0.9217122395833334}, {"start": 2381.85, "end": 2382.07, "word": " لي", "probability": 0.269775390625}, {"start": 2382.07, "end": 2382.45, "word": " any", "probability": 0.66796875}, {"start": 2382.45, "end": 2383.23, "word": " complex", "probability": 0.72607421875}, {"start": 2383.23, "end": 2383.85, "word": " number", "probability": 0.94140625}, {"start": 2383.85, "end": 2384.19, "word": " z", "probability": 0.697265625}, {"start": 2384.19, "end": 2384.71, "word": " is", "probability": 0.95068359375}, {"start": 2384.71, "end": 2385.51, "word": " written", "probability": 0.91064453125}, {"start": 2385.51, "end": 2386.11, "word": " as", "probability": 0.9755859375}, {"start": 2386.11, "end": 2387.11, "word": " بكتبه", "probability": 0.90380859375}, {"start": 2387.11, "end": 2387.33, "word": " على", "probability": 0.87158203125}, {"start": 2387.33, "end": 2388.11, "word": " شكل", "probability": 0.923583984375}, {"start": 2388.11, "end": 2388.93, "word": " عددين", "probability": 0.9534912109375}, {"start": 2388.93, "end": 2389.85, "word": " مركبين", "probability": 0.9381103515625}, {"start": 2389.85, "end": 2390.89, "word": " واحد", "probability": 0.792236328125}, {"start": 2390.89, "end": 2391.13, "word": " a", "probability": 0.767578125}, {"start": 2391.13, "end": 2391.71, "word": " والتاني", "probability": 0.8211669921875}, {"start": 2391.71, "end": 2392.07, "word": " ib", "probability": 0.3779296875}, {"start": 2392.07, "end": 2392.47, "word": " يعني", "probability": 0.9443359375}, {"start": 2392.47, "end": 2392.91, "word": " جزء", "probability": 0.9952799479166666}, {"start": 2392.91, "end": 2393.63, "word": " حقيقي", "probability": 0.98681640625}, {"start": 2393.63, "end": 2394.21, "word": " وجزء", "probability": 0.9251302083333334}], "temperature": 1.0}, {"id": 98, "seek": 241159, "start": 2394.53, "end": 2411.59, "text": "تخيلي قد يكون أحدهم بالصفر ماعنديش مشكلة، ممكن يكون الـA بالزرع و بالثالث يصبح الـIB هو العدد المركب، ممكن يطلع B بالزرع و يظل عند A فقط، و بعد قليل هقولك أن الـA هذا كمان complex number", "tokens": [2655, 9778, 26895, 1829, 12174, 3215, 7251, 30544, 5551, 24401, 16095, 20666, 9381, 5172, 2288, 19446, 3615, 1863, 16254, 8592, 37893, 28820, 3660, 12399, 3714, 43020, 7251, 30544, 2423, 39184, 32, 20666, 11622, 2288, 3615, 4032, 20666, 12984, 6027, 12984, 7251, 9381, 49628, 2423, 39184, 39081, 31439, 18863, 3215, 3215, 9673, 31747, 3555, 12399, 3714, 43020, 7251, 9566, 1211, 3615, 363, 20666, 11622, 2288, 3615, 4032, 7251, 19913, 1211, 43242, 316, 6156, 47432, 12399, 4032, 39182, 12174, 20292, 1211, 8032, 39648, 4117, 14739, 2423, 39184, 32, 23758, 9122, 2304, 7649, 3997, 1230], "avg_logprob": -0.2884744700565133, "compression_ratio": 1.634020618556701, "no_speech_prob": 0.0, "words": [{"start": 2394.53, "end": 2395.63, "word": "تخيلي", "probability": 0.705902099609375}, {"start": 2395.63, "end": 2395.91, "word": " قد", "probability": 0.828369140625}, {"start": 2395.91, "end": 2396.45, "word": " يكون", "probability": 0.989990234375}, {"start": 2396.45, "end": 2397.09, "word": " أحدهم", "probability": 0.8678385416666666}, {"start": 2397.09, "end": 2397.73, "word": " بالصفر", "probability": 0.90478515625}, {"start": 2397.73, "end": 2398.25, "word": " ماعنديش", "probability": 0.8677734375}, {"start": 2398.25, "end": 2399.05, "word": " مشكلة،", "probability": 0.790679931640625}, {"start": 2399.05, "end": 2399.43, "word": " ممكن", "probability": 0.95556640625}, {"start": 2399.43, "end": 2399.75, "word": " يكون", "probability": 0.931640625}, {"start": 2399.75, "end": 2400.09, "word": " الـA", "probability": 0.6017252604166666}, {"start": 2400.09, "end": 2400.43, "word": " بالزرع", "probability": 0.48980712890625}, {"start": 2400.43, "end": 2400.55, "word": " و", "probability": 0.552734375}, {"start": 2400.55, "end": 2400.87, "word": " بالثالث", "probability": 0.5244903564453125}, {"start": 2400.87, "end": 2401.05, "word": " يصبح", "probability": 0.7862955729166666}, {"start": 2401.05, "end": 2401.95, "word": " الـIB", "probability": 0.5894368489583334}, {"start": 2401.95, "end": 2402.73, "word": " هو", "probability": 0.7236328125}, {"start": 2402.73, "end": 2403.19, "word": " العدد", "probability": 0.89990234375}, {"start": 2403.19, "end": 2404.11, "word": " المركب،", "probability": 0.7471923828125}, {"start": 2404.11, "end": 2404.37, "word": " ممكن", "probability": 0.960205078125}, {"start": 2404.37, "end": 2404.81, "word": " يطلع", "probability": 0.971923828125}, {"start": 2404.81, "end": 2405.05, "word": " B", "probability": 0.478271484375}, {"start": 2405.05, "end": 2405.59, "word": " بالزرع", "probability": 0.83062744140625}, {"start": 2405.59, "end": 2405.71, "word": " و", "probability": 0.99072265625}, {"start": 2405.71, "end": 2406.17, "word": " يظل", "probability": 0.8863932291666666}, {"start": 2406.17, "end": 2406.61, "word": " عند", "probability": 0.9736328125}, {"start": 2406.61, "end": 2407.17, "word": " A", "probability": 0.873046875}, {"start": 2407.17, "end": 2408.15, "word": " فقط،", "probability": 0.86669921875}, {"start": 2408.15, "end": 2408.23, "word": " و", "probability": 0.495361328125}, {"start": 2408.23, "end": 2408.51, "word": " بعد", "probability": 0.91943359375}, {"start": 2408.51, "end": 2409.01, "word": " قليل", "probability": 0.9554036458333334}, {"start": 2409.01, "end": 2409.47, "word": " هقولك", "probability": 0.8610026041666666}, {"start": 2409.47, "end": 2409.65, "word": " أن", "probability": 0.43896484375}, {"start": 2409.65, "end": 2409.93, "word": " الـA", "probability": 0.9246419270833334}, 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"end": 2545.62, "word": " بالضبط", "probability": 0.8951416015625}, {"start": 2545.62, "end": 2546.12, "word": " تماما", "probability": 0.97998046875}], "temperature": 1.0}, {"id": 106, "seek": 257211, "start": 2546.33, "end": 2572.11, "text": "اختلف ولا واحد فيهم معاني التانية يعني لو اختلف الجزء الحقيقي عن الجزء الحقيقي فبتصيروا ايه اعداد تخيل مثله ذلك لو قلتلك واحد زائد اتنين I و هنا قلتلك تلاتة زائد اتنين I اختلف ولا لا اختلفوا يبقى هدول not equal و هكذا طيب نجي للنقطة الرابعة النقطة الرابعة بيقول Complex function", "tokens": [47283, 2655, 46538, 49429, 36764, 24401, 8978, 16095, 20449, 7649, 1829, 16712, 7649, 10632, 37495, 22653, 45164, 1975, 46456, 46538, 25724, 11622, 38207, 21542, 38436, 38436, 18871, 25724, 11622, 38207, 21542, 38436, 38436, 6156, 3555, 2655, 9381, 13546, 14407, 1975, 1829, 3224, 1975, 22488, 18513, 6055, 9778, 26895, 50113, 43761, 29910, 23275, 45164, 12174, 1211, 2655, 23275, 36764, 24401, 30767, 16373, 3215, 1975, 2655, 1863, 9957, 286, 4032, 34105, 12174, 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"text": "الرمز W of X تُكتب عليه شكل جزء حقيقي كذلك و جزء تخيله بس مش عدد، دالة في X والتانية دالة في X", "tokens": [6027, 2288, 2304, 11622, 343, 295, 1783, 6055, 10859, 4117, 2655, 3555, 47356, 13412, 28820, 10874, 11622, 38207, 11331, 38436, 38436, 9122, 8848, 23275, 4032, 10874, 11622, 38207, 6055, 9778, 26895, 3224, 4724, 3794, 37893, 6225, 3215, 3215, 12399, 11778, 6027, 3660, 8978, 1783, 16070, 2655, 7649, 10632, 11778, 6027, 3660, 8978, 1783], "avg_logprob": -0.3087384380676128, "compression_ratio": 1.3675213675213675, "no_speech_prob": 0.0, "words": [{"start": 2574.46, "end": 2575.3, "word": "الرمز", "probability": 0.6676788330078125}, {"start": 2575.3, "end": 2575.72, "word": " W", "probability": 0.37353515625}, {"start": 2575.72, "end": 2576.02, "word": " of", "probability": 0.06854248046875}, {"start": 2576.02, "end": 2576.28, "word": " X", "probability": 0.8974609375}, {"start": 2576.28, "end": 2579.6, "word": " تُكتب", "probability": 0.73369140625}, {"start": 2579.6, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i9JeLMWGd-k_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i9JeLMWGd-k_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..56e5e24513d0d16f2ad1fab4c408ea709ef0da81
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/i9JeLMWGd-k_raw.srt
@@ -0,0 +1,1600 @@
+1
+00:00:20,690 --> 00:00:25,190
+بسم الله الرحمن الرحيم انتهينا من chapter 3 اللى
+
+2
+00:00:25,190 --> 00:00:29,510
+بتحدث عن موضوعين اللى هو ال vector spaces و ال
+
+3
+00:00:29,510 --> 00:00:34,130
+linear transformations وانتقلنا الان الى chapter 4
+
+4
+00:00:34,130 --> 00:00:39,150
+و هو ال chapter الثالث من ال linear algebra لأن
+
+5
+00:00:39,150 --> 00:00:43,670
+المادة اللى معانا معادلات تفاضلية وجبر خطي يبقى
+
+6
+00:00:43,670 --> 00:00:49,110
+هذا هو ال chapter الثالث والاخير من الجبر الخطيفي
+
+7
+00:00:49,110 --> 00:00:53,330
+هذا الشفر بدنا ناخد two sections هذا أول section
+
+8
+00:00:53,330 --> 00:00:57,250
+بين إيدينا اللي هو ال characteristic values
+
+9
+00:00:57,250 --> 00:01:01,750
+والsection التاني اللي هو ال diagonalization خلينا
+
+10
+00:01:01,750 --> 00:01:03,990
+الآن مع ال section الأول أربعة و واحدة اللي هو ال
+
+11
+00:01:03,990 --> 00:01:10,970
+characteristic values يعني القيم المميزة أو القيم
+
+12
+00:01:10,970 --> 00:01:16,730
+المميزةايش القيم المميزة؟ طبعا القيم المميزة
+
+13
+00:01:16,730 --> 00:01:22,670
+لمصفوفة ما هي المقصود فيها التعريف بيقول ما ياتي
+
+14
+00:01:22,670 --> 00:01:31,410
+هاعطي تعريف لقيم المميزة والمتجهات المميزة لمصفوفة
+
+15
+00:01:32,200 --> 00:01:39,160
+التعريف الأول هو القيم المميزة لمصفوفة بيقول افترض
+
+16
+00:01:39,160 --> 00:01:45,360
+ال A هي مصفوفة مربعة نظامها N في M number lambda
+
+17
+00:01:45,360 --> 00:01:50,920
+يبقى هذا العدد هو real numberالعدد هذا قد يكون عدد
+
+18
+00:01:50,920 --> 00:01:57,540
+حقيقي وقد يكون عدد تخيلي complex number يبقى سواء
+
+19
+00:01:57,540 --> 00:02:01,140
+كان عدد حقيقي و طبعا هنعطي أمثلة ان شاء الله على
+
+20
+00:02:01,140 --> 00:02:06,520
+لندن تطلع مرة قيمة حقيقية و مرة قيمة تخيليةيوجد
+
+21
+00:02:06,520 --> 00:02:11,120
+رمبر لامضة real or complex يعني يا إما عدد حقيقي
+
+22
+00:02:11,120 --> 00:02:15,800
+يا إما عدد مُركّب is called an eigenvalue بسميه
+
+23
+00:02:15,800 --> 00:02:20,180
+الـ eigenvalue أو الـ characteristic value القيمة
+
+24
+00:02:20,180 --> 00:02:25,160
+المميزة لمن؟ للمصفوفة إيه؟ if there exists a non
+
+25
+00:02:25,160 --> 00:02:31,200
+-zero vector x موجود في الـ RMيبقى ال X ده non
+
+26
+00:02:31,200 --> 00:02:34,560
+-zero عمره ما هيساوي zero دلوقت دروا بالكم non
+
+27
+00:02:34,560 --> 00:02:41,160
+-zero vector X موجود في Rn بحيث أن ال A في ال X
+
+28
+00:02:41,160 --> 00:02:45,560
+يساوي ال land ده في X ال land يا بنات A مصفوفة
+
+29
+00:02:45,560 --> 00:02:51,450
+نظامها N في N وال X هذي vector موجود وين؟فى RN
+
+30
+00:02:51,450 --> 00:02:57,630
+يعني كأنه مصفوفة فيها N من الصفوف وعمود واحد لو
+
+31
+00:02:57,630 --> 00:03:03,870
+ضربت اتنين في بعض يفلع مصفوفة المصفوفة هذه يمكن
+
+32
+00:03:03,870 --> 00:03:08,410
+اللاجئ بين جميع أنصارها عامل مشترك اخده برا اخده
+
+33
+00:03:08,410 --> 00:03:13,690
+برا مين هو لندن لندن بيضل فى ال vector X ان حدث
+
+34
+00:03:13,690 --> 00:03:20,050
+ذلك بقول يبقى لندن هي قيمة مميزة للمصفوفة Aيبقى
+
+35
+00:03:20,050 --> 00:03:24,650
+لاندا اللي عندى هذه عدد لكن X هذا vector يعني
+
+36
+00:03:24,650 --> 00:03:31,730
+مصفوفة تتكون من N من الصفوف وعمود واحد تمام إذا
+
+37
+00:03:31,730 --> 00:03:35,730
+جدرت أكتب هذه على الشكل اللي عندنا هذا يبقى لاندا
+
+38
+00:03:35,730 --> 00:03:43,640
+هذه مالها شو اسمهاEigenvalue او characteristic
+
+39
+00:03:43,640 --> 00:03:52,200
+value بشرط ال X non zero vector نجي
+
+40
+00:03:52,200 --> 00:03:57,330
+التعريف التانيEvery non-zero vector x الموجود في
+
+41
+00:03:57,330 --> 00:04:02,450
+Rn satisfy the question بحقق لهذا الهدف is called
+
+42
+00:04:02,450 --> 00:04:05,890
+the eigenvector او ال characteristic vector
+
+43
+00:04:12,430 --> 00:04:16,970
+أيوة يعني نفس المعادلة اللى عندنا هي نفس المعادلة
+
+44
+00:04:16,970 --> 00:04:22,770
+هذه يبقى ال X اللى قلنا عليه non zero vector ال X
+
+45
+00:04:22,770 --> 00:04:27,630
+اللى هو non zero vector اللى بحقق المعادلة هذه
+
+46
+00:04:27,630 --> 00:04:34,670
+بسميه المتجه المميز يبقى السؤال هو هل ممكن لل
+
+47
+00:04:34,670 --> 00:04:37,890
+characteristic vector في يوم من الأيام يكون ال
+
+48
+00:04:37,890 --> 00:04:43,870
+zero vectorفي الشمكانية قال non-zero vector يبقى
+
+49
+00:04:43,870 --> 00:04:49,430
+لا يمكن المتجه الصفري أن يكون eigenvector يبقى ال
+
+50
+00:04:49,430 --> 00:04:53,870
+eigenvalue يا بنات هو عدد حقيقي أو عدد تخيلي لكن
+
+51
+00:04:53,870 --> 00:04:58,750
+ال eigenvector هو مصفوفة مكونة من N من الصفوف مثلا
+
+52
+00:04:58,750 --> 00:05:04,720
+او M من الصفوف وعمود واحدهو اللى بيحقق مين بيحقق
+
+53
+00:05:04,720 --> 00:05:07,940
+المعادلة اللى عندنا هذه يبقى المعادلة هذه يابا
+
+54
+00:05:07,940 --> 00:05:12,520
+اكتبها بالشكل هذا او الشكل هذا او الشكل هذا الشكل
+
+55
+00:05:12,520 --> 00:05:16,140
+هذا من وين اجا هذه البنات لو جيبتها على الشجرة
+
+56
+00:05:16,140 --> 00:05:23,120
+تنقش بالصغيرلاندا اكس ناقص ax يساوي زيرو يعني في
+
+57
+00:05:23,120 --> 00:05:29,060
+الها مش هيك لو جيت قولت لاندا اكس ناقص ax بدي ساوي
+
+58
+00:05:29,060 --> 00:05:33,460
+مين بدي ساوي زيرو في عامل مشترك ممكن ناخده منهم
+
+59
+00:05:33,460 --> 00:05:38,780
+اللي هو من اللي هو ال X طب أخده برا ولا أخده يعني
+
+60
+00:05:38,780 --> 00:05:44,420
+أخده على اليمين ولا أخده على الإشمال أشمال
+
+61
+00:05:44,420 --> 00:05:49,210
+يعني أخده هنا براتاخدوا على اليمين ليش؟ ان عرمالية
+
+62
+00:05:49,210 --> 00:05:55,550
+ضرب المصوفات ليست إبدالية، دي مش بمزاج يمين وشمال،
+
+63
+00:05:55,550 --> 00:05:59,770
+إجباري هو على اليمين، جاي بيبقى بتخليه على اليمين،
+
+64
+00:05:59,770 --> 00:06:03,430
+إذا لو أخدتوا عامل مشترك، بيظل يمين هنا عندنا
+
+65
+00:06:03,430 --> 00:06:06,790
+لندا، لندا بس ولا لندا ..
+
+66
+00:06:13,110 --> 00:06:19,530
+هل يمكن الرقم أني أطرحه من المصوفة في الشمكانية
+
+67
+00:06:19,530 --> 00:06:24,610
+يبقى بطرح مصوفة من المصوفة يبقى lambda I ناقص ال A
+
+68
+00:06:24,610 --> 00:06:29,190
+كله في X بده يساوي Zero يبقى هاي المعادلة اللي فوق
+
+69
+00:06:29,190 --> 00:06:35,070
+اللي احنا جايلين عليهاطبعا ياما هنكتبها خلال شغلنا
+
+70
+00:06:35,070 --> 00:06:39,210
+في هذا ال chapter بالطريقة اللي عندنا هذه تمام
+
+71
+00:06:39,210 --> 00:06:43,470
+يبقى هي عرفنا ال eigen value وال eigen vectors
+
+72
+00:06:43,470 --> 00:06:48,910
+بدنا نبدأ ناخد أمثلة على ذلك نبدأ بأول مثال أول
+
+73
+00:06:48,910 --> 00:06:56,290
+مثال مثال بسيط يبقى example one example one بيقول
+
+74
+00:06:56,290 --> 00:07:05,110
+ما ياتي Fالمصوفة ايه؟ هي ال identity matrix اللي
+
+75
+00:07:05,110 --> 00:07:13,950
+هي the identity matrix لو كانت هذه مصوفة الوحدة
+
+76
+00:07:13,950 --> 00:07:26,170
+then the only the only eigen value eigen
+
+77
+00:07:26,170 --> 00:07:36,000
+valueis one and
+
+78
+00:07:36,000 --> 00:07:42,320
+hence every
+
+79
+00:07:42,320 --> 00:07:54,700
+non zero vector every non zero vector X اللي موجود
+
+80
+00:07:54,700 --> 00:08:04,500
+في RN isand eigen vector
+
+81
+00:08:04,500 --> 00:08:12,820
+السبب because ان
+
+82
+00:08:12,820 --> 00:08:19,020
+ال I في ال X يسوى
+
+83
+00:08:21,030 --> 00:08:26,090
+أحنا قلنا ال X هدى وين موجودة ال R N يبقى X هدى
+
+84
+00:08:26,090 --> 00:08:30,550
+vector X واحد X اتنى لغاية X N مضروب في مصفوفة
+
+85
+00:08:30,550 --> 00:08:35,090
+الواحدهاش بيعطينى المصفوفة X بالشكل اللى عندنا هدى
+
+86
+00:08:35,090 --> 00:08:41,290
+اللى بقدر اكتبها على الشكل واحد مضروب في مين في X
+
+87
+00:08:41,290 --> 00:08:45,810
+ومن هنا ال Eigen value اللى عندنا مين اللى هى
+
+88
+00:08:45,810 --> 00:08:52,200
+الواحد يبقى هدى أتفة أنواع مين الأمثلةيبقى لو كانت
+
+89
+00:08:52,200 --> 00:08:58,140
+ال a هي مصفوفة الوحدة عندنا هنا يبقى بناء عليه ال
+
+90
+00:08:58,140 --> 00:09:03,610
+eigen value هيالواحد الصحي مفيش غيره لكن ال
+
+91
+00:09:03,610 --> 00:09:08,690
+eigenvectors أكتر كلهم eigenvectors مع عدمين ال
+
+92
+00:09:08,690 --> 00:09:12,890
+zero vector روح نقول أهنس every non zero vector
+
+93
+00:09:12,890 --> 00:09:17,490
+موجود في ال RN عبارة عن eigenvector هذا الشغل
+
+94
+00:09:17,490 --> 00:09:24,250
+البسيط طيب نشتغل شغل أحسن من هنا يبقى example two
+
+95
+00:09:31,250 --> 00:09:37,990
+LED المصوفة ايه اللي هي عبارة عن واحد ستة خمس
+
+96
+00:09:37,990 --> 00:09:40,910
+اتنين بالشكل اللي عندنا هنا
+
+97
+00:09:43,790 --> 00:09:50,570
+ال X بده يساوي ال vector اللي هو مين؟ ستة وناقص
+
+98
+00:09:50,570 --> 00:09:57,690
+خمسة و ال Y هو ال vector اللي هو مين؟ ثلاثة وسلب
+
+99
+00:09:57,690 --> 00:10:04,110
+اتنين كل هذا اللي موجود وين؟ في R2 المطلوب الأول
+
+100
+00:10:04,110 --> 00:10:12,990
+بيقولي find the eigen value
+
+101
+00:10:37,730 --> 00:10:42,430
+هل هدول بيكونوا eigenvectors of a ولا لأ
+
+102
+00:10:53,800 --> 00:10:59,920
+سؤال مرة ثانية سؤال بيقول مياتي عندي مصفوفة نظامها
+
+103
+00:10:59,920 --> 00:11:05,320
+اتنين في اتنين سميتها ايه؟ اخدت vector ماقلتش عنه
+
+104
+00:11:05,320 --> 00:11:09,760
+لا إيه كان و لا غيره vector موجود في اعراء اتنين
+
+105
+00:11:09,760 --> 00:11:14,920
+اللي بقدر اقول ستة و سالب خمسة او مصفوفة عمودية
+
+106
+00:11:14,920 --> 00:11:19,100
+اللي هي ستة و سالب خمسة و vector تاني موجود في
+
+107
+00:11:19,100 --> 00:11:23,050
+اعراء اتنين اللي هو تلاتة و سالب اتنينمطلبين
+
+108
+00:11:23,050 --> 00:11:28,030
+جاليهات لل eigenvalue للمصوفة من a مطلب الأول مطلب
+
+109
+00:11:28,030 --> 00:11:32,070
+التاني بيقول هل ال X و Y هدول بيكونوا eigenvectors
+
+110
+00:11:32,070 --> 00:11:36,710
+ام لا طبعا يمكن يطلعوا eigenvectors و يمكن ما
+
+111
+00:11:36,710 --> 00:11:41,010
+يطلعوش لما نشوف هل بنقدر نكتب على الصيغة اللي
+
+112
+00:11:41,010 --> 00:11:45,610
+عندنا هذه ولا لأ و بعد هيك يمكن يجي في بالنا تساؤل
+
+113
+00:11:45,610 --> 00:11:50,160
+خليه لما نوصله بصير خيريبقى النقطة الأولى قاللي
+
+114
+00:11:50,160 --> 00:11:54,000
+هاتلي ال eigen value لمين للمصمم باجي بقوله أنا
+
+115
+00:11:54,000 --> 00:11:59,660
+بدي أخد ال a في ال x هشوف إيش بتعطينا يبقى بداجي
+
+116
+00:11:59,660 --> 00:12:05,640
+أقوله ال a في ال x يساوي ال a موجودة اللي هي واحد
+
+117
+00:12:05,640 --> 00:12:12,720
+ستة خمس اتنين ال x عندنا قداشر ستة ناقص خمسة
+
+118
+00:12:12,720 --> 00:12:13,740
+بالشكل اللي عندنا
+
+119
+00:12:19,890 --> 00:12:25,610
+هل بقدر اكتب الرقم في ال vector اللي عندنا هذا و
+
+120
+00:12:25,610 --> 00:12:31,490
+لا لأ حسب ال definition هل
+
+121
+00:12:31,490 --> 00:12:34,950
+بقدر اكتب الرقم في ال vector اللي عندنا هذا و لا
+
+122
+00:12:34,950 --> 00:12:39,150
+لأ حسب ال definitionتعالوا نضرب المصفتين هدول
+
+123
+00:12:39,150 --> 00:12:43,710
+ونشوف إيه الشناتين يبقى الصف الأول في العمود الأول
+
+124
+00:12:43,710 --> 00:12:50,550
+واحد في ستة بستة وهنا ناقص تلاتين بيظل جداش ناقص
+
+125
+00:12:50,550 --> 00:12:54,960
+أربعة وعشرينيبقى هذا الصف الأول في العمون الصف
+
+126
+00:12:54,960 --> 00:12:59,900
+الثاني في العمون خمسة في ستة بتلاتين ناقص عشرة
+
+127
+00:12:59,900 --> 00:13:05,620
+بيظل قداشر عشرين بالشكل اللي عندنا هذا بنقدر ناخد
+
+128
+00:13:05,620 --> 00:13:09,760
+عامل مشترك، إيش العامل المشترك اللي مابيل يتنام؟
+
+129
+00:13:11,370 --> 00:13:14,350
+أربعة لو أخدت أربعة بيصير هنا سالب بس أنا عندي
+
+130
+00:13:14,350 --> 00:13:20,090
+سالب وين؟ تحت يبقى خد سالب أربعة من الكل يبقى سالب
+
+131
+00:13:20,090 --> 00:13:26,850
+أربعة بيظل عندنا قداش ستة و هنا قداش ناقص خمسة
+
+132
+00:13:26,850 --> 00:13:31,660
+بالشكل اللي عندنا هنا يبقى هذا X ولا لا؟مش هو X
+
+133
+00:13:31,660 --> 00:13:37,440
+اللي عندنا؟ إذا حصل ضرب لإتنين كتبته على صيغة رقم
+
+134
+00:13:37,440 --> 00:13:43,460
+مضروب في الـ X يبقى Lambda بكم؟ سالب أربعة يبقى
+
+135
+00:13:43,460 --> 00:13:52,640
+هنا Lambda تساوي السالب أربعة اللي هي is the eigen
+
+136
+00:13:52,640 --> 00:14:04,450
+value ofthe matrix المُعطَر طب لو غيرنا المصفوف
+
+137
+00:14:04,450 --> 00:14:08,630
+هذه بمصفوفها تانية بضل ال land هذه ولا بتتغير؟
+
+138
+00:14:10,080 --> 00:14:15,780
+بتتغير لأن هذه كل واحدة خاصة بمصفوفتها إذا لو غيرت
+
+139
+00:14:15,780 --> 00:14:19,940
+المصفوفة بتتغير قيمة land يعني بتبقى اشتاب ده ليش
+
+140
+00:14:19,940 --> 00:14:23,400
+انا اقول the eigen value of the matrix ايه؟ غيرت
+
+141
+00:14:23,400 --> 00:14:28,660
+ال matrix اتغير مين؟ بتتغير قيمة ال land يبقى هذا
+
+142
+00:14:28,660 --> 00:14:34,780
+المطلوب الأول اللي هو نمرة a نمرة bنمرى بيقول هل
+
+143
+00:14:34,780 --> 00:14:39,120
+ال X و ال Y Eigen Vectors ولا لا؟ بدأ أسألكوا
+
+144
+00:14:39,120 --> 00:14:43,800
+السؤال التالي هل ال X Eigen Vector ولا لا؟ ليش له
+
+145
+00:14:43,800 --> 00:14:49,320
+non-zero اتنين حقق المعادلة اللي عندنا هذه صحيح
+
+146
+00:14:49,320 --> 00:14:54,960
+ولا لا؟ يبقى باجي يقول is the Eigen Value and ال X
+
+147
+00:14:54,960 --> 00:15:02,980
+بده يساوي ستة ناقص خمسة is an Eigen Vector
+
+148
+00:15:05,910 --> 00:15:10,650
+المصوفة ايه؟ طب بدي اجي لنمر بيه؟ بدي اشتغل نفسي
+
+149
+00:15:10,650 --> 00:15:18,120
+الشغل فايش بدي اجي اقوله؟ بدي اخد ال a في ال yطبعا
+
+150
+00:15:18,120 --> 00:15:23,540
+إذا لما أخد ال A في ال Y بده ساوي المصوفة واحد ستة
+
+151
+00:15:23,540 --> 00:15:29,620
+خمسة اتنين فمين في ال Y عنده تلاتة و سالبي اتنين
+
+152
+00:15:29,620 --> 00:15:34,260
+بالشكل اللي عندنا هذا يبقى تاع لنضرب الصف الأول في
+
+153
+00:15:34,260 --> 00:15:39,820
+العمود يبقى تلاتة وعندي ناقص اتناش في ضلج الدرجة
+
+154
+00:15:49,280 --> 00:15:55,740
+السؤال هو هل تستطيع ان تأخذ عامل مشترك يطلع عندنا
+
+155
+00:15:55,740 --> 00:15:57,100
+هذا ال vector؟
+
+156
+00:15:59,630 --> 00:16:07,630
+يبقى هذا لا يساوي لاندا في من؟ في تلاتة سالي
+
+157
+00:16:07,630 --> 00:16:15,770
+باتنين for any number لاندا
+
+158
+00:16:15,770 --> 00:16:21,210
+لأي number لاندا هذا الكلام مش موجود عندي معناته
+
+159
+00:16:21,210 --> 00:16:26,650
+هذا ال vector Eigen vectorيبقى هذا لا يمكن أن يكون
+
+160
+00:16:26,650 --> 00:16:34,390
+eigenvector في يوم من الأيام يبقى هنا ال y تساوي
+
+161
+00:16:34,390 --> 00:16:45,170
+تلاتة وسلب اتنين is not an eigenvector
+
+162
+00:16:46,610 --> 00:16:50,330
+يبقى معناته هذا الكلام الـEigenvector يعتمد على
+
+163
+00:16:50,330 --> 00:16:53,970
+مين الـEigenvalue إذا عندي إيش فيه Eigenvalue
+
+164
+00:16:53,970 --> 00:16:57,010
+معناته فيه Eigenvector مافيش Eigenvalue يبقى مافيش
+
+165
+00:16:57,010 --> 00:17:04,490
+Eigenvector تمام؟ يبقى هذا مثال بسيط واضح إنه معنى
+
+166
+00:17:04,490 --> 00:17:07,930
+الـEigenvalue والـEigenvector اللي أعطينا
+
+167
+00:17:07,930 --> 00:17:12,830
+تعريفاتهم أو تعريفاتهما قبل قليل
+
+168
+00:17:15,770 --> 00:17:21,710
+نجي للنقطة الثانية كيف بدنا نوجد ال eigenvalues
+
+169
+00:17:21,710 --> 00:17:29,170
+هطرح حد على صيغة السؤال التالي يبقى how to find
+
+170
+00:17:29,170 --> 00:17:38,970
+كيف بدك توجد the eigen أو ال characteristic values
+
+171
+00:17:38,970 --> 00:17:40,990
+of
+
+172
+00:17:44,020 --> 00:17:49,800
+ن بي ن ماتريكس
+
+173
+00:17:49,800 --> 00:17:55,820
+ماتريكس
+
+174
+00:17:55,820 --> 00:18:06,520
+A هذا هو السؤال الإجابة كالتالي answer خطوة
+
+175
+00:18:06,520 --> 00:18:09,200
+الأولى rewrite
+
+176
+00:18:12,220 --> 00:18:22,260
+عاد كتابة المعادلة equation ax يساوي lambda x in
+
+177
+00:18:22,260 --> 00:18:26,500
+the form في
+
+178
+00:18:26,500 --> 00:18:34,900
+الشكل التالي اللي هو lambda I ناقص ال A في ال X
+
+179
+00:18:34,900 --> 00:18:42,620
+بده يساوي Zero وسميلي هذه المعادلة رقم 6خطوة
+
+180
+00:18:42,620 --> 00:18:49,740
+التانية since ال X does not equal to zero يبقى ال
+
+181
+00:18:49,740 --> 00:18:54,340
+system يبقى
+
+182
+00:18:54,340 --> 00:19:00,720
+ال system star has
+
+183
+00:19:00,720 --> 00:19:07,380
+a non zero solution
+
+184
+00:19:10,280 --> 00:19:19,940
+if and only if if and only if determinant ل lambda
+
+185
+00:19:19,940 --> 00:19:28,580
+I ناقص ال A بده يساوي zero و هذه المعادلة رقم واحد
+
+186
+00:19:28,580 --> 00:19:31,620
+the
+
+187
+00:19:31,620 --> 00:19:46,390
+solution the solution of thatEquation one بيعطينا
+
+188
+00:19:46,390 --> 00:19:56,530
+الـ Eigen values اللي
+
+189
+00:19:56,530 --> 00:20:04,230
+هي اللي عندها command definition equation
+
+190
+00:20:07,100 --> 00:20:15,120
+المعادلة determined ل lambda I ناقص ال A بده يساوي
+
+191
+00:20:15,120 --> 00:20:20,600
+Zero is called the
+
+192
+00:20:20,600 --> 00:20:31,560
+characteristic equation المعادلة
+
+193
+00:20:31,560 --> 00:20:35,540
+المميزة أو ال polynomial
+
+194
+00:20:40,780 --> 00:20:53,460
+pronomial equation of a matrix a مصفوفة a that is
+
+195
+00:20:53,460 --> 00:21:05,410
+in ال P of لاندا بدي اساوي determinantللاندا اي
+
+196
+00:21:05,410 --> 00:21:15,210
+ناقص ال a اللي هي بدأ تساوي لاندا زيرو زيرو زيرو
+
+197
+00:21:15,210 --> 00:21:23,870
+لاندا زيرو زيرو زيرو زيرو لاندا بالشكل اللي عندنا
+
+198
+00:21:23,870 --> 00:21:32,470
+هنا ناقص a11 a12 a1n a21
+
+199
+00:21:44,090 --> 00:21:49,930
+بالشكل اللي عندنا هذا و اللي بقدر اقول وتساوي
+
+200
+00:21:49,930 --> 00:22:04,840
+مصفوفة واحدة يبقى لاندا ناقص a11نقص a12 ناقص a1n
+
+201
+00:22:09,510 --> 00:22:22,010
+A21 ناقص A21 و بعدين لاندا ناقص A22 و ناقص A2N و
+
+202
+00:22:22,010 --> 00:22:31,530
+نظل ماشيين لغاية ناقص AN1 ناقص AN2 و نظل ماشيين
+
+203
+00:22:31,530 --> 00:22:35,750
+لغاية لاندا ناقص ANN
+
+204
+00:23:08,940 --> 00:23:10,340
+اممم
+
+205
+00:23:17,590 --> 00:23:22,050
+الان بنطرح السؤال اللى بين ادينا هذا ونحاول نجاوب
+
+206
+00:23:22,050 --> 00:23:29,070
+على هذا السؤال بخطوتين لا ثالثة لهما السؤال هو how
+
+207
+00:23:29,070 --> 00:23:33,690
+to find the eigenvalues of an n by n matrix ايه
+
+208
+00:23:33,690 --> 00:23:38,110
+ماهي الوسيلة العملية مشان جيب ال eigenvalues
+
+209
+00:23:38,110 --> 00:23:44,140
+لمصوفة مع نظامها n في nاللي جابها في نقطتنا النقطة
+
+210
+00:23:44,140 --> 00:23:49,020
+الأولى بيقول يا ليها write the equation AX بيستوي
+
+211
+00:23:49,020 --> 00:23:53,180
+Lambda X in the form قعدت كتابة المعادلة اللي
+
+212
+00:23:53,180 --> 00:23:57,080
+عندنا تبع تعريف ال Eigen value على الشكل اللي
+
+213
+00:23:57,080 --> 00:24:01,240
+عندنا هذا و هذا شفناها كيف قبل قليل كتبناها سمنها
+
+214
+00:24:01,240 --> 00:24:05,280
+المعادلة Star الآن المعادلة Star هدى homogeneous
+
+215
+00:24:05,280 --> 00:24:10,360
+system ولا non homogeneous system؟هوموجينيا ال
+
+216
+00:24:10,360 --> 00:24:13,880
+system مدام هوموجينيا ال system يا عندى ال trivial
+
+217
+00:24:13,880 --> 00:24:18,740
+solution يا اما عندى عدد لنهائى من الحلول انا بدى
+
+218
+00:24:18,740 --> 00:24:22,540
+استبعد ل trivial solution لان قلت الفكتور هذا non
+
+219
+00:24:22,540 --> 00:24:28,420
+zero فكتور معناته الحل الصفري مستبعد فايش قال ليه؟
+
+220
+00:24:28,800 --> 00:24:32,860
+بما أن الـ X لا يمكن أن تساوي 0 يعني الحل الصفري
+
+221
+00:24:32,860 --> 00:24:39,580
+مستبعد يبقى ال system has a non-zero solution إذا
+
+222
+00:24:39,580 --> 00:24:43,540
+كان ال determinant هذا بيساوي قداش؟ Zero إذا
+
+223
+00:24:43,540 --> 00:24:48,080
+المحدد تبع المصوف هذا بيساوي Zero بيكون عندى اللي
+
+224
+00:24:48,080 --> 00:24:54,040
+هو حل غير صفري لمين؟ لسystem اللي عندنا هذا
+
+225
+00:24:57,620 --> 00:25:05,030
+الحل تبع المحدد هذابيعطيني قيم ال eigenvalues ليش؟
+
+226
+00:25:05,030 --> 00:25:10,350
+لأن هذه معادلة هذه أعداد هذه مصفوفة الوحدة المجهول
+
+227
+00:25:10,350 --> 00:25:14,710
+من عندى lambda إذا بفكها دى و بجيبله قيم lambda
+
+228
+00:25:14,710 --> 00:25:17,870
+يمكن تطلع معادلة من الدرجة التانية يمكن من الدرجة
+
+229
+00:25:17,870 --> 00:25:21,350
+التالتية يمكن من الدرجة الرابعة حسب نوع المصفوفة
+
+230
+00:25:21,350 --> 00:25:26,120
+اللى عندى فلو كانت المصفوفة من الدرجة الثانيةيبقى
+
+231
+00:25:26,120 --> 00:25:29,840
+automatic لازم تطلع المعادلة من الدرجة الثانية إذا
+
+232
+00:25:29,840 --> 00:25:33,300
+المصوفة نظامها تلاتة في تلاتة بتطلع من الدرجة
+
+233
+00:25:33,300 --> 00:25:38,960
+التالتة و هكذا تمام إلى آخرى طيب ما علينانجي
+
+234
+00:25:38,960 --> 00:25:42,940
+التعريف التاني بقول المعادلة اللي عندنا هذه اللي
+
+235
+00:25:42,940 --> 00:25:46,860
+هو determinant لهذه بيسوي zero بسميها ال
+
+236
+00:25:46,860 --> 00:25:50,460
+characteristic equation او ال polynomial equation
+
+237
+00:25:50,460 --> 00:25:56,020
+يبقى كثيرة الحدود او معادلة كثيرة الحدود او
+
+238
+00:25:56,020 --> 00:26:02,120
+المعادلة المميزة لمين للمصوفة ايه that is مين هي
+
+239
+00:26:02,120 --> 00:26:09,120
+لما اقولP of لندا يعني دالة في لندا بتطلع بدلالة
+
+240
+00:26:09,120 --> 00:26:13,100
+لندا من هى هى ال determinant للندا ايه النقص ايه
+
+241
+00:26:13,100 --> 00:26:17,480
+النقص ايه وان اللندا ايه يبقى اللندا مضروبة في مين
+
+242
+00:26:17,480 --> 00:26:24,610
+في مصوفة الوحدةناقص الـA كتبتها بعناصرها يبقى بدي
+
+243
+00:26:24,610 --> 00:26:29,370
+أطرح المصفتين من بعض بيصير كل عنصر باطرحهم من
+
+244
+00:26:29,370 --> 00:26:34,590
+نظيره Zero ناقص يبقى البجر بيصير ناقص ما عدا عناصر
+
+245
+00:26:34,590 --> 00:26:37,270
+القطة الرئيسية القطة الرئيسية بيصير لاندا ناقص ايه
+
+246
+00:26:37,270 --> 00:26:42,380
+one oneلاندا ناقص a22 ناقص لاندا a33 الاخر حاجة
+
+247
+00:26:42,380 --> 00:26:47,440
+لاندا ناقص a ان ان والباقي عناصر المصفوفة هم هم بس
+
+248
+00:26:47,440 --> 00:26:53,380
+بغير مين إشارتهم السبب بسبب سبق المصفوفة بمين
+
+249
+00:26:53,380 --> 00:26:58,500
+بإشارة سالب يبقى الصورة العامة لهذه المصفوفة تصبح
+
+250
+00:26:58,500 --> 00:27:03,280
+على الصورة اللي عندها هي القطرة الرئيسي كله لاندا
+
+251
+00:27:03,280 --> 00:27:07,690
+ناقص عناصر القطرة الرئيسيوالباقي هي المصوفة A بس
+
+252
+00:27:07,690 --> 00:27:12,090
+بإشارة من؟ بإشارة set الآن الكلام اللي بقوله هذا
+
+253
+00:27:12,090 --> 00:27:16,970
+بدنا نروح نطبقه على أرض الواقع يبقى لما نيجي نحسب
+
+254
+00:27:16,970 --> 00:27:22,010
+قيمة lambda هنا يا بنات يمكن تطلع عدد حقيقي ويمكن
+
+255
+00:27:22,010 --> 00:27:27,990
+تطلع عددتخيلي كما ذكرنا في التعريف قبل قليل تمام
+
+256
+00:27:27,990 --> 00:27:32,250
+إذا بدنا نروح نجرب نخلي مرة يطلع عدد حقيقي و مرة
+
+257
+00:27:32,250 --> 00:27:36,390
+يطلع تخيلي و نشوف كيف بدنا نجيب ال eigenvalues و
+
+258
+00:27:36,390 --> 00:27:40,690
+ال eigenvectors في هذه الحلقة هنبدأ بعدد حقيقي
+
+259
+00:27:40,690 --> 00:27:44,070
+لإنه أسلف شوية و المرة الجاية ان شاء الله بنجيب
+
+260
+00:27:44,070 --> 00:27:52,110
+اللعنة ده بعدد تخيلي يبقى example oneexample one
+
+261
+00:27:52,110 --> 00:27:59,610
+هذا سؤال واحد من الكتاب بقول find the eigenvalues
+
+262
+00:27:59,610 --> 00:28:05,450
+find the eigenvalues
+
+263
+00:28:05,450 --> 00:28:08,730
+and eigenvectors
+
+264
+00:28:16,270 --> 00:28:21,330
+والـ Eigenvectors of the
+
+265
+00:28:21,330 --> 00:28:26,730
+matrix للمصفوفة
+
+266
+00:28:26,730 --> 00:28:29,930
+التي تساوى
+
+267
+00:28:41,860 --> 00:28:45,840
+يبقى بدل الـ Eigenvalues والـ Eigenvectors لمين؟
+
+268
+00:28:45,840 --> 00:28:47,740
+للمصوفة اللي عندنا هذه
+
+269
+00:28:53,790 --> 00:28:57,090
+كيف بدي أجيب الـ Eigenvalues؟ هذه المعادلة اللي
+
+270
+00:28:57,090 --> 00:29:02,510
+عندنا يبقى أنا بدي أذهب لمين لـ lambda I ناقص A X
+
+271
+00:29:02,510 --> 00:29:07,210
+بده يساوي Zero و بعد هيك إذا قلت X non-zero يبقى
+
+272
+00:29:07,210 --> 00:29:10,890
+بدي ال determinant لهذه و أخليه يساوي مين؟ ال Zero
+
+273
+00:29:10,890 --> 00:29:17,690
+إذا أنا بدي أبدأ بال determinantلمين؟ لان ده I
+
+274
+00:29:17,690 --> 00:29:23,070
+ناقص ال A كله و اقول هذا الكلام بده يساوي قداش؟
+
+275
+00:29:23,070 --> 00:29:28,770
+بده يساوي Zero طيب مشان هيك تعالى نشوف لان ده في I
+
+276
+00:29:28,770 --> 00:29:33,550
+و نشوف ال A، اه ال A موجود عندىإذا بقدر أعوض تعويض
+
+277
+00:29:33,550 --> 00:29:37,470
+مباشر في الأخيرة اللي تحت هذه مانديش أقعد أكل
+
+278
+00:29:37,470 --> 00:29:42,270
+كأكتير يبقى بقدر أكتب على طول الخط يبقى هاي
+
+279
+00:29:42,270 --> 00:29:47,910
+المصوفة اللي عندنا هاي اللي عندنا ناقص a11 a11
+
+280
+00:29:47,910 --> 00:29:54,750
+بقداشسالف واحد يبقى بصير زائد واحد هذا ناقص واحد
+
+281
+00:29:54,750 --> 00:30:00,450
+زي ما هو هذا ناقص اربعة زي ما هو هذه لندن ناقص
+
+282
+00:30:00,450 --> 00:30:03,990
+اتنين هيجفلنا الجوز تمام؟
+
+283
+00:30:07,360 --> 00:30:13,640
+للاندا اي ناقص الاي له بده ساوي زيرو يعني معناه
+
+284
+00:30:13,640 --> 00:30:19,840
+هذا الكلام انه عندي المحدد لاندا زائد واحد ناقص
+
+285
+00:30:19,840 --> 00:30:26,500
+واحد ناقص اربعة لاندا ناقص اتنين كل هذا الكلام بده
+
+286
+00:30:26,500 --> 00:30:32,060
+ساوي مين؟ بده ساوي زيروإذا لو فكّت المحدد هذا حاصل
+
+287
+00:30:32,060 --> 00:30:36,860
+ضرب عناصر القطر الرئيسي ناقص حاصل ضرب عناصر القطر
+
+288
+00:30:36,860 --> 00:30:43,680
+الثانوي هذا بيعطيك Lambda زائد واحد فLambda ناقص
+
+289
+00:30:43,680 --> 00:30:49,580
+اتنين ناقص أربعة بيساوي مين؟ بيساوي Zero طبعا ناقص
+
+290
+00:30:49,580 --> 00:30:53,040
+واحد فناقص أربعة بيزايد أربعة الرئيسي ناقص الثانوي
+
+291
+00:30:53,040 --> 00:30:56,440
+تجيني كمان إشارة ناقص فبصير الناقص بالشكل اللي
+
+292
+00:30:56,440 --> 00:31:01,360
+عندنا هذايبقى انا عندى معادلة من اى درجة ثانية
+
+293
+00:31:01,360 --> 00:31:05,400
+يبقى انا بدى احلى المعادلة هذه مشان احلى المعادلة
+
+294
+00:31:05,400 --> 00:31:11,300
+هذه بدى اروح افكها يبقى هذه لاندا تربية زائد لاندا
+
+295
+00:31:11,300 --> 00:31:17,270
+ونقص اثنين لاندا بطلع قداشنقص لاندا و عندك ناقص
+
+296
+00:31:17,270 --> 00:31:23,190
+اتنين ناقص اربعة بده يساوي zero او بمعنى اخر بده
+
+297
+00:31:23,190 --> 00:31:29,790
+يصير لاندا تربية ناقص لاندا ناقص ستة يساوي zero او
+
+298
+00:31:29,790 --> 00:31:36,960
+لو حللتها كحاصل ضرب قوسين يساوي zero هنا لانداوهنا
+
+299
+00:31:36,960 --> 00:31:43,380
+لاندا وهنا اتنين في تلاتة بستة وواحدة ناقص وواحدة
+
+300
+00:31:43,380 --> 00:31:48,200
+زايد اتنين لاندا وناقص تلاتة تحليل مية المية يبقى
+
+301
+00:31:48,200 --> 00:31:54,560
+بناء عليه بقوله the eigen values
+
+302
+00:31:54,560 --> 00:31:58,320
+are
+
+303
+00:32:00,560 --> 00:32:06,900
+اللي هم مين لاندا تساوي ناقص اتنين and لاندا تساوي
+
+304
+00:32:06,900 --> 00:32:13,600
+كدهش تلاتة يبقى جيبت ال eigen vectors اللي عندنا
+
+305
+00:32:14,480 --> 00:32:19,200
+جبت ال eigenvectors اللي عندنا تمام يبقى جبت ال
+
+306
+00:32:19,200 --> 00:32:23,840
+eigenvalues لسه ال eigenvectors ما جبتهمش اه تمام
+
+307
+00:32:23,840 --> 00:32:29,120
+بدنا نروح ندور على مين على ال eigenvectors لكل
+
+308
+00:32:29,120 --> 00:32:33,280
+لنضة من اللنضات الأتنين هدونأه يعني كانوا ضايل
+
+309
+00:32:33,280 --> 00:32:38,040
+عليه لسه مسألتين مش مسألة واحدة كل landa لها
+
+310
+00:32:38,040 --> 00:32:43,040
+eigenvectors خاصة بها تمام يبقى أنا بدي أمسك أول
+
+311
+00:32:43,040 --> 00:32:48,300
+واحدة فيهم يبقى باجي بقول هنا إذا كانت ال landa
+
+312
+00:32:48,300 --> 00:32:51,480
+تساوي الناقص اتنين then
+
+313
+00:32:54,310 --> 00:33:01,150
+أخذ الـ land في هذا كله من المصوفة اللي عندنا هذه
+
+314
+00:33:01,150 --> 00:33:07,710
+صحيح ولا لأ؟ و ال X موجود وين؟ موجود في R2 يبقى X1
+
+315
+00:33:07,710 --> 00:33:14,410
+و X2 اشعرفك R2 لأن المصوفة نظامها 2 في 2 يبقى باجي
+
+316
+00:33:14,410 --> 00:33:18,670
+بقول بداجي على المصوفة هذه هي يا بنات بالتفصيل
+
+317
+00:33:18,670 --> 00:33:26,000
+المرة هذه يبقى هي ناقص 2 زائد 1وهي ناقص واحد وهي
+
+318
+00:33:26,000 --> 00:33:34,660
+ناقص اربعة وهي ناقص اتنين ناقص اتنين في X واحد X
+
+319
+00:33:34,660 --> 00:33:41,340
+اتنين بده ساوي Zero و Zeroيبقى انا راجع اتعوض في
+
+320
+00:33:41,340 --> 00:33:47,560
+مين؟ في المعادلة star عن مين؟ عن قيم lambda واخد
+
+321
+00:33:47,560 --> 00:33:52,360
+lambda الأولى اشوف هذه ايش بدها تجيبلي يبقى هذه
+
+322
+00:33:52,360 --> 00:33:58,900
+معناه يا بنت المصفوفة ناقص واحد ناقص واحد ناقص
+
+323
+00:33:58,900 --> 00:34:07,180
+اربعة ناقص اربعة X واحد X اتنين يساوي Zero و Zero
+
+324
+00:34:07,180 --> 00:34:11,710
+بالشكل اللي عندناهذه العمود لو جيت فكيتها يبقاش
+
+325
+00:34:11,710 --> 00:34:21,330
+بيصير ناقص x1 ناقص x2 و العمود التاني ناقص 4x1
+
+326
+00:34:21,330 --> 00:34:29,550
+ناقص 4x2 هي هذه كلها بدها تساوي مين؟ Zero و Zero
+
+327
+00:34:29,550 --> 00:34:38,050
+هذا معناهانه ناقص X1 ناقص X2 بده يساوي Zero وناقص
+
+328
+00:34:38,050 --> 00:34:48,710
+4X1 ناقص 4X2 بده يساوي Zero هذه لو جيت ضربت الأولى
+
+329
+00:34:48,710 --> 00:34:56,450
+في سالب واحد ايش بيصير X1 زيد X2 يساوي Zero هذه لو
+
+330
+00:34:56,450 --> 00:35:03,640
+ضربتها في سالب رابعبصير نفس المعادلة هذه صح ولا لأ
+
+331
+00:35:03,640 --> 00:35:07,660
+يبقى التان تانة صاروا مش معادلتين هذه مين معادلة
+
+332
+00:35:07,660 --> 00:35:14,900
+واحدة يبقى هذا معناه انه x واحد يساوي قداش سالب x
+
+333
+00:35:14,900 --> 00:35:22,000
+اتنين اذا لو كانت x اتنين ب a x واحد قداش سالب a
+
+334
+00:35:22,000 --> 00:35:32,360
+يبقى هنا بقوله fالـ X2 تساوي A ثم X1 يساوي سالب A
+
+335
+00:35:32,360 --> 00:35:43,060
+يبقى باجي بقوله The Eigen vectors are in the form
+
+336
+00:35:43,060 --> 00:35:46,880
+يبقى
+
+337
+00:35:46,880 --> 00:35:56,420
+على الشكل التالي X1 بقدرش عندي سالب Aو اكس اتنين
+
+338
+00:35:56,420 --> 00:36:03,140
+تبقى اكس
+
+339
+00:36:03,140 --> 00:36:07,250
+اكس اكس اكس اكس اكس اكس اكس اكس اكسيبقى هي جيب له
+
+340
+00:36:07,250 --> 00:36:12,370
+ال eigenvectors كل ال vectors اللي بتبقى على الشكل
+
+341
+00:36:12,370 --> 00:36:16,030
+هذا يعني الرقم من ال set of real numbers اللي هو a
+
+342
+00:36:16,030 --> 00:36:20,610
+مضروب في سالب واحد واحد بيجيب لل eigenvectors
+
+343
+00:36:20,610 --> 00:36:27,170
+تبعات مين تبعات lambda تساوي سلب اتنين فقطلأنه في
+
+344
+00:36:27,170 --> 00:36:30,030
+السؤال قال هي اتلقى كل ال eigenvalues و ال
+
+345
+00:36:30,030 --> 00:36:34,370
+eigenvectors للمصوفة هذه انا جبت لسه ل lambda 2 زي
+
+346
+00:36:34,370 --> 00:36:39,050
+ما جبت ل lambda 2 بتروح اجيب لمام ل lambda 3 يبقى
+
+347
+00:36:39,050 --> 00:36:46,590
+كله بالشكل اللي هنا كم واحد هدولبس المراكبة الأولى
+
+348
+00:36:46,590 --> 00:36:52,390
+هي سالب المراكبة الثانية كل العناصر اللى بالشكل
+
+349
+00:36:52,390 --> 00:36:55,150
+هذا بيكونوا eigenvectors واحنا شفنا في السؤال اللى
+
+350
+00:36:55,150 --> 00:36:59,690
+جابله قبل قليل مش كل vector هو eigenvector يعني
+
+351
+00:36:59,690 --> 00:37:04,120
+بعضهم بنفع يكون eigenvectors وبعضهمبنفعل فى السؤال
+
+352
+00:37:04,120 --> 00:37:07,280
+اللى جابله ال X طلع Eigen vector لكن ال Y طلع
+
+353
+00:37:07,280 --> 00:37:11,980
+Eigen vector إذا يا بنات مش كل vector بنفع يكون
+
+354
+00:37:11,980 --> 00:37:15,760
+Eigen vector للمصحوفة اللى موجودة البعض بنفع
+
+355
+00:37:15,760 --> 00:37:19,980
+والبعض بنفعش مين اللى بينفعه فى السؤال هذا كل ال
+
+356
+00:37:19,980 --> 00:37:23,700
+vectors اللى على الشكل area number مضروب فى سالب
+
+357
+00:37:23,700 --> 00:37:28,320
+واحد وواحد طيب نجى للحالة الثانية
+
+358
+00:37:45,930 --> 00:37:51,970
+أخذنا لاندا تساوي سالب اتنين بدأت ياخد الان F
+
+359
+00:37:51,970 --> 00:37:57,370
+لاندا تساوي تلاتة اللي هو القيمة الثانية اللي
+
+360
+00:37:57,370 --> 00:38:03,110
+طلعناها then لاندا
+
+361
+00:38:03,110 --> 00:38:11,610
+I نقص ال A في X بدأت تساوي zero impliesبتجي لنفس
+
+362
+00:38:11,610 --> 00:38:14,170
+المصوفة اللي عندنا هذي بدي أشيل اللاندة و أحط
+
+363
+00:38:14,170 --> 00:38:21,050
+مكانها مالها تلاتة يبقى تلاتة زائد واحد و سالب
+
+364
+00:38:21,050 --> 00:38:29,290
+واحد و سالب أربعة و تلاتة ناقص اتنين هذه كلها في X
+
+365
+00:38:29,290 --> 00:38:36,650
+واحد X اتنين كله بدي يساوي مين؟ Zero و Zero تلاتة
+
+366
+00:38:36,650 --> 00:38:42,480
+زائد واحد كدهش؟أربعة و هنا سالب واحد و هنا سالب
+
+367
+00:38:42,480 --> 00:38:49,920
+أربعة و هنا واحد كله x واحد x اتنين بدي يسوى من
+
+368
+00:38:49,920 --> 00:38:56,670
+Zero و Zeroنضرب المصافتين هدول في بعض يبقى الصف
+
+369
+00:38:56,670 --> 00:39:01,990
+الأول في العمود الأول اربعة اكس واحد ناقص اكس
+
+370
+00:39:01,990 --> 00:39:09,430
+اتنين صف التاني ناقص اربعة اكس واحد زائد اكس اتنين
+
+371
+00:39:09,430 --> 00:39:15,760
+كله بده يساوي من؟ Zero و Zeroاللي هناخد مقارنة بين
+
+372
+00:39:15,760 --> 00:39:21,160
+الموصفين يبقى العناصر المتنظرة متساوية يبقى الاربع
+
+373
+00:39:21,160 --> 00:39:26,960
+X واحد ناقص X اتنين يساوي كده؟ Zero المعادلة
+
+374
+00:39:26,960 --> 00:39:33,340
+التانية ناقص اربع X واحد زيد X اتنين يساوي Zero
+
+375
+00:39:34,460 --> 00:39:37,680
+المعادلة اللي تحت لو ضربها في السلب بصير هي
+
+376
+00:39:37,680 --> 00:39:41,860
+المعادلة اللي فوق إذا هذول مش معادلتين وإنما في
+
+377
+00:39:41,860 --> 00:39:46,440
+الواقع عبارة عن معادلة واحدة يبقى هذا معناه أن
+
+378
+00:39:46,440 --> 00:39:52,480
+أربعة اكس واحد ناقص اكس اتنين يساوي Zero إذا اكس
+
+379
+00:39:52,480 --> 00:39:58,390
+اتنين يساوي مين؟ أربعة اكس واحديبقى بناء عليه لو
+
+380
+00:39:58,390 --> 00:40:05,350
+كانت ال X واحد بده يساوي ال A then X اتنين بده
+
+381
+00:40:05,350 --> 00:40:11,450
+يساوي اربعة A يبقى بقدر اجيب الشكل العام لل Eigen
+
+382
+00:40:11,450 --> 00:40:18,190
+vectors اذا بناء عليه بروح بقوله the Eigen vectors
+
+383
+00:40:18,190 --> 00:40:28,950
+are in the form في الشكل التالياللي هو مين ال X
+
+384
+00:40:28,950 --> 00:40:34,650
+واحد وال X اتنين اللي أنا قلت عليهم الآن A واحد او
+
+385
+00:40:34,650 --> 00:40:41,750
+X واحد هي A X اتنين هي اربعة A واللي هو A في واحد
+
+386
+00:40:41,750 --> 00:40:46,800
+ومين واربعةيبقى بالنسبة للاندة التانية اللى تساوي
+
+387
+00:40:46,800 --> 00:40:51,860
+التلاتة شكل ال eigenvectors أي real number بس
+
+388
+00:40:51,860 --> 00:40:56,940
+مايكونش صفرها اي real number غير ال zero بدي اضربه
+
+389
+00:40:56,940 --> 00:41:00,740
+في من في ال vector واحد واربعة بيعطيني ال
+
+390
+00:41:00,740 --> 00:41:06,300
+eigenvectors قداش هدول عددهم؟ما لا نهاية، إذا عندي
+
+391
+00:41:06,300 --> 00:41:09,420
+ما لا نهاية من الـEigenvectors، ورغم أن
+
+392
+00:41:09,420 --> 00:41:13,740
+الـEigenvalues تنتين، لكن الـEigenvectors التابعة
+
+393
+00:41:13,740 --> 00:41:17,020
+لكل واحدة فيهم، عبارة عن العدد لا نهائي من
+
+394
+00:41:17,020 --> 00:41:20,620
+الـEigenvectors، يبقى هكذا، جمتوا الـEigenvalues
+
+395
+00:41:20,620 --> 00:41:25,760
+وEigenvectors، وهذا يعتبر من الأسئلة السهلة، لأنه
+
+396
+00:41:25,760 --> 00:41:32,460
+ما فيهاcomplex numbers يعني هذه مالها أعداد حقيقية
+
+397
+00:41:32,460 --> 00:41:38,100
+real numbers أعداد حقيقية طبعا الآن بدنا نيجي على
+
+398
+00:41:38,100 --> 00:41:42,520
+سؤال ال complex لكن السؤال زي ما انتوا شايفين at
+
+399
+00:41:42,520 --> 00:41:47,040
+least بده ربع ساعة طبعا إذا مافيش إمكانية للمرة
+
+400
+00:41:47,040 --> 00:41:51,400
+القادمة ان شاء الله بنكمل بيعطيكوا العفو
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/iuDuvfspJA8_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/iuDuvfspJA8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4ed40755a2383613e662e319ed1229be07e3dc32
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/iuDuvfspJA8_postprocess.srt
@@ -0,0 +1,2132 @@
+1
+00:00:19,940 --> 00:00:26,190
+بسم الله الرحمن الرحيمهذه المحاضرة نفضل ان تكون
+
+2
+00:00:26,190 --> 00:00:31,170
+محاضرة مناقشة بسبب الامتحان اللى عندنا اليوم
+
+3
+00:00:31,170 --> 00:00:36,770
+الساعتين دون فقبل ان نبدأ المناقشة انا بحب ان نشير
+
+4
+00:00:36,770 --> 00:00:41,690
+الى رقم القاعة اللى سيكون فيها الامتحان لان اللى
+
+5
+00:00:41,690 --> 00:00:47,890
+كان نزلكه في الأول N411 تغيرت وقسمته الى قاعتين
+
+6
+00:00:47,890 --> 00:00:54,640
+القاعة الأولى اللى هى ال Nمتين و اتنين والقاعة
+
+7
+00:00:54,640 --> 00:01:00,580
+التانية N متين و خمسةيبقى تتوجهوا الى هتين
+
+8
+00:01:00,580 --> 00:01:05,240
+القاعتين بدلا من القاع الى N411 اللى كانت نازلة
+
+9
+00:01:05,240 --> 00:01:10,300
+سابقا لكم اي واحدة متين اتنين طبعا ان متين واثنين
+
+10
+00:01:10,300 --> 00:01:15,080
+كبيرة شوية ان متين وخمسة صغيرة شوية فغالب يتوجهوا
+
+11
+00:01:15,080 --> 00:01:20,540
+الى N202 ان شاء الله تعالى يبقى هذا بالنسبة لمين
+
+12
+00:01:20,540 --> 00:01:27,240
+لامتحانه ذكرناان الامتحان هيكون في نهاية chapter 2
+
+13
+00:01:27,240 --> 00:01:31,040
+اللي هو اخر two sections بالاضافة الى chapter 3
+
+14
+00:01:31,040 --> 00:01:36,760
+كله اعطيتكم مجموعة من النماذج حوالي خمسة نماذج من
+
+15
+00:01:36,760 --> 00:01:41,040
+الامتحانات السابقة كي تتدربوا عليها و لا انسى
+
+16
+00:01:41,040 --> 00:01:47,960
+نناقش بعض هذه النماذج فمثلا في امتحان اللي هو تبع
+
+17
+00:01:47,960 --> 00:01:58,870
+2007 يعطيني السؤال رقم 2و جاي اللي Tمن M22 إلى M22
+
+18
+00:01:58,870 --> 00:02:24,610
+Linear Transformation معرفة بشكل تالي
+
+19
+00:02:31,090 --> 00:02:39,290
+طلب المطلوب الأول T عبارة عن Linear Transformation
+
+20
+00:02:40,530 --> 00:02:43,490
+مش هنثبت له هذه الـ Linear Transformation بده أروح
+
+21
+00:02:43,490 --> 00:02:49,030
+أثبت الخاصيتين الخاصية الأولى لو أخدت element من
+
+22
+00:02:49,030 --> 00:02:52,430
+ال set of real numbers اللي هو يعني خاتة scalar و
+
+23
+00:02:52,430 --> 00:02:58,750
+بنديله رمز C كعادتنا أو K أو أي رمز آخر تمام و
+
+24
+00:02:58,750 --> 00:03:02,990
+أخدنا element من ال M22 و ضربنا الاتنين هدول في
+
+25
+00:03:02,990 --> 00:03:08,590
+بعض و أثرنا عليهم بT بده يساوي C في T of ال
+
+26
+00:03:08,590 --> 00:03:13,540
+element اللي أخدنا هذايبقى بقى بقى بقى بقى بقى
+
+27
+00:03:13,540 --> 00:03:19,880
+solution
+
+28
+00:03:22,670 --> 00:03:27,950
+وطبعا هذا نمر ايه من المثالة بدي اثبت ان هذه T is
+
+29
+00:03:27,950 --> 00:03:32,870
+a linear transformation فباجي بقوله لو كانت ال C
+
+30
+00:03:32,870 --> 00:03:39,470
+موجودة في ال set of real numbers and ال A اللي هي
+
+31
+00:03:39,470 --> 00:03:48,430
+موجودة او ال A اللي تساوي A11, A12, A21, A22 اللي
+
+32
+00:03:48,430 --> 00:03:58,430
+موجودة في ال M22بعد ذلك بدي أخد T of C في الـ A
+
+33
+00:03:58,430 --> 00:04:03,550
+إذا و طلعت والله الـ C لحالها في T of A بيكون
+
+34
+00:04:03,550 --> 00:04:09,110
+اتحققنا الخاصية الأولى فماجي بقوله هذا الكلام بدي
+
+35
+00:04:09,110 --> 00:04:18,570
+يساوي T فيC مضربها في كل حد من حدود المصوفة
+
+36
+00:04:18,570 --> 00:04:19,590
+بالاستثناء
+
+37
+00:04:31,060 --> 00:04:34,960
+الان بداية ال definition اللى انا كاتبه بدي اجي
+
+38
+00:04:34,960 --> 00:04:39,000
+اعوض في العلاقة اللى احنا كاتبينها يبقى بما ان انا
+
+39
+00:04:39,000 --> 00:04:44,640
+عليها بدي اعطيني CA11-CA22
+
+40
+00:04:44,640 --> 00:04:51,380
+هنا Zero هنا Zero وهنا CA12
+
+41
+00:04:51,380 --> 00:04:54,400
+-CA21
+
+42
+00:04:54,400 --> 00:04:58,590
+بالشكل اللى عندنا هنايبقى هاي كتابنا ناتج على
+
+43
+00:04:58,590 --> 00:05:03,570
+الشكل اللي عندنا هذا بالضبط هنا الـC ممكن أخدها
+
+44
+00:05:03,570 --> 00:05:09,230
+عامل مشترك من الكل المضروبة في جميع أناصر المصوفة
+
+45
+00:05:09,230 --> 00:05:14,920
+لأن الـ0 هذا باعتبر الـC في 0إذا لو أخدت الـ C
+
+46
+00:05:14,920 --> 00:05:21,880
+عامل مشترك يبقى بدي أوطيني هذا الـ C في a11-a22
+
+47
+00:05:21,880 --> 00:05:28,240
+وهنا 0 وهنا 0 وهنا a12-a21
+
+48
+00:05:28,650 --> 00:05:33,210
+يبقى هذا الكلام بدي يساوي C هذا ال element اللي هو
+
+49
+00:05:33,210 --> 00:05:41,690
+T of A يبقى T of A وبناء عليه الخاصية الأولى تحققت
+
+50
+00:05:41,690 --> 00:05:48,870
+من خواص ال linear transformationيبقى هذه هي النقطة
+
+51
+00:05:48,870 --> 00:05:55,310
+الأولى، بدي أجي للنقطة الثانية، بدي أجي أخد مصرفين
+
+52
+00:05:55,310 --> 00:06:04,070
+A وB موجودة في ال M22 و بدي أجي أخد المجموع تبعهم
+
+53
+00:06:05,760 --> 00:06:13,480
+بدي اخد ال a زائد ال b اللي عبارة عن مهم a11 a12
+
+54
+00:06:13,480 --> 00:06:24,560
+a21 a22 زائد اللي هي b11 b12 b21
+
+55
+00:06:27,190 --> 00:06:36,950
+بتوتو يبقى اصبح T لما تأثر على ال A زائد ال B يسوى
+
+56
+00:06:36,950 --> 00:06:43,320
+تأثير T على نجمع هدولالجمع طبع العناصر المتناغرة
+
+57
+00:06:43,320 --> 00:06:56,620
+مع بعضها وهنا a12 زائد b12 وهنا a21 زائد b21 وهنا
+
+58
+00:06:56,620 --> 00:07:04,840
+a22 زائد b22 بالشكل اللي عندنا هناالان بدى أري على
+
+59
+00:07:04,840 --> 00:07:08,680
+التعريف تبع ال function اللى عندنا اللى هى T T لما
+
+60
+00:07:08,680 --> 00:07:13,560
+تأثر على ال element بده يساوي الفرق بين عناصر
+
+61
+00:07:13,560 --> 00:07:20,100
+القطر الرئيسى و الفرق بين عناصر القطر الثانوي يبقى
+
+62
+00:07:20,100 --> 00:07:28,330
+هذا الكلام بده يساوي هى المصفوفةيبقى a11 زائد b11
+
+63
+00:07:28,330 --> 00:07:33,270
+هذا العنصر الأول ناقص العنصر التاني و كل واحد
+
+64
+00:07:33,270 --> 00:07:42,050
+هحطله إشارة سالب يبقى ناقص a22 ناقص b22 العنصر
+
+65
+00:07:42,050 --> 00:07:47,440
+اللي بعده zero العنصر اللي هنا zeroالعنصر الثاني
+
+66
+00:07:47,440 --> 00:07:56,600
+اللي هو a12 زائد b12 ناقص هدخلها لكل واحد من هدول
+
+67
+00:07:56,600 --> 00:08:05,860
+يبقى ناقص a21 ناقص b21 الشكل اللي عندنا هنا هذا
+
+68
+00:08:05,860 --> 00:08:12,740
+الكلام يساويهذه مصفوفة واحدة ممكن احولها الى مجموع
+
+69
+00:08:12,740 --> 00:08:17,400
+مصفوفين بدون مشاكل بدي اخد اللي فيهم ال اهات مع
+
+70
+00:08:17,400 --> 00:08:21,220
+بعض و اللي فيهم ال بيهات مع بعض يبقى باجي بقول
+
+71
+00:08:21,220 --> 00:08:29,700
+المصفوفة الاولى هي a11 ناقص a22 هذا بدي اخليه zero
+
+72
+00:08:29,700 --> 00:08:38,450
+هذا بدي اخليه zeroهنا a12 ناقص a21 زائد المصفوفة
+
+73
+00:08:38,450 --> 00:08:46,610
+التانية بقى عندى b11 minus b22 وهنا زيرو زي ما هو
+
+74
+00:08:46,610 --> 00:08:55,870
+وهنا بقى عندى b12 ناقص b21 بالشكل اللى عندنا هنا
+
+75
+00:08:57,010 --> 00:09:04,250
+الأولى هي صورة من مصفوفة A يبجى هذه هي عبارة عن T
+
+76
+00:09:04,250 --> 00:09:11,150
+of A التانية هي صورة المصفوفة من B إذا تحققت
+
+77
+00:09:11,150 --> 00:09:16,230
+الخاصيتين الإتنين هدول إذا بقوله So T is a linear
+
+78
+00:09:16,230 --> 00:09:24,290
+transformation يبجى هنا SoT is a linear
+
+79
+00:09:24,290 --> 00:09:30,070
+transformation وانتهينا من المطلوب الأول من المثلة
+
+80
+00:09:30,070 --> 00:09:37,060
+بدنا نيجي لمن؟ للمطلوب التاني نمربينمرة بي وهذا
+
+81
+00:09:37,060 --> 00:09:40,520
+اللي أنتوا بدكوا إياه أساسا من السؤال يعني هذا شغل
+
+82
+00:09:40,520 --> 00:09:45,280
+روتيني الكل بتقدر يسويه بدون أي مشكلة المطلوب
+
+83
+00:09:45,280 --> 00:09:48,660
+التاني جالي هاتلي ال basis و ال dimension لل
+
+84
+00:09:48,660 --> 00:09:56,960
+kernel of T يبقى نمرة بي بدنا ال kernel of T ال
+
+85
+00:09:56,960 --> 00:10:04,680
+basis لل kernel عفوا بدنا ال basis of
+
+86
+00:10:04,950 --> 00:10:15,010
+الـ Kernel لـ T and ال dimension لمين للكرنل of T
+
+87
+00:10:15,010 --> 00:10:21,170
+بالشكل اللي عندنا طيب احنا مش هنجيب ال bases لكرنل
+
+88
+00:10:21,170 --> 00:10:26,680
+لاننا نعرف ما هو شكل الكرنلطيب إذا بدنا نروح نعطي
+
+89
+00:10:26,680 --> 00:10:32,140
+تعريف الكيرن لو نبدأ نطبق هذا التعريف يبقى انا لو
+
+90
+00:10:32,140 --> 00:10:39,000
+جيت هنا و قولت الكيرن التي هي كل المصحفات A اللي
+
+91
+00:10:39,000 --> 00:10:46,600
+موجودة في ال M22 such that T of A بده يساوي من؟
+
+92
+00:10:46,600 --> 00:10:53,210
+بده يساوي Z صحيح ولا لا؟يبقى هذا بده يعطيني كل
+
+93
+00:10:53,210 --> 00:11:01,670
+المصفوفات اللي على الشكل A11, A12, A21, A22 اللي
+
+94
+00:11:01,670 --> 00:11:07,350
+موجودة في ال M22 و such that ال T of A هي صورتها
+
+95
+00:11:07,640 --> 00:11:16,800
+يبقى باجي بقوله ال T of A هي عبارة عن A11-A22 00
+
+96
+00:11:16,800 --> 00:11:25,740
+A12-A21 كله بده يساوي 0 يعني مين ال 0؟ هي المصفوفة
+
+97
+00:11:25,740 --> 00:11:32,090
+الصفرية اللي عندنا بهذا الشكلتمام اذا انا عندي
+
+98
+00:11:32,090 --> 00:11:38,450
+مصفتين متساويتين اذا بدروح أساوي العناصر المتناضرة
+
+99
+00:11:38,450 --> 00:11:47,670
+ببعضها يبقى بناء عليه a11 a22-a22 بده يساوي 0
+
+100
+00:11:47,670 --> 00:11:56,910
+والتانية a12-a21 بده يساوي 0هذا بده يعطينا ان ال
+
+101
+00:11:56,910 --> 00:12:04,170
+a11 بده تساوي ال a22 و كذلك ال a12 بده يساوي ال
+
+102
+00:12:04,170 --> 00:12:05,630
+a21
+
+103
+00:12:07,340 --> 00:12:13,540
+كويس إذا بقدر أحط الآن شكل العناصر اللي عندي هذه
+
+104
+00:12:13,540 --> 00:12:18,500
+العناصر اللي موجودة وين في ال kernel يبقى أصبح
+
+105
+00:12:18,500 --> 00:12:25,660
+عندي ال kernel اللتي بدي يكون على الشكل التالي كل
+
+106
+00:12:25,660 --> 00:12:32,840
+العناصر اللي على الشكل التالي a11 تسوى a22 يعني لو
+
+107
+00:12:32,840 --> 00:12:40,150
+قلت هنا a و قلت هنا aو A to 1 لو قلت هذه بي و قلت
+
+108
+00:12:40,150 --> 00:12:45,190
+هذه بي بالشكل اللي عندنا هذا ساتش ذات ال A و ال B
+
+109
+00:12:45,190 --> 00:12:51,770
+موجودة في ال set of real numbers نمسح
+
+110
+00:12:51,770 --> 00:12:58,660
+هذه خلاصنا يبقى كله عارف قاعات الامتحان اليوميبقى
+
+111
+00:12:58,660 --> 00:13:04,940
+ما عليك الى تتوجهى الى احدتين القاعتين 202 و205 في
+
+112
+00:13:04,940 --> 00:13:10,600
+مبنى المدينة المنورة نرجع لسؤالنا يبقى أصبح ال
+
+113
+00:13:10,600 --> 00:13:16,080
+kernel كل المصففات اللى موجودة في ال M22 بحيث
+
+114
+00:13:16,080 --> 00:13:21,240
+عناصر القطر الرئيسى are equal وعناصر القطر الثانوي
+
+115
+00:13:21,240 --> 00:13:22,220
+are equal
+
+116
+00:13:28,300 --> 00:13:32,100
+يبقى عناصر القطر الرئيسي ار اكول وعناصر القطر
+
+117
+00:13:32,100 --> 00:13:34,740
+الثانوي اتنين ار اكول
+
+118
+00:13:38,520 --> 00:13:43,300
+الان هذا هو الست اللي في ال kernels يبقى ال
+
+119
+00:13:43,300 --> 00:13:47,200
+kernels التي كل المصوفات اللي من الدرجة من الرتبة
+
+120
+00:13:47,200 --> 00:13:50,820
+الثانية والعناصر قطر الرئيس are equal وعناصر قطر
+
+121
+00:13:50,820 --> 00:13:57,160
+الثانوي are equal بدنا ندور على bases لأ بدنا ندور
+
+122
+00:13:57,160 --> 00:14:01,400
+بقول المرة الأخيرة بدنا ندور على bases وإلا ديروا
+
+123
+00:14:01,400 --> 00:14:08,010
+بالكميبقى بقول هنا بدي اروح ادور على basis لهذا ال
+
+124
+00:14:08,010 --> 00:14:12,770
+kernel بقول كويس مشان ادور على basis يبقى اي
+
+125
+00:14:12,770 --> 00:14:16,850
+مصفوفة بده تبقى على الشكل اللي عندنا هذا لكن هذا
+
+126
+00:14:16,850 --> 00:14:25,480
+الشكل بقدر اكتبه هنا كتالياللي هو ال a b b a بقدر
+
+127
+00:14:25,480 --> 00:14:33,680
+اقول يساوي mass of two a zero zero a زائد zero b b
+
+128
+00:14:33,680 --> 00:14:40,760
+zero بالشكل اللي عندنا هذا هذا معناه ان a في واحد
+
+129
+00:14:40,760 --> 00:14:49,860
+zero zero واحد زائد b في zero واحد واحد zeroيبقى
+
+130
+00:14:49,860 --> 00:14:54,620
+بناء عليه المصففين اللي اتنين هذول are linearly
+
+131
+00:14:54,620 --> 00:15:00,810
+dependent ولا linearly independentindependent يبقى
+
+132
+00:15:00,810 --> 00:15:05,330
+مادامي independent واحنا عندنا ال M22 يبقى هدول
+
+133
+00:15:05,330 --> 00:15:10,130
+بيشكلولي bases ليش؟ لسببين سببين اتنين are
+
+134
+00:15:10,130 --> 00:15:15,890
+linearly independent تمام النقطة الثانية انه اي
+
+135
+00:15:15,890 --> 00:15:19,150
+element في ال kernel هو linear combination من اين؟
+
+136
+00:15:19,150 --> 00:15:24,230
+يعني الاتنين هدول اسبين لل kernel بوردون من؟
+
+137
+00:15:24,310 --> 00:15:28,230
+الكرنال يبقى معناه هذا الكلام اتنين هدول بيشكلولي
+
+138
+00:15:28,230 --> 00:15:34,730
+basis لل kernel يبقى باجي بقوله لان since بما ان
+
+139
+00:15:34,730 --> 00:15:42,750
+اللي هو واحد زيرو زيرو واحد and العنصر التاني زيرو
+
+140
+00:15:42,750 --> 00:15:51,640
+واحد واحد زيرو are linearly independent طبعابنقدر
+
+141
+00:15:51,640 --> 00:15:58,120
+نثبتهم هدول ولا لا؟ عن طريق مين؟
+
+142
+00:15:58,120 --> 00:16:03,560
+كونسان في الأول و كونسان في التاني و نطلع الكونسان
+
+143
+00:16:03,560 --> 00:16:11,120
+هدول بقى بالزيرو يبقى هذي check بدك تروحي راجع في
+
+144
+00:16:11,120 --> 00:16:18,580
+الدار و تعمليها تمام؟ and any element
+
+145
+00:16:20,320 --> 00:16:35,020
+in الـ kernel التي is a linear combination of
+
+146
+00:16:35,020 --> 00:16:47,660
+اللي هو main 1001 and 0110 يبقى هنا هذا بدي يعطينا
+
+147
+00:16:47,660 --> 00:16:56,900
+the setاليمين عناصرها 1 0 0 1 والعنصر التاني 0 1 1
+
+148
+00:16:56,900 --> 00:17:10,240
+0 is a basis for kernel Latin يعني هدول يمثلولي
+
+149
+00:17:10,240 --> 00:17:14,160
+مين؟ يمثلولي ال basis للكيرنل بناء عليها ال
+
+150
+00:17:14,160 --> 00:17:18,580
+dimension جداشر لإتنينيبقى باجي بقوله اذا ال
+
+151
+00:17:18,580 --> 00:17:24,680
+dimension للكيرن اللتي كله بده يساوي كده؟ بده
+
+152
+00:17:24,680 --> 00:17:33,520
+يساوي اتنين لحد هنا انتهى هذا السؤال ايوة هنجاوبك
+
+153
+00:17:33,520 --> 00:17:42,460
+بس اصبر شوية بس نخلص الشجة هذه ايوة
+
+154
+00:17:42,460 --> 00:17:47,690
+وين اللي بتسأل؟عشان أحكي عليكم في الانجليزية ان كل
+
+155
+00:17:47,690 --> 00:17:52,750
+واحد فيه مضاعفات تانية صح؟ اه يعني قصدك تقولي
+
+156
+00:17:52,750 --> 00:17:56,310
+واحدة فيهم اتنين برضه ماشي، ماشي الحالة، ولا واحدة
+
+157
+00:17:56,310 --> 00:18:00,050
+فيهم مضاعفة احنا نقول لك تشك بأي طريقة بدك إياها،
+
+158
+00:18:00,050 --> 00:18:03,070
+اللي بتقدر عليها سويها، طبعا عندنا بدل الطريقة
+
+159
+00:18:03,070 --> 00:18:08,400
+تلاتة، خاصة لما يكون عشان دي اتنين فقطإن هو لو أحد
+
+160
+00:18:08,400 --> 00:18:12,240
+فيهم مضعفات التانية لو حطيت constant و constant و
+
+161
+00:18:12,240 --> 00:18:15,380
+جمعة و سويت بال zero دي يطلع ال constants هدول
+
+162
+00:18:15,380 --> 00:18:19,440
+بيها أسفار أو لو كان عندي محدد بس هنا مفيش عندي
+
+163
+00:18:19,440 --> 00:18:24,960
+محدد آه تمام بدي يكون محدد لا يساوي zero ما علينا
+
+164
+00:18:24,960 --> 00:18:29,560
+طيب هذا كان هو السؤال رقم اتنين من هذا لمت عنه
+
+165
+00:18:29,560 --> 00:18:33,760
+السؤال رقم تلاتةبقول show that if ال F is
+
+166
+00:18:33,760 --> 00:18:38,020
+invertible then the determinant لل A inverse بده
+
+167
+00:18:38,020 --> 00:18:44,100
+يساوي واحد على ال determinant ل A بدنا سؤال التالف
+
+168
+00:18:44,100 --> 00:18:52,220
+طبعا question three نمرا A بيقول show that أن ال
+
+169
+00:18:52,220 --> 00:18:59,410
+determinantللـ A inverse بدي سوى واحد على الـ
+
+170
+00:18:59,410 --> 00:19:04,310
+determinant لمن؟ للـ A والـ A invertible matrix
+
+171
+00:19:04,310 --> 00:19:08,630
+يعني لما اقول invertible matrix يعني الـ A has an
+
+172
+00:19:08,630 --> 00:19:14,730
+inverse يعني المصوفة A لها معكوث مادام لها معكوث
+
+173
+00:19:14,730 --> 00:19:20,360
+يبقى سهل جدا الإثبات مش مستاهللما يكون ال A لها
+
+174
+00:19:20,360 --> 00:19:26,020
+معكوس يبقى بدروح اقوله انه
+
+175
+00:19:26,020 --> 00:19:36,300
+since بما ان ال A is invertable لها معكوس we have
+
+176
+00:19:36,300 --> 00:19:44,040
+ان ال A انفرسمالها existيبقى هذه موجودة مادام
+
+177
+00:19:44,040 --> 00:19:49,600
+exist بقدر اقول يبقى ال a في ال a inverse بدي سوى
+
+178
+00:19:49,600 --> 00:19:55,040
+مين ال a inverse في ال a بدي سوى مين ال identity
+
+179
+00:19:55,040 --> 00:20:02,610
+elementخُد المحدد للطرفين يبقى هذا يعطينا ان ال
+
+180
+00:20:02,610 --> 00:20:10,670
+determinant لمن ل A inverse A يساوي ال determinant
+
+181
+00:20:10,670 --> 00:20:15,960
+لمصفوف من الواحدةمن خواص ال determinant ال
+
+182
+00:20:15,960 --> 00:20:19,100
+determinant اللي حصل ضرب مصوفتين يساوي ال
+
+183
+00:20:19,100 --> 00:20:23,300
+determinant للمصوفة الأولى في ال determinant
+
+184
+00:20:23,300 --> 00:20:29,020
+للمصوفة الثانية ومحدد مصوفتي الواحدة بجداش بواحدة
+
+185
+00:20:29,020 --> 00:20:33,880
+صحية طيب هدول عبارة عن real numbers مش مصوفات
+
+186
+00:20:33,880 --> 00:20:38,360
+المحدد قيمة عددية إذا بقدر أقول أجسم على ال
+
+187
+00:20:38,360 --> 00:20:43,920
+determinant لإيه؟ بنفع؟بنفع ليش؟ لأن invertible
+
+188
+00:20:43,920 --> 00:20:49,240
+يعني محددها ليه يمكن أن يساوي zero مدام المحدد لا
+
+189
+00:20:49,240 --> 00:20:52,940
+يمكن أن يساوي zero إذا بجسم عليه without problems
+
+190
+00:20:52,940 --> 00:20:58,380
+يبقى هذا الكلام بده يعطينا أن ال determinant لل A
+
+191
+00:20:58,380 --> 00:21:04,060
+inverse بده يساوي واحد على ال determinant ل A
+
+192
+00:21:04,060 --> 00:21:09,190
+وانتهى الفرقانيبقى هذه النقطة الأولى من السؤال
+
+193
+00:21:09,190 --> 00:21:15,990
+النقطة الثانية هذه نظرية معاكم صح؟ اه مش نظرية حتى
+
+194
+00:21:15,990 --> 00:21:20,630
+هو السؤال محلول في ال exercises وانا حلته لكم يبقى
+
+195
+00:21:20,630 --> 00:21:25,590
+لا داعي لتضيع الوقت فيه هذه النقطة يعني يجي للنقطة
+
+196
+00:21:25,590 --> 00:21:30,190
+الثانية من هذا السؤال النقطة الثانية اللي هي نمربي
+
+197
+00:21:30,800 --> 00:21:35,120
+بقول determinant a basis and dimension for the
+
+198
+00:21:35,120 --> 00:21:40,900
+subspace spanned by the vectors يبقى ال U is
+
+199
+00:21:40,900 --> 00:21:42,680
+spanned
+
+200
+00:21:43,910 --> 00:21:49,750
+by the vectors الـ vectors اللي هم واحد واحد واحد
+
+201
+00:21:49,750 --> 00:21:59,870
+واتنين سالب واحد واحد واربع سالب خمسة واحد بالشكل
+
+202
+00:21:59,870 --> 00:22:04,070
+اللي عندنا يبقى فيه عند أنا ال subspace تولد بهذه
+
+203
+00:22:04,070 --> 00:22:07,570
+ال vectors السؤال بيقول هات ال basis و ال
+
+204
+00:22:07,570 --> 00:22:14,390
+dimension لل subspace اللي عندنا يبقى هنا finda
+
+205
+00:22:14,390 --> 00:22:24,230
+bases for you and a dimension لمن لليوم
+
+206
+00:22:45,960 --> 00:22:51,020
+طيب الان قال لي ان يتولد بهذه ال vector هاتل ال
+
+207
+00:22:51,020 --> 00:22:54,620
+basis و ال dimension اذا ال basis هم العناصر
+
+208
+00:22:54,620 --> 00:23:00,940
+التلاتة و ال dimension تلاتة صحيح؟ ايوة فهذا كلام
+
+209
+00:23:00,940 --> 00:23:05,260
+خطأ، خطأ كيف؟ احنا عناصر ال basis كلهم are
+
+210
+00:23:05,260 --> 00:23:09,880
+linearly independent فهل ال vectors هدول linearly
+
+211
+00:23:09,880 --> 00:23:14,220
+dependent ولا linearly independent احنا مش عارفين
+
+212
+00:23:14,800 --> 00:23:18,460
+إذا بدى نتأكد هل هدول linearly dependent ولا
+
+213
+00:23:18,460 --> 00:23:22,520
+linearly independent لأ انطلع linearly independent
+
+214
+00:23:22,520 --> 00:23:28,580
+بيكون خلاصنا طب انطلع linearly dependent يبقى
+
+215
+00:23:28,580 --> 00:23:34,360
+مانفعش بدي أخد مين؟ اتنين منهم هاتأكد في الأول هل
+
+216
+00:23:34,360 --> 00:23:37,700
+هدول linearly dependent ولا linearly independent
+
+217
+00:23:38,240 --> 00:23:42,560
+أعتقد أن هما دول linearly dependent تأكدتوا منهم؟
+
+218
+00:23:42,560 --> 00:23:46,780
+طيب على أي حال بأي طريقة من الطرق اللي انت
+
+219
+00:23:46,780 --> 00:23:54,420
+بتعرفيها بدك محدد بدك كذا بس المحدد بطلعش او بطلع
+
+220
+00:23:54,420 --> 00:23:57,660
+لا يساوي zero ان طلع لا يساوي zero بجه دول
+
+221
+00:23:57,660 --> 00:24:02,400
+linearly independent لكن المحدد بطلع قداش قيمة
+
+222
+00:24:02,400 --> 00:24:10,100
+عددية تمام؟ مدام قيمة عدديةيبقى هذا لا يؤكد انهم
+
+223
+00:24:10,100 --> 00:24:15,260
+linearly dependent صح ولا لا؟ ليش؟ لأن الشرط انه
+
+224
+00:24:15,260 --> 00:24:18,880
+لو كانوا linearly dependent إذا المحدد بدي ساوي
+
+225
+00:24:18,880 --> 00:24:24,580
+zero لكن العكس ليس بالضرورة صحيحا يبقى حكاية هذه
+
+226
+00:24:24,580 --> 00:24:28,280
+الطريقة بتنفعش يبقى بدول كونصان في الأول و كونصان
+
+227
+00:24:28,280 --> 00:24:32,660
+في التاني و كونصان في التالت و اعمل system وحل و
+
+228
+00:24:32,660 --> 00:24:38,580
+اثبت ان C1 وC2 وC3مش كلهم أصفر و يمكن و لا واحد
+
+229
+00:24:38,580 --> 00:24:46,500
+فيهم صفر تمام يبقى هنا بنانيجي نقول لك تشيرك that
+
+230
+00:24:46,500 --> 00:24:59,700
+these vectors are linearly dependent ارايحك
+
+231
+00:24:59,700 --> 00:25:04,950
+شوية بدل من تاخده تلاتة؟خد اتنين منهم و قول كنصا
+
+232
+00:25:04,950 --> 00:25:09,190
+في الأول و كنصا في التاني و سويهم بالتالت وبالتالي
+
+233
+00:25:09,190 --> 00:25:12,850
+بصير عندي system of non homogeneous differential
+
+234
+00:25:12,850 --> 00:25:19,170
+equation من معادلتين وبالتالي صار عندي معادلتين في
+
+235
+00:25:19,170 --> 00:25:27,280
+ثلاثةمجاهيل، مظبوط، إذا هذي linearly dependent على
+
+236
+00:25:27,280 --> 00:25:31,500
+طول القطر ما علينا، طيب احنا بقول تشكي بجه أي
+
+237
+00:25:31,500 --> 00:25:38,880
+وسيلة تنشأتي لأ
+
+238
+00:25:38,880 --> 00:25:42,880
+يعني انهم linearly dependent قد يكون و قد لا يكون
+
+239
+00:25:42,880 --> 00:25:47,320
+بس لكن في حالة ان M تساوي Mالبتجاهين if and only
+
+240
+00:25:47,320 --> 00:25:50,880
+if the elements are dependent if and only if the
+
+241
+00:25:50,880 --> 00:25:55,440
+determinant is zero يعني بتجاهين إيش يعني بتجاهين؟
+
+242
+00:25:58,510 --> 00:26:01,890
+كويس هذه حسنا بس في الأول كنا بيقول كلام هذا مش
+
+243
+00:26:01,890 --> 00:26:05,630
+متأكدين منه نظرية الأولى بيقول مش كنا مش متأكدين
+
+244
+00:26:05,630 --> 00:26:10,850
+ماعنا مشكلة في هذه الحالة no problem يعني بأي
+
+245
+00:26:10,850 --> 00:26:14,550
+وسيلة بس بدك تبينيلي شو الطريقة اللي استخدمتيها
+
+246
+00:26:14,550 --> 00:26:19,870
+تمام؟ كويس؟ طيب على أي حال هدول linearly dependent
+
+247
+00:26:19,870 --> 00:26:25,030
+يبقى بدي أخد أي اتنين منهم يبقى بدي بقوله clearly
+
+248
+00:26:26,450 --> 00:26:33,670
+إن الواحد والواحد والواحد and الاتنين وثالث واحد
+
+249
+00:26:33,670 --> 00:26:39,830
+وواحد اتنين وثالث واحد وواحد are linearly
+
+250
+00:26:39,830 --> 00:26:54,290
+independent السبب because any one of them is not
+
+251
+00:26:55,040 --> 00:27:02,480
+multiple of the
+
+252
+00:27:02,480 --> 00:27:08,760
+other يبقى معناته اتنين بيشكلولي ايش؟ اتنين
+
+253
+00:27:08,760 --> 00:27:19,070
+بيشكلولي bases تمام يبقى the اللي هو the setاللي
+
+254
+00:27:19,070 --> 00:27:25,250
+هي مين؟ واحد و واحد و واحد و اتنين و سالب واحد و
+
+255
+00:27:25,250 --> 00:27:35,670
+واحد for a basis for you مادام basis يبقى ضال
+
+256
+00:27:35,670 --> 00:27:40,350
+علينا مين ال dimension يبقى ال dimension لل you
+
+257
+00:27:40,350 --> 00:27:44,990
+بده يسوي كده اش اتنين وكفى الله المؤمنين على
+
+258
+00:27:44,990 --> 00:27:45,690
+الخيارة
+
+259
+00:27:51,600 --> 00:28:00,140
+بنجي لها الخيارات كل ما أكل ورقة هذه كل ما قعد
+
+260
+00:28:00,140 --> 00:28:05,160
+عليها الورقة هذه الخيارات علشان نناقشهم مع بعض و
+
+261
+00:28:05,160 --> 00:28:10,690
+مافيش دعاية لكتابها دعاية اخدوا محاضرة لكتابةشافة
+
+262
+00:28:10,690 --> 00:28:16,730
+و بنقول في عندي ثمان نقاط واحدة منهم اللي هي رقم
+
+263
+00:28:16,730 --> 00:28:22,190
+خمسة مش داخلة في الامتحان لكن السبع نقاط الأخرى
+
+264
+00:28:22,190 --> 00:28:26,230
+كلها داخلة في الامتحان طلعولي في النقطة الأولى
+
+265
+00:28:26,800 --> 00:28:31,000
+النقطة الأولى بيقولي ده ست وميعطيني three vectors
+
+266
+00:28:31,000 --> 00:28:34,820
+واحد واحد واحد ال vector التاني واحد واحد زيرو
+
+267
+00:28:34,820 --> 00:28:39,940
+والتاني واحد زيرو زيرو اول نقطة form a basis for
+
+268
+00:28:39,940 --> 00:28:45,120
+R3 فتحته
+
+269
+00:28:45,120 --> 00:28:49,820
+اتحان
+
+270
+00:28:49,820 --> 00:28:56,590
+2007 هو نفسه اللي معاكوا السؤال الأخير رقم 4أه
+
+271
+00:28:56,590 --> 00:28:59,890
+بيقولي mark each of the following statements by
+
+272
+00:28:59,890 --> 00:29:04,570
+true or false يبقى احنا بنحط اللي قدام كل جملة من
+
+273
+00:29:04,570 --> 00:29:13,390
+هذه الجمل اما صح او خطأ خديلة
+
+274
+00:29:13,390 --> 00:29:14,290
+الورقة دي
+
+275
+00:29:21,920 --> 00:29:27,200
+إذا احنا في عنا ثماني جمال بنحط قبل سبعة منهم صح
+
+276
+00:29:27,200 --> 00:29:31,700
+أو خطأ الجملة الأولى بيقولي that's it واحد وواحد
+
+277
+00:29:31,700 --> 00:29:35,480
+وواحد العنصر التاني واحد وواحد وزيرو العنصر التالت
+
+278
+00:29:35,480 --> 00:29:41,020
+واحد زيرو زيرو form a basis for are three يبقى هذا
+
+279
+00:29:41,020 --> 00:29:47,200
+بيشكللي أساس لل are three الإجابة هل صح ام خطأيبقى
+
+280
+00:29:47,200 --> 00:29:52,500
+بدنا نروح ناخدلهم مين المحدد المحدد بيطلع جداش
+
+281
+00:29:52,500 --> 00:29:58,740
+جداش اللي معاكم رقم صح ولا لا يعني لا يساوي zero
+
+282
+00:29:58,740 --> 00:30:05,480
+إذا هدول مالهم linearly independent عددهم تلاتة و
+
+283
+00:30:05,480 --> 00:30:11,260
+ال basis أصل ل R3 تلاتة إذا هدول بنفع يكونوا basis
+
+284
+00:30:11,260 --> 00:30:17,460
+يبقى الإجابة مالها ال true واضح كلامي هنا؟عشان مش
+
+285
+00:30:17,460 --> 00:30:20,860
+فاهم ايش قولناه و مش واضح انه ايش كلام اللي قولناه
+
+286
+00:30:20,860 --> 00:30:25,580
+طيب ننتقل الى النقطة الثانية يعطيني T من R2 الى
+
+287
+00:30:25,580 --> 00:30:30,960
+Two Linear Transformation معرفة كتالة جميع العناصر
+
+288
+00:30:30,960 --> 00:30:36,700
+في الـR2 صورتها Zero و Zero يعني مين يعني ال Zero
+
+289
+00:30:36,700 --> 00:30:41,900
+Element تمام ايش بيقول اذا ال dimension لل range
+
+290
+00:30:41,900 --> 00:30:47,160
+of T بدي ساوي Zero سؤالنا هولما تبقى الـLinear
+
+291
+00:30:47,160 --> 00:30:51,760
+Transformation من R2 إلى R2 جميع العلاصر بدأت تذهب
+
+292
+00:30:51,760 --> 00:30:57,440
+إلى الـ0 كم هو الـRange؟ فيه غيره؟ يبقى
+
+293
+00:30:57,440 --> 00:31:00,380
+الـTrivial، مافيش فيه إلا الـTrivial Element اللي
+
+294
+00:31:00,380 --> 00:31:04,500
+هو العنصر الصفري واخدنا قاعدة إذا الـSubspace
+
+295
+00:31:04,500 --> 00:31:07,300
+مافيش فيه إلا العنصر الصفري يبقى الـDimension اللي
+
+296
+00:31:07,300 --> 00:31:14,000
+بده يساوي جدر الـ0 إذا العبارة هذه الصحيحة trueنجل
+
+297
+00:31:14,000 --> 00:31:19,120
+اللي هي النقطة الثالثة بيقول if the Wronskin of F1
+
+298
+00:31:19,120 --> 00:31:26,380
+و F2 بده ساوي zero لكل ال X الموجود في R يبقى هدول
+
+299
+00:31:26,380 --> 00:31:32,630
+إجباري linearly dependentطبعا خطأ قد يكون و قد لا
+
+300
+00:31:32,630 --> 00:31:39,650
+يكون يبقى هذا خطأ يبقى false النقطة الرابعة يعطيني
+
+301
+00:31:39,650 --> 00:31:44,910
+أربعة عناصر ال S تساوي العنصر الأول واحد واحد
+
+302
+00:31:44,910 --> 00:31:49,280
+العنصر التاني اتنين و تلاتةالعنصر التالت أربعة و
+
+303
+00:31:49,280 --> 00:31:53,700
+خمسة تلت عناصر مش أربعة بقول إذن ال S ليه المجموعة
+
+304
+00:31:53,700 --> 00:31:58,940
+هذه المخونة من ثلاثة عناصر form a linearly
+
+305
+00:31:58,940 --> 00:32:07,270
+independent set in R2يبقى هذه false ليش؟ لأنه عدد
+
+306
+00:32:07,270 --> 00:32:12,130
+العناصر اللي أخدها أكتر من عدد العناصر في ال basis
+
+307
+00:32:12,130 --> 00:32:19,310
+تبع R2 ال R2 ال basis تبع يتكون من عنصرين هدول
+
+308
+00:32:19,310 --> 00:32:23,330
+linearly independent لو أضفت عليهم كمان عنصر
+
+309
+00:32:23,330 --> 00:32:28,060
+بصيروا linearlyيبقى أي مجموعة من العناصر أخدنا
+
+310
+00:32:28,060 --> 00:32:34,160
+نظري عددها ان كانوا linearly independent لو أضفت
+
+311
+00:32:34,160 --> 00:32:38,600
+عليهم كمان عنصر بصيروا ماله linearly dependent إذا
+
+312
+00:32:38,600 --> 00:32:46,050
+هذه العبارة رقم أربعة wrong، false، مش صحيحةبنجي
+
+313
+00:32:46,050 --> 00:32:52,890
+لنقطة رقم ستة بيقول if a is an n by n matrix and k
+
+314
+00:32:52,890 --> 00:32:56,570
+is a non zero real number then ال determinant لكي
+
+315
+00:32:56,570 --> 00:33:03,510
+في a بده يساوي الكي في determinant ل a ايش رايكوا
+
+316
+00:33:03,510 --> 00:33:11,310
+في هذه؟ مش مظبوطة؟ كي و أس ان بيغيريها وليها ايش
+
+317
+00:33:11,310 --> 00:33:16,380
+رايكوا بالعبارة هذه؟خلّيني أذكركم لإجابة الصحية
+
+318
+00:33:16,380 --> 00:33:22,760
+لما نضرب عنصر في مصفوفة خلّي بالك هنا لما نضرب
+
+319
+00:33:22,760 --> 00:33:27,560
+عنصر في مصفوفة، فنضربه في جميع أناصر المصفوفة لكن
+
+320
+00:33:27,560 --> 00:33:34,100
+لو ضربنا عنصر فيه محدد، فنضربه في الصف أو في عمود
+
+321
+00:33:34,100 --> 00:33:40,180
+تمام؟ المصفوفة هذه نظامها N في Nيبقى الصحيح أن الـ
+
+322
+00:33:40,180 --> 00:33:45,440
+determinant للـ K في A يكون K أس N في الـ
+
+323
+00:33:45,440 --> 00:33:49,820
+determinant لمام إلى K يبقى هذا العبارة عبارة
+
+324
+00:33:49,820 --> 00:33:55,360
+خاطئة فالس النقطة السابعة بيقول فالـ A is
+
+325
+00:33:55,360 --> 00:33:59,940
+invertible matrix then ال determinant للـ A
+
+326
+00:33:59,940 --> 00:34:04,300
+transpose يسوى ال determinant للـ A inverse
+
+327
+00:34:04,300 --> 00:34:05,500
+transpose
+
+328
+00:34:09,960 --> 00:34:13,490
+بعد شوية المفروض غلطأحنا اللي أثبتناها في المسائل
+
+329
+00:34:13,490 --> 00:34:17,470
+اللي أنا بذكرها كويس كان ال determinant ل A
+
+330
+00:34:17,470 --> 00:34:22,390
+inverse transpose يساوي determinant ل A transpose
+
+331
+00:34:22,390 --> 00:34:27,030
+inverse مظبوط؟ هذه مش ليها بتفرج لكن احنا ممكن
+
+332
+00:34:27,030 --> 00:34:32,070
+نثبتها رياضيا كذلك يعني نثبت رياضيا ان ال
+
+333
+00:34:32,070 --> 00:34:37,010
+determinant ل A transpose لا يساوي ال determinant
+
+334
+00:34:37,010 --> 00:34:42,910
+ل A inverse transpose كيف؟ كالتاليجل ال A
+
+335
+00:34:42,910 --> 00:34:48,370
+invertible matrix مظبوط يبقى ال A inverse معكوز A
+
+336
+00:34:48,370 --> 00:34:52,770
+مام exist يعني معنى هذا الكلام ان ال A في ال A
+
+337
+00:34:52,770 --> 00:34:58,540
+inverse بدي ساوي مصوفة الواحدةبدنا ندخل الـ
+
+338
+00:34:58,540 --> 00:35:02,820
+Transpose لأن في السؤال جال الـ A determinant للـ
+
+339
+00:35:02,820 --> 00:35:06,400
+A Transpose والـ determinant للـ A inverse
+
+340
+00:35:06,400 --> 00:35:10,640
+Transpose إذا بناءً عليه لو روحت أنا أخدتلي ال
+
+341
+00:35:10,640 --> 00:35:15,460
+Transpose للطرفين بصير ال A في ال A inverse
+
+342
+00:35:15,460 --> 00:35:20,940
+Transpose يسوى مصفوفة الوحدة Transposeيبقى لو جيت
+
+343
+00:35:20,940 --> 00:35:27,000
+حسب خواصة لترانسبوز هذه a inverse transpose في ال
+
+344
+00:35:27,000 --> 00:35:32,500
+a transpose بدي اساوي ال I transpose اللي هي من؟
+
+345
+00:35:32,500 --> 00:35:37,960
+ال I itself الان بدي أخد ال determinant للطرفين
+
+346
+00:35:37,960 --> 00:35:42,540
+إذا لو روحت أخدت determinant للطرفين بدي أصير ال
+
+347
+00:35:42,540 --> 00:35:46,720
+determinant لل a inverse transpose
+
+348
+00:35:52,920 --> 00:36:00,080
+Determinant لمن؟ للمصوفة I هذا معناه ايه؟ معناه ان
+
+349
+00:36:00,080 --> 00:36:06,580
+ال determinant لل A inverse اترانسبوز في ال
+
+350
+00:36:06,580 --> 00:36:13,540
+determinant لل A transpose بدي سوى 1 صحيحيبقى بناء
+
+351
+00:36:13,540 --> 00:36:19,880
+عليه صارت determinant للـ A inverse transpose واحد
+
+352
+00:36:19,880 --> 00:36:24,660
+على ال determinant للـ A transpose وما قالليش واحد
+
+353
+00:36:24,660 --> 00:36:28,100
+قاللي لا تساوي ال determinant للـ A transpose يبقى
+
+354
+00:36:28,100 --> 00:36:33,660
+هذا عين الخطأ يبقى الإجابة خاطئة وهيبرهنها لكوا
+
+355
+00:36:33,900 --> 00:36:38,300
+برهان إذا كنا حابين برهان لكن لو كان حسب ال
+
+356
+00:36:38,300 --> 00:36:42,200
+exercise اللي ذكرناه في بداية حديثنا برضه كلامنا
+
+357
+00:36:42,200 --> 00:36:45,780
+صحيح طبعا مش واضطر منك البارحة اللي مضطر بستحكم
+
+358
+00:36:45,780 --> 00:36:50,980
+نقول يا اه يا لأ حسب معلوماتك او من خلال دراستك
+
+359
+00:36:52,330 --> 00:36:55,630
+النقطة الثامنة والاخيرة بيقول لي any set which
+
+360
+00:36:55,630 --> 00:37:00,390
+contains a zero vector must be linearly dependent
+
+361
+00:37:00,390 --> 00:37:04,330
+يعني
+
+362
+00:37:04,330 --> 00:37:08,710
+أي مجموعة تحتوي على الصفر فهي linearly dependent
+
+363
+00:37:08,710 --> 00:37:16,050
+يبقى هذا هو الامتحان الأول الامتحان 2007 نيجي
+
+364
+00:37:16,050 --> 00:37:18,170
+لامتحان 2005
+
+365
+00:37:37,930 --> 00:37:45,230
+الفين و خمسة السؤال الأول بيقول
+
+366
+00:37:45,230 --> 00:37:46,430
+show that
+
+367
+00:38:03,950 --> 00:38:08,390
+مش معاكم؟ مش معاكم الـlinear dependence و
+
+368
+00:38:08,390 --> 00:38:12,010
+الـlinear independence؟
+
+369
+00:38:12,010 --> 00:38:16,470
+كيف؟ لما هو معاهم كان من ضمنها
+
+370
+00:38:18,930 --> 00:38:26,290
+سبعة، خمسة، ألفين وخمسة معاك يا وليه يا عزيزي؟
+
+371
+00:38:26,290 --> 00:38:29,670
+غريب والله انت معايا .. على أي حال مش مشكلة مش
+
+372
+00:38:29,670 --> 00:38:33,740
+مشكلةأصلا في بنات عايزة يسألوني في أحد الأسئلة
+
+373
+00:38:33,740 --> 00:38:38,640
+فيهم فحبي تحله للكل تمام؟ بيقول يبينلي أنه
+
+374
+00:38:38,640 --> 00:38:43,000
+العنصرين الأثنين هدول are linearly independent إذا
+
+375
+00:38:43,000 --> 00:38:48,120
+سهل أخد المحدد صحيح؟ يبقى باجي بقوله بدي أخد
+
+376
+00:38:48,120 --> 00:38:55,190
+المحدد تبع الأثنين هدوليبقى المحدد اللي هو من sin
+
+377
+00:38:55,190 --> 00:39:05,850
+x وcos x وتفاضل sin بcos x وتفاضل cos بسالب sin x
+
+378
+00:39:05,850 --> 00:39:12,110
+يساويطبعا هذه سالب ساين تربيع ال X سالب كوساين
+
+379
+00:39:12,110 --> 00:39:17,390
+تربيع ال X يبقى لو أخذت سالب عام المشترك بصير ساين
+
+380
+00:39:17,390 --> 00:39:23,410
+تربيع ال X زائد كوساين تربيع ال X اللي يبقى ده لا
+
+381
+00:39:23,410 --> 00:39:31,850
+يساوي Zero يبقى هنا سواء ساين ال X and كوساين ال X
+
+382
+00:39:31,850 --> 00:39:39,440
+are linearly independentهذا نمرى A، نمرى Bنمرة
+
+383
+00:39:39,440 --> 00:39:44,800
+بيقول لتل بي بتساوي R3 يبقى R3 هو ال vector space
+
+384
+00:39:44,800 --> 00:39:52,340
+اللي عندنا اخدي ال W اخدي ال W هي عبارة عن كل
+
+385
+00:39:52,340 --> 00:40:02,900
+العناصر X1 و X2 و X3 الموجودة في ال R3 بحيث ان ال
+
+386
+00:40:02,900 --> 00:40:10,580
+X1 بده يساوي مين بده يساوي ال X2Be a subspace of
+
+387
+00:40:10,580 --> 00:40:14,220
+V, find a basis of W and its dimension
+
+388
+00:40:31,500 --> 00:40:35,080
+طبعا الأمانات هذه لو ال W بدي أعيد صياغتها مرة
+
+389
+00:40:35,080 --> 00:40:42,520
+ثانية بقول هذه على الشكل ان ال X1 يسوى X2 يبقى X1
+
+390
+00:40:42,520 --> 00:40:50,680
+و X1 و X3بصدش ذات ال X واحد وال X ثلاثة موجودة في
+
+391
+00:40:50,680 --> 00:40:56,020
+ال set of real numbers مظبوط يبقى هذا الشكل قال لي
+
+392
+00:40:56,020 --> 00:41:00,240
+اثبتلي ان هذا عبارة اوهات لل basis و اوهات لل
+
+393
+00:41:00,240 --> 00:41:05,540
+dimension لهذا ال subspace بقوله كويس يبقى انا
+
+394
+00:41:05,540 --> 00:41:15,110
+باجي بقوله لو كانتال X1 مثلا تساوي A وال X3 تساوي
+
+395
+00:41:15,110 --> 00:41:22,330
+B ثم ال W بقدر اكتبه على الشكل التالي كل العناصر
+
+396
+00:41:22,330 --> 00:41:29,890
+اللي على الشكل A و A و B بحيث ال A و ال B موجودة
+
+397
+00:41:29,890 --> 00:41:32,270
+وين في ال set of real number
+
+398
+00:41:34,950 --> 00:41:40,690
+طيب بدي اشوف ال basis لهذا ال subspace بقوله تمام
+
+399
+00:41:40,690 --> 00:41:47,510
+لو جتلي اي element موجود في ال w وليكن a و a و b
+
+400
+00:41:47,510 --> 00:41:52,850
+مش هذا element موجود في اليدي بقدر اكتبه على الشكل
+
+401
+00:41:52,850 --> 00:42:03,370
+التالي مجموع عنصرين a و a و 0 زائد 0 و 0 و bمظبوط
+
+402
+00:42:03,370 --> 00:42:09,690
+يعني بناء عليه بقدر اقول هذا a في واحد و واحد و
+
+403
+00:42:09,690 --> 00:42:18,550
+زيرو زائد b في من في زيرو و زيرو و واحد طبعا كويس
+
+404
+00:42:18,550 --> 00:42:24,630
+اي element في ال w قدرت اكتب على صيغة linear
+
+405
+00:42:24,630 --> 00:42:29,790
+combination من الاتنين هدولإذا اللي اتنين هدول
+
+406
+00:42:29,790 --> 00:42:35,170
+بيولدولي عناصر main الـW كلها، اتنين هدول إذا
+
+407
+00:42:35,170 --> 00:42:38,390
+طلعوا linearly dependent عندنا مشكلة، طلعوا
+
+408
+00:42:38,390 --> 00:42:41,930
+linearly independent يبقى no problem، تمام؟
+
+409
+00:42:41,930 --> 00:42:46,030
+بيكونوا هم ال business على فوقهم، طلع هنا فيهم، هل
+
+410
+00:42:46,030 --> 00:42:52,010
+لو ضربت أي عدد في أي من هم بطلع التاني؟ مش إمكانية
+
+411
+00:42:52,140 --> 00:42:57,020
+يهم اذا كنت تروح تشوف اي طريقة تانية او تساوي بـ0
+
+412
+00:42:57,020 --> 00:43:03,580
+واطلع قيمة A وB اذا بتقدري تمام يبقى بقدر اقول the
+
+413
+00:43:03,580 --> 00:43:04,280
+vectors
+
+414
+00:43:07,310 --> 00:43:13,510
+اللي هم مين؟ واحد و واحد و زيرو and زيرو و زيرو
+
+415
+00:43:13,510 --> 00:43:21,470
+واحد are linearly independent يبقى مادام هيك يبقى
+
+416
+00:43:21,470 --> 00:43:28,090
+ال basesبدو يساوي اللي هو main واحد و واحد و zero
+
+417
+00:43:28,090 --> 00:43:33,870
+و zero و zero و واحد يبقى هدول شكلولي basis ل main
+
+418
+00:43:33,870 --> 00:43:38,450
+لل subspace اللي هو w بناء عليه ال dimension كده
+
+419
+00:43:38,450 --> 00:43:44,410
+اشتغلت اتنين يبقى باجي بقوله ال dimension ل ال W
+
+420
+00:43:44,410 --> 00:43:49,430
+بدو يساوي اتنين وانتهينا من هذه المسألة
+
+421
+00:43:52,840 --> 00:43:57,820
+لو طلع Linearly Dependent بيضلش إلا مين؟ واحد يبقى
+
+422
+00:43:57,820 --> 00:44:02,200
+واحد بيكون هو business بدي يولدهم وهذا مستحيل في
+
+423
+00:44:02,200 --> 00:44:07,200
+مثل هذا الشكل إلا إذا a ساوة بيه لو a ساوة بيه
+
+424
+00:44:07,200 --> 00:44:13,220
+بيطلع كلام مظبط أو ال a كانت مجموعة لإتنين a الأول
+
+425
+00:44:13,220 --> 00:44:17,860
+والثاني أو الفرق فيما بينهما يعني إذا المراكبة
+
+426
+00:44:17,860 --> 00:44:22,100
+التالتة جيبناها من خلال المراكبات الإتنين هدوةبصير
+
+427
+00:44:22,100 --> 00:44:26,380
+كلامنا فيه ان مافيش يبقى مافيش تمام هذا السؤال
+
+428
+00:44:26,380 --> 00:44:29,980
+الأول و طبعا حاطينه السؤال الأول لشانه سهل في
+
+429
+00:44:29,980 --> 00:44:35,420
+الصدارة حتى يفتح و نفس الطالب السؤال التاني غير
+
+430
+00:44:35,420 --> 00:44:40,260
+مطلوب كله عدايا generalizable السؤال التالت على ال
+
+431
+00:44:40,260 --> 00:44:49,200
+linear transformation يعطيني T السؤال التالت Tمن
+
+432
+00:44:49,200 --> 00:45:04,520
+R2 إلى R3 مُعرّف كالتالي defined by T of X1 و X2
+
+433
+00:45:04,520 --> 00:45:15,980
+بده يساوي X1 زائد X2 و X1 ناقص X2 وتلاتة X1
+
+434
+00:45:18,680 --> 00:45:21,300
+أثبت لي المطلوب الأول أن تكون T Linear
+
+435
+00:45:21,300 --> 00:45:26,200
+Transformation أظن هذه سهلة أثبت أنها Linear
+
+436
+00:45:26,200 --> 00:45:29,340
+Transformation سهلة مباشرة الخطواتين اللي أثبتناهم
+
+437
+00:45:29,340 --> 00:45:36,420
+قبل قليل يبقى هذلك قال هاتلي matrix A بحيث أن T of
+
+438
+00:45:36,420 --> 00:45:49,640
+X يساوي A X find a matrix A such thatبحيث هو ان T
+
+439
+00:45:49,640 --> 00:45:57,500
+of X بده يساوي من AX هذا المطلوب الأول المطلوب
+
+440
+00:45:57,500 --> 00:46:04,060
+التاني جلهات لل kernel وال dimension find ال
+
+441
+00:46:04,060 --> 00:46:13,340
+kernel التي and ال dimension لل kernel of T
+
+442
+00:46:38,300 --> 00:46:42,500
+هذا السؤال سألوني فيه مجموعة من الطلبات و سألوني
+
+443
+00:46:42,500 --> 00:46:47,460
+فيه و قلنا لهم طب احنا خدنا سؤال يقول لا مش زيهم
+
+444
+00:46:47,460 --> 00:46:53,500
+قلنا كام؟والسؤال اللي زيه اعطناك T ل element محدد
+
+445
+00:46:53,500 --> 00:46:56,960
+و اعطينا صوته و T ل element ثاني و اعطينا صورته
+
+446
+00:46:56,960 --> 00:47:00,980
+تمام؟ طب ما هذا لسه احسن من اللي اعطناه انا مش
+
+447
+00:47:00,980 --> 00:47:05,120
+عارف شكل ال T و طلبت منك شكل ال T بس هذا سهل هذا
+
+448
+00:47:05,120 --> 00:47:09,160
+بيعطيني شكل ال Tوبالتالي قال لي هاتلي ال matrix
+
+449
+00:47:09,160 --> 00:47:14,520
+بقوله تمام حاليا أنا في قدامي في القاعة كل طالبات
+
+450
+00:47:14,520 --> 00:47:19,660
+موجودة لو جلسلة واحدة كل واحدة تاخدلها عنصرين شكل
+
+451
+00:47:19,660 --> 00:47:24,340
+مختلفات عن بعض واتنين nearly independent مش عبارة
+
+452
+00:47:24,340 --> 00:47:29,540
+عن basis وروحنا حسبنا المصروفة بتطلع كلنا نفس
+
+453
+00:47:29,540 --> 00:47:36,190
+المصروفة ولا كل واحد بيطلع لمصروفة شكلنفس المصفوفة
+
+454
+00:47:36,190 --> 00:47:42,710
+ال X بتغيره لكن نفس المصفوفة لأن الصورة العامة T
+
+455
+00:47:42,710 --> 00:47:46,430
+of X بدي تسوي X يبقى كل linear transformation
+
+456
+00:47:46,430 --> 00:47:50,130
+مرتبطة بمصفوفة معينة غيرنا ال linear
+
+457
+00:47:50,130 --> 00:47:54,530
+transformation تتغير منهم المصفوفة لذلك بدي أقول
+
+458
+00:47:54,530 --> 00:47:58,910
+لك غامضي وخديلك أي عنصرين بس بشرط يكونوا linearly
+
+459
+00:47:58,910 --> 00:48:03,800
+independent تمام؟باجي بقول بده اخد عنصرين وين
+
+460
+00:48:03,800 --> 00:48:10,740
+موجودات في R2 يبقى باجي بقول ل let مثلا ها واحد
+
+461
+00:48:10,740 --> 00:48:18,280
+وزيرو مثلا و مثلا واحد وواحد على سبيل المثال بلاش
+
+462
+00:48:18,280 --> 00:48:28,140
+نبعد كتير هذي
+
+463
+00:48:28,140 --> 00:48:33,770
+مش مصفوفة هذي R2طب مش هذا ال form مظبوط؟ اه مظبوط
+
+464
+00:48:33,770 --> 00:48:37,890
+صح اه لما مفسدت x1 على جنب و x2 على جنب و سحبتها
+
+465
+00:48:37,890 --> 00:48:43,690
+عامل مشترك بيطلع عندي basis مش فاهم كيف يعني لما
+
+466
+00:48:43,690 --> 00:48:49,190
+مفسدت x1 على x2 جسمتي؟ لأ مصفوف مصفوف بقى يعني هذا
+
+467
+00:48:49,190 --> 00:48:54,390
+التعبير اللي فوق عيش عملتي مصفوف مصفوف
+
+468
+00:48:57,890 --> 00:49:02,850
+فصلتهم إلى مجموع مقدرين مافيش مشكلة عادة بس بدك
+
+469
+00:49:02,850 --> 00:49:05,710
+تذهب لإن هو هذا ال basis بعدين لكن أحنا بيقول لو
+
+470
+00:49:05,710 --> 00:49:09,530
+أخدت أي عنصرين و أدور عناصر سهلة في الإحسان مش
+
+471
+00:49:09,530 --> 00:49:14,030
+أدور رقام كبيرة يبقى بدي أخد مثلا واحد أو حتى 01
+
+472
+00:49:14,030 --> 00:49:18,030
+اللي هو ال standard basis بنفع ولا مانفعش؟ بنفع
+
+473
+00:49:18,030 --> 00:49:20,670
+يعني واحد أخد ال standard basis و أنا مابديش أخد
+
+474
+00:49:20,670 --> 00:49:24,250
+ال standard basis بدي أخد basis تانيبس هي اللي
+
+475
+00:49:24,250 --> 00:49:30,670
+بتحكيها بيزل لمشكلة R2 وR3 يعني هي بتحكي ببسط ال
+
+476
+00:49:30,670 --> 00:49:35,630
+X1 وX2 في المعادلة لإنها بيزل لـ R2 لإنها بيزل لـ
+
+477
+00:49:35,630 --> 00:49:36,690
+R2 لإنها بيزل لـ R2 لإنها بيزل لـ R2 لإنها بيزل لـ
+
+478
+00:49:36,690 --> 00:49:37,770
+R2 لإنها بيزل لـ R2 لإنها بيزل لـ R2 لإنها بيزل لـ
+
+479
+00:49:37,770 --> 00:49:38,590
+R2 لإنها بيزل لـ R2 لإنها بيزل لـ R2 لإنها بيزل لـ
+
+480
+00:49:38,590 --> 00:49:42,390
+R2 لإنها بيزل لـ R2 لإنها بيزل لـ R2 لإنها بيزل لـ
+
+481
+00:49:42,390 --> 00:49:52,190
+R2 لإنها
+
+482
+00:49:52,190 --> 00:49:55,200
+بيزل لـlinearly dependent و لا linearly
+
+483
+00:49:55,200 --> 00:50:01,470
+independentيبقى هؤلاء ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+484
+00:50:01,470 --> 00:50:02,270
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+485
+00:50:02,270 --> 00:50:02,870
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+486
+00:50:02,870 --> 00:50:10,610
+ا ا ا ا ا ا ا ا ا
+
+487
+00:50:10,610 --> 00:50:10,650
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+488
+00:50:10,650 --> 00:50:11,130
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+489
+00:50:11,130 --> 00:50:11,830
+ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا ا
+
+490
+00:50:11,830 --> 00:50:15,590
+ا ا
+
+491
+00:50:15,590 --> 00:50:25,890
+ا ا ا ا ا ا ا ا ا ا ا
+
+492
+00:50:25,890 --> 00:50:33,920
+ا ا ا ا او هنا تلاتة، مظبوط؟ and T of واحد و واحد
+
+493
+00:50:33,920 --> 00:50:44,040
+بده يساوي اتنين و zero و تلاتة، مظبوط؟ كويسيبقى
+
+494
+00:50:44,040 --> 00:50:50,560
+انا عندي ال T of X بده يساوي ال A of X هذا معناه
+
+495
+00:50:50,560 --> 00:50:56,980
+ال A اللي بديها في مين؟ في 1011
+
+496
+00:50:56,980 --> 00:51:06,180
+بده يساوي مين؟ بده يساوي الصورة 113203
+
+497
+00:51:06,180 --> 00:51:10,080
+يعني احنا بنكملمثل ما كان عندنا في المثال بالضبط
+
+498
+00:51:10,080 --> 00:51:15,320
+تماما يبقى انا بدي المصوفة ايه بروح بضرب في مين؟
+
+499
+00:51:15,320 --> 00:51:19,860
+في معكوس المصوفة اللي عندنا يبقى ايه اللي
+
+500
+00:51:19,860 --> 00:51:26,480
+بدواياها؟ بدها تساوي 1233
+
+501
+00:51:26,480 --> 00:51:31,720
+هنا 1101 inverse
+
+502
+00:51:33,490 --> 00:51:37,550
+المحدد تبع المصوفة هذه كده يا شباب انا واحد صحيح
+
+503
+00:51:37,550 --> 00:51:43,630
+تمام اذا بناء عليه بقدر اقول هذا الكلام بده يساوي
+
+504
+00:51:43,630 --> 00:51:50,360
+واحد اتنين واحد زيرو تلاتة تلاتة فيهذه المحددة
+
+505
+00:51:50,360 --> 00:51:53,420
+تبعها واحد يبقى بالانكسام على واحد ماعنديش مشكلة
+
+506
+00:51:53,420 --> 00:51:57,940
+طيب بدي أجيب ال adjoint تبعها ببدل عناصر القطر
+
+507
+00:51:57,940 --> 00:52:03,320
+الرئيسي مكان بعض بظلهم زي ما هم و بغير إشارات
+
+508
+00:52:03,320 --> 00:52:09,880
+عناصر القطرالثانوي يبقى هذا هو المعكوس تبع المصوفة
+
+509
+00:52:09,880 --> 00:52:14,560
+دي نضرب الاتنين في بعض نشوف إيش اللي بيحصل صف
+
+510
+00:52:14,560 --> 00:52:19,780
+الأول في العمود الأول اللي هو بواحد الصف الأول في
+
+511
+00:52:19,780 --> 00:52:24,680
+العمود الثاني اللي هو كمان واحد لإنه سالب واحد
+
+512
+00:52:24,680 --> 00:52:28,860
+واتنين بيبقى واحد الصف الثاني في العمود الأول اللي
+
+513
+00:52:28,860 --> 00:52:33,360
+هو بواحد الصف الثاني في العمود الثاني اللي هو
+
+514
+00:52:33,360 --> 00:52:38,870
+بسالب واحدالصف التالت في العمود الأول اللي هو
+
+515
+00:52:38,870 --> 00:52:43,470
+بالتلاتة الصف التالت في العمود يبقى التاني اللي هو
+
+516
+00:52:43,470 --> 00:52:49,170
+بالمين F0 يبقى هذه المصوفة A السؤال اللي كنت بقوله
+
+517
+00:52:50,520 --> 00:52:54,480
+أنا أخدت الـ two elements هدول، لو أخدتلي standard
+
+518
+00:52:54,480 --> 00:52:58,660
+elements، في مشكلة؟ مافي مشكلة، لازم تطلع نفس
+
+519
+00:52:58,660 --> 00:53:03,380
+المصوفة لو أخدت عنصرين غير هدول، كمان عنصرين تانية
+
+520
+00:53:03,380 --> 00:53:08,520
+غيرهم، بتتغير المصوفة؟ لن تتغير، يبقى المصوفة ايه؟
+
+521
+00:53:08,520 --> 00:53:14,340
+مصوفة ثابتة كما هي، بظل من عندك ال kernel وال
+
+522
+00:53:14,340 --> 00:53:20,220
+dimension لمن؟ للكرنلالكيرنر اللي بدنا نسوي بـ0
+
+523
+00:53:20,220 --> 00:53:28,520
+يبقى
+
+524
+00:53:28,520 --> 00:53:35,040
+باختصار الكيرنر اللي بد يكون T of X1 و X2 بد يسوي
+
+525
+00:53:35,040 --> 00:53:38,680
+0 هذا معناه ان X1
+
+526
+00:53:44,730 --> 00:53:49,790
+يبقى X1 ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2
+
+527
+00:53:49,790 --> 00:53:50,370
+ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2
+
+528
+00:53:50,370 --> 00:53:53,250
+ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2
+
+529
+00:53:53,250 --> 00:53:56,150
+ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2
+
+530
+00:53:56,150 --> 00:53:56,970
+ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2
+
+531
+00:53:56,970 --> 00:53:59,530
+ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2 ناقص X2
+
+532
+00:53:59,530 --> 00:54:03,030
+ناقص X2 نا
+
+533
+00:54:05,620 --> 00:54:09,680
+والعنصر الصفري يبقى dimension يساوي 0
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/mteISRbTvzU.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/mteISRbTvzU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..815ce8a306cfb9915b73e94c6537c93dba1a9df3
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/mteISRbTvzU.srt
@@ -0,0 +1,1550 @@
+1
+00:00:19,490 --> 00:00:24,710
+بسم الله الرحمن الرحيم عدنا على بداية المرة الماضية
+
+2
+00:00:24,710 --> 00:00:29,750
+بدأنا بـ الـ linear differential equation و أخذنا 
+
+3
+00:00:29,750 --> 00:00:35,090
+بعض التعريفات الأساسية ثم أخذنا مثالا واحدا والآن
+
+4
+00:00:35,090 --> 00:00:40,140
+نكمل على نفس الموضوع، الـ remark بتقول لو كان V هو
+
+5
+00:00:40,140 --> 00:00:45,220
+vector space of no dimension لما نقول no dimension
+
+6
+00:00:45,220 --> 00:00:49,800
+معناه infinite dimensional vector space يعني الـ
+
+7
+00:00:49,800 --> 00:00:55,020
+basis له عدد العناصر فيه يساوي مالانهاية من 
+
+8
+00:00:55,020 --> 00:00:59,540
+العناصر فهذا يا إما بسميه infinite dimensional vector
+
+9
+00:00:59,540 --> 00:01:04,080
+space يا إما بسميه vector space with no dimension
+
+10
+00:01:04,080 --> 00:01:09,660
+ما له بعد محدد أو ما له بعد محدود because then we
+
+11
+00:01:09,660 --> 00:01:13,480
+can find a subspace بنقدر نجد subspace من الـ
+
+12
+00:01:13,480 --> 00:01:17,760
+vector space V of finite dimension يعني الـ vector
+
+13
+00:01:17,760 --> 00:01:22,600
+space اللي الـ dimension له infinite ممكن أجيب منه
+
+14
+00:01:22,600 --> 00:01:27,620
+subspaces الـ dimension له يكون finite بدنا نعطي 
+
+15
+00:01:27,620 --> 00:01:33,260
+مثالا على ذلك، بيقول المثال بيلي إن E أُس X و E أُس
+
+16
+00:01:33,260 --> 00:01:37,960
+2X هما حلين لمين؟ للـ differential equation عندنا
+
+17
+00:01:37,960 --> 00:01:41,860
+اللي هي الـ homogeneous differential equation رقم 1
+
+18
+00:01:42,390 --> 00:01:47,590
+مطلوب أن نف بدنا الـ dimension للـ solutions space of
+
+19
+00:01:47,590 --> 00:01:50,490
+the given differential equation طبعا الـ solution
+
+20
+00:01:50,490 --> 00:01:55,410
+space هو عبارة عن subspace من الـ vector space
+
+21
+00:01:55,410 --> 00:02:02,370
+الأساسي الذي يحتوي على اللي هو المعادلات اللي لها
+
+22
+00:02:02,370 --> 00:02:07,110
+المشتقات أنونية بعد، هي كل الـ solution تبع الـ
+
+23
+00:02:07,110 --> 00:02:10,690
+initial value problem هذه لما نحط عليها الشرطين
+
+24
+00:02:10,690 --> 00:02:14,930
+الأثنين هدول، فبأجي بقول مايتي بدي أثبت الخطوة
+
+25
+00:02:14,930 --> 00:02:20,190
+الأولى أن هدول هما عبارة عن حلين لمين؟ للمعادلة
+
+26
+00:02:20,190 --> 00:02:24,930
+عندنا رقم واحد، يبقى بأجي بقول لو أي دالة من هذه
+
+27
+00:02:24,930 --> 00:02:29,990
+الدوال حققت المعادلة يبقى بتبقى هي عبارة عن حل
+
+28
+00:02:29,990 --> 00:02:35,830
+طبعا الـ E أُس X بنعرف أن مشتقتها مرة مرتين تلاتة مالانهاية كلها كله بـ E أُس X إذا بناء عليه بأجي بقوله E 
+
+29
+00:02:35,830 --> 00:02:43,850
+أُس X ناقص تلاتة E أُس X زائد اتنين E أُس X يساوي
+
+30
+00:02:43,850 --> 00:02:52,250
+اللي هو تلاتة E أُس X ناقص تلاتة E أُس X بده يساوي
+
+31
+00:02:52,250 --> 00:02:57,730
+كده صفر، يبقى F1 of X يساوي E أُس X is a solution of
+
+32
+00:03:09,620 --> 00:03:17,930
+equation 1 المعادلة الأساسية اللي عندنا، الآن لو جيت
+
+33
+00:03:17,930 --> 00:03:25,750
+للـ F2 of X بده يساوي E أُس 2X بدي أجيب F2 prime
+
+34
+00:03:25,750 --> 00:03:31,490
+of X يبقى اتنين E أُس 2X الـ exponential كما هي
+
+35
+00:03:31,490 --> 00:03:36,670
+مضروبة في مشتقة الأس تبع الـ exponential هذا بدي
+
+36
+00:03:36,670 --> 00:03:43,670
+يعطينا أن المشتقة الثانية F2 double prime of X F2W'
+
+37
+00:03:44,210 --> 00:03:51,410
+of X بده يساوي 4E أُس 2X
+
+38
+00:03:51,410 --> 00:03:56,310
+لما ناخد المعلومات التي حصلنا عليها ونعوض في
+
+39
+00:03:56,310 --> 00:04:01,250
+المعادلة 1 ونشوف هل بتعطينا صفر ولا لا يبقى
+
+40
+00:04:01,250 --> 00:04:08,170
+المعادلة عندنا Y''-3Y'+2Y
+
+41
+00:04:09,360 --> 00:04:16,880
+Y'' لي F2'' اللي هي مين؟ أربعة في E أُس 2X
+
+42
+00:04:16,880 --> 00:04:23,440
+ناقص تلاتة في الـ Y' اللي هو اتنين E أُس 2X
+
+43
+00:04:23,440 --> 00:04:30,810
+زائدي اتنين E أُس 2X يساوي، أربعة و اتنين اللي 
+
+44
+00:04:30,810 --> 00:04:36,130
+هو ستة E أُس 2X سالب تلاتة في اتنين بسالب
+
+45
+00:04:36,130 --> 00:04:41,490
+ستة E أُس 2X بده يساوي قداش؟ بده يساوي زيرو
+
+46
+00:04:41,490 --> 00:04:47,550
+يبقى يساوي، الـ Y2 أو الـ F2 of X
+
+47
+00:04:51,580 --> 00:05:04,820
+الـ F2 of X بده يساوي E أُس 2X is a solution of the 
+
+48
+00:05:04,820 --> 00:05:11,970
+differential equation 1، يبقى المطلوب الأول يبين لي
+
+49
+00:05:11,970 --> 00:05:15,850
+أن الدالتين الاتنين هم حلين لهذه المعادلة، انتهينا 
+
+50
+00:05:15,850 --> 00:05:27,630
+منها، يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+51
+00:05:27,630 --> 00:05:34,010
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+52
+00:05:34,010 --> 00:05:38,690
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى As a function of
+
+53
+00:05:38,690 --> 00:05:44,550
+x الحل الأول E أُس X، والـ second الحل الثاني E أُس 2X
+
+54
+00:05:44,550 --> 00:05:49,490
+مشتقة الـ E أُس X بـ E أُس X، مشتقة الـ E أُس 
+
+55
+00:05:49,490 --> 00:05:57,070
+2X بـ 2E أُس 2X، نجي نفك هذا المحدد يبقى
+
+56
+00:05:57,070 --> 00:06:04,890
+2E أُس 3X ناقص E أُس 3X يساوي E أُس
+
+57
+00:06:04,890 --> 00:06:09,950
+3X وهذا لا يمكن أن يساوي Zero في يوم من 
+
+58
+00:06:09,950 --> 00:06:15,890
+الأيام لجميع قيم X بلا استثناء لأن الـ exponential
+
+59
+00:06:15,890 --> 00:06:20,410
+function زي ما أخذنا في كل قلص P هي دائما وأبدا
+
+60
+00:06:20,950 --> 00:06:25,130
+قيمة موجبة، يعني أكبر من مين؟ أكبر من الـ zero
+
+61
+00:06:25,130 --> 00:06:28,990
+المنحنى تبعها لو روحنا ورسمنا إذا كنتم الذاكرين
+
+62
+00:06:28,990 --> 00:06:34,350
+كان دائما أو أبدا أعلى الـ x axis ويمر بالنقطة
+
+63
+00:06:34,350 --> 00:06:39,930
+اللي هي zero وواحد، مادام لا يساوي zero يبقى so E 
+
+64
+00:06:39,930 --> 00:06:47,730
+أُس X and E أُس 2X are linearly independent، ما
+
+65
+00:06:47,730 --> 00:06:50,590
+دام الـ linearly independent يبقى الاتنين هدول
+
+66
+00:06:50,590 --> 00:06:57,450
+بيشكّلوا basis للـ solution space يبقى هذا بده يعطينا
+
+67
+00:06:57,450 --> 00:07:10,990
+أن the set E أُس X و E أُس 2X is a basis for
+
+68
+00:07:10,990 --> 00:07:13,830
+the solution
+
+69
+00:07:26,810 --> 00:07:37,430
+مادام basis يبقى بأجي بقول the dimension of this
+
+70
+00:07:37,430 --> 00:07:43,190
+subspace is 
+
+71
+00:07:43,190 --> 00:07:54,930
+two، while بينما the dimension of
+
+72
+00:07:54,930 --> 00:08:01,190
+the space FN is infinite
+
+73
+00:08:05,040 --> 00:08:09,540
+يبقى هاي الـ space الأساسي تبع الـ functions هو main
+
+74
+00:08:09,540 --> 00:08:13,840
+ما لا نهاية، أخذنا منه الـ subspace طلع الـ dimension 
+
+75
+00:08:13,840 --> 00:08:19,100
+له يساوي two، وهذا ما قلناه في الـ remark، ممكن 
+
+76
+00:08:19,100 --> 00:08:22,820
+يكون عندي vector space الـ dimension له infinite
+
+77
+00:08:22,820 --> 00:08:27,220
+ولاّزم أن الـ subspace الـ dimension لهم يكون ما له
+
+78
+00:08:27,220 --> 00:08:33,750
+يكون finite، طيب انتهينا من اللي هو نقطة B، نقطة C 
+
+79
+00:08:33,750 --> 00:08:36,930
+قال هات الـ solution لـ الـ initial value problem
+
+80
+00:08:36,930 --> 00:08:41,150
+بقوله كويس اللي بيجيب الدجاجل أنا أمرأي الـ C احنا
+
+81
+00:08:41,150 --> 00:08:50,330
+عندنا الحل، the general solution of the
+
+82
+00:08:50,330 --> 00:09:02,040
+differential equation one is Y يساوي C1 في E أُس X زي 
+
+83
+00:09:02,040 --> 00:09:11,860
+C2 في E أُس 2X لأن هذا الحل يمثل الشكل العام لحل
+
+84
+00:09:11,860 --> 00:09:16,380
+المعادلة، أي حل بدي يكون كونستانتاني في E أُس X زي
+
+85
+00:09:16,380 --> 00:09:23,890
+كونستانتاني في E أُس 2X، هذه الـ E أُس X وE أُس 2X عبارة 
+
+86
+00:09:23,890 --> 00:09:29,930
+عن basis للـ solution space يعني أي solution هي عملية 
+
+87
+00:09:29,930 --> 00:09:31,010
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+88
+00:09:31,010 --> 00:09:32,310
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+89
+00:09:32,310 --> 00:09:33,310
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+90
+00:09:33,310 --> 00:09:36,490
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+91
+00:09:36,490 --> 00:09:36,970
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+92
+00:09:36,970 --> 00:09:42,510
+عملية عملية عملية عملية عملية عملية، طيب هذا شكل الـ 
+
+93
+00:09:42,510 --> 00:09:47,270
+general solution، أنا عندي هنا شرطين، يبقى الشرط 
+
+94
+00:09:47,270 --> 00:09:52,230
+الأول سهل، الشرط الثاني بيلزمه اشتقاق يبقى بأجي 
+
+95
+00:09:52,230 --> 00:09:59,470
+بقول الآن هذا بده يعطينا أن Y prime يساوي C1 مقدار
+
+96
+00:09:59,470 --> 00:10:03,690
+ثابت، مشتقة الـ exponential بالـ exponential كما هي 
+
+97
+00:10:03,690 --> 00:10:13,510
+C2 مقدار ثابت E أُس 2X مشتقتها 2E أُس 2X بالدجاجل، الـ condition
+
+98
+00:10:13,510 --> 00:10:18,790
+الأول يقول لي Y عند الـ zero بده يساوي 4 implies
+
+99
+00:10:18,790 --> 00:10:23,650
+أن 4 تساوي C1 في E أُس 0
+
+100
+00:10:25,590 --> 00:10:30,490
+زائد C2 في الـ E أُس 0 كذلك في الـ Main اللي هي 
+
+101
+00:10:30,490 --> 00:10:37,310
+بواحد، الآن بدنا نيجي لمين؟ للـ Y' عند الـ Main عند 
+
+102
+00:10:37,310 --> 00:10:42,610
+الـ 0 كذلك، يبقى بده أشيل كل X وأحط مكانها Zero
+
+103
+00:10:42,610 --> 00:10:50,160
+اللي هي تساوي واحد، اللي هي تساوي C1 زائد 2C2
+
+104
+00:10:50,160 --> 00:10:55,420
+إذا صار عندنا معادلتين على الشكل التالي اللي هو
+
+105
+00:10:55,420 --> 00:11:01,560
+4 يساوي C1 زائد C2 
+
+106
+00:11:03,420 --> 00:11:06,940
+يبقى سالب C2 ضربنا المعادلة الأولى في سالب
+
+107
+00:11:06,940 --> 00:11:14,000
+المعادلة الثانية كما هي، C1 زائد 2C2، بنروح
+
+108
+00:11:14,000 --> 00:11:20,980
+نجمع الاتنين هدول، مع السلامة، وهدول بيضل منهم بس C2
+
+109
+00:11:20,980 --> 00:11:27,930
+فقط وهدا بيضل منها قداش؟ سالب تلاتة، يبقى لما تبقى C2 
+
+110
+00:11:27,930 --> 00:11:32,790
+بسالب تلاتة ارجع عوض في أي من المعادلتين، هذا
+
+111
+00:11:32,790 --> 00:11:38,550
+بيعطينا أن 4 تساوي C1 وC2 اللي هي بسالب
+
+112
+00:11:38,550 --> 00:11:44,490
+تلاتة، هذا بدي يعطيك أن C1 تساوي قداش؟ سبعة، يبقى
+
+113
+00:11:44,490 --> 00:11:50,230
+بناء عليه بقوله solution of
+
+114
+00:12:14,390 --> 00:12:28,120
+الحل اللي قدامنا على اللوحة، أي تساؤل؟ إيش 
+
+115
+00:12:28,120 --> 00:12:34,470
+السؤال؟ ما فهمتش إن الـ infinite والـ specific، بتذكر 
+
+116
+00:12:34,470 --> 00:12:41,630
+أن احنا في الـ chapter الماضي بجينا نقول أن بجينا 
+
+117
+00:12:41,630 --> 00:12:44,030
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+118
+00:12:44,030 --> 00:12:44,170
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+119
+00:12:44,170 --> 00:12:45,670
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+120
+00:12:45,670 --> 00:12:46,870
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+121
+00:12:46,870 --> 00:12:50,370
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+122
+00:12:50,370 --> 00:12:52,130
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+123
+00:12:52,130 --> 00:12:56,370
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا، ن
+
+124
+00:12:56,550 --> 00:13:01,830
+ما لانهائي من الـ vectors إذا احنا هنا في شكل مشابه
+
+125
+00:13:01,830 --> 00:13:06,190
+احنا عندنا معادلة، المعادلة لها عدد لانهائي من 
+
+126
+00:13:06,190 --> 00:13:11,370
+الحلول، بدليل إن الـ C1 والـ C2 حط القيم اللي بدك إياها 
+
+127
+00:13:11,370 --> 00:13:15,870
+تمام؟ كويس، لكن عدد لانهائي من الحلول اللي هم bases
+
+128
+00:13:15,870 --> 00:13:21,690
+الـ bases يتكون من قداش؟ من two elements الـ vector 
+
+129
+00:13:21,690 --> 00:13:27,830
+الأساسي اللي هو الـ FN هذا with no dimension مرة
+
+130
+00:13:27,830 --> 00:13:31,750
+علينا أخذنا منه functions جاب ليك إذا كنت مليان جد 
+
+131
+00:13:31,750 --> 00:13:35,390
+ما بدك إيش ما يطلع على بالك موجود فيه، يبقى هذا 
+
+132
+00:13:35,390 --> 00:13:40,210
+infinite dimension، طلعت منه دالتين، واحدة E أُس X
+
+133
+00:13:40,210 --> 00:13:45,080
+والثانية E أُس 2X، الاتنين اللي جتهم linearly 
+
+134
+00:13:45,080 --> 00:13:52,060
+independent، اتنين يعني كونّوا الـ basis للـ solution 
+
+135
+00:13:52,060 --> 00:13:57,260
+تبع المعادلة اللي عندنا يعني في solutions آخرين شو
+
+136
+00:13:57,260 --> 00:14:03,360
+شكلهم؟ الشكل العام لهم هاهم تمام؟ كم واحد هدول؟ ما 
+
+137
+00:14:03,360 --> 00:14:09,040
+لانهاية، حط C1 وC2 زي ما بدك تمام؟ كله بيعطيني
+
+138
+00:14:09,040 --> 00:14:13,460
+إيه؟ بيعطيني شكل للحل، يعني أي حل كتبته على صيغة 
+
+139
+00:14:13,460 --> 00:14:17,160
+linear combination من مين؟ من الاتنين هدول، يبقى
+
+140
+00:14:17,160 --> 00:14:22,680
+الـ business يتكون فقط تبع الـ solutions من عنصرين،
+
+141
+00:14:22,680 --> 00:14:27,200
+يبقى الـ dimension له يساوي اتنين والـ FN الـ 
+
+142
+00:14:27,200 --> 00:14:31,620
+dimension له قداش؟ infinity بطلع الـ subspace الـ
+
+143
+00:14:31,620 --> 00:14:36,260
+dimension له اتنين من الـ space اللي الـ dimension له
+
+144
+00:14:36,260 --> 00:14:43,880
+ما لا نهاية، هاي واضحة؟ حد بيتسأل ثاني؟ فبنتقل للنقطة
+
+145
+00:14:43,880 --> 00:14:45,500
+الأخيرة من هذا الـ section
+
+146
+00:15:11,410 --> 00:15:25,010
+theorem نظرية، let the F1 والـ F2 هو لغاية الـ FN be in
+
+147
+00:15:25,010 --> 00:15:35,550
+solutions solutions of the order
+
+148
+00:15:35,550 --> 00:15:46,650
+differential equation differential equation اللي هي 
+
+149
+00:15:46,650 --> 00:15:49,410
+على الشكل التالي A0
+
+150
+00:16:01,000 --> 00:16:08,520
+زائد ونظل ماشين لغاية ما نصل إلى N minus one as a
+
+151
+00:16:08,520 --> 00:16:15,060
+function of X prime زائد a N of X في الـ Y بده
+
+152
+00:16:15,060 --> 00:16:16,200
+يساوي zero
+
+153
+00:16:20,480 --> 00:16:31,040
+interval I على فترة ما where حيث الـ AI as a
+
+154
+00:16:31,040 --> 00:16:40,600
+function of X are continuous functions
+
+155
+00:16:40,600 --> 00:16:54,470
+يبقى دوال متواصلة for all I لجميع قيم I and ضروري
+
+156
+00:16:54,470 --> 00:17:01,450
+الـ A node of X لا يساوي Main لا يساوي zero then
+
+157
+00:17:01,450 --> 00:17:16,190
+ومن ثم F F الـ F one والـ F two والـ FN بعدين أنا
+
+158
+00:17:16,190 --> 00:17:23,030
+ماشي لغاية الـ FN are linearly dependent than
+
+159
+00:17:23,030 --> 00:17:32,770
+الرونسكيان as a function of X بده يساوي 0 for all X 
+
+160
+00:17:32,770 --> 00:17:43,890
+اللي موجودة في الـ interval I and if the functions
+
+161
+00:17:45,220 --> 00:17:56,480
+إذا الـ functions f1 وf2 وfn are linearly
+
+162
+00:17:56,480 --> 00:18:05,100
+independent then الرونسكيان as a function of X لا
+
+163
+00:18:05,100 --> 00:18:12,960
+يساوي 0 for all x اللي موجودة وين؟ في الـ interval I
+
+164
+00:19:33,960 --> 00:19:38,460
+أظن واضح أن هذه النظرية لم تأتي بجديد، مكررة من 
+
+165
+00:19:38,460 --> 00:19:43,380
+الـ chapter الماضي، أجت وين؟ أجت فيه الـ chapter اللي عندنا
+
+166
+00:19:43,380 --> 00:19:48,460
+يبقى دوال من F1 لغاية Fn اللي هم عبارة عن حلول
+
+167
+00:19:48,460 --> 00:19:52,460
+للمعادلة التفاضلية من الرتبة N، بس كنا هناك بنقول على 
+
+168
+00:19:52,460 --> 00:19:55,840
+vectors هنا بدنا نقولهم على مين؟ على حلول يعني
+
+169
+00:19:55,840 --> 00:20:00,640
+قعدنا النظرية إعادة فقط بحيث تناسب المعادلات
+
+170
+00:20:00,640 --> 00:20:05,440
+التفاضلية، يبقى لو كانوا هدول هم عدد من الحلول
+
+171
+00:20:05,440 --> 00:20:11,040
+يساوي رتبة المعادلة التفاضلية اللي عندنا هذه حيث
+
+172
+00:20:11,040 --> 0
+
+201
+00:22:58,030 --> 00:23:05,230
+one ونظل ماشيين لغاية  a n minus ال one Y to the 
+
+202
+00:23:05,230 --> 00:23:12,230
+derivative of prime زائد a n y بده يساوي capital F
+
+203
+00:23:12,230 --> 00:23:17,790
+of X وهذه سأسميها المعادلة واحد يبقى الآن في هذا
+
+204
+00:23:17,790 --> 00:23:22,740
+ال section المعاملات كلها ثوابت وما لهاش علاقة في
+
+205
+00:23:22,740 --> 00:23:29,640
+المعادلة بمعاملات متغيرة لسه هذا الكلام ثاني سنصل 
+
+206
+00:23:29,640 --> 00:23:34,800
+إليه قبل نهاية هذا الفيديو إن شاء الله يمكن أن آخذ
+
+207
+00:23:34,800 --> 00:23:41,220
+المعاملات ثوابت في الأول وبعدين نكمل where حيث ال
+
+208
+00:23:41,220 --> 00:23:52,720
+a i are constants ثوابت constants and  الـ A Note
+
+209
+00:23:52,720 --> 00:23:59,040
+كمان لا يساوي Zero لكي تبقى معادلة من الرتبة النونية
+
+210
+00:23:59,040 --> 00:24:09,970
+F capital D تساوي المشتقة بالنسبة لـ X و D² تعني
+
+211
+00:24:09,970 --> 00:24:16,730
+المشتقة الثانية بالنسبة لـ X وظللنا ماشيين لغاية ما
+
+212
+00:24:16,730 --> 00:24:24,110
+وصلنا إلى D n هي المشتقة النونية بالنسبة لـ X
+
+213
+00:24:26,270 --> 00:24:36,470
+equation one is written as is written as بروح
+
+214
+00:24:36,470 --> 00:24:46,610
+بكتبها على من على الشكل التالي بكتبها a not d n
+
+215
+00:24:46,610 --> 00:25:08,980
+زائد a one d n minus ال one زائد زائد دي أو
+
+216
+00:25:08,980 --> 00:25:10,240
+دي وخلصنا
+
+217
+00:25:12,500 --> 00:25:20,800
+أين كل هذا الكلام مضروبا في من؟ في ال Y بده يساوي
+
+218
+00:25:20,800 --> 00:25:26,920
+capital F of X بالشكل اللي عندنا هذا أو اختصارا
+
+219
+00:25:26,920 --> 00:25:34,840
+بقدر أقول L of Y بدها تساوي من؟ بدها تساوي capital
+
+220
+00:25:34,840 --> 00:25:37,280
+F of X where
+
+221
+00:25:43,820 --> 00:25:50,640
+حيث where اللي 
+
+222
+00:25:50,640 --> 00:26:02,100
+هو ال L بده يساوي a0dn a1dn minus ال one زائد ونظل 
+
+223
+00:26:02,100 --> 00:26:09,660
+ماشيين لغاية اللي هو a n minus ال one دي زائد ال a
+
+224
+00:26:09,660 --> 00:26:22,270
+n is called هذا بنسميه linear أو
+
+225
+00:26:22,270 --> 00:26:29,670
+بدل ال linear بسميها polynomial polynomial
+
+226
+00:26:29,670 --> 00:26:34,990
+differential operator
+
+227
+00:26:34,990 --> 00:26:40,030
+differential linear operator with
+
+228
+00:26:43,830 --> 00:26:52,510
+constant coefficients بمعاملات
+
+229
+00:26:52,510 --> 00:27:01,250
+ثابتة homogeneous
+
+230
+00:27:01,250 --> 00:27:08,110
+linear differential equation
+
+231
+00:27:12,470 --> 00:27:20,130
+أو equation one is a
+
+232
+00:27:20,130 --> 00:27:25,550
+a n y to the derivative n a one y to the
+
+233
+00:27:25,550 --> 00:27:34,330
+derivative n minus one زائد a n minus one y prime
+
+234
+00:27:34,330 --> 00:27:44,010
+زائد a n y is equal to zero وهذه اسمها اللي من 
+
+235
+00:27:44,010 --> 00:27:47,030
+المعادلة رقم اتنين
+
+236
+00:28:26,900 --> 00:28:31,680
+يبقى احنا بنجي لـ section خمسة اتنين ونبدأ الآن 
+
+237
+00:28:31,680 --> 00:28:36,080
+نشتغل شغل معادلات تفاضلية فعلية يعني ال section
+
+238
+00:28:36,080 --> 00:28:41,920
+اللي فات كان مجرد شوية تعريفات أو رابط لمين؟ لل
+
+239
+00:28:41,920 --> 00:28:45,340
+chapter اللي فات بمين؟ بهذا ال chapter لكن من هنا
+
+240
+00:28:45,340 --> 00:28:49,600
+بدنا نبدأ ابتداء من هذا ال section ونبدأ نشتغل شغل 
+
+241
+00:28:49,600 --> 00:28:54,570
+معادلات تفاضلية يقول إن الأنصار ضالين ال equation 
+
+242
+00:28:54,570 --> 00:28:59,030
+differential بمعاملات ثابتة هي معادلة على الشكل
+
+243
+00:28:59,030 --> 00:29:02,810
+اللي عندنا اللي هو شكل واحد ال a node و ال a one و
+
+244
+00:29:02,810 --> 00:29:07,530
+لغاية ال a n minus one و ال a n كلهم ثوابت الدالة 
+
+245
+00:29:07,530 --> 00:29:12,010
+ال f of x يبقى دالة في x ما لهاش علاقة في y اللي 
+
+246
+00:29:12,010 --> 00:29:16,030
+بعد اليساوي اللي جاب لي اليساوي كلها مشتقات بالنسبة
+
+247
+00:29:16,030 --> 00:29:20,410
+لـ y ماعدا آخر اثنين والدالة الأخيرة كلها دالة في x
+
+248
+00:29:20,410 --> 00:29:24,840
+ما لهاش علاقة بـ y حيث ال a i are constant وال a node 
+
+249
+00:29:24,840 --> 00:29:27,800
+لا يساوي zero وجدنا ليش ال a node لا يساوي zero
+
+250
+00:29:27,800 --> 00:29:33,080
+حتى تبقى المعادلة منها رتبة أنونية بقول لو حطيت
+
+251
+00:29:33,080 --> 00:29:37,910
+capital D هو عبارة عن المشتقة الأولى بالنسبة لـ X دي 
+
+252
+00:29:37,910 --> 00:29:41,330
+تربيع المشتقة الثانية دي تكعيب المشتقة الثالثة
+
+253
+00:29:41,330 --> 00:29:46,010
+وهكذا لغاية ما وصلت لدى أنهي المشتقة النونية
+
+254
+00:29:46,010 --> 00:29:50,490
+بالنسبة لـ X يبقى المعادلة رقم واحد بقدر أكتبها على 
+
+255
+00:29:50,490 --> 00:29:56,600
+الشكل التالي a node كما هي وهذه المشتركة بدي أكتبها 
+
+256
+00:29:56,600 --> 00:30:02,880
+dny بس و يوري حطيه تبارك كأنه أخذ عامل مشترك من 
+
+257
+00:30:02,880 --> 00:30:10,900
+الكل اللي بعدها a1dn-1y و اللي بعدها و اللي بعدها
+
+258
+00:30:10,900 --> 00:30:12,860
+لغاية هذه a1dn-1y
+
+259
+00:30:17,610 --> 00:30:22,290
+يبقى Y كإن أخذ عامل مشترك من مين؟ من الكل بده يسوي
+
+260
+00:30:22,290 --> 00:30:28,510
+capital F of X هذه بالشكل الطويل ممكن أختصرها بـ L
+
+261
+00:30:28,510 --> 00:30:34,930
+of Y بده يساوي من؟ F of X مين هو الـ L هو العنوان
+
+262
+00:30:34,930 --> 00:30:39,840
+اللي احنا رفعينه هناللـ polynomial operator المؤثر
+
+263
+00:30:39,840 --> 00:30:46,300
+على الخط اللي على شكل كثيرة حدود يبقى الـ L of Y 
+
+264
+00:30:46,300 --> 00:30:52,740
+معناته كل اللي بين قوسين هذا بدي أديله الرمز L هاي 
+
+265
+00:30:52,740 --> 00:30:59,000
+L كل المقدار بين مين؟ بين القوسين يبقى هذا مؤثر
+
+266
+00:30:59,000 --> 00:31:03,670
+تفاضل يبدأ من المشتقة القنونية لغاية المشتقة الأولى
+
+267
+00:31:03,670 --> 00:31:09,830
+لغاية الدالة بدون مين؟ بدون اشتقاق كويس يبقى هذا is
+
+268
+00:31:09,830 --> 00:31:15,070
+called a linear polynomial أو بسميه linear
+
+269
+00:31:15,070 --> 00:31:19,530
+differential operator يبقى linear والله polynomial
+
+270
+00:31:19,530 --> 00:31:24,710
+لاثنين المقصود فيهم اثنين نفس الشيء لمين؟ للمعادلة
+
+271
+00:31:24,710 --> 00:31:30,480
+ال تفاضلية بمعاملات ثابتة الآن أنا المعادلة رقم واحد 
+
+272
+00:31:30,480 --> 00:31:34,540
+هذي بسميها ال non homogeneous تمام ال non
+
+273
+00:31:34,540 --> 00:31:39,300
+homogeneous بيقول أترحي شوية سنرجع لكِ في المستقبل
+
+274
+00:31:39,300 --> 00:31:43,400
+خلال هذا الشبطة يبقى أنا بروح آخذ فقط مين؟
+
+275
+00:31:52,010 --> 00:31:54,790
+المعاملات الثوابت هي المعاملات الثوابت وليست دوال
+
+276
+00:31:54,790 --> 00:31:55,390
+f x
+
+277
+00:32:00,570 --> 00:32:04,530
+اثنين أخذت ال homogeneous وسبت ال non homogeneous
+
+278
+00:32:04,530 --> 00:32:08,570
+ال non homogeneous لها شغل آخر هناخده في آخر هذا 
+
+279
+00:32:08,570 --> 00:32:13,130
+chapter أو آخر two sections من هذا ال chapter يبقى
+
+280
+00:32:13,130 --> 00:32:16,170
+احنا بدنا نبدأ نشتغل عالميا على ال homogeneous
+
+281
+00:32:16,170 --> 00:32:20,130
+روحنا أخذنا ال homogeneous differential equation
+
+282
+00:32:20,130 --> 00:32:25,710
+فكانت على الشكل اللي عندنا هذا الآن بدروح أدور على 
+
+283
+00:32:25,710 --> 00:32:32,950
+شكل الحل العام للمعادلة رقم 2 بدروح أفترض من عندي
+
+284
+00:32:32,950 --> 00:32:38,310
+حل وأشوف هذا الحل بيوصلنا لوين يبقى بدجي أقول له
+
+285
+00:32:38,310 --> 00:32:51,210
+هنا let Y تساوي E أس RX بيه solution of the
+
+286
+00:32:51,210 --> 00:32:56,370
+differential equation 2
+
+287
+00:33:00,720 --> 00:33:05,380
+بارامتر رقم اثنين ثلاثة أربعة ناقص خمسة قد ما يكون 
+
+288
+00:33:05,380 --> 00:33:12,280
+يبقى الـ R ال number مين ما يكون يكون تمام الـ X هي 
+
+289
+00:33:12,280 --> 00:33:18,040
+ال متغير اللي عندنا يبقى لأن بروح أجيب المشتقة
+
+290
+00:33:18,040 --> 00:33:22,180
+الأولى والثانية والثالثة والرابعة والخامسة و
+
+291
+00:33:22,180 --> 00:33:29,520
+النونية إلى آخره يبقى بأجي بقول له هنا then بدي آخذ
+
+292
+00:33:29,520 --> 00:33:35,760
+Y' يبقى الـ exponential كما هي مضروبة في مين؟ في 
+
+293
+00:33:35,760 --> 00:33:44,760
+مشتقة الأس بدي آخذ المشتقة الثانية Y W' يبقى Y W' 
+
+294
+00:33:45,320 --> 00:33:50,760
+بدي أساوي R ما لهاش دعوة وهذه مشتقتها بدي أجيب كمان
+
+295
+00:33:50,760 --> 00:33:58,130
+R بصير R تربيع E أس RX ولو دلت حوصل لمين؟ للمشتقة 
+
+296
+00:33:58,130 --> 00:34:05,190
+الثالثة يبقى R تكعيب E أس RX ولو دلت مستمر حوصل 
+
+297
+00:34:05,190 --> 00:34:11,850
+للمشتقة النونية يبقى R to the power in E أس RX
+
+298
+00:34:14,120 --> 00:34:18,580
+بتأخذ المعلومات اللي عندي هذه وروح اعوض في مين؟ في
+
+299
+00:34:18,580 --> 00:34:25,400
+المعادلة رقم اثنين يبقى بأجي بقول الصعب اسم تت يوت
+
+300
+00:34:25,400 --> 00:34:33,340
+and equation اثنين we get نحصل على علامات ال a node 
+
+301
+00:34:33,340 --> 00:34:43,570
+كما هي والـ Y to the derivative N هي R n E أس RX
+
+302
+00:34:44,690 --> 00:34:55,790
+اللي بعدها زائد A 1 R أس N minus 1 E أس RX زائد
+
+303
+00:34:55,790 --> 00:35:03,110
+ونظل ماشيين لغاية ما نوصل لحد قبل الأخير A N minus
+
+304
+00:35:03,110 --> 00:35:14,730
+1 R E أس RX اليمين المشتقولة زائد A n في E أس RX
+
+305
+00:35:14,730 --> 00:35:21,410
+كما هي بده يساوي Zero لا يمكن أن تساوي صفر في يوم 
+
+306
+00:35:21,410 --> 00:35:26,090
+من الأيام إذا الأبانات بنجي للمعادلة اللي عندنا 
+
+307
+00:35:26,090 --> 00:35:32,450
+هذه كون الـ E أس RX لا تساوي Zero إذا بقدر أقسم
+
+308
+00:35:32,450 --> 00:35:37,050
+طرفين المعادلة عليها إذا لو قسمنا طرفين المعادلة
+
+309
+00:35:37,050 --> 00:35:41,810
+على E أس RX تصبح المعادلة على الشكل التالي
+
+310
+00:36:01,520 --> 00:36:07,860
+نعمل محاسبة مع نفسنا احنا المعادلة رقم اثنين عندنا 
+
+311
+00:36:07,860 --> 00:36:15,180
+هذه معادلة تفاضلية من الرتبة النونية اللي توصلنا 
+
+312
+00:36:15,180 --> 00:36:19,580
+عليها هذه. هذه معادلة تفاضلية؟ لا، هذه معادلة 
+
+313
+00:36:19,580 --> 00:36:25,180
+عادية من أي درجة؟ من الدرجة النونية. إذا هذه 
+
+314
+00:36:25,180 --> 00:36:31,390
+المعادلة لها كام حل؟ لها n من الحلول سواء كانوا مكرر 
+
+315
+00:36:31,390 --> 00:36:36,010
+بعضهم أو مش مكرر أو كلهم مكررات بهم نيل إذا هذه 
+
+316
+00:36:36,010 --> 00:36:41,910
+معادلة من الدرجة النونية يبقى لها n من الحلول
+
+317
+00:36:41,910 --> 00:36:47,570
+تمام هذه المعادلة بسميها المعادلة المساعدة ال
+
+318
+00:36:47,570 --> 00:36:51,220
+auxiliary equation أول أكتبها لك أول
+
+319
+00:36:51,220 --> 00:36:55,940
+characteristic equation المعادلة المميزة للمعادلة
+
+320
+00:36:55,940 --> 00:37:01,500
+الرقم اثنين والآن بدنا نيجي نتكلم عن حلول هذه
+
+321
+00:37:01,500 --> 00:37:08,740
+المعادلة يبقى بأجي بقول له this equation this
+
+322
+00:37:08,740 --> 00:37:18,120
+equation هذه المعادلة is called بنسميها
+
+323
+00:37:18,120 --> 00:37:18,940
+Z
+
+324
+00:37:43,620 --> 00:37:51,700
+المعادلة المميزة للمعادلة اللي عندنا هذه بنات هتلعب 
+
+325
+00:37:51,700 --> 00:37:56,420
+عمود في قري في شغلنا خلال هذا ال section وال 
+
+326
+00:37:56,420 --> 00:38:03,360
+sections القادمة كذلك طب المعادلة هذه معادلة من
+
+327
+00:38:03,360 --> 00:38:09,680
+الدرجة النونية إذا لها إيه من الحلول؟ الحلول هذه
+
+328
+00:38:09,680 --> 00:38:18,140
+يمكن يطلع كلهم ريال كلهم أغار قيم حقيقية وكلهم
+
+329
+00:38:18,140 --> 00:38:22,400
+يكونوا ولا واحد زي الثاني يبقى الاحتمال الأول 
+
+330
+00:38:22,400 --> 00:38:27,480
+يطلعوا كلهم .. هكتبوا كلهم
+
+331
+00:38:27,480 --> 00:38:32,160
+يبقى أنا بقول الاحتمال الأول إن الحلوين يكونوا are
+
+332
+00:38:32,160 --> 00:38:36,700
+real and distinct ولا واحد زي الثاني الاحتمال
+
+333
+00:38:36,700 --> 00:38:44,060
+الثاني إنه يطلع حل واحد مكرر n من المرات يبقى 
+
+334
+00:38:44,060 --> 00:38:49,980
+repeated roots جذور مكررة لإحتمالية إنهم يطلعوا
+
+335
+00:38:49,980 --> 00:38:55,180
+complex و complex بيطلعوا complex conjugate إن طلع 
+
+336
+00:38:55,180 --> 00:39:00,580
+حل هيكون واحد مرافق له هيك طبيعة من الحلول تبع ال
+
+337
+00:39:00,580 --> 00:39:05,600
+complex طبعا لما أقول لك ال element يساوي a زائد ib
+
+338
+00:39:05,600 --> 00:39:11,540
+ال conjugate تبعه a ناقص ib طبعا أنا أتعرض له ما أعرفش
+
+339
+00:39:11,540 --> 00:39:14,600
+اليوم والله مش اليوم الله عليه ممكن نلحق اليوم 
+
+340
+00:39:14,600 --> 00:39:22,070
+تمام هي ثلاثة حلول ويمكن أن يكون الحل مزيد ما بين 
+
+341
+00:39:22,070 --> 00:39:26,350
+ال complex وما بين الريال كيف يعني؟ لو قلنا إن 
+
+342
+00:39:26,350 --> 00:39:31,570
+عشرة يمكن يطلع عندي عشرة حلول العشرة حلول يمكن 
+
+343
+00:39:31,570 --> 00:39:36,710
+أربعة ريال وستة complex أو اثنين complex وثمانية 
+
+344
+00:39:36,710 --> 00:39:42,190
+ريال وهكذا يبقى بدعم الريال بالريال وبدعم 
+
+345
+00:39:42,190 --> 00:39:46,610
+ال complex بال complex كما سنرى من خلال هذه
+
+346
+00:39:46,610 --> 00:39:51,770
+الأمثلة التي سنعطيها بعد قليلبقى أنا بالذات 
+
+347
+00:39:51,770 --> 00:39:55,810
+بالأقل احتمالاتي الثلاثة وبعد هيك بدنا نمسك
+
+348
+00:39:55,810 --> 00:39:59,910
+الاحتمال الأول بنكمل بال section بصير الاحتمال 
+
+349
+00:39:59,910 --> 00:40:05,010
+الثاني هو section جديد لأنه له شغله لوحده وهكذا
+
+350
+00:40:05,010 --> 00:40:15,160
+إذا هانيجي بأجي بقول له equation equation هذي نسميها 
+
+351
+00:40:15,160 --> 00:40:20,360
+بنات ال star لجديد اللي عندنا يبقى equation star
+
+352
+00:40:20,360 --> 00:40:29,540
+has n roots كونها من الدرجة النونية إذا لها n من 
+
+353
+00:40:29,540 --> 00:40:39,660
+الجذور and these roots وهذه الجذور are found
+
+354
+00:40:43,720 --> 00:40:57,660
+as follow يبقى بنوجدها كالتالي تمام نملا 
+
+355
+00:40:57,660 --> 00:41:04,340
+واحد the roots الجذور
+
+356
+00:41:04,340 --> 00:41:10,900
+are real and different
+
+357
+00:41:13,720 --> 00:41:23,340
+يبقى حقيقية ومختلفة that is r واحد لا يساوي r 
+
+358
+00:41:23,340 --> 00:41:32,620
+اثنين لا يساوي لا يساوي r n الاحتمال
+
+359
+00:41:32,620 --> 00:41:42,340
+الثاني the roots are real and repeated حقيقية 
+
+360
+00:41:42,340 --> 00:42:00,280
+ومكررة رمز
+
+361
+00:42:00,280 --> 00:42:09,380
+r مثلا لإحتمال الثالث the roots are complex 
+
+362
+00:42:10,270 --> 00:42:16,050
+conjugate تخيليه 
+
+363
+00:42:16,050 --> 00:42:30,630
+مترافقة that is if R1 بدي تساوي A زائد IB then 
+
+364
+00:42:33,300 --> 00:42:45,860
+R2 بيبقى A ناقص IB and so on وهكذا والـ I هو الجذر 
+
+365
+00:42:45,860 --> 00:42:48,600
+التربيع لمين؟ لسالب واحد
+
+366
+00:43:10,450 --> 00:43:18,010
+in this section يبقى in this section يبقى in this
+
+367
+00:43:18,010 --> 00:43:20,530
+section يبقى in this section يبقى in this section
+
+368
+00:43:20,530 --> 00:43:21,870
+يبقى in this section يبقى in this section يبقى in
+
+369
+00:43:21,870 --> 00:43:21,910
+this section يبقى in this section يبقى in this
+
+370
+00:43:21,910 --> 00:43:22,390
+section يبقى in this section يبقى in this section
+
+371
+00:43:22,390 --> 00:43:25,830
+يبقى in this section يبقى in this section يبقى in
+
+372
+00:43:25,830 --> 00:43:27,790
+this section يبقى in this section يبقى in this
+
+373
+00:43:27,790 --> 00:43:29,070
+section يبقى in this section يبقى in this section
+
+374
+00:43:29,070 --> 00:43:36,650
+يبقى in this section يبقى in this section يبقى
+
+375
+00:43:36,650 --> 00:43:38,730
+in this section يبقى in this section يبقى in this
+
+376
+00:43:38,730 --> 00:43:44,160
+section يبقى in this section يب
+
+401
+00:47:47,410 --> 00:47:51,730
+المعادلة رقم اثنين لما عوضنا صارت المعادلة على
+
+402
+00:47:51,730 --> 00:47:56,880
+الشكل اللي عندنا هذا جسمنا كله على USRX وصلنا 
+
+403
+00:47:56,880 --> 00:48:00,880
+للمعادلة هذه سمينا هذه المعادلة المميزة أو
+
+404
+00:48:00,880 --> 00:48:05,220
+المعادلة المساعدة للمعادلة رقم 2 يعني احنا طلعنا
+
+405
+00:48:05,220 --> 00:48:09,900
+من معادلة تفاضلية من الرتبة النونية إلى معادلة
+
+406
+00:48:09,900 --> 00:48:16,360
+عادية من الدرجة رقم N يبقى هذه المعادلة لها N من
+
+407
+00:48:16,360 --> 00:48:24,060
+الحلول هذه الحلول ممكن تكون حقيقية ومختلفة ولا 
+
+408
+00:48:24,060 --> 00:48:30,820
+واحد زي الثاني ممكن تكون حقيقية ومكررة كل الحلول
+
+409
+00:48:30,820 --> 00:48:35,280
+اللي عددهم N كل واحد زي الثاني تمام ما عندي مشكلة
+
+410
+00:48:35,280 --> 00:48:39,900
+بدي أسميه مثلا R الحالة الثالثة كل اثنين بيكونوا 
+
+411
+00:48:39,900 --> 00:48:46,080
+complex conjugate مع بعض فبيكون الحل R1A زائد IB
+
+412
+00:48:46,080 --> 00:48:52,240
+والثاني R2A ناقص IB وهكذا والـ I هو الجذر التربيعي
+
+413
+00:48:52,240 --> 00:48:57,080
+لمن لسان واحد في هذا الـ section بدنا ناخد الحالة 
+
+414
+00:48:57,080 --> 00:49:01,600
+الأولى فقط هذه الحالة هيقبلها section لحالها وهذه
+
+415
+00:49:01,600 --> 00:49:05,900
+section لحالها تماما يبقى لو أخذنا الحالة الأولى
+
+416
+00:49:05,900 --> 00:49:11,780
+أن الجذور كانت حقيقية ومختلفة ففرضنا أن الجذور هي من 
+
+417
+00:49:11,780 --> 00:49:17,620
+R1 لغاية RN بـ the distinct solutions الحلول
+
+418
+00:49:17,620 --> 00:49:24,500
+المختلفة لمن للمعادلة اللي قدامنا هذه يبقى الحلول
+
+419
+00:49:24,500 --> 00:49:30,560
+التابعة للمعادلة رقم اثنين هي Y واحد بيكون E أس R
+
+420
+00:49:30,560 --> 00:49:36,380
+واحد X Y اثنين E أس R اثنين X لأنه قلنا R واحد
+
+421
+00:49:36,380 --> 00:49:43,260
+تختلف عن R اثنين يفرضنا الحل أصلا على الشكل Y تساوي
+
+422
+00:49:43,260 --> 00:49:48,480
+E أس R X يبقى الحكي الشكل كان على الشكل هذا طلعنا 
+
+423
+00:49:48,480 --> 00:49:54,260
+مختلفة ولو عزيزي الثاني يبقى هذا حل هذا حل هذا حل 
+
+424
+00:49:54,260 --> 00:50:00,340
+وهكذا يبقى عندي N من الحلول المختلفة إذا الحلول
+
+425
+00:50:00,340 --> 00:50:05,700
+هذه في سيكشن ثلاثة أربعة إذا بتذكر وأخذنا الدالة a
+
+426
+00:50:05,700 --> 00:50:10,440
+واحد x a اثنين x أثبتنا إن ما دول linearly
+
+427
+00:50:13,320 --> 00:50:18,840
+آخر مثال كان في سيكشن ثلاثة أربعة يبقى هدول ال
+
+428
+00:50:18,840 --> 00:50:22,640
+functions are linearly independent بيكونوا main
+
+429
+00:50:22,640 --> 00:50:28,080
+بيكونوا basis لمجموعة الحلول للمعادلة اللي عندنا 
+
+430
+00:50:28,080 --> 00:50:33,060
+رقم اثنين ما دام بيكونوا الـ basis يبقى الحل العام
+
+431
+00:50:33,060 --> 00:50:37,220
+أو أي حل بدي يكون على مين كونه صنف الأول زائد كونه 
+
+432
+00:50:37,220 --> 00:50:40,440
+صنف الثاني زائد كونه صنف الثالث زائد كونه صنف 
+
+433
+00:50:40,440 --> 00:50:44,120
+الشكل اللي عندنا ده يبقى بناء عليه لو كان عندي
+
+434
+00:50:44,120 --> 00:50:49,530
+معادلة تفاضلية من الرتبة النونية ورحت جبت 
+
+435
+00:50:49,530 --> 00:50:54,270
+المعادلة المساعدة اللي هي رقم star ولجيت الحلول
+
+436
+00:50:54,270 --> 00:50:59,270
+are real and different يبقى الشكل العام للحل بيكون
+
+437
+00:50:59,270 --> 00:51:03,690
+على الشكل هذا complex اللي هو شكل آخر repeated 
+
+438
+00:51:03,690 --> 00:51:08,890
+اللي هو شكل آخر هذا ما سنعرفه مستقبلا يبقى هنا stop
+
+439
+00:51:08,890 --> 00:51:13,670
+المحاضرة الثانية هنبدأ ناخد أمثلة عالمين مختلفة على
+
+440
+00:51:13,670 --> 00:51:16,870
+هذه الحالة أعطيكم العفو 
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/mteISRbTvzU_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/mteISRbTvzU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e419d43a30ea7e866fd6810428e2a39acbc7cc1a
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/mteISRbTvzU_raw.srt
@@ -0,0 +1,1788 @@
+1
+00:00:19,490 --> 00:00:24,710
+بسم الله الرحمن الرحيم عودنا على بدأ المرة الماضية
+
+2
+00:00:24,710 --> 00:00:29,750
+بدأنا ب ال linear differential equation و أخدنا
+
+3
+00:00:29,750 --> 00:00:35,090
+بعض التعريفات الأساسية ثم أخدنا مثالا واحدا و الآن
+
+4
+00:00:35,090 --> 00:00:40,140
+بنكمل على نفس الموضوعالرمارك بتقول لو كان V هو
+
+5
+00:00:40,140 --> 00:00:45,220
+vector space of no dimension لما نقول no dimension
+
+6
+00:00:45,220 --> 00:00:49,800
+معناته infinite dimensional vector space يعني ال
+
+7
+00:00:49,800 --> 00:00:55,020
+basis له عدد العناصر فيه يساويمالة نهاية من
+
+8
+00:00:55,020 --> 00:00:59,540
+العناصر فهذا يا بسميه infinite dimensional vector
+
+9
+00:00:59,540 --> 00:01:04,080
+space يا اما بسميه vector space with no dimension
+
+10
+00:01:04,080 --> 00:01:09,660
+مالوش بعد محدد او مالوش بعد محدود because then we
+
+11
+00:01:09,660 --> 00:01:13,480
+can find a subspace بنقدر نجد subspace من ال
+
+12
+00:01:13,480 --> 00:01:17,760
+vector space V of finite dimensionيعني الـ vector
+
+13
+00:01:17,760 --> 00:01:22,600
+space اللي ال dimension إله infinite ممكن أجيب منه
+
+14
+00:01:22,600 --> 00:01:27,620
+subspaces ال dimension إله يكون finite بدنا نعطي
+
+15
+00:01:27,620 --> 00:01:33,260
+مثال على ذلك بيقول المثال بيلي إن E أوس X و E أوس
+
+16
+00:01:33,260 --> 00:01:37,960
+2X هما حلاني لمين لل differential equation عندنا
+
+17
+00:01:37,960 --> 00:01:41,860
+اللي هي ال homogeneous differential equation رقم 1
+
+18
+00:01:42,390 --> 00:01:47,590
+مطلوب اتنف بدنا ال dimension لل solutions space of
+
+19
+00:01:47,590 --> 00:01:50,490
+the given differential equation طبعا ال solution
+
+20
+00:01:50,490 --> 00:01:55,410
+space هو عبارة عن subspace من ال vector space
+
+21
+00:01:55,410 --> 00:02:02,370
+الأساسي الذي يحتوي على اللي هو المعادلات اللي لها
+
+22
+00:02:02,370 --> 00:02:07,110
+المشتقات أنونية بعد هي كتل ال solution تبع ال
+
+23
+00:02:07,110 --> 00:02:10,690
+initial value problem هذه لما نحط عليها الشرطين
+
+24
+00:02:10,690 --> 00:02:14,930
+الأثنين هدولفباجي بقول مياتي بدي أثبت الخطوة
+
+25
+00:02:14,930 --> 00:02:20,190
+الأولى ان هدول هما عبارة عن حلين لمين للمعادلة
+
+26
+00:02:20,190 --> 00:02:24,930
+عندنا رقم واحد يبقى باجي بقول لو اي دولة من هذه
+
+27
+00:02:24,930 --> 00:02:29,990
+الدولة حققت المعادلة يبقى بتبقى هي عبارة عن حل
+
+28
+00:02:29,990 --> 00:02:35,830
+طبعا ال EU6 بنعرف ان مشتقتها مرة مرتين تلاتة مالة
+
+29
+00:02:35,830 --> 00:02:43,850
+نهاية كلهاكله ب E أُس X إذا بناء عليه باجي بقوله E
+
+30
+00:02:43,850 --> 00:02:52,250
+أُس X ناقص تلاتة E أُس X زائد اتنين E أُس X يساوي
+
+31
+00:02:52,250 --> 00:02:57,730
+اللي هو تلاتة E أُس X ناقص تلاتة E أُس X بده يساوي
+
+32
+00:02:57,730 --> 00:03:09,620
+كده عشانيبقى F1 of X يساوي EO6 is a solution of
+
+33
+00:03:09,620 --> 00:03:17,930
+equation 1 المعادلة الأساسية اللي عندناالان لو جيت
+
+34
+00:03:17,930 --> 00:03:25,750
+لل F2 of X بدى يسوى E أس اتنين X بدى اجيب F2 prime
+
+35
+00:03:25,750 --> 00:03:31,490
+of X يبقى اتنين E أس اتنين X ال exponential كما هي
+
+36
+00:03:31,490 --> 00:03:36,670
+مضروبة في مشتقة الأس تبع ال exponential هذا بدى
+
+37
+00:03:36,670 --> 00:03:43,670
+يعطينا ان المشتقة الثانية F2 double prime of XF2W'
+
+38
+00:03:44,210 --> 00:03:51,410
+of X بده يساوي 4E2X
+
+39
+00:03:51,410 --> 00:03:56,310
+لما ناخد المعلومات اللتي حصلنا عليها و نعوض في
+
+40
+00:03:56,310 --> 00:04:01,250
+المعادلة 1 و نشوف هل بتعطينا صفر ولا لا يبقى
+
+41
+00:04:01,250 --> 00:04:08,170
+المعادلة عندنا YW'-3Y'2Y
+
+42
+00:04:09,360 --> 00:04:16,880
+YW' لي FW' اللي هي مين؟ أربعة في E أس اتنين X
+
+43
+00:04:16,880 --> 00:04:23,440
+ماقصة ثلاثة في ال Y' اللي هو اتنين E أس اتنين X
+
+44
+00:04:23,440 --> 00:04:30,810
+زائدي اتنين E أس اتنين X يساويأربعة و اتنين اللي
+
+45
+00:04:30,810 --> 00:04:36,130
+هو ستة اي اصي اتنين اكس سالب تلاتة في اتنين بسالب
+
+46
+00:04:36,130 --> 00:04:41,490
+ستة اي اصي اتنين اكس بده يساوي جداش بده يساوي زيرو
+
+47
+00:04:41,490 --> 00:04:47,550
+يبقى يساوي ال Y2 او ال F2 of X
+
+48
+00:04:51,580 --> 00:05:04,820
+الـ F2 of X بده يسوي E أُس 2X is a solution of the
+
+49
+00:05:04,820 --> 00:05:11,970
+differential equation 1يبقى المطلوب الأول يبين لي
+
+50
+00:05:11,970 --> 00:05:15,850
+أن الدليلين الاتنين هم حلين لهذه المعادلة انتهينا
+
+51
+00:05:15,850 --> 00:05:27,630
+منها يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+52
+00:05:27,630 --> 00:05:34,010
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+53
+00:05:34,010 --> 00:05:34,010
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+54
+00:05:34,010 --> 00:05:34,010
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+55
+00:05:34,010 --> 00:05:38,690
+يبقى يبقى يبقى يبقى يبقى يبقى يبقىAs a function of
+
+56
+00:05:38,690 --> 00:05:44,550
+x الحل الأول e والسكس الحل التاني e أوس اتنين x
+
+57
+00:05:44,550 --> 00:05:49,490
+مشتقة ال e والسكس بال e والسكس مشتقة ال e أوس
+
+58
+00:05:49,490 --> 00:05:57,070
+اتنين x ب 2e أوس اتنين xنجي نفك هذا المحدد يبقى
+
+59
+00:05:57,070 --> 00:06:04,890
+اتنين E أس ثلاثة X ناقص E أس ثلاثة X يساوي E أس
+
+60
+00:06:04,890 --> 00:06:09,950
+ثلاثة X وهذا لا يمكن أن يساوي Zero في يوم من
+
+61
+00:06:09,950 --> 00:06:15,890
+الأيام لجميع قيم X بلا استثناء لأن ال exponential
+
+62
+00:06:15,890 --> 00:06:20,410
+function زي ما أخدنا في كل قلص P هي دائما وأبدا
+
+63
+00:06:20,950 --> 00:06:25,130
+قيمة موجبة يعني اكبر من مين اكبر من ال zero
+
+64
+00:06:25,130 --> 00:06:28,990
+المنحنة تبعها لو روحنا و رسمنا اذا كنتم الذاكرين
+
+65
+00:06:28,990 --> 00:06:34,350
+كان دائما او ابدا اعلى ال x axis و يمر بالنقطة
+
+66
+00:06:34,350 --> 00:06:39,930
+اللي هي zero و واحد مادام لا يساوي zero يبقى so E
+
+67
+00:06:39,930 --> 00:06:47,730
+أس X and E أس اتنين X are linearly independentما
+
+68
+00:06:47,730 --> 00:06:50,590
+دام الينيار اللي independent يبقى الاتنين هدولش
+
+69
+00:06:50,590 --> 00:06:57,450
+بشكله basis لل solution space يبقى هذا بده يعطينا
+
+70
+00:06:57,450 --> 00:07:10,990
+انه the set E أس X و E أس اتنين X is a basis for
+
+71
+00:07:10,990 --> 00:07:13,830
+the solution
+
+72
+00:07:26,810 --> 00:07:37,430
+مدام بيزن يبقى باجي بقول the dimension of this
+
+73
+00:07:37,430 --> 00:07:43,190
+subspace is
+
+74
+00:07:43,190 --> 00:07:54,930
+twowhile بينما the dimension of
+
+75
+00:07:54,930 --> 00:08:01,190
+the space FN is infinite
+
+76
+00:08:05,040 --> 00:08:09,540
+يبقى هاي ال space الأساسي تبع ال functions هو main
+
+77
+00:08:09,540 --> 00:08:13,840
+ما لا نهاية أخدنا منه ال subspace طلع ال dimension
+
+78
+00:08:13,840 --> 00:08:19,100
+له يسوى main to وهذا ما قلناه في ال remark ممكن
+
+79
+00:08:19,100 --> 00:08:22,820
+يكون عندي vector space ال dimension له infinite
+
+80
+00:08:22,820 --> 00:08:27,220
+ولاجب ان ال subspace ال dimension لهم يكون ماله
+
+81
+00:08:27,220 --> 00:08:33,750
+يكون finiteطيب انتهينا من اللي هو نقطة B نقطة C
+
+82
+00:08:33,750 --> 00:08:36,930
+قال هات ال solution ل ال initial value problem
+
+83
+00:08:36,930 --> 00:08:41,150
+بقوله كويس اللي بيجيب الداجل انا امرأي ال C احنا
+
+84
+00:08:41,150 --> 00:08:50,330
+عندنا الحل the general solution of the
+
+85
+00:08:50,330 --> 00:09:02,040
+differential equation one isY يسوى C1 في E وSix زي
+
+86
+00:09:02,040 --> 00:09:11,860
+C2 في E اقصى 2X لأن هذا الحل يمثل الشكل العام لحل
+
+87
+00:09:11,860 --> 00:09:16,380
+المعادلة اي حل بدي يكون كونستانتاني في E وSix زي
+
+88
+00:09:16,380 --> 00:09:23,890
+كونستانتاني في E اقصى 2Xهذه الـ 6EOS6 وEOS2X عبارة
+
+89
+00:09:23,890 --> 00:09:29,930
+عن بيزز للـ solution space يعني أي سلوشن هي عملية
+
+90
+00:09:29,930 --> 00:09:31,010
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+91
+00:09:31,010 --> 00:09:32,310
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+92
+00:09:32,310 --> 00:09:33,310
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+93
+00:09:33,310 --> 00:09:36,490
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+94
+00:09:36,490 --> 00:09:36,970
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+95
+00:09:36,970 --> 00:09:36,970
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+96
+00:09:36,970 --> 00:09:36,970
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+97
+00:09:36,970 --> 00:09:42,510
+عملية عملية عملية عملية عملية عمليةطيب هذا شكل ال
+
+98
+00:09:42,510 --> 00:09:47,270
+general solution أنا عندي هنا شرطين يبقى الشرط
+
+99
+00:09:47,270 --> 00:09:52,230
+الأول سهل الشرط التاني بيلزمه اشتقاق يبقى باجي
+
+100
+00:09:52,230 --> 00:09:59,470
+بقول الآن هذا بده يعطينا ان y prime يساويC1 مقدار
+
+101
+00:09:59,470 --> 00:10:03,690
+ثابت مجتقة الـ exponential بالـ exponential كما هي
+
+102
+00:10:03,690 --> 00:10:13,510
+C2 مقدار ثابت E2X مجتقتها 2E2X بالدجل ال condition
+
+103
+00:10:13,510 --> 00:10:18,790
+الأول يقول لي Y عند الـ zero بده يساوي 4 implies
+
+104
+00:10:18,790 --> 00:10:23,650
+أن 4 تساوي C1 في E0
+
+105
+00:10:25,590 --> 00:10:30,490
+زائد C2 في الـ E و الـ 0 كذلك في الـ Main اللي هي
+
+106
+00:10:30,490 --> 00:10:37,310
+بواحد الآن بدنا نيجي للمين للـ Y' عند الـ Main عند
+
+107
+00:10:37,310 --> 00:10:42,610
+الـ 0 كذلك يبقى بده أشيل كل X و أحط مكانها Zero
+
+108
+00:10:42,610 --> 00:10:50,160
+اللي هي تساوي واحد اللي هي تساوي C1زائد اتنين C2
+
+109
+00:10:50,160 --> 00:10:55,420
+إذا صار عندنا معادلتين على الشكل التالي اللي هو
+
+110
+00:10:55,420 --> 00:11:01,560
+سالب أربعة يساوي سالب C1 سالب C2
+
+111
+00:11:03,420 --> 00:11:06,940
+يبقى سالب C2 ضربنا المعادلة الأولى في سالب
+
+112
+00:11:06,940 --> 00:11:14,000
+المعادلة التانية كما هي C1 زائد اتنين C2 بنروح
+
+113
+00:11:14,000 --> 00:11:20,980
+نجمع الاتنين هدول مع السلامة وهدول بيضل منهم بس C2
+
+114
+00:11:20,980 --> 00:11:27,930
+فقط وهدى بيضل منها قداش سالب تلاتةيبقى لما تبقى C2
+
+115
+00:11:27,930 --> 00:11:32,790
+بسالب تلاتة ارجع عوض في اي من المعادلتين هذا
+
+116
+00:11:32,790 --> 00:11:38,550
+بيعطينا انه اربعة تساوي C1 و C2 اللي هي بسالب
+
+117
+00:11:38,550 --> 00:11:44,490
+تلاتة هذا بدي يعطيك انه C1 تساوي قداش سبعة يبقى
+
+118
+00:11:44,490 --> 00:11:50,230
+بناء عليه بقوله solution of
+
+119
+00:12:14,390 --> 00:12:28,120
+الحل اللي قدامنا على اللوحةأي تساؤل؟ ايش
+
+120
+00:12:28,120 --> 00:12:34,470
+السؤال؟ مافهمتاش ان ال infinite و ال specificبتذكر
+
+121
+00:12:34,470 --> 00:12:41,630
+انه احنا في ال chapter الماضى بجينا نقول انه بجينا
+
+122
+00:12:41,630 --> 00:12:44,030
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+123
+00:12:44,030 --> 00:12:44,170
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+124
+00:12:44,170 --> 00:12:45,670
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+125
+00:12:45,670 --> 00:12:46,870
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+126
+00:12:46,870 --> 00:12:50,370
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+127
+00:12:50,370 --> 00:12:52,130
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا
+
+128
+00:12:52,130 --> 00:12:56,370
+نقول بيجينا نقول بيجينا نقول بيجينا نقول بيجينا ن
+
+129
+00:12:56,550 --> 00:13:01,830
+ما لنهائي من الـ vectors إذا إحنا هنا في شكل مشابه
+
+130
+00:13:01,830 --> 00:13:06,190
+إحنا عندنا معادلة المعادلة لها عدد لنهائي من
+
+131
+00:13:06,190 --> 00:13:11,370
+الحلول بدليل إن الـC1 وC2 حط القيم اللي بدك إياها
+
+132
+00:13:11,370 --> 00:13:15,870
+تمام؟ كويس لكن عدد لنهائي من الحلول اللي هم bases
+
+133
+00:13:15,870 --> 00:13:21,690
+ال bases يتكون من جداش من two elements ال vector
+
+134
+00:13:21,690 --> 00:13:27,830
+الأساسي اللي هو ال FN هذاwith no dimension مرة
+
+135
+00:13:27,830 --> 00:13:31,750
+علينا اخدنا منه functions جاب ليك اذا كنت مليان جد
+
+136
+00:13:31,750 --> 00:13:35,390
+ما بدك ايش ما يطلع على بالك موجود فيه يبجى هذا
+
+137
+00:13:35,390 --> 00:13:40,210
+infinite dimension طلعت منه دالتين واحدة EO6
+
+138
+00:13:40,210 --> 00:13:45,080
+والتانية EO2Xالاتنين اللي جيتهم linearly
+
+139
+00:13:45,080 --> 00:13:52,060
+independent اتنين يعني كونولي ال basis لل solution
+
+140
+00:13:52,060 --> 00:13:57,260
+تبع المعادلة اللي عندنا يعني في solutions اخرين شو
+
+141
+00:13:57,260 --> 00:14:03,360
+شكلهم الشكل العام لهم هاهم تمام كم واحد هدول؟ما
+
+142
+00:14:03,360 --> 00:14:09,040
+لنهاية، حط C1 و C2 زي ما بدك، تمام؟ كله بيعطيني
+
+143
+00:14:09,040 --> 00:14:13,460
+إيه؟ بيعطيني شكل للحل، يعني أي حل كتبته على صيغة
+
+144
+00:14:13,460 --> 00:14:17,160
+linear combination من مين؟ من الاتنين هدول، يبقى
+
+145
+00:14:17,160 --> 00:14:22,680
+ال business يتكون فقط تبع ال solutions من عنصرين،
+
+146
+00:14:22,680 --> 00:14:27,200
+يبقى ال dimension له يساويتنين وال F ان ال
+
+147
+00:14:27,200 --> 00:14:31,620
+dimension له جداش infinity بطلع ال subspace ال
+
+148
+00:14:31,620 --> 00:14:36,260
+dimension له تنين من ال space اللي ال dimension له
+
+149
+00:14:36,260 --> 00:14:43,880
+مالاني هاي واضحة؟ حد بتسأل تاني؟ فبنتقل للنقطة
+
+150
+00:14:43,880 --> 00:14:45,500
+الأخيرة من هذا ال section
+
+151
+00:15:11,410 --> 00:15:25,010
+theorem نظرية لت ال F1 وال F2 هو لغاية ال FN بي in
+
+152
+00:15:25,010 --> 00:15:35,550
+solutions solutions of the order
+
+153
+00:15:35,550 --> 00:15:46,650
+differential equationDifferential equation اللي هي
+
+154
+00:15:46,650 --> 00:15:49,410
+على الشكل التالي A0
+
+155
+00:16:01,000 --> 00:16:08,520
+زائد ونظل ماشين لغاية ما نصل الى ن minus one as a
+
+156
+00:16:08,520 --> 00:16:15,060
+function of x prime زائد a n of x في ال y بده
+
+157
+00:16:15,060 --> 00:16:16,200
+يساوي zero
+
+158
+00:16:20,480 --> 00:16:31,040
+interval I على فترة ما where حيث ال AI as a
+
+159
+00:16:31,040 --> 00:16:40,600
+function of X are continuous functions
+
+160
+00:16:40,600 --> 00:16:54,470
+يبقى دوال متواصلة for all Iلجميع قيم I and ضروري
+
+161
+00:16:54,470 --> 00:17:01,450
+ال A node of X لا يساوي main لا يساوي zero then
+
+162
+00:17:01,450 --> 00:17:16,190
+ومن ثم F F ال F one وال F two وال F Nبعدين انا
+
+163
+00:17:16,190 --> 00:17:23,030
+ماشي لغاية ال FN are linearly dependent than
+
+164
+00:17:23,030 --> 00:17:32,770
+الرنسكين as a function of X بده يساوي 0 for all X
+
+165
+00:17:32,770 --> 00:17:43,890
+اللي موجودة في ال interval I and if the functions
+
+166
+00:17:45,220 --> 00:17:56,480
+إذا ال functions f1 و f2 و fn are linearly
+
+167
+00:17:56,480 --> 00:18:05,100
+independent then الرنسكان as a function of x لا
+
+168
+00:18:05,100 --> 00:18:12,960
+يساوي 0 for all x اللي موجودة وين في ال interval I
+
+169
+00:19:33,960 --> 00:19:38,460
+أظن واضح أن هذه النظرية لم تأتي بجديد مكررة من
+
+170
+00:19:38,460 --> 00:19:43,380
+الشبتر الماضي أجت وين أجت فيه الشبتر اللي عندنا
+
+171
+00:19:43,380 --> 00:19:48,460
+يبقى دوال من F1 لغاية Fn اللي هم عبارة عن حلول
+
+172
+00:19:48,460 --> 00:19:52,460
+للمعادلة التفاضلية من الرتبة بس كنا هناك بنقول على
+
+173
+00:19:52,460 --> 00:19:55,840
+vectors هنا بدنا نقولهم على مين على حلول يعني
+
+174
+00:19:55,840 --> 00:20:00,640
+قعدنا النظرية إعادة فقطبحيث تناسب المعادلات
+
+175
+00:20:00,640 --> 00:20:05,440
+التفاضلية يبقى لو كانوا هدول هم عدد من الحلول
+
+176
+00:20:05,440 --> 00:20:11,040
+يساوي رتبة المعادلة التفاضلية اللي عندنا هذه حيث
+
+177
+00:20:11,040 --> 00:20:15,640
+ال A1 وال A2 وكل هذه عبارة عن دوال متصلة في
+
+178
+00:20:15,640 --> 00:20:21,740
+المتغير X لجميع قيم I ولحد الأول المعامل هو A node
+
+179
+00:20:21,740 --> 00:20:25,780
+of X شرطنا لا يساوي Zero لأن لو ساوى Zero بتنزل
+
+180
+00:20:25,780 --> 00:20:29,890
+الرتبة من الرتبة N إلى الرتبةin minus one و هذا
+
+181
+00:20:29,890 --> 00:20:34,650
+الكلام مابدناهش هي يبقى في عندنا نقطتين هذول لو
+
+182
+00:20:34,650 --> 00:20:39,050
+كانوا linearly dependent يبقى الرونسكين تبعهم بده
+
+183
+00:20:39,050 --> 00:20:45,110
+يساوي zero لكن العكس ليس صحيحا تمام طبعا و
+
+184
+00:20:45,110 --> 00:20:50,230
+أثبتناها قبل هيك انه لو كان الرونسكين يساوي zero
+
+185
+00:20:50,230 --> 00:20:55,370
+ليس بالضرورة ان يكونوا هذول linearly dependent لكن
+
+186
+00:20:55,370 --> 00:20:57,090
+لو كانوا linearly dependent
+
+187
+00:21:00,030 --> 00:21:03,970
+النقطة الثانية لو كان هؤلاء الليارلي independent
+
+188
+00:21:03,970 --> 00:21:10,790
+يبقى ال رونسكين تبعهم لا يساوي 0 لكل ال X الموجودة
+
+189
+00:21:10,790 --> 00:21:14,090
+في القاعدة ما علينا هذا X أساعد على ال section
+
+190
+00:21:14,090 --> 00:21:18,910
+والبرهان مش لازمةطيب ننتقل الأن إلى ال section
+
+191
+00:21:18,910 --> 00:21:27,530
+الجديد اللي هو polynomial operators يبقى المؤثرات
+
+192
+00:21:27,530 --> 00:21:31,910
+اللي على شكل كثيرات الحدود أو ال linear operators
+
+193
+00:21:31,910 --> 00:21:37,210
+المؤثرات الخطوية في بعض الناس بكتب بدل polynomial
+
+194
+00:21:37,210 --> 00:21:43,640
+بكتبوا linearoperators يبقى linear والله
+
+195
+00:21:43,640 --> 00:21:50,120
+polynomial مقصود ابو هو هو بنحاول نعرف ما هو ال
+
+196
+00:21:50,120 --> 00:21:57,180
+linear operator أو ال polynomial
+
+197
+00:21:57,180 --> 00:22:01,800
+operator اللي عندنا ونرطب المعادلات التفاضلية
+
+198
+00:22:01,800 --> 00:22:06,680
+فبعدين بقول and and order
+
+199
+00:22:16,310 --> 00:22:22,650
+معادلة تفاضلية الخطية with constant coefficients
+
+200
+00:22:22,650 --> 00:22:32,570
+with constant coefficients بمعاملات
+
+201
+00:22:32,570 --> 00:22:42,330
+ثابتة has the formas the fourth نفس الشكل اللي
+
+202
+00:22:42,330 --> 00:22:46,670
+عناه بناته بس بدنا نخلق ان بطن نخليهم دوال في X و
+
+203
+00:22:46,670 --> 00:22:52,330
+ان انا بده اخليهم مين ثوابت يبقى a node y to the
+
+204
+00:22:52,330 --> 00:22:58,030
+derivative n a one y to the derivative n minus ال
+
+205
+00:22:58,030 --> 00:23:05,230
+one ونظل ماشيين لغاية a n minus ال oneY to the
+
+206
+00:23:05,230 --> 00:23:12,230
+derivative of prime زائد ANY بده يساوي capital F
+
+207
+00:23:12,230 --> 00:23:17,790
+of X وهذه ساميليها المعادلة واحد يبقى الآن في هذا
+
+208
+00:23:17,790 --> 00:23:22,740
+ال section المعاملات كلها مثوبة وما لاش علاقةفي
+
+209
+00:23:22,740 --> 00:23:29,640
+المعادلة بمعاملات متغيرة لسه هذه الكلام تاني سنصل
+
+210
+00:23:29,640 --> 00:23:34,800
+إليه قبل نهاية هذا الفيديو ان شاء الله يمكن أن أخد
+
+211
+00:23:34,800 --> 00:23:41,220
+المعاملة ثوابت في الأول و بعدين نكمل where حيث ال
+
+212
+00:23:41,220 --> 00:23:52,720
+AI are constants ثوابت constants andالـ A Note
+
+213
+00:23:52,720 --> 00:23:59,040
+كمان لا يسوى Zero لكي تبقى معدلة من الرتبة النونية
+
+214
+00:23:59,040 --> 00:24:09,970
+Fcapital D تساوي المشتقة بالنسبة ال X وD² تعني
+
+215
+00:24:09,970 --> 00:24:16,730
+المشتقة الثانية بالنسبة ال X وضلنا ماشيين لغاية ما
+
+216
+00:24:16,730 --> 00:24:24,110
+وصلنا الى DN هي المشتقة النونية بالنسبة ال X
+
+217
+00:24:26,270 --> 00:24:36,470
+equation one is written as is written as بروح
+
+218
+00:24:36,470 --> 00:24:46,610
+بكتبها على من على الشكل التالي بكتبها a not d n
+
+219
+00:24:46,610 --> 00:25:08,980
+زائد a one d n minus ال one زائد زائددي او
+
+220
+00:25:08,980 --> 00:25:10,240
+دي وخلصنا
+
+221
+00:25:12,500 --> 00:25:20,800
+اين كل هذا الكلام مضروبا في من؟ في ال Y بده يساوي
+
+222
+00:25:20,800 --> 00:25:26,920
+capital F of X بالشكل اللي عندنا هذا او اختصارا
+
+223
+00:25:26,920 --> 00:25:34,840
+بقدر اقول L of Y بدها تساوي من؟ بدها تساوي capital
+
+224
+00:25:34,840 --> 00:25:37,280
+F of X where
+
+225
+00:25:43,820 --> 00:25:50,640
+حيث where اللي
+
+226
+00:25:50,640 --> 00:26:02,100
+هو ال L بده يساوي a0dn a1dn minus ال one زائد ونظل
+
+227
+00:26:02,100 --> 00:26:09,660
+ماشيين لغاية اللي هو a n minus ال one دي زائد ال a
+
+228
+00:26:09,660 --> 00:26:22,270
+nis called هذا بنسميه linear أو
+
+229
+00:26:22,270 --> 00:26:29,670
+بدل ال linear بسميها polynomial polynomial
+
+230
+00:26:29,670 --> 00:26:34,990
+differential operator
+
+231
+00:26:34,990 --> 00:26:40,030
+differential linear operator with
+
+232
+00:26:43,830 --> 00:26:52,510
+constant coefficients بمعاملات
+
+233
+00:26:52,510 --> 00:27:01,250
+ثابتة homogenous
+
+234
+00:27:01,250 --> 00:27:08,110
+linear differential equation
+
+235
+00:27:12,470 --> 00:27:20,130
+او اكويشن وان از a
+
+236
+00:27:20,130 --> 00:27:25,550
+نود y to the derivative n a one y to the
+
+237
+00:27:25,550 --> 00:27:34,330
+derivative n minus one زائد a n minus one y prime
+
+238
+00:27:34,330 --> 00:27:44,010
+زائد a n y is equal to zeroوهذه اسمها اللي من
+
+239
+00:27:44,010 --> 00:27:47,030
+المعادلة رقم اتنين
+
+240
+00:28:26,900 --> 00:28:31,680
+يبقى احنا بننجي ل section خمسة اتنين ونبدأ الان
+
+241
+00:28:31,680 --> 00:28:36,080
+نشتغل شغل معادلات تفاضلية فعلية يعني ال section
+
+242
+00:28:36,080 --> 00:28:41,920
+اللي فات كان مجرد شوية تعريفات او رابط لمين لل
+
+243
+00:28:41,920 --> 00:28:45,340
+chapter اللي فات بمين بهذا ال chapter لكن من هنا
+
+244
+00:28:45,340 --> 00:28:49,600
+بدنا نبدأ ابتداء من هذا ال section ونبدأ نشتغل شغل
+
+245
+00:28:49,600 --> 00:28:54,570
+معادلات تفاضليةيقول ان الانصار ضالين ال equation
+
+246
+00:28:54,570 --> 00:28:59,030
+differential بمعاملات ثابتة هي معادلة على الشكل
+
+247
+00:28:59,030 --> 00:29:02,810
+اللى عندنا اللى هو شكل واحد ال a node و ال a one و
+
+248
+00:29:02,810 --> 00:29:07,530
+لغاية ال a n minus one و ال a n كلهم ثوابت الدالة
+
+249
+00:29:07,530 --> 00:29:12,010
+ال f of x يبقى دالة في x مالهاش علاقة في y اللى
+
+250
+00:29:12,010 --> 00:29:16,030
+بعد اليساوي اللى جابلى اليساوي كلها مشتقات بالنسبة
+
+251
+00:29:16,030 --> 00:29:20,410
+ل y ماعدى آخر تين والدالة الأخيرة كلها دالة في x
+
+252
+00:29:20,410 --> 00:29:24,840
+مالهاش علاقة بyحيث ال AI are constant وال A node
+
+253
+00:29:24,840 --> 00:29:27,800
+لا يساوي zero وجدنا ليش ال A node لا يساوي zero
+
+254
+00:29:27,800 --> 00:29:33,080
+حتى تبقى المعادلة منها رتبة أنونية بقول لو حطيت
+
+255
+00:29:33,080 --> 00:29:37,910
+capital D هو عبارة عن المشتقة الأولى بالنسبة ل Xدى
+
+256
+00:29:37,910 --> 00:29:41,330
+تربيع المشتقة التانية دى تكعيب المشتقة التالتة
+
+257
+00:29:41,330 --> 00:29:46,010
+وهكذا لغاية ما وصلت لدى انهى المشتقة النونية
+
+258
+00:29:46,010 --> 00:29:50,490
+بالنسبة ل X يبقى المعادلة رقم واحد بقدر اكتبها على
+
+259
+00:29:50,490 --> 00:29:56,600
+الشكل التالي a node كما هىوهذه المشتركة بدي اكتبها
+
+260
+00:29:56,600 --> 00:30:02,880
+dny بس و يوري حطيه تبارك كأنه خدت عامل مشترك من
+
+261
+00:30:02,880 --> 00:30:10,900
+الكل اللي بعدها a1dn-1y و اللي بعدها و اللي بعدها
+
+262
+00:30:10,900 --> 00:30:12,860
+لغاية هذه a1dn-1y
+
+263
+00:30:17,610 --> 00:30:22,290
+يبقى Y كإن أخدت عامل مشترك من مين من الكل بده يسوي
+
+264
+00:30:22,290 --> 00:30:28,510
+capital F of X هذه بالشكل الطويل ممكن أختصرها ب L
+
+265
+00:30:28,510 --> 00:30:34,930
+of Y بده يسوي من F of X مين هو ال L هو العنوان
+
+266
+00:30:34,930 --> 00:30:39,840
+اللي احنا رفعينه هناللـ polynomial operator المؤثر
+
+267
+00:30:39,840 --> 00:30:46,300
+على الخط اللي على شكل كثيرة حدود يبقى ال L of Y
+
+268
+00:30:46,300 --> 00:30:52,740
+معناته كل اللي بين قوسين هذا بدي تديله الرمز L هاي
+
+269
+00:30:52,740 --> 00:30:59,000
+L كل المقدار بين مين؟ بين القوسين يبقى هذا مؤثر
+
+270
+00:30:59,000 --> 00:31:03,670
+تفاضل يبدأ من المشتقة القنونيةلغاية المشتقة الأولى
+
+271
+00:31:03,670 --> 00:31:09,830
+لغاية الدالة بدون مين بدون اشتقاق كويس يبقى هذا is
+
+272
+00:31:09,830 --> 00:31:15,070
+called a linear polynomial او بسميه linear
+
+273
+00:31:15,070 --> 00:31:19,530
+differential operator يبقى linear والله polynomial
+
+274
+00:31:19,530 --> 00:31:24,710
+لاتنين المقصود فيهم اتنين نفس الشيء لمين للمعادلة
+
+275
+00:31:24,710 --> 00:31:30,480
+التفاضلية بمعاملات ثابتةالان انا المعادلة رقم واحد
+
+276
+00:31:30,480 --> 00:31:34,540
+هذي بسميها ال non homogeneous تمام ال non
+
+277
+00:31:34,540 --> 00:31:39,300
+homogeneous بيقول اتريحي شوية سنرجعلكي في المستقبل
+
+278
+00:31:39,300 --> 00:31:43,400
+خلال هذا الشبطة يبقى انا بروح اخد فقط مين
+
+279
+00:31:52,010 --> 00:31:54,790
+المعاملة الثوابت هي المعاملة الثوابت وليست دوال
+
+280
+00:31:54,790 --> 00:31:55,390
+فكس
+
+281
+00:32:00,570 --> 00:32:04,530
+إتنين أخدت ال homogenous و سبت ال non homogenous
+
+282
+00:32:04,530 --> 00:32:08,570
+ال non homogenous لها شغل اخر هناخده في اخر هذا
+
+283
+00:32:08,570 --> 00:32:13,130
+chapter او اخر two sections من هذا ال chapter يبقى
+
+284
+00:32:13,130 --> 00:32:16,170
+احنا بدنا نبدأ نشتغل عالميا على ال homogenous
+
+285
+00:32:16,170 --> 00:32:20,130
+روحنا أخدنا ال homogenous differential equation
+
+286
+00:32:20,130 --> 00:32:25,710
+فكانت على الشكل اللي عندنا هذاالان بدروح ادور على
+
+287
+00:32:25,710 --> 00:32:32,950
+شكل الحل العام للمعادلة رقم 2 بدروح افترض من عندي
+
+288
+00:32:32,950 --> 00:32:38,310
+حل واشوف هذا الحل بيوصلنا لوين يبقى بداجي اقوله
+
+289
+00:32:38,310 --> 00:32:51,210
+هنا letY تساوي E وصة RX بيه solution of the
+
+290
+00:32:51,210 --> 00:32:56,370
+differential equation 2
+
+291
+00:33:00,720 --> 00:33:05,380
+بارامتر رقم اتنين تلاتة اربعة ناقص خمسة قد ما يكون
+
+292
+00:33:05,380 --> 00:33:12,280
+يبقى ال R ال number مين ما يكون يكون تمام ال X هي
+
+293
+00:33:12,280 --> 00:33:18,040
+ال متغير اللي عندنا يبقى لان بروح اجيب المشتقة
+
+294
+00:33:18,040 --> 00:33:22,180
+الأولى و التانية و التالتة و الرابعة و الخمسة و
+
+295
+00:33:22,180 --> 00:33:29,520
+النونية الى اخره يبقى باجي بقوله هنا thenبدي أخد
+
+296
+00:33:29,520 --> 00:33:35,760
+Y' يبقى الـ exponential كما هي مضروبة في مين؟ في
+
+297
+00:33:35,760 --> 00:33:44,760
+مشتقة الأس بدي أخد المشتقة الثانية YW' يبقى YW'
+
+298
+00:33:45,320 --> 00:33:50,760
+بدي أساوي R مالهاش دعوة وهذه مشتقتها بدي أجيب كمان
+
+299
+00:33:50,760 --> 00:33:58,130
+R بصير R تربية E أس RXولو دلت حوصل لمين للمشتقة
+
+300
+00:33:58,130 --> 00:34:05,190
+التالتة يبقى R تكعيب E أُس RX ولو دلت مستمر حوصل
+
+301
+00:34:05,190 --> 00:34:11,850
+للمشتقة النونية يبقى R to the power in E أُس RX
+
+302
+00:34:14,120 --> 00:34:18,580
+بتاخد المعلومات اللي عندي هذه وروح اعوض في مين في
+
+303
+00:34:18,580 --> 00:34:25,400
+المعادلة رقم اتنين يبقى باجي بقول الصعب اسم تت يوت
+
+304
+00:34:25,400 --> 00:34:33,340
+and equation اتنين we get نحصل علامات ال a node
+
+305
+00:34:33,340 --> 00:34:43,570
+كما هيوالـ Y to the derivative N هي RN E أُس RX
+
+306
+00:34:44,690 --> 00:34:55,790
+اللي بعدها زائد A1 R أس N minus 1 E أس RX زائد
+
+307
+00:34:55,790 --> 00:35:03,110
+ونظل ماشيين لغاية ما نوصل لحد قبل الأخير A N minus
+
+308
+00:35:03,110 --> 00:35:14,730
+1 R E أس RX اليمينالمشتقلولة زائد AN في E أُس RX
+
+309
+00:35:14,730 --> 00:35:21,410
+كما هي بده يساوي Zeroلا يمكن أن تساوي صفر في يوم
+
+310
+00:35:21,410 --> 00:35:26,090
+من الأيام إذا الأبانات بنجي للمعادلة اللي عندنا
+
+311
+00:35:26,090 --> 00:35:32,450
+هذه كون ال E أُس RX لا تساوي Zero إذا بقدر أقسم
+
+312
+00:35:32,450 --> 00:35:37,050
+طرفين المعادلة عليها إذا لو قسمنا طرفين المعادلة
+
+313
+00:35:37,050 --> 00:35:41,810
+على E أُس RX تصبح المعادلة على الشكل التالي
+
+314
+00:36:01,520 --> 00:36:07,860
+نعمل محاسبة مع نفسنا احنا المعادلة رقم اتنين عنا
+
+315
+00:36:07,860 --> 00:36:15,180
+هذه معادلة تفاضليةمن الرتبة النونية اللي توصلنا
+
+316
+00:36:15,180 --> 00:36:19,580
+عليها هذه. هذه معادلة تفاضلية؟ لأ، هذه معادلة
+
+317
+00:36:19,580 --> 00:36:25,180
+عادية من أي درجة؟ من الدرجة النونية. إذا هذه
+
+318
+00:36:25,180 --> 00:36:31,390
+المعادلة لها كام حل؟إن من الحلول سواء كانوا مكرر
+
+319
+00:36:31,390 --> 00:36:36,010
+بعضهم أو مش مكرر أو كلهم مكررات بهمنيل إذا هذه
+
+320
+00:36:36,010 --> 00:36:41,910
+معادلة من الدرجة النونية يبقى لها إن من الحلول
+
+321
+00:36:41,910 --> 00:36:47,570
+تمام هذه المعادلة بسميها المعادلة المساعدة ال
+
+322
+00:36:47,570 --> 00:36:51,220
+accelerator equationأول اكتبها لك اول
+
+323
+00:36:51,220 --> 00:36:55,940
+characteristic equation المعادلة المميزة للمعادلة
+
+324
+00:36:55,940 --> 00:37:01,500
+الرقم اتنين والان بدنا نيجي نتكلم عن حلول هذه
+
+325
+00:37:01,500 --> 00:37:08,740
+المعادلة يبقى باجي بقوله this equation this
+
+326
+00:37:08,740 --> 00:37:18,120
+equation هذه المعادلة is called بنسميها
+
+327
+00:37:18,120 --> 00:37:18,940
+Z
+
+328
+00:37:43,620 --> 00:37:51,700
+المعادلة المميزة للمعادلة اللي عندناهذه بنات هتلعب
+
+329
+00:37:51,700 --> 00:37:56,420
+عمود في قري في شغلنا خلال هذا ال section و ال
+
+330
+00:37:56,420 --> 00:38:03,360
+sections القادمة كذلك طب المعادلة هذه معادلة من
+
+331
+00:38:03,360 --> 00:38:09,680
+الدرجة النونية إذا لها إيه من الحلول؟ الحلول هذه
+
+332
+00:38:09,680 --> 00:38:18,140
+يمكن يطلع كلهم ريال كلهم أغار قيم حقيقيةوالكلهم
+
+333
+00:38:18,140 --> 00:38:22,400
+يكونوا ولا واحد زي التاني يبقى الاحتمال الأول
+
+334
+00:38:22,400 --> 00:38:27,480
+يطلعوا كلهم .. هكتبوا كلهم
+
+335
+00:38:27,480 --> 00:38:32,160
+يبقى انا بقول الاحتمال الأول ان الحلوين يكونوا are
+
+336
+00:38:32,160 --> 00:38:36,700
+real and destined ولا واحد زي التاني الاحتمال
+
+337
+00:38:36,700 --> 00:38:44,060
+الثاني انه يطلع حل واحد مكرر ان من المراتيبقى
+
+338
+00:38:44,060 --> 00:38:49,980
+repeated roots جذور مكررة لإحتمالية انهم يطلعوا
+
+339
+00:38:49,980 --> 00:38:55,180
+complex و complex بيطلعوا complex conjugate ان طلع
+
+340
+00:38:55,180 --> 00:39:00,580
+حل هيكون واحد مرافق له هيك طبيعة من الحلول تبع ال
+
+341
+00:39:00,580 --> 00:39:05,600
+complex طبعا لما اقولك ال elementيساوي a زائد ib
+
+342
+00:39:05,600 --> 00:39:11,540
+الكونججت تبع a ناقص ib طبعا انا اتعرض له ماعرفش
+
+343
+00:39:11,540 --> 00:39:14,600
+اليوم والله مش اليوم الله عليه ممكن نلحق اليوم
+
+344
+00:39:14,600 --> 00:39:22,070
+تمام هاي ثلاثة حلول ويمكنان يكون الحل مزيد ما بين
+
+345
+00:39:22,070 --> 00:39:26,350
+ال complex وما بين الريال، كيف يعني؟ لو قلنا ان
+
+346
+00:39:26,350 --> 00:39:31,570
+عشرة يمكن يطلع عندي عشرة حلول، العشرة حلول يمكن
+
+347
+00:39:31,570 --> 00:39:36,710
+أربعة ريال وستة complexأو اتنين كومبليكس وتمانية
+
+348
+00:39:36,710 --> 00:39:42,190
+ريال وهكذا يبقى بدعم الريال بالريال وبدعم
+
+349
+00:39:42,190 --> 00:39:46,610
+الكومبليكس بالكومبليكس كما سنرى من خلال هذه
+
+350
+00:39:46,610 --> 00:39:51,770
+الأمثلة التي سنعطيها بعد قليليبقى أنا بالذات
+
+351
+00:39:51,770 --> 00:39:55,810
+بالأقل احتمالاتي الثلاثة وبعد هيك بدنا نمسك
+
+352
+00:39:55,810 --> 00:39:59,910
+الاحتمال الأول بنكمل بال section بصير الاحتمال
+
+353
+00:39:59,910 --> 00:40:05,010
+الثاني هو section جديد لأنه له شغله لوحده وهكذا
+
+354
+00:40:05,010 --> 00:40:15,160
+اذا هانيجي باجي بقوله equationEquation هذي نسميها
+
+355
+00:40:15,160 --> 00:40:20,360
+بنات الـ star لجديد اللي عندنا يبقى equation star
+
+356
+00:40:20,360 --> 00:40:29,540
+has n roots كونها من الدرجة النونية إذا إلها n من
+
+357
+00:40:29,540 --> 00:40:39,660
+الجذور and these roots و هذه الجذور are found
+
+358
+00:40:43,720 --> 00:40:57,660
+as follow يبقى بنوجودها كالتالي تمام نملا
+
+359
+00:40:57,660 --> 00:41:04,340
+واحد the roots الجذور
+
+360
+00:41:04,340 --> 00:41:10,900
+are real and different
+
+361
+00:41:13,720 --> 00:41:23,340
+يبقى حقيقية ومختلفة that is ر واحد لا يساوي ر
+
+362
+00:41:23,340 --> 00:41:32,620
+اتنين لا يساوي لا يساوي ر ان الاحتمال
+
+363
+00:41:32,620 --> 00:41:42,340
+الثاني the roots are real and repeatedحقيقية
+
+364
+00:41:42,340 --> 00:42:00,280
+ومكررة رمز
+
+365
+00:42:00,280 --> 00:42:09,380
+ر مثلا لإحتمال الثالث the roads are complex
+
+366
+00:42:10,270 --> 00:42:16,050
+conjugate تخيليه
+
+367
+00:42:16,050 --> 00:42:30,630
+مترافقة that is if R1 بدي تساوي A زائد IB then
+
+368
+00:42:33,300 --> 00:42:45,860
+R2 بيبقى A ناقص IB and so on وهكذا والـ I هو الجذر
+
+369
+00:42:45,860 --> 00:42:48,600
+التربيه لمين لسالب واحد
+
+370
+00:43:10,450 --> 00:43:18,010
+in this section يبقى in this section يبقى in this
+
+371
+00:43:18,010 --> 00:43:20,530
+section يبقى in this section يبقى in this section
+
+372
+00:43:20,530 --> 00:43:21,870
+يبقى in this section يبقى in this section يبقى in
+
+373
+00:43:21,870 --> 00:43:21,910
+this section يبقى in this section يبقى in this
+
+374
+00:43:21,910 --> 00:43:22,390
+section يبقى in this section يبقى in this section
+
+375
+00:43:22,390 --> 00:43:25,830
+يبقى in this section يبقى in this section يبقى in
+
+376
+00:43:25,830 --> 00:43:27,790
+this section يبقى in this section يبقى in this
+
+377
+00:43:27,790 --> 00:43:29,070
+section يبقى in this section يبقى in this section
+
+378
+00:43:29,070 --> 00:43:36,650
+يبقى in this section يبقى in this section يبقى
+
+379
+00:43:36,650 --> 00:43:38,730
+in this section يبقى in this section يبقى in this
+
+380
+00:43:38,730 --> 00:43:38,730
+section يبقى in this section يبقى in this section
+
+381
+00:43:38,730 --> 00:43:38,730
+يبقى in this section يبقى in this section يبقى in
+
+382
+00:43:38,730 --> 00:43:38,730
+this section يبقى in this section يبقى in this
+
+383
+00:43:38,730 --> 00:43:44,160
+section يبقى in this section يبقىequation اتنين if
+
+384
+00:43:44,160 --> 00:43:56,420
+the roots اذا كانت الجذور of equation star are
+
+385
+00:43:56,420 --> 00:44:02,240
+real and different
+
+386
+00:44:12,770 --> 00:44:22,290
+يبقى باجي بقول let R1 وR2 وRN بيه
+
+387
+00:44:22,290 --> 00:44:28,830
+the destined solutions
+
+388
+00:44:28,830 --> 00:44:33,130
+of
+
+389
+00:44:33,130 --> 00:44:37,090
+the differential
+
+390
+00:44:41,500 --> 00:44:48,420
+of the equation للمعادلة
+
+391
+00:44:48,420 --> 00:44:59,560
+of the equation ل A0 R1 RN زائد A1 RN minus 1 زائد
+
+392
+00:44:59,560 --> 00:45:17,590
+AN minus 1 R زائد AN تساوي 0then the solutions of
+
+393
+00:45:17,590 --> 00:45:25,270
+the
+
+394
+00:45:25,270 --> 00:45:36,340
+differential equation اتنين ا why oneيساوي E أس R
+
+395
+00:45:36,340 --> 00:45:44,920
+one X و Y two يساوي E أس R two X ونظل ماشين لغاية
+
+396
+00:45:44,920 --> 00:45:57,580
+Y in يساوي E أس R in X these solutions are
+
+397
+00:45:57,580 --> 00:46:10,500
+linearly independentيبقى هذه from section تلاتة
+
+398
+00:46:10,500 --> 00:46:18,080
+اربعة the general solution
+
+399
+00:46:18,080 --> 00:46:22,380
+of
+
+400
+00:46:22,380 --> 00:46:32,400
+the differential equation to is
+
+401
+00:46:36,220 --> 00:46:46,340
+يبقى Y ساوي C1 E أُس R1 X زائد C2 E أُس R2 X زائد
+
+402
+00:46:46,340 --> 00:46:52,720
+CN E أُس RN X بالشكل اللي عنها
+
+403
+00:47:25,110 --> 00:47:30,210
+بنرجع لكلام اللي احنا كتبناه هذا مرة ثانية طبعا
+
+404
+00:47:30,210 --> 00:47:33,630
+احنا بدنا بالمعادلة التفاضلية ذات المعاملات
+
+405
+00:47:33,630 --> 00:47:39,330
+الثابتة فرضنا ان Y تسوى E أسار X هو عبارة عن حل
+
+406
+00:47:39,330 --> 00:47:43,910
+لهذه المعادلة جيبنا المشتقة الأولى للحل المشتقة
+
+407
+00:47:43,910 --> 00:47:47,410
+التانية التالتة الرابعة النونية جينا عوضنا في
+
+408
+00:47:47,410 --> 00:47:51,730
+المعادلة رقم اتنين لما عوضنا صارت المعادلة على
+
+409
+00:47:51,730 --> 00:47:56,880
+الشكل اللي عندنا هذاجسمنا كله على USRX وصلنا
+
+410
+00:47:56,880 --> 00:48:00,880
+للمعادلة هذه سمينا هذه المعادلة المميزة او
+
+411
+00:48:00,880 --> 00:48:05,220
+المعادلة المساعدة للمعادلة رقم 2 يعني احنا طلعنا
+
+412
+00:48:05,220 --> 00:48:09,900
+من معادلة تفاضلية من الرتبة النونية إلى معادلة
+
+413
+00:48:09,900 --> 00:48:16,360
+عادية من الدرجة الرقم N يبقى هذه المعادلة لها N من
+
+414
+00:48:16,360 --> 00:48:24,060
+الحلول هذه الحلولممكن تكون حقيقية و مختلفة ولا
+
+415
+00:48:24,060 --> 00:48:30,820
+واحد زي التاني ممكن تكون حقيقية و مكررة كل الحلول
+
+416
+00:48:30,820 --> 00:48:35,280
+اللي عددهم ان كل واحد زي التاني تمام ماعندي مشكلة
+
+417
+00:48:35,280 --> 00:48:39,900
+بدي أسميه مثلا R الحالة التالتةكل اتنين بيكونوا
+
+418
+00:48:39,900 --> 00:48:46,080
+complex conjugate مع بعض فبيكون الحل R1A زيد IB
+
+419
+00:48:46,080 --> 00:48:52,240
+والتاني R2A ناقص IB وهكذا وال I هو الجدر التربيه
+
+420
+00:48:52,240 --> 00:48:57,080
+لمين لسان واحدفي هذا ال section بدنا ناخد الحالة
+
+421
+00:48:57,080 --> 00:49:01,600
+الأولى فقط هذه الحالة هيقبلها section لحالها وهذه
+
+422
+00:49:01,600 --> 00:49:05,900
+section لحالها تماما يبقى لو أخدنا الحالة الأولى
+
+423
+00:49:05,900 --> 00:49:11,780
+ان الجذور كانت حقيقية ومختلفة ففرط ان الجذور هي من
+
+424
+00:49:11,780 --> 00:49:17,620
+R1 لغاية RN بـthe destined solutions الحلول
+
+425
+00:49:17,620 --> 00:49:24,500
+المختلفة لمين للمعادلة اللى قدامنا هذهيبقى الحلول
+
+426
+00:49:24,500 --> 00:49:30,560
+تبعت المعادلة رقم اتنين هي Y واحد بيكون E أس R
+
+427
+00:49:30,560 --> 00:49:36,380
+واحد X Y اتنين E أس R اتنين X لأنه قلنا R واحد
+
+428
+00:49:36,380 --> 00:49:43,260
+تقلف عن R اتنين يفرضنا الحل أصلا على الشكل Y تساوي
+
+429
+00:49:43,260 --> 00:49:48,480
+E أس R X يبقى الحكي الشكل كان على الشكل هذار طلعت
+
+430
+00:49:48,480 --> 00:49:54,260
+مختلفة و لو عزيزي التاني يبقى هذا حل هذا حل هذا حل
+
+431
+00:49:54,260 --> 00:50:00,340
+و هكذا يبقى اندي ان من الحلول المختلفة إذا الحلول
+
+432
+00:50:00,340 --> 00:50:05,700
+هذه في سيكشن تلاتة اربع إذا بتذكر و أخدنا الدالة a
+
+433
+00:50:05,700 --> 00:50:10,440
+اصر one x a اصر two x أثبتنا إن ما دول linearly
+
+434
+00:50:13,320 --> 00:50:18,840
+أخر مثال كان في سيكشن تلاتة أربع يبقى هدول ال
+
+435
+00:50:18,840 --> 00:50:22,640
+functions are linearly dependent يكونوله main
+
+436
+00:50:22,640 --> 00:50:28,080
+بيكونوله basis لمجموعة الحلول للمعادلة اللي عندنا
+
+437
+00:50:28,080 --> 00:50:33,060
+رقم اتنينما دام بيكونولي ال basis يبقى الحل العام
+
+438
+00:50:33,060 --> 00:50:37,220
+أو أي حل بدي يكون على مين كونه صنف الأول زايد كونه
+
+439
+00:50:37,220 --> 00:50:40,440
+صنف التاني زايد كونه صنف التالت زايد كونه صنف
+
+440
+00:50:40,440 --> 00:50:44,120
+الشكل اللي عندنا ده يبقى بناء عليه لو كان عندي
+
+441
+00:50:44,120 --> 00:50:49,530
+معادلة تفاضلية من الرتبة النونيةو روحت جبت
+
+442
+00:50:49,530 --> 00:50:54,270
+المعادلة المساعدة اللي هي رقم star و لجيت الحلول
+
+443
+00:50:54,270 --> 00:50:59,270
+are real and different يبقى الشكل العام للحل بيكون
+
+444
+00:50:59,270 --> 00:51:03,690
+على الشكل هذا complex اللي هو شكل آخر repeated
+
+445
+00:51:03,690 --> 00:51:08,890
+اللي هو شكل آخر هذا ما سنعرفه مستقبل يبقى هنا stop
+
+446
+00:51:08,890 --> 00:51:13,670
+المحاضرة الثانية هنبدأ ناخد أمثل عالمين مختلفة على
+
+447
+00:51:13,670 --> 00:51:16,870
+هذه الحالة أعطيكوا العفو
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..711f692400c1884ae40fa089ead7d984baed7784
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_raw.json
@@ -0,0 +1 @@
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83.27, "word": " لا", "probability": 0.8642578125}, {"start": 83.27, "end": 83.99, "word": " يكون", "probability": 0.957763671875}, {"start": 83.99, "end": 84.45, "word": " zero", "probability": 0.408935546875}, {"start": 84.45, "end": 85.09, "word": " vector", "probability": 0.94091796875}, {"start": 85.09, "end": 86.43, "word": " بسميه", "probability": 0.8641357421875}, {"start": 86.43, "end": 86.65, "word": " الـ", "probability": 0.67822265625}, {"start": 86.65, "end": 86.93, "word": " eigen", "probability": 0.5458984375}, {"start": 86.93, "end": 87.53, "word": " vector", "probability": 0.8095703125}, {"start": 87.53, "end": 88.53, "word": " واخدنا", "probability": 0.8822021484375}, {"start": 88.53, "end": 88.99, "word": " المرة", "probability": 0.960205078125}, {"start": 88.99, "end": 89.47, "word": " الماضية", "probability": 0.9772135416666666}, {"start": 89.47, "end": 89.67, "word": " على", "probability": 0.88623046875}, {"start": 89.67, "end": 90.07, "word": " ذلك", 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{"start": 96.97, "end": 97.27, "word": " لما", "probability": 0.866943359375}, {"start": 97.27, "end": 97.55, "word": " نأتي", "probability": 0.74560546875}, {"start": 97.55, "end": 97.95, "word": " ناخد", "probability": 0.8377278645833334}, {"start": 97.95, "end": 98.43, "word": " مثال", "probability": 0.962890625}, {"start": 98.43, "end": 98.95, "word": " رقم", "probability": 0.9837239583333334}, {"start": 98.95, "end": 99.33, "word": " اتنين", "probability": 0.8497314453125}, {"start": 99.33, "end": 99.75, "word": " ونشوف", "probability": 0.85400390625}, {"start": 99.75, "end": 100.07, "word": " هل", "probability": 0.840087890625}, {"start": 100.07, "end": 100.21, "word": " ال", "probability": 0.64453125}, {"start": 100.21, "end": 100.41, "word": " land", "probability": 0.974609375}, {"start": 100.41, "end": 100.67, "word": " هي", "probability": 0.91357421875}, {"start": 100.67, "end": 101.21, "word": " complex", "probability": 0.90771484375}], "temperature": 1.0}, {"id": 4, "seek": 12891, "start": 101.64, "end": 128.92, "text": "والله real وإذا طلعت cumless كيف بدنا نشتغل في هذا الموضوع هل زي ال real و الله بيختلف عنه تمام يبقى بنيجي لمثال اتنين بيقول find the eigenvalues and eigenvectors of the matrix A سالب واحد واتنين سالب واحد وواحد يبقى احنا بدنا نروح للمعادلة اللي هو ابتدينا فيها المرة الماضية وهي المعادلة lambda I ناقص A", "tokens": [2407, 6027, 43761, 957, 4032, 28814, 15730, 23032, 1211, 34268, 12713, 1832, 9122, 33911, 47525, 8315, 8717, 8592, 2655, 17082, 1211, 8978, 23758, 9673, 2407, 11242, 45367, 8032, 1211, 30767, 1829, 2423, 957, 4032, 21984, 4724, 1829, 46456, 46538, 18871, 3224, 46811, 10943, 7251, 3555, 4587, 7578, 44945, 1829, 7435, 1829, 32767, 12984, 6027, 1975, 2655, 1863, 9957, 4724, 1829, 39648, 915, 264, 10446, 46033, 293, 10446, 303, 5547, 295, 264, 8141, 316, 8608, 6027, 3555, 36764, 24401, 4032, 9307, 1863, 9957, 8608, 6027, 3555, 36764, 24401, 4032, 14407, 24401, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 47525, 8315, 8717, 32887, 5016, 5296, 19528, 3615, 18513, 37977, 13672, 1829, 31439, 48127, 2655, 16254, 8315, 8978, 11296, 9673, 25720, 9673, 46958, 10632, 37037, 1829, 9673, 3615, 18513, 37977, 13607, 286, 8717, 995, 4587, 9381, 316], "avg_logprob": -0.1524305623990518, "compression_ratio": 1.7536231884057971, "no_speech_prob": 0.0, "words": [{"start": 101.64, "end": 102.18, "word": "والله", "probability": 0.6170247395833334}, {"start": 102.18, "end": 102.54, "word": " real", "probability": 0.326416015625}, {"start": 102.54, "end": 103.28, "word": " وإذا", "probability": 0.8063151041666666}, {"start": 103.28, "end": 103.66, "word": " طلعت", "probability": 0.9168294270833334}, {"start": 103.66, "end": 104.12, "word": " cumless", "probability": 0.57275390625}, {"start": 104.12, "end": 104.4, "word": " كيف", "probability": 0.92431640625}, {"start": 104.4, "end": 104.78, "word": " بدنا", "probability": 0.88720703125}, {"start": 104.78, "end": 105.3, "word": " نشتغل", "probability": 0.9740234375}, {"start": 105.3, 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"end": 214.8, "word": " هذه", "probability": 0.461669921875}, {"start": 214.8, "end": 215.06, "word": " لو", "probability": 0.84423828125}, {"start": 215.06, "end": 215.38, "word": " جيت", "probability": 0.906005859375}, {"start": 215.38, "end": 216.0, "word": " فاكدت", "probability": 0.75009765625}, {"start": 216.0, "end": 216.8, "word": " بتعطيني", "probability": 0.761328125}, {"start": 216.8, "end": 217.3, "word": " لاندا", "probability": 0.4203287760416667}, {"start": 217.3, "end": 217.82, "word": " تربية", "probability": 0.8624674479166666}, {"start": 217.82, "end": 218.38, "word": " ناقص", "probability": 0.9659423828125}, {"start": 218.38, "end": 218.82, "word": " واحد", "probability": 0.9619140625}, {"start": 218.82, "end": 219.4, "word": " ليه؟", "probability": 0.6354166666666666}, {"start": 219.4, "end": 219.92, "word": " لأن", "probability": 0.785400390625}, {"start": 219.92, "end": 220.74, "word": " تحليل", "probability": 0.9613037109375}, {"start": 220.74, "end": 221.24, "word": " فرق", "probability": 0.875}, {"start": 221.24, "end": 221.58, "word": " بين", "probability": 0.9833984375}, {"start": 221.58, "end": 222.48, "word": " المربعين", "probability": 0.8624267578125}, {"start": 222.48, "end": 223.6, "word": " رجعتها", "probability": 0.9046630859375}, {"start": 223.6, "end": 223.74, "word": " إلى", "probability": 0.6708984375}, {"start": 223.74, "end": 224.28, "word": " أصلها", "probability": 0.9404296875}, {"start": 224.28, "end": 224.64, "word": " قبل", "probability": 0.99169921875}, {"start": 224.64, "end": 225.54, "word": " التحليل", "probability": 0.9862060546875}, {"start": 225.54, "end": 226.58, "word": " زائد", "probability": 0.8134765625}, {"start": 226.58, "end": 227.18, "word": " اتنين", "probability": 0.856201171875}, {"start": 227.18, "end": 227.62, "word": " يبقى", "probability": 0.9637451171875}, {"start": 227.62, "end": 228.26, "word": " تساوي", "probability": 0.9578857421875}, {"start": 228.26, "end": 228.8, "word": " لاندا", "probability": 0.931640625}, {"start": 228.8, "end": 229.46, "word": " تربية", "probability": 0.9676106770833334}, {"start": 229.46, "end": 230.38, "word": " زائد", "probability": 0.9591471354166666}, {"start": 230.38, "end": 230.86, "word": " واحد", "probability": 0.988037109375}, {"start": 230.86, "end": 231.02, "word": " اللي", "probability": 0.892822265625}, {"start": 231.02, "end": 231.46, "word": " بتروح", "probability": 0.94189453125}, {"start": 231.46, "end": 231.94, "word": " أسويها", "probability": 0.8602294921875}, {"start": 231.94, "end": 232.8, "word": " من؟", "probability": 0.55029296875}, {"start": 232.8, "end": 233.66, "word": " بالزيرو", "probability": 0.666717529296875}], "temperature": 1.0}, {"id": 9, "seek": 26149, "start": 233.95, "end": 261.49, "text": "يبقى بناء عليه بصير لاندا تربيع يسوى قدر؟ سالب واحد هل يُعقل إن مجموعة كمية مربع يعطيني قيمة سالبة؟ إذا هذه لا يمكن أن تكون real number وإنما complex number يبقى هذا معناه إن لاندا تسوى الجدر التربيع إلى مين؟ لسالب واحد", "tokens": [1829, 3555, 4587, 7578, 44945, 16606, 47356, 4724, 9381, 13546, 5296, 7649, 28259, 6055, 2288, 21292, 3615, 7251, 3794, 2407, 7578, 12174, 3215, 2288, 22807, 8608, 6027, 3555, 36764, 24401, 8032, 1211, 7251, 10859, 3615, 4587, 1211, 36145, 3714, 7435, 2304, 2407, 27884, 9122, 2304, 10632, 3714, 25513, 3615, 37495, 9566, 1829, 22653, 12174, 32640, 3660, 8608, 6027, 49401, 22807, 11933, 15730, 29538, 20193, 7251, 43020, 14739, 6055, 30544, 957, 1230, 4032, 28814, 1863, 15042, 3997, 1230, 7251, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 36145, 5296, 7649, 28259, 6055, 3794, 2407, 7578, 25724, 3215, 2288, 16712, 2288, 21292, 3615, 30731, 3714, 9957, 22807, 5296, 3794, 6027, 3555, 36764, 24401], "avg_logprob": -0.2259290527116071, "compression_ratio": 1.6696428571428572, "no_speech_prob": 0.0, "words": [{"start": 233.95, "end": 234.67, "word": "يبقى", "probability": 0.7972412109375}, {"start": 234.67, "end": 235.07, "word": " بناء", "probability": 0.84521484375}, 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285.42, "end": 307.62, "text": "بتلاقيهم اتنين مالهم مترافقين يعني العدد التخيلي دائما هو بقول a زائد bi حيث ال i له الجذر الترميه لسالب واحد الحل التاني بكون a ناقص bi السالب للجزء التخيلي وليس للجزء الحقيقي", "tokens": [3555, 2655, 15040, 4587, 1829, 16095, 1975, 2655, 1863, 9957, 3714, 6027, 16095, 44650, 23557, 5172, 4587, 9957, 37495, 22653, 18863, 3215, 3215, 16712, 9778, 1829, 20292, 11778, 16373, 15042, 31439, 4724, 39648, 257, 30767, 16373, 3215, 3228, 11331, 1829, 12984, 2423, 741, 46740, 25724, 8848, 2288, 16712, 2288, 2304, 1829, 3224, 5296, 3794, 6027, 3555, 36764, 24401, 21542, 1211, 16712, 7649, 1829, 4724, 30544, 257, 8717, 995, 4587, 9381, 3228, 21136, 6027, 3555, 24976, 7435, 11622, 38207, 16712, 9778, 1829, 20292, 4032, 20292, 3794, 24976, 7435, 11622, 38207, 21542, 38436, 38436], "avg_logprob": -0.22899865014578707, "compression_ratio": 1.8304093567251463, "no_speech_prob": 0.0, "words": [{"start": 285.42, "end": 286.18, "word": "بتلاقيهم", "probability": 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بيساوي واحد ناقص I في ال A", "tokens": [10721, 2407, 7251, 3794, 995, 45865, 36764, 24401, 8717, 995, 4587, 9381, 286, 8978, 9154, 8978, 2423, 1783, 17, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 45164, 25961, 2423, 1783, 17, 7251, 3794, 995, 45865, 316, 50113, 15040, 550, 2423, 1783, 16, 4724, 1829, 3794, 995, 45865, 36764, 24401, 8717, 995, 4587, 9381, 286, 8978, 2423, 316], "avg_logprob": -0.19935344930352836, "compression_ratio": 1.5163934426229508, "no_speech_prob": 0.0, "words": [{"start": 693.85, "end": 694.41, "word": "أو", "probability": 0.7198486328125}, {"start": 694.41, "end": 695.67, "word": " يساوي", "probability": 0.83203125}, {"start": 695.67, "end": 696.47, "word": " واحد", "probability": 0.78466796875}, {"start": 696.47, "end": 697.39, "word": " ناقص", "probability": 0.98291015625}, {"start": 697.39, "end": 697.81, "word": " I", "probability": 0.77978515625}, {"start": 697.81, "end": 698.09, "word": " في", "probability": 0.96240234375}, {"start": 698.09, "end": 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بناء", "probability": 0.825439453125}, {"start": 732.27, "end": 732.91, "word": " عليه", "probability": 0.94482421875}, {"start": 732.91, "end": 733.91, "word": " so", "probability": 0.496826171875}, {"start": 733.91, "end": 734.95, "word": " the", "probability": 0.8984375}, {"start": 734.95, "end": 736.51, "word": " eigen", "probability": 0.8056640625}, {"start": 736.51, "end": 738.41, "word": " vectors", "probability": 0.6806640625}, {"start": 738.41, "end": 740.07, "word": " are", "probability": 0.9580078125}, {"start": 740.07, "end": 741.31, "word": " in", "probability": 0.9580078125}, {"start": 741.31, "end": 742.39, "word": " the", "probability": 0.92529296875}, {"start": 742.39, "end": 743.65, "word": " form", "probability": 0.95703125}], "temperature": 1.0}, {"id": 31, "seek": 76981, "start": 744.57, "end": 769.81, "text": "هذا اكس واحد وهذا اكس اتنين بده يساوي اكس واحد كده اش قولنا واحد ناقص I في ال A اكس اتنين اللي هي بمين ب A لو أخدت ال A عامل مشترك يبقى بصير عندي واحد ناقص I واحد ناقص I وهنا واحد", "tokens": [3224, 15730, 1975, 4117, 3794, 36764, 24401, 37037, 15730, 1975, 4117, 3794, 1975, 2655, 1863, 9957, 47525, 3224, 7251, 3794, 995, 45865, 1975, 4117, 3794, 36764, 24401, 9122, 3215, 3224, 1975, 8592, 12174, 12610, 8315, 36764, 24401, 8717, 995, 4587, 9381, 286, 8978, 2423, 316, 1975, 4117, 3794, 1975, 2655, 1863, 9957, 13672, 1829, 39896, 4724, 2304, 9957, 4724, 316, 45164, 5551, 9778, 3215, 2655, 2423, 316, 6225, 10943, 1211, 37893, 2655, 31747, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 18871, 16254, 36764, 24401, 8717, 995, 4587, 9381, 286, 36764, 24401, 8717, 995, 4587, 9381, 286, 37037, 8315, 36764, 24401], "avg_logprob": -0.2060643517144836, "compression_ratio": 2.026143790849673, "no_speech_prob": 0.0, "words": [{"start": 744.57, "end": 746.05, "word": "هذا", "probability": 0.4945068359375}, {"start": 746.05, "end": 746.41, "word": " اكس", "probability": 0.6378987630208334}, {"start": 746.41, "end": 747.01, "word": " واحد", "probability": 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760.09, "word": " أخدت", "probability": 0.851318359375}, {"start": 760.09, "end": 760.33, "word": " ال", "probability": 0.91943359375}, {"start": 760.33, "end": 760.57, "word": " A", "probability": 0.951171875}, {"start": 760.57, "end": 761.09, "word": " عامل", "probability": 0.955078125}, {"start": 761.09, "end": 761.79, "word": " مشترك", "probability": 0.9431966145833334}, {"start": 761.79, "end": 762.59, "word": " يبقى", "probability": 0.970703125}, {"start": 762.59, "end": 763.09, "word": " بصير", "probability": 0.9383138020833334}, {"start": 763.09, "end": 763.55, "word": " عندي", "probability": 0.766357421875}, {"start": 763.55, "end": 764.23, "word": " واحد", "probability": 0.992431640625}, {"start": 764.23, "end": 765.15, "word": " ناقص", "probability": 0.994873046875}, {"start": 765.15, "end": 765.77, "word": " I", "probability": 0.994140625}, {"start": 765.77, "end": 766.73, "word": " واحد", "probability": 0.935302734375}, {"start": 766.73, "end": 767.37, "word": " ناقص", "probability": 0.9853515625}, {"start": 767.37, "end": 767.73, "word": " I", "probability": 0.990234375}, {"start": 767.73, "end": 768.79, "word": " وهنا", "probability": 0.792236328125}, {"start": 768.79, "end": 769.81, "word": " واحد", "probability": 0.980224609375}], "temperature": 1.0}, {"id": 32, "seek": 78346, "start": 769.94, "end": 783.46, "text": "يبقى هذا ال call vector اللي هو يعتبر من ال eigen vector طيب هذا واحد ولا اتنين ولا تلاتة ولا عشرة ولا مية؟ كدهش؟", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 818, 8062, 13672, 1829, 31439, 7251, 34268, 26890, 9154, 2423, 10446, 8062, 23032, 1829, 3555, 23758, 36764, 24401, 49429, 1975, 2655, 1863, 9957, 49429, 6055, 1211, 9307, 3660, 49429, 6225, 8592, 25720, 49429, 3714, 10632, 22807, 9122, 3215, 3224, 8592, 22807], "avg_logprob": -0.18701171378294626, "compression_ratio": 1.4108527131782946, "no_speech_prob": 0.0, "words": [{"start": 769.94, "end": 770.68, "word": "يبقى", "probability": 0.919921875}, {"start": 770.68, "end": 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"probability": 0.69287109375}, {"start": 778.48, "end": 778.96, "word": " واحد", "probability": 0.939453125}, {"start": 778.96, "end": 779.22, "word": " ولا", "probability": 0.7060546875}, {"start": 779.22, "end": 779.68, "word": " اتنين", "probability": 0.9224853515625}, {"start": 779.68, "end": 779.94, "word": " ولا", "probability": 0.96630859375}, {"start": 779.94, "end": 780.44, "word": " تلاتة", "probability": 0.896240234375}, {"start": 780.44, "end": 780.62, "word": " ولا", "probability": 0.9765625}, {"start": 780.62, "end": 781.04, "word": " عشرة", "probability": 0.9490559895833334}, {"start": 781.04, "end": 781.28, "word": " ولا", "probability": 0.97705078125}, {"start": 781.28, "end": 782.14, "word": " مية؟", "probability": 0.87060546875}, {"start": 782.14, "end": 783.46, "word": " كدهش؟", "probability": 0.86396484375}], "temperature": 1.0}, {"id": 33, "seek": 81056, "start": 785.22, "end": 810.56, "text": "infinite number of eigenvectors يبقى هذا عدد لانهائي من 100 من ال eigenvectors اللي عندنا ليش هو السؤال قال هات ال eigenvalues و ال eigenvectors يعني ال eigenvectors بتبقى في الشكل هذا هذا ال eigenvectors المناظرة لمين المناظرة للامدة تساوي I", "tokens": [259, 5194, 642, 1230, 295, 10446, 303, 5547, 7251, 3555, 4587, 7578, 23758, 6225, 3215, 3215, 5296, 7649, 3224, 16373, 1829, 9154, 2319, 9154, 2423, 10446, 303, 5547, 13672, 1829, 43242, 8315, 32239, 8592, 31439, 21136, 33604, 6027, 50239, 8032, 9307, 2423, 10446, 46033, 4032, 2423, 10446, 303, 5547, 37495, 22653, 2423, 10446, 303, 5547, 39894, 3555, 4587, 7578, 8978, 25124, 28820, 23758, 23758, 2423, 10446, 303, 5547, 9673, 1863, 5718, 116, 25720, 32767, 9957, 9673, 1863, 5718, 116, 25720, 5296, 37440, 41891, 6055, 3794, 995, 45865, 286], "avg_logprob": -0.25175560994094676, "compression_ratio": 1.8195876288659794, "no_speech_prob": 0.0, "words": [{"start": 785.22, "end": 786.26, "word": "infinite", "probability": 0.53741455078125}, {"start": 786.26, "end": 786.78, "word": " number", "probability": 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794.04, "end": 794.54, "word": " عندنا", "probability": 0.9072265625}, {"start": 794.54, "end": 795.56, "word": " ليش", "probability": 0.60772705078125}, {"start": 795.56, "end": 795.74, "word": " هو", "probability": 0.388916015625}, {"start": 795.74, "end": 796.0, "word": " السؤال", "probability": 0.865234375}, {"start": 796.0, "end": 796.28, "word": " قال", "probability": 0.84228515625}, {"start": 796.28, "end": 796.56, "word": " هات", "probability": 0.6368408203125}, {"start": 796.56, "end": 796.68, "word": " ال", "probability": 0.397705078125}, {"start": 796.68, "end": 797.62, "word": " eigenvalues", "probability": 0.6793212890625}, {"start": 797.62, "end": 797.78, "word": " و", "probability": 0.818359375}, {"start": 797.78, "end": 797.9, "word": " ال", "probability": 0.66650390625}, {"start": 797.9, "end": 798.8, "word": " eigenvectors", "probability": 0.9713541666666666}, {"start": 798.8, "end": 800.82, "word": " يعني", "probability": 0.6944580078125}, {"start": 800.82, "end": 800.96, "word": " ال", "probability": 0.90966796875}, {"start": 800.96, "end": 802.14, "word": " eigenvectors", "probability": 0.9659830729166666}, {"start": 802.14, "end": 802.56, "word": " بتبقى", "probability": 0.9564208984375}, {"start": 802.56, "end": 802.68, "word": " في", "probability": 0.84521484375}, {"start": 802.68, "end": 803.08, "word": " الشكل", "probability": 0.97314453125}, {"start": 803.08, "end": 803.38, "word": " هذا", "probability": 0.90673828125}, {"start": 803.38, "end": 803.74, "word": " هذا", "probability": 0.3212890625}, {"start": 803.74, "end": 803.96, "word": " ال", "probability": 0.9755859375}, {"start": 803.96, "end": 805.08, "word": " eigenvectors", "probability": 0.9661458333333334}, {"start": 805.08, "end": 806.52, "word": " المناظرة", "probability": 0.873046875}, {"start": 806.52, "end": 807.18, "word": " لمين", "probability": 0.88134765625}, {"start": 807.18, "end": 808.42, "word": " المناظرة", "probability": 0.886328125}, {"start": 808.42, "end": 809.14, "word": " للامدة", "probability": 0.6720377604166666}, {"start": 809.14, "end": 810.04, "word": " تساوي", "probability": 0.9312744140625}, {"start": 810.04, "end": 810.56, "word": " I", "probability": 0.76171875}], "temperature": 1.0}, {"id": 34, "seek": 83856, "start": 811.04, "end": 838.56, "text": "لسة كمان في Eigen vectors أخرى مناظرة لـ lambda تساوي من يعني احنا كأنه بدنا نبدأ مسألة جديدة زي المسألة هذه بالضبط تماما وقت اش لما lambda تساوي I بدنا نروح نجيب ال Eigen vectors المناظرة لها بدنا نيجي الآن if lambda تساوي ناقص I", "tokens": [1211, 3794, 3660, 9122, 2304, 7649, 8978, 30586, 18875, 5551, 34740, 7578, 3714, 8315, 19913, 25720, 5296, 39184, 13607, 6055, 3794, 995, 45865, 9154, 37495, 22653, 1975, 5016, 8315, 9122, 33456, 3224, 47525, 8315, 8717, 44510, 10721, 47524, 10721, 37977, 10874, 16254, 41891, 30767, 1829, 9673, 3794, 10721, 37977, 29538, 20666, 11242, 3555, 9566, 46811, 10943, 995, 4032, 38149, 1975, 8592, 5296, 15042, 13607, 6055, 3794, 995, 45865, 286, 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"probability": 0.9765625}], "temperature": 1.0}, {"id": 35, "seek": 87049, "start": 841.23, "end": 870.49, "text": "بدي اعيد هذا الكلام من جديد بدي احط مباشرة دغري يعني بدي اكتب هذا و لسه اعيد لا بدي احط لاندا دغري لاندا بناقص I يبقى بصير عندنا هنا ناقص I زائد واحد و هنا ناقص اتنين و هنا واحد و هنا ناقص I ناقص واحد كله في X واحد X اتنين بدي ساوي", "tokens": [3555, 16254, 1975, 3615, 25708, 23758, 2423, 28820, 10943, 9154, 10874, 16254, 3215, 4724, 16254, 1975, 5016, 9566, 3714, 3555, 33599, 25720, 11778, 17082, 16572, 37495, 22653, 4724, 16254, 1975, 4117, 2655, 3555, 23758, 4032, 5296, 3794, 3224, 1975, 3615, 25708, 20193, 4724, 16254, 1975, 5016, 9566, 5296, 7649, 28259, 11778, 17082, 16572, 5296, 7649, 28259, 4724, 8315, 4587, 9381, 286, 7251, 3555, 4587, 7578, 4724, 9381, 13546, 43242, 8315, 34105, 8717, 995, 4587, 9381, 286, 30767, 16373, 3215, 36764, 24401, 4032, 34105, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957, 4032, 34105, 36764, 24401, 4032, 34105, 8717, 995, 4587, 9381, 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"word": " the", "probability": 0.853515625}, {"start": 1127.54, "end": 1129.64, "word": " matrix", "probability": 0.96142578125}, {"start": 1129.64, "end": 1130.58, "word": " A", "probability": 0.98193359375}], "temperature": 1.0}, {"id": 49, "seek": 115533, "start": 1131.86, "end": 1155.34, "text": "نمر بي find the eigen vectors of the matrix A نمر سي بيقول find a basis for the corresponding", "tokens": [1863, 29973, 4724, 1829, 915, 264, 10446, 18875, 295, 264, 8141, 316, 8717, 29973, 8608, 1829, 4724, 1829, 39648, 915, 257, 5143, 337, 264, 11760], "avg_logprob": -0.3810096245545607, "compression_ratio": 1.1368421052631579, "no_speech_prob": 0.0, "words": [{"start": 1131.86, "end": 1132.36, "word": "نمر", "probability": 0.509033203125}, {"start": 1132.36, "end": 1133.34, "word": " بي", "probability": 0.5731201171875}, {"start": 1133.34, "end": 1135.4, "word": " find", "probability": 0.2498779296875}, {"start": 1135.4, "end": 1136.12, "word": " the", "probability": 0.79541015625}, 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1786.03, "word": " في", "probability": 0.80322265625}, {"start": 1786.03, "end": 1786.67, "word": " الحقيقة", "probability": 0.9913736979166666}, {"start": 1786.67, "end": 1787.17, "word": " ماعنديش", "probability": 0.94189453125}, {"start": 1787.17, "end": 1787.35, "word": " إلا", "probability": 0.77001953125}, {"start": 1787.35, "end": 1788.01, "word": " قيمتين", "probability": 0.9935302734375}, {"start": 1788.01, "end": 1789.17, "word": " وليست", "probability": 0.8740234375}, {"start": 1789.17, "end": 1789.73, "word": " ثلاث", "probability": 0.9705810546875}], "temperature": 1.0}, {"id": 78, "seek": 181667, "start": 1790.23, "end": 1816.67, "text": "يبقى باجي بقول صاروا ال eigen values هو لاندا تساوي زيرو لاندا تساوي اتنين إذا بدي أجي أخد الحالة الأولى لو كانت لاندا تساوي زيرو then يبقى بدي أرجع على المعادلة الأساسية اللي عندنا هنا و أجي أحط بدالها لاندا بقداش بزيرو يبقى بدي أصير المعادلة لاندا I", "tokens": [1829, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 20328, 9640, 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"end": 1809.23, "word": " أحط", "probability": 0.9666341145833334}, {"start": 1809.23, "end": 1810.03, "word": " بدالها", "probability": 0.939453125}, {"start": 1810.03, "end": 1810.51, "word": " لاندا", "probability": 0.9544270833333334}, {"start": 1810.51, "end": 1811.37, "word": " بقداش", "probability": 0.74755859375}, {"start": 1811.37, "end": 1812.41, "word": " بزيرو", "probability": 0.7972412109375}, {"start": 1812.41, "end": 1813.05, "word": " يبقى", "probability": 0.9591064453125}, {"start": 1813.05, "end": 1813.23, "word": " بدي", "probability": 0.732421875}, {"start": 1813.23, "end": 1813.81, "word": " أصير", "probability": 0.8229166666666666}, {"start": 1813.81, "end": 1815.03, "word": " المعادلة", "probability": 0.9949951171875}, {"start": 1815.03, "end": 1816.11, "word": " لاندا", "probability": 0.90869140625}, {"start": 1816.11, "end": 1816.67, "word": " I", "probability": 0.83349609375}], "temperature": 1.0}, {"id": 79, "seek": 184523, "start": 1816.79, "end": 1845.23, "text": "ناقص ال a في ال x بدها تساوي zero has the form يبقى بدها تاخد الشكل التالي هذا lambda I ناقص ال a يبقى بده أشيل lambda و أحط مكانها جداش zero بصير عند هنا مين ناقص واحد ناقص اتنين ناقص تلاتة واحد ناقص اربعة ناقص تلاتة ناقص واحد اتنين واحد", "tokens": [1863, 995, 4587, 9381, 2423, 257, 8978, 2423, 2031, 47525, 11296, 6055, 3794, 995, 45865, 4018, 575, 264, 1254, 7251, 3555, 4587, 7578, 47525, 11296, 6055, 47283, 3215, 25124, 28820, 16712, 6027, 1829, 23758, 13607, 286, 8717, 995, 4587, 9381, 2423, 257, 7251, 3555, 4587, 7578, 47525, 3224, 5551, 8592, 26895, 13607, 4032, 5551, 5016, 9566, 3714, 41361, 11296, 10874, 3215, 33599, 4018, 4724, 9381, 13546, 43242, 34105, 3714, 9957, 8717, 995, 4587, 9381, 36764, 24401, 8717, 995, 4587, 9381, 1975, 2655, 1863, 9957, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 36764, 24401, 8717, 995, 4587, 9381, 1975, 25513, 27884, 8717, 995, 4587, 9381, 6055, 1211, 9307, 3660, 8717, 995, 4587, 9381, 36764, 24401, 1975, 2655, 1863, 9957, 36764, 24401], "avg_logprob": -0.23360655359068855, "compression_ratio": 2.0, "no_speech_prob": 0.0, "words": [{"start": 1816.79, "end": 1817.95, "word": "ناقص", "probability": 0.62396240234375}, {"start": 1817.95, "end": 1818.25, "word": " ال", "probability": 0.30908203125}, {"start": 1818.25, "end": 1818.61, "word": " a", "probability": 0.2266845703125}, {"start": 1818.61, "end": 1819.15, "word": " في", "probability": 0.5556640625}, {"start": 1819.15, "end": 1819.41, "word": " ال", "probability": 0.771484375}, {"start": 1819.41, "end": 1819.73, "word": " x", "probability": 0.5068359375}, {"start": 1819.73, "end": 1820.15, "word": " بدها", "probability": 0.56146240234375}, {"start": 1820.15, "end": 1820.67, "word": " تساوي", "probability": 0.89599609375}, {"start": 1820.67, "end": 1821.09, "word": " zero", "probability": 0.275146484375}, {"start": 1821.09, "end": 1821.81, "word": " has", "probability": 0.67919921875}, {"start": 1821.81, "end": 1822.13, "word": " the", "probability": 0.59716796875}, {"start": 1822.13, "end": 1823.03, "word": " form", "probability": 0.94921875}, {"start": 1823.03, "end": 1824.25, "word": " يبقى", "probability": 0.899658203125}, {"start": 1824.25, "end": 1824.53, "word": " بدها", "probability": 0.85107421875}, {"start": 1824.53, "end": 1824.99, "word": " تاخد", "probability": 0.8953450520833334}, {"start": 1824.99, "end": 1825.51, "word": " الشكل", "probability": 0.971923828125}, {"start": 1825.51, "end": 1825.95, "word": " التالي", "probability": 0.8098958333333334}, {"start": 1825.95, "end": 1826.55, "word": " هذا", "probability": 0.794921875}, {"start": 1826.55, "end": 1827.05, "word": " lambda", "probability": 0.2398681640625}, {"start": 1827.05, "end": 1827.45, "word": " I", "probability": 0.5126953125}, {"start": 1827.45, "end": 1828.13, "word": " ناقص", "probability": 0.975341796875}, {"start": 1828.13, "end": 1828.37, "word": " ال", "probability": 0.84814453125}, {"start": 1828.37, "end": 1828.61, "word": " a", "probability": 0.7333984375}, {"start": 1828.61, "end": 1829.23, "word": " يبقى", "probability": 0.8397216796875}, {"start": 1829.23, "end": 1829.61, "word": " بده", "probability": 0.66845703125}, {"start": 1829.61, "end": 1829.81, "word": " أشيل", "probability": 0.7858072916666666}, {"start": 1829.81, "end": 1830.09, "word": " lambda", "probability": 0.70068359375}, {"start": 1830.09, "end": 1830.27, "word": " و", "probability": 0.53125}, {"start": 1830.27, "end": 1830.51, "word": " أحط", "probability": 0.8453776041666666}, {"start": 1830.51, "end": 1830.97, "word": " مكانها", "probability": 0.620849609375}, {"start": 1830.97, "end": 1831.61, "word": " جداش", "probability": 0.7508138020833334}, {"start": 1831.61, "end": 1832.51, "word": " zero", "probability": 0.370361328125}, {"start": 1832.51, "end": 1832.89, "word": " بصير", "probability": 0.7389322916666666}, {"start": 1832.89, "end": 1833.07, "word": " عند", "probability": 0.76513671875}, {"start": 1833.07, "end": 1833.31, "word": " هنا", "probability": 0.7255859375}, {"start": 1833.31, "end": 1833.59, "word": " مين", "probability": 0.6866455078125}, {"start": 1833.59, "end": 1834.19, "word": " ناقص", "probability": 0.958740234375}, {"start": 1834.19, "end": 1834.67, "word": " واحد", "probability": 0.968994140625}, {"start": 1834.67, "end": 1835.29, "word": " ناقص", "probability": 0.9814453125}, {"start": 1835.29, "end": 1835.71, "word": " اتنين", "probability": 0.96923828125}, {"start": 1835.71, "end": 1836.37, "word": " ناقص", "probability": 0.9796142578125}, {"start": 1836.37, "end": 1837.35, "word": " تلاتة", "probability": 0.94775390625}, {"start": 1837.35, "end": 1838.25, "word": " واحد", "probability": 0.9521484375}, {"start": 1838.25, "end": 1839.19, "word": " ناقص", "probability": 0.995361328125}, {"start": 1839.19, "end": 1839.87, "word": " اربعة", "probability": 0.7376302083333334}, {"start": 1839.87, "end": 1840.65, "word": " ناقص", "probability": 0.9886474609375}, {"start": 1840.65, "end": 1841.67, "word": " تلاتة", "probability": 0.98291015625}, {"start": 1841.67, "end": 1842.71, "word": " ناقص", "probability": 0.9947509765625}, {"start": 1842.71, "end": 1843.31, "word": " واحد", "probability": 0.984619140625}, {"start": 1843.31, "end": 1844.35, "word": " اتنين", "probability": 0.990234375}, {"start": 1844.35, "end": 1845.23, "word": " واحد", "probability": 0.97216796875}], "temperature": 1.0}, {"id": 80, "seek": 185838, "start": 1845.58, "end": 1858.38, "text": "بالشكل اللي عندنا ده يبقى شيلت لاندا وحطيت مكانها zero وهنا X واحد X اتنين X تلاتة بده يساوي zero zero zero", "tokens": [3555, 6027, 8592, 28820, 13672, 1829, 43242, 8315, 11778, 3224, 7251, 3555, 4587, 7578, 13412, 26895, 2655, 5296, 7649, 28259, 4032, 5016, 9566, 36081, 3714, 41361, 11296, 4018, 37037, 8315, 1783, 36764, 24401, 1783, 1975, 2655, 1863, 9957, 1783, 6055, 1211, 9307, 3660, 47525, 3224, 7251, 3794, 995, 45865, 4018, 4018, 4018], "avg_logprob": -0.24307193283764822, "compression_ratio": 1.4146341463414633, 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"word": " X", "probability": 0.5107421875}, {"start": 1851.48, "end": 1852.2, "word": " واحد", "probability": 0.6478271484375}, {"start": 1852.2, "end": 1852.82, "word": " X", "probability": 0.78271484375}, {"start": 1852.82, "end": 1853.6, "word": " اتنين", "probability": 0.9061279296875}, {"start": 1853.6, "end": 1854.22, "word": " X", "probability": 0.95556640625}, {"start": 1854.22, "end": 1855.1, "word": " تلاتة", "probability": 0.8807373046875}, {"start": 1855.1, "end": 1855.7, "word": " بده", "probability": 0.644287109375}, {"start": 1855.7, "end": 1856.2, "word": " يساوي", "probability": 0.8896484375}, {"start": 1856.2, "end": 1856.78, "word": " zero", "probability": 0.4423828125}, {"start": 1856.78, "end": 1857.76, "word": " zero", "probability": 0.78515625}, {"start": 1857.76, "end": 1858.38, "word": " zero", "probability": 0.875}], "temperature": 1.0}, {"id": 81, "seek": 188741, "start": 1859.93, "end": 1887.41, "text": "إذاً هذا بدي يقودني إلى الشكل التالي بدي أضرب المصففين 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يبقى الآن بناء عليه بقوله the eigenvalues the eigenvectors the eigenvectors corresponding", "tokens": [1211, 15042, 10874, 1829, 3555, 8315, 13672, 7649, 2655, 9154, 34105, 47525, 8315, 8717, 44510, 10721, 8717, 29973, 7578, 4724, 1829, 3224, 7251, 3555, 4587, 7578, 6024, 48506, 44945, 16606, 47356, 4724, 39648, 3224, 264, 10446, 46033, 264, 10446, 303, 5547, 264, 10446, 303, 5547, 11760], "avg_logprob": -0.2973736676763981, "compression_ratio": 1.406015037593985, "no_speech_prob": 0.0, "words": [{"start": 2104.56, "end": 2104.94, "word": "لما", "probability": 0.59246826171875}, {"start": 2104.94, "end": 2105.36, "word": " جيبنا", "probability": 0.80987548828125}, {"start": 2105.36, "end": 2105.82, "word": " اللانت", "probability": 0.4422200520833333}, {"start": 2105.82, "end": 2106.0, "word": " من", "probability": 0.7880859375}, {"start": 2106.0, "end": 2106.56, "word": " هنا", "probability": 0.9814453125}, {"start": 2106.56, "end": 2107.38, "word": " بدنا", "probability": 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اتنين بناقص a و اكس تلاتة بناقص a و اكس تلاتة بناقص a", "tokens": [995, 4117, 3794, 1975, 2655, 1863, 9957, 1975, 4117, 3794, 6055, 1211, 9307, 3660, 47525, 3224, 7251, 3794, 995, 45865, 1975, 4117, 3794, 36764, 24401, 44945, 995, 4587, 9381, 257, 4032, 1975, 4117, 3794, 1975, 2655, 1863, 9957, 44945, 995, 4587, 9381, 257, 4032, 1975, 4117, 3794, 6055, 1211, 9307, 3660, 44945, 995, 4587, 9381, 257, 4032, 1975, 4117, 3794, 6055, 1211, 9307, 3660, 44945, 995, 4587, 9381, 257], "avg_logprob": -0.2794642925262451, "compression_ratio": 2.13953488372093, "no_speech_prob": 0.0, "words": [{"start": 2148.93, "end": 2149.41, "word": "اكس", "probability": 0.5290985107421875}, {"start": 2149.41, "end": 2149.97, "word": " اتنين", "probability": 0.8868408203125}, {"start": 2149.97, "end": 2151.09, "word": " اكس", "probability": 0.9404296875}, {"start": 2151.09, "end": 2151.89, "word": " تلاتة", "probability": 0.9183349609375}, {"start": 2151.89, "end": 2152.99, "word": " بده", "probability": 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"word": " تلاتة", "probability": 0.9580078125}, {"start": 2410.03, "end": 2410.75, "word": " اكس", "probability": 0.6763509114583334}, {"start": 2410.75, "end": 2411.39, "word": " واحد", "probability": 0.9287109375}, {"start": 2411.39, "end": 2411.91, "word": " اكس", "probability": 0.9765625}, {"start": 2411.91, "end": 2412.57, "word": " اتنين", "probability": 0.95947265625}, {"start": 2412.57, "end": 2413.37, "word": " اكس", "probability": 0.96875}, {"start": 2413.37, "end": 2414.25, "word": " تلاتة", "probability": 0.9788818359375}, {"start": 2414.25, "end": 2414.89, "word": " بده", "probability": 0.29229736328125}, {"start": 2414.89, "end": 2415.35, "word": " يساوي", "probability": 0.8934326171875}, {"start": 2415.35, "end": 2416.05, "word": " زيرو", "probability": 0.5941569010416666}, {"start": 2416.05, "end": 2417.19, "word": " زيرو", "probability": 0.9348958333333334}, {"start": 2417.19, "end": 2418.23, "word": " زيرو", "probability": 0.9601236979166666}], "temperature": 1.0}, {"id": 104, "seek": 243758, "start": 2422.46, "end": 2437.58, "text": "أنا جيت على المعادلة الأصلية لان دا اي ناقص ا كله في اكس بده يسوى زيرو و كتبتها في شكل المصوفات ا التالية اللي عندنا هنا يبقى بده اروح اضرب المصوفتين هدول في بعض", "tokens": [10721, 8315, 10874, 36081, 15844, 9673, 3615, 18513, 37977, 16247, 9381, 1211, 10632, 5296, 7649, 11778, 995, 1975, 1829, 8717, 995, 4587, 9381, 1975, 28242, 3224, 8978, 1975, 4117, 3794, 47525, 3224, 7251, 3794, 2407, 7578, 30767, 13546, 2407, 4032, 9122, 2655, 3555, 2655, 11296, 8978, 13412, 28820, 9673, 9381, 38688, 9307, 1975, 16712, 6027, 10632, 13672, 1829, 43242, 8315, 34105, 7251, 3555, 4587, 7578, 47525, 3224, 1975, 32887, 5016, 1975, 11242, 25513, 9673, 9381, 38688, 2655, 9957, 8032, 3215, 12610, 8978, 45030, 11242], "avg_logprob": -0.33345587674309224, "compression_ratio": 1.7100591715976332, "no_speech_prob": 0.0, "words": [{"start": 2422.46, "end": 2422.92, "word": "أنا", "probability": 0.2025146484375}, {"start": 2422.92, "end": 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"word": " بده", "probability": 0.4879150390625}, {"start": 2428.2, "end": 2428.6, "word": " يسوى", "probability": 0.740234375}, {"start": 2428.6, "end": 2429.08, "word": " زيرو", "probability": 0.727294921875}, {"start": 2429.08, "end": 2429.5, "word": " و", "probability": 0.787109375}, {"start": 2429.5, "end": 2430.18, "word": " كتبتها", "probability": 0.9205078125}, {"start": 2430.18, "end": 2430.34, "word": " في", "probability": 0.875}, {"start": 2430.34, "end": 2430.74, "word": " شكل", "probability": 0.9716796875}, {"start": 2430.74, "end": 2431.86, "word": " المصوفات", "probability": 0.89404296875}, {"start": 2431.86, "end": 2432.4, "word": " ا", "probability": 0.3720703125}, {"start": 2432.4, "end": 2433.36, "word": " التالية", "probability": 0.9314778645833334}, {"start": 2433.36, "end": 2433.52, "word": " اللي", "probability": 0.8291015625}, {"start": 2433.52, "end": 2434.04, "word": " عندنا", "probability": 0.8955078125}, {"start": 2434.04, "end": 2434.18, "word": " هنا", 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"end": 2441.31, "word": " ياخدوني", "probability": 0.653515625}, {"start": 2441.31, "end": 2441.85, "word": " الشكل", "probability": 0.89599609375}, {"start": 2441.85, "end": 2442.57, "word": " التالي", "probability": 0.9378255208333334}, {"start": 2442.57, "end": 2443.53, "word": " يبقى", "probability": 0.9627685546875}, {"start": 2443.53, "end": 2443.87, "word": " هذا", "probability": 0.849609375}, {"start": 2443.87, "end": 2444.77, "word": " x1", "probability": 0.53662109375}, {"start": 2444.77, "end": 2448.05, "word": "-2x2", "probability": 0.795654296875}, {"start": 2448.05, "end": 2450.95, "word": "-3x3", "probability": 0.982666015625}, {"start": 2450.95, "end": 2451.97, "word": " الصف", "probability": 0.92041015625}, {"start": 2451.97, "end": 2452.83, "word": " التاني", "probability": 0.8868815104166666}, {"start": 2452.83, "end": 2453.47, "word": " اللي", "probability": 0.702392578125}, {"start": 2453.47, "end": 2453.67, "word": " هو", "probability": 0.984375}, {"start": 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"-3x3", "probability": 0.948974609375}, {"start": 2494.59, "end": 2495.25, "word": " يساوي", "probability": 0.5925197601318359}, {"start": 2495.25, "end": 2495.67, "word": " 0", "probability": 0.54052734375}, {"start": 2495.67, "end": 2496.79, "word": " x1", "probability": 0.823974609375}, {"start": 2496.79, "end": 2498.73, "word": "-2x2", "probability": 0.974365234375}, {"start": 2498.73, "end": 2500.05, "word": "-x3", "probability": 0.9864908854166666}, {"start": 2500.05, "end": 2500.75, "word": " يساوي", "probability": 0.71868896484375}, {"start": 2500.75, "end": 2501.15, "word": " 0", "probability": 0.94140625}, {"start": 2501.15, "end": 2502.37, "word": " x1", "probability": 0.624267578125}, {"start": 2502.37, "end": 2503.39, "word": "-x2", "probability": 0.49212646484375}, {"start": 2503.39, "end": 2507.81, "word": "-x3", "probability": 0.6522165934244791}, {"start": 2507.81, "end": 2508.49, "word": " يساوي", "probability": 0.801727294921875}, {"start": 2508.49, "end": 2510.03, 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{"start": 2743.07, "end": 2743.51, "word": " هل", "probability": 0.97900390625}, {"start": 2743.51, "end": 2743.95, "word": " هدول", "probability": 0.9666341145833334}, {"start": 2743.95, "end": 2744.63, "word": " linearly", "probability": 0.97509765625}, {"start": 2744.63, "end": 2745.67, "word": " dependent", "probability": 0.91943359375}, {"start": 2745.67, "end": 2746.55, "word": " ولا", "probability": 0.62939453125}, {"start": 2746.55, "end": 2747.21, "word": " linearly", "probability": 0.96240234375}, {"start": 2747.21, "end": 2748.87, "word": " independent", "probability": 0.970703125}, {"start": 2748.87, "end": 2750.29, "word": " independent", "probability": 0.734375}, {"start": 2750.29, "end": 2751.17, "word": " لأن", "probability": 0.779052734375}, {"start": 2751.17, "end": 2751.61, "word": " ولا", "probability": 0.724609375}, {"start": 2751.61, "end": 2752.39, "word": " واحد", "probability": 0.98681640625}, {"start": 2752.39, "end": 2753.01, "word": " فيهم", "probability": 0.97265625}, {"start": 2753.01, "end": 2754.55, "word": " مضاعفات", "probability": 0.92705078125}, {"start": 2754.55, "end": 2755.35, "word": " الآخر", "probability": 0.90185546875}, {"start": 2755.35, "end": 2757.51, "word": " يبقى", "probability": 0.98046875}, {"start": 2757.51, "end": 2758.03, "word": " the", "probability": 0.65869140625}, {"start": 2758.03, "end": 2759.77, "word": " two", "probability": 0.95947265625}, {"start": 2759.77, "end": 2761.83, "word": " vectors", "probability": 0.93994140625}], "temperature": 1.0}, {"id": 119, "seek": 279231, "start": 2763.41, "end": 2792.31, "text": "منهم اتنين واحد زيرو and اللي هو تلاتة زيرو واحد are linearly independent because any one of them is not a multiple", "tokens": [27842, 16095, 1975, 2655, 1863, 9957, 36764, 24401, 30767, 13546, 2407, 293, 13672, 1829, 31439, 6055, 1211, 9307, 3660, 30767, 13546, 2407, 36764, 24401, 366, 43586, 6695, 570, 604, 472, 295, 552, 307, 406, 257, 3866], "avg_logprob": -0.20101351512444987, "compression_ratio": 1.2276422764227641, "no_speech_prob": 0.0, "words": [{"start": 2763.41, "end": 2764.21, "word": "منهم", "probability": 0.55126953125}, {"start": 2764.21, "end": 2765.49, "word": " اتنين", "probability": 0.8978271484375}, {"start": 2765.49, "end": 2766.37, "word": " واحد", "probability": 0.92138671875}, {"start": 2766.37, "end": 2767.33, "word": " زيرو", "probability": 0.6722819010416666}, {"start": 2767.33, "end": 2768.53, "word": " and", "probability": 0.35205078125}, {"start": 2768.53, "end": 2769.69, "word": " اللي", "probability": 0.819091796875}, {"start": 2769.69, "end": 2770.03, "word": " هو", "probability": 0.97412109375}, {"start": 2770.03, "end": 2771.19, "word": " تلاتة", "probability": 0.941650390625}, {"start": 2771.19, "end": 2772.07, "word": " زيرو", "probability": 0.8699544270833334}, {"start": 2772.07, "end": 2772.89, "word": " واحد", "probability": 0.98095703125}, {"start": 2772.89, "end": 2773.87, "word": " are", "probability": 0.6318359375}, {"start": 2773.87, "end": 2774.99, "word": " linearly", "probability": 0.94384765625}, {"start": 2774.99, "end": 2776.01, "word": " independent", "probability": 0.935546875}, {"start": 2776.01, "end": 2777.61, "word": " because", "probability": 0.88232421875}, {"start": 2777.61, "end": 2779.97, "word": " any", "probability": 0.62353515625}, {"start": 2779.97, "end": 2781.45, "word": " one", "probability": 0.95654296875}, {"start": 2781.45, "end": 2782.89, "word": " of", "probability": 0.9794921875}, {"start": 2782.89, "end": 2784.47, "word": " them", "probability": 0.93017578125}, {"start": 2784.47, "end": 2787.93, "word": " is", "probability": 0.96337890625}, {"start": 2787.93, "end": 2790.09, "word": " not", "probability": 0.95849609375}, {"start": 2790.09, "end": 2791.33, "word": " a", "probability": 0.82080078125}, {"start": 2791.33, "end": 2792.31, "word": " multiple", "probability": 0.88818359375}], "temperature": 1.0}, {"id": 120, "seek": 280788, "start": 2795.06, "end": 2807.88, "text": "of multiple of the other هذا بدي اعطيك ان ال basis المطلوب", "tokens": [2670, 3866, 295, 264, 661, 23758, 4724, 16254, 1975, 3615, 9566, 1829, 4117, 16472, 2423, 5143, 9673, 9566, 1211, 37746], "avg_logprob": -0.35881695293244864, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 2795.06, "end": 2796.46, "word": "of", "probability": 0.129638671875}, {"start": 2796.46, "end": 2797.86, "word": " multiple", "probability": 0.7705078125}, {"start": 2797.86, "end": 2798.68, "word": " of", "probability": 0.96142578125}, {"start": 2798.68, "end": 2799.68, "word": " the", "probability": 0.84326171875}, {"start": 2799.68, "end": 2800.96, "word": " other", "probability": 0.830078125}, {"start": 2800.96, "end": 2804.52, "word": " هذا", "probability": 0.634765625}, {"start": 2804.52, "end": 2804.88, "word": " بدي", "probability": 0.471405029296875}, {"start": 2804.88, "end": 2805.44, "word": " اعطيك", "probability": 0.91513671875}, {"start": 2805.44, "end": 2805.78, "word": " ان", "probability": 0.681640625}, {"start": 2805.78, "end": 2806.0, "word": " ال", "probability": 0.89306640625}, {"start": 2806.0, "end": 2806.36, "word": " basis", "probability": 0.541015625}, {"start": 2806.36, "end": 2807.88, "word": " المطلوب", "probability": 0.9766845703125}], "temperature": 1.0}, {"id": 121, "seek": 282870, "start": 2809.64, "end": 2828.7, "text": "is the set يبقى هو عبارة عن المجموعة بحط فيها ال vector الأول اتنين واحد زيرو و بروح بحط ال vector التاني تلاتة زيرو واحد الشكل اللي عندنا هنا", "tokens": [271, 264, 992, 7251, 3555, 4587, 7578, 31439, 6225, 3555, 9640, 3660, 18871, 9673, 7435, 2304, 2407, 27884, 4724, 5016, 9566, 8978, 11296, 2423, 8062, 16247, 12610, 1975, 2655, 1863, 9957, 36764, 24401, 30767, 13546, 2407, 4032, 4724, 32887, 5016, 4724, 5016, 9566, 2423, 8062, 16712, 7649, 1829, 6055, 1211, 9307, 3660, 30767, 13546, 2407, 36764, 24401, 25124, 28820, 13672, 1829, 43242, 8315, 34105], "avg_logprob": -0.1149639423076923, "compression_ratio": 1.5324675324675325, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2809.64, "end": 2810.42, "word": "is", "probability": 0.3671875}, {"start": 2810.42, "end": 2811.84, "word": " the", "probability": 0.79150390625}, {"start": 2811.84, "end": 2813.2, "word": " set", "probability": 0.9677734375}, {"start": 2813.2, "end": 2814.26, "word": " يبقى", "probability": 0.8509521484375}, {"start": 2814.26, "end": 2814.52, "word": " هو", "probability": 0.791015625}, {"start": 2814.52, "end": 2815.0, "word": " عبارة", "probability": 0.9862060546875}, {"start": 2815.0, "end": 2815.2, "word": " عن", "probability": 0.99658203125}, {"start": 2815.2, "end": 2816.06, "word": " المجموعة", "probability": 0.908984375}, {"start": 2816.06, "end": 2817.04, "word": " بحط", "probability": 0.94921875}, {"start": 2817.04, "end": 2817.4, "word": " فيها", "probability": 0.981201171875}, {"start": 2817.4, "end": 2817.56, "word": " ال", "probability": 0.96435546875}, {"start": 2817.56, "end": 2817.9, "word": " vector", "probability": 0.92578125}, {"start": 2817.9, "end": 2818.56, "word": " الأول", "probability": 0.9365234375}, {"start": 2818.56, "end": 2819.82, "word": " اتنين", "probability": 0.845703125}, {"start": 2819.82, "end": 2820.76, "word": " واحد", "probability": 0.934814453125}, {"start": 2820.76, "end": 2821.38, "word": " زيرو", "probability": 0.73583984375}, {"start": 2821.38, "end": 2821.92, "word": " و", "probability": 0.76904296875}, {"start": 2821.92, "end": 2822.24, "word": " بروح", "probability": 0.9152018229166666}, {"start": 2822.24, "end": 2822.66, "word": " بحط", "probability": 0.97021484375}, {"start": 2822.66, "end": 2822.8, "word": " ال", "probability": 0.9638671875}, {"start": 2822.8, "end": 2823.12, "word": " vector", "probability": 0.98876953125}, {"start": 2823.12, "end": 2823.9, "word": " التاني", "probability": 0.9461263020833334}, {"start": 2823.9, "end": 2825.48, "word": " تلاتة", "probability": 0.943115234375}, {"start": 2825.48, "end": 2826.42, "word": " زيرو", "probability": 0.9275716145833334}, {"start": 2826.42, "end": 2827.46, "word": " واحد", "probability": 0.98095703125}, {"start": 2827.46, "end": 2828.04, "word": " الشكل", "probability": 0.890869140625}, {"start": 2828.04, "end": 2828.2, "word": " اللي", "probability": 0.9287109375}, {"start": 2828.2, "end": 2828.5, "word": " عندنا", "probability": 0.93896484375}, {"start": 2828.5, "end": 2828.7, "word": " هنا", "probability": 0.935546875}], "temperature": 1.0}, {"id": 122, "seek": 285189, "start": 2834.93, "end": 2851.89, "text": "حد فيكوا لايه تساؤل هنا؟ يعني كل أندعها بيقابلها vector space خاص بها، يبقى كأنه فيها two vector أو two eigenspaces، حد فيكوا لايه تساؤل؟ طيب أعطيكوا العافية", "tokens": [5016, 3215, 8978, 4117, 14407, 20193, 1829, 3224, 6055, 3794, 5718, 97, 1211, 34105, 22807, 37495, 22653, 28242, 14739, 3215, 3615, 11296, 4724, 1829, 4587, 16758, 1211, 11296, 8062, 1901, 16490, 33546, 4724, 11296, 12399, 7251, 3555, 4587, 7578, 9122, 33456, 3224, 8978, 11296, 732, 8062, 34051, 732, 9728, 694, 79, 2116, 12399, 11331, 3215, 8978, 4117, 14407, 20193, 1829, 3224, 6055, 3794, 5718, 97, 1211, 22807, 23032, 1829, 3555, 5551, 3615, 9566, 1829, 4117, 14407, 18863, 31845, 10632], "avg_logprob": -0.3011718798428774, "compression_ratio": 1.58125, "no_speech_prob": 0.0, "words": [{"start": 2834.93, "end": 2835.21, "word": "حد", "probability": 0.2136688232421875}, {"start": 2835.21, "end": 2835.53, "word": " فيكوا", "probability": 0.6068522135416666}, {"start": 2835.53, "end": 2835.69, "word": " لايه", "probability": 0.6537272135416666}, {"start": 2835.69, "end": 2836.15, "word": " تساؤل", "probability": 0.817041015625}, {"start": 2836.15, "end": 2837.31, "word": " هنا؟", "probability": 0.78125}, {"start": 2837.31, "end": 2837.59, "word": " يعني", "probability": 0.900634765625}, {"start": 2837.59, "end": 2838.21, "word": " كل", "probability": 0.97216796875}, {"start": 2838.21, "end": 2839.13, "word": " أندعها", "probability": 0.5771484375}, {"start": 2839.13, "end": 2840.53, "word": " بيقابلها", "probability": 0.9200846354166666}, {"start": 2840.53, "end": 2840.99, "word": " vector", "probability": 0.85400390625}, {"start": 2840.99, "end": 2841.69, "word": " space", "probability": 0.9404296875}, {"start": 2841.69, "end": 2842.35, "word": " خاص", "probability": 0.982421875}, {"start": 2842.35, "end": 2843.09, "word": " بها،", "probability": 0.705078125}, {"start": 2843.09, "end": 2843.35, "word": " يبقى", "probability": 0.887451171875}, {"start": 2843.35, "end": 2843.85, "word": " كأنه", "probability": 0.9226888020833334}, {"start": 2843.85, "end": 2844.13, "word": " فيها", "probability": 0.6807861328125}, {"start": 2844.13, "end": 2844.85, "word": " two", "probability": 0.1781005859375}, {"start": 2844.85, "end": 2846.11, "word": " vector", "probability": 0.80322265625}, {"start": 2846.11, "end": 2846.45, "word": " أو", "probability": 0.65625}, {"start": 2846.45, "end": 2846.79, "word": " two", "probability": 0.9140625}, {"start": 2846.79, "end": 2848.39, "word": " eigenspaces،", "probability": 0.73955078125}, {"start": 2848.39, "end": 2848.59, "word": " حد", "probability": 0.926513671875}, {"start": 2848.59, "end": 2848.93, "word": " فيكوا", "probability": 0.9734700520833334}, {"start": 2848.93, "end": 2849.09, "word": " لايه", "probability": 0.9708658854166666}, {"start": 2849.09, "end": 2850.63, "word": " تساؤل؟", "probability": 0.8650716145833334}, {"start": 2850.63, "end": 2851.01, "word": " طيب", "probability": 0.8704427083333334}, {"start": 2851.01, "end": 2851.49, "word": " أعطيكوا", "probability": 0.7643636067708334}, {"start": 2851.49, "end": 2851.89, "word": " العافية", "probability": 0.8748372395833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2852.5715, "duration_after_vad": 2727.8693749999948}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..120457340de4bc632e8f46f5df75e71adaa79b1c
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/ugJHqxp4YY0_raw.srt
@@ -0,0 +1,1756 @@
+1
+00:00:20,940 --> 00:00:25,680
+بسم الله الرحمن الرحيم نرجع الآن لل section
+
+2
+00:00:25,680 --> 00:00:30,820
+ابتدناه المرة الماضية وهو اول section من chapter 4
+
+3
+00:00:30,820 --> 00:00:36,040
+لاتحدث عن نقطتين فقط النقطة الأولى هي ال
+
+4
+00:00:36,040 --> 00:00:40,380
+eigenvalues والنقطة الثانية هي ال eigenvectors
+
+5
+00:00:40,380 --> 00:00:47,140
+وقولنا لو عندي matrix A تجب مصفوفة مربعة نضام n في
+
+6
+00:00:47,140 --> 00:00:51,040
+n اتنين في اتنينتلاتة في تلاتة اربعة في اربعة معنا
+
+7
+00:00:51,040 --> 00:00:58,040
+مشكلة يبقى باجي بقول المعادلة ل A X يساوي لاندا X
+
+8
+00:00:58,040 --> 00:01:02,420
+يعني اذا جدرنا نضرب المصفوفة A في المصفوفة X
+
+9
+00:01:02,420 --> 00:01:08,500
+لمصفوفة مجاهيل اعطاني لاندا وهو رقم real number او
+
+10
+00:01:08,500 --> 00:01:12,700
+complex number اعطاني لاندا X يبقى لاندا في هذه
+
+11
+00:01:12,700 --> 00:01:18,570
+الحالة بسميها هنا بسميها ال eigen valueالـ vector
+
+12
+00:01:18,570 --> 00:01:24,450
+x الذي يحقق هذه المعادلة بشرط أن لا يكون zero
+
+13
+00:01:24,450 --> 00:01:29,470
+vector بسميه الـ eigen vector واخدنا المرة الماضية
+
+14
+00:01:29,470 --> 00:01:33,450
+على ذلك مثال واحدة وهذا المثال طلعت أن ال land
+
+15
+00:01:33,450 --> 00:01:38,950
+مالها real number تمام؟ لما نأتي ناخد مثال رقم
+
+16
+00:01:38,950 --> 00:01:43,280
+اتنين ونشوف هل ال land هي complexوالله real وإذا
+
+17
+00:01:43,280 --> 00:01:46,660
+طلعت cumless كيف بدنا نشتغل في هذا الموضوع هل زي
+
+18
+00:01:46,660 --> 00:01:51,340
+ال real و الله بيختلف عنه تمام يبقى بنيجي لمثال
+
+19
+00:01:51,340 --> 00:01:54,920
+اتنين بيقول find the eigenvalues and eigenvectors
+
+20
+00:01:54,920 --> 00:01:59,680
+of the matrix A سالب واحد واتنين سالب واحد وواحد
+
+21
+00:01:59,680 --> 00:02:04,180
+يبقى احنا بدنا نروح للمعادلة اللي هو ابتدينا فيها
+
+22
+00:02:04,180 --> 00:02:10,350
+المرة الماضية وهي المعادلة lambda I ناقص Aطبعا
+
+23
+00:02:10,350 --> 00:02:16,130
+يبقى هذا الكلام بدها تساوي لاندا اي اللي هي الرقم
+
+24
+00:02:16,130 --> 00:02:20,590
+ال real او ال complex لاندا مضروب في مصوفة الوحدة
+
+25
+00:02:20,590 --> 00:02:27,390
+يبقى هذا عبارة عن لاندا زيرو زيرو لاندا ناقص
+
+26
+00:02:27,390 --> 00:02:33,230
+المصوفة ايه زي ما هي قدامنا هناك بالشكل اللي عندنا
+
+27
+00:02:33,230 --> 00:02:37,430
+هذا طيب هذا النتج بده يساوي بده يساوي المصوفة
+
+28
+00:02:37,430 --> 00:02:43,600
+التاليةلاندا ناقص ناقص واحد يبقى باللاندا ا زايد
+
+29
+00:02:43,600 --> 00:02:49,780
+واحد زيرو ناقص اتنين بناقص اتنين زيرو ناقص ناقص
+
+30
+00:02:49,780 --> 00:02:55,820
+واحد بواحد لاندا ناقص واحد باللاندا ناقص واحد
+
+31
+00:02:55,820 --> 00:03:00,340
+بالشكل اللي عندنا هذا بعد هيك بنروح ناخد ال
+
+32
+00:03:00,340 --> 00:03:06,020
+determinant لهذه المعادلة لو نسوي بالزيرو يبقى
+
+33
+00:03:06,020 --> 00:03:13,160
+باجي بقول ال determinantالمين للاندا اي ناقص ال a
+
+34
+00:03:13,160 --> 00:03:19,460
+بدل سوى المحدد لاندا plus one minus two one لاندا
+
+35
+00:03:19,460 --> 00:03:26,340
+minus one بدل نفك المحدد هذا حاصل ضرب عناصر القطر
+
+36
+00:03:26,340 --> 00:03:35,060
+الرئيسيناقص حاصل ضرب عناصر القطر الثانوي هذه لو
+
+37
+00:03:35,060 --> 00:03:39,920
+جيت فاكدت بتعطيني لاندا تربية ناقص واحد ليه؟ لأن
+
+38
+00:03:39,920 --> 00:03:44,640
+تحليل فرق بين المربعين رجعتها إلى أصلها قبل
+
+39
+00:03:44,640 --> 00:03:50,380
+التحليل زائد اتنين يبقى تساوي لاندا تربية زائد
+
+40
+00:03:50,380 --> 00:03:55,750
+واحد اللي بتروح أسويها من؟ بالزيرويبقى بناء عليه
+
+41
+00:03:55,750 --> 00:04:02,970
+بصير لاندا تربيع يسوى قدر؟ سالب واحد هل يُعقل إن
+
+42
+00:04:02,970 --> 00:04:07,770
+مجموعة كمية مربع يعطيني قيمة سالبة؟ إذا هذه لا
+
+43
+00:04:07,770 --> 00:04:13,690
+يمكن أن تكون real number وإنما complex number يبقى
+
+44
+00:04:13,690 --> 00:04:20,190
+هذا معناه إن لاندا تسوى الجدر التربيع إلى مين؟
+
+45
+00:04:20,190 --> 00:04:24,950
+لسالب واحدالجدر التربية إلى سالب واحد اللي هو زائد
+
+46
+00:04:24,950 --> 00:04:30,930
+او ناقص I حيث I اللي هو الجدر التربية إلى سالب
+
+47
+00:04:30,930 --> 00:04:37,350
+واحد I الحرف الأول من كلمة imaginary تخيّلي يبقى
+
+48
+00:04:37,350 --> 00:04:42,190
+قيمة لاندا يا اما واحد يا اما سالب واحد ودائما
+
+49
+00:04:42,190 --> 00:04:47,040
+وابدا بيطلع عندى حلين تخيليينبتلاقيهم اتنين مالهم
+
+50
+00:04:47,040 --> 00:04:54,040
+مترافقين يعني العدد التخيلي دائما هو بقول a زائد
+
+51
+00:04:54,040 --> 00:04:59,780
+bi حيث ال i له الجذر الترميه لسالب واحد الحل
+
+52
+00:04:59,780 --> 00:05:06,180
+التاني بكون a ناقص bi السالب للجزء التخيلي وليس
+
+53
+00:05:06,180 --> 00:05:13,060
+للجزء الحقيقيطبعا في سؤالنا هذا بي بي زيرو بيضل ا
+
+54
+00:05:13,060 --> 00:05:16,700
+ا بي زيرو بيضلش عندنا إلا مين إلا بي لي زيد أو
+
+55
+00:05:16,700 --> 00:05:23,280
+ناقص واحد في اي يبقى صار عندى قيمتين للامدة وكل
+
+56
+00:05:23,280 --> 00:05:29,260
+واحدة فيهم عبارة عن قيمة تخيلية يبقى الآن بدى أبدأ
+
+57
+00:05:29,260 --> 00:05:34,700
+أروح أدور على مين على ال eigenvectors فبنقول ما
+
+58
+00:05:34,700 --> 00:05:39,070
+ياتىأحنا الآن طلعنا الـ eigen values اللي لاندا
+
+59
+00:05:39,070 --> 00:05:42,650
+بزايد أو ناقص I و بنروح ندور على مين على ال eigen
+
+60
+00:05:42,650 --> 00:05:46,290
+vectors فبرجع للمعادلة الأصلية اللي عندي هي لاندا
+
+61
+00:05:46,290 --> 00:05:49,970
+I ناقص A فكس بده ساوي مين بده ساوي Zero اللي من
+
+62
+00:05:49,970 --> 00:05:54,770
+خلالها بدنا نجيب مين ال eigen vectors يبقى بده
+
+63
+00:05:54,770 --> 00:06:00,390
+أروح أصيغ هذه صياغة عملية لاندا I ناقص A هي جاهزة
+
+64
+00:06:00,390 --> 00:06:05,160
+عندي صح؟يبقى انا بدى احطها كما هي يبقى هذا بدى
+
+65
+00:06:05,160 --> 00:06:12,440
+يعطينا lambda plus one ناقص اتنين واحد lambda ناقص
+
+66
+00:06:12,440 --> 00:06:19,700
+واحد في x لي x واحد و x اتنين بدى يساوي مين؟ Zero
+
+67
+00:06:19,700 --> 00:06:25,970
+و Zeroالان بدنا ناخد النقطة الأولى لو كانت ال land
+
+68
+00:06:25,970 --> 00:06:31,590
+هذه تساوي I ايش اللي بد يحصل في هذه المعادلة اذا
+
+69
+00:06:31,590 --> 00:06:36,490
+بد اشيل كل land او احط مكانها مين I زي ما عملنا
+
+70
+00:06:36,490 --> 00:06:40,570
+المرة اللي فاتت في حالة ال real لما ال land كانت
+
+71
+00:06:40,570 --> 00:06:48,860
+real numberيبقى بناء عليه ستصبح هذه كتالة I plus
+
+72
+00:06:48,860 --> 00:06:57,300
+one سالب اتنين واحد I minus one I minus one في X
+
+73
+00:06:57,300 --> 00:07:04,710
+واحد X اتنين كله بده يساوي من؟ Zero و Zeroبنروح
+
+74
+00:07:04,710 --> 00:07:08,830
+اضرب المصفتين الاتنين هدول في بعض يبقى لو ضربت
+
+75
+00:07:08,830 --> 00:07:12,410
+المصفتين هدول بيصير الصف الأول في العمود الأول
+
+76
+00:07:12,410 --> 00:07:20,490
+يبقى I plus one في main في X one ناقص اتنين X two
+
+77
+00:07:20,490 --> 00:07:28,290
+صف الثاني في العمود الأول يبقى X one زائداللي هو I
+
+78
+00:07:28,290 --> 00:07:34,970
+minus ال 1 في ال X2 كله بده يساوي من؟ Zero و Zero
+
+79
+00:07:34,970 --> 00:07:40,870
+من هذا الكلام بده اطلع بالمعادلتين التاليتين ل I
+
+80
+00:07:40,870 --> 00:07:46,730
+زائد واحد في X واحد ناقص اتنين X اتنين يساوي Zero
+
+81
+00:07:46,730 --> 00:07:53,350
+المعادلة التانية X واحد زائد I ناقص واحد
+
+82
+00:08:00,610 --> 00:08:05,190
+شرايك المعادلات ان هذول زي بعض مختلفات تماما
+
+83
+00:08:10,930 --> 00:08:16,310
+بختلف عن بعض شكلا لكن في الحقيقة الاتنين are the
+
+84
+00:08:16,310 --> 00:08:21,190
+same كيف are the same يعني لو جيت ضربت المعادلة
+
+85
+00:08:21,190 --> 00:08:26,190
+هذه في مقدار ثابت و طلعت اللي فوق مش التان تان
+
+86
+00:08:26,190 --> 00:08:30,390
+بيكونوا نفس الشيء يبقى هدول اتنين نفس الشيء تعالى
+
+87
+00:08:30,390 --> 00:08:34,590
+نضرب المعادلة التانية في I plus one و نشوف تطلع
+
+88
+00:08:34,590 --> 00:08:39,290
+المعادلة اللي فوق ولا لأ يبقى هنا فاجب اقوله ما
+
+89
+00:08:39,290 --> 00:08:39,970
+يأتي
+
+90
+00:08:50,090 --> 00:08:54,790
+يبقى دول اتنين نفس الشيء ليش؟
+
+91
+00:08:55,660 --> 00:08:59,840
+بدا اجعل معادلة ثانية واضربها في I زائد واحد يبقى
+
+92
+00:08:59,840 --> 00:09:09,120
+I زائد واحد في X واحد زائد I زائد واحد في I ناقص
+
+93
+00:09:09,120 --> 00:09:15,460
+واحد في X اتنين بده يساوي Zero هذه بده تعطينا I
+
+94
+00:09:15,460 --> 00:09:24,300
+plus one في X oneهذا الفرق بين المربعين يبقى كذلك
+
+95
+00:09:24,300 --> 00:09:32,460
+بالصير زائد I تربيع ناقص واحد في ال X اتنين بده
+
+96
+00:09:32,460 --> 00:09:40,000
+يساوي Zero هذا بده يعطينا I زائد واحد في ال X واحد
+
+97
+00:09:40,000 --> 00:09:46,930
+قداش ال I تربيع يا بنات من هنا لو ربعت الطرفينسالب
+
+98
+00:09:46,930 --> 00:09:54,970
+واحد ستصبح سالب اتنين يبقى هذه I تربية عندى من هنا
+
+99
+00:09:54,970 --> 00:09:59,950
+بسالب واحد سالب واحد و سالب واحد بسالب اتنين يبقى
+
+100
+00:09:59,950 --> 00:10:05,250
+هذه سالب اتنين X اتنين تساوي Zero أليست هي
+
+101
+00:10:05,250 --> 00:10:10,690
+المعادلة الأولى؟يبقى دول معادلة شكل مش زي بعض لكن
+
+102
+00:10:10,690 --> 00:10:15,810
+في الحقيقة لما انضربت في العدد اللي عنده I plus
+
+103
+00:10:15,810 --> 00:10:20,150
+one طلعت نفس المعادلة الثانية كويس يبقى دول مش
+
+104
+00:10:20,150 --> 00:10:25,100
+معادلة وانما في الحقيقةمعادلة واحدة مافيش غيرها
+
+105
+00:10:25,100 --> 00:10:30,220
+طيب هذه المعادلة الواحدة بقدر اجيب منها x واحد
+
+106
+00:10:30,220 --> 00:10:35,680
+بدلالة x اتنين او x اتنين بدلالة اتنين بدلالة x
+
+107
+00:10:35,680 --> 00:10:40,960
+واحد يبقى بناء عليه هذه صارت معادلة واحدة يبقى
+
+108
+00:10:40,960 --> 00:10:45,100
+سواء قلت المعادلة الأولى والله المعادلة الثانية
+
+109
+00:10:45,100 --> 00:10:50,780
+الاتنين are the sameفبناء عليه لو روحت مشان ماخليش
+
+110
+00:10:50,780 --> 00:10:54,540
+عندي كسور بدل ما اخد المعادلة الأولى بدي اخد
+
+111
+00:10:54,540 --> 00:11:01,220
+المعادلة الثانية لو اخدنا المعادلة الثانية يبقى x
+
+112
+00:11:01,220 --> 00:11:10,340
+واحد تساوي اللي هو مين؟يبقى هذه المعادلة
+
+113
+00:11:10,340 --> 00:11:16,040
+الآن بناء على الكلام اللي قلته تكفي المعادلة X1
+
+114
+00:11:16,040 --> 00:11:23,580
+زائد I ناقص واحد في X2 بيساوي Zero او ان شئتم
+
+115
+00:11:23,580 --> 00:11:32,560
+فقولوا ان X1 يساوي ناقص I ناقص واحد في X2 بهذا
+
+116
+00:11:32,560 --> 00:11:41,130
+الشكلأو يساوي واحد ناقص I في من في ال X2 يبقى بناء
+
+117
+00:11:41,130 --> 00:11:50,670
+عليه لو كان ال X2 يساوي A مثلا then ال X1 بيساوي
+
+118
+00:11:50,670 --> 00:11:59,370
+واحد ناقص I في ال Aيبقى جبت من قيمة كل من x1 و x2
+
+119
+00:11:59,370 --> 00:12:07,330
+بواسطة ال number الهمان a a0 a1 a2 ما بعرف المهم a
+
+120
+00:12:07,330 --> 00:12:12,910
+any real number ماحطيتش عليه قيود يبقى بناء عليه
+
+121
+00:12:12,910 --> 00:12:27,010
+so the eigen vectors are in the formهذا اكس واحد
+
+122
+00:12:27,010 --> 00:12:32,130
+وهذا اكس اتنين بده يساوي اكس واحد كده اش قولنا
+
+123
+00:12:32,130 --> 00:12:39,470
+واحد ناقص I في ال A اكس اتنين اللي هي بمين ب A لو
+
+124
+00:12:39,470 --> 00:12:45,770
+أخدت ال A عامل مشترك يبقى بصير عندي واحد ناقص I
+
+125
+00:12:45,770 --> 00:12:53,080
+واحد ناقص I وهنا واحديبقى هذا ال call vector اللي
+
+126
+00:12:53,080 --> 00:12:59,680
+هو يعتبر من ال eigen vector طيب هذا واحد ولا اتنين
+
+127
+00:12:59,680 --> 00:13:03,460
+ولا تلاتة ولا عشرة ولا مية؟ كدهش؟
+
+128
+00:13:05,220 --> 00:13:10,280
+infinite number of eigenvectors يبقى هذا عدد
+
+129
+00:13:10,280 --> 00:13:15,560
+لانهائي من 100 من ال eigenvectors اللي عندنا ليش
+
+130
+00:13:15,560 --> 00:13:18,800
+هو السؤال قال هات ال eigenvalues و ال eigenvectors
+
+131
+00:13:18,800 --> 00:13:23,960
+يعني ال eigenvectors بتبقى في الشكل هذا هذا ال
+
+132
+00:13:23,960 --> 00:13:30,560
+eigenvectors المناظرة لمين المناظرة للامدة تساوي I
+
+133
+00:13:31,040 --> 00:13:36,040
+لسة كمان في Eigen vectors أخرى مناظرة لـ lambda
+
+134
+00:13:36,040 --> 00:13:41,840
+تساوي من يعني احنا كأنه بدنا نبدأ مسألة جديدة زي
+
+135
+00:13:41,840 --> 00:13:47,300
+المسألة هذه بالضبط تماما وقت اش لما lambda تساوي I
+
+136
+00:13:47,300 --> 00:13:53,720
+بدنا نروح نجيب ال Eigen vectors المناظرة لها بدنا
+
+137
+00:13:53,720 --> 00:13:58,560
+نيجي الآن if lambda تساوي ناقص I
+
+138
+00:14:01,230 --> 00:14:06,010
+بدي اعيد هذا الكلام من جديد بدي احط مباشرة دغري
+
+139
+00:14:06,010 --> 00:14:09,810
+يعني بدي اكتب هذا و لسه اعيد لا بدي احط لاندا دغري
+
+140
+00:14:09,810 --> 00:14:17,530
+لاندا بناقص I يبقى بصير عندنا هنا ناقص I زائد واحد
+
+141
+00:14:17,530 --> 00:14:25,290
+و هنا ناقص اتنين و هنا واحد و هنا ناقص I ناقص واحد
+
+142
+00:14:25,290 --> 00:14:34,940
+كله في X واحد X اتنين بدي ساويZero و Zeroبنفك
+
+143
+00:14:34,940 --> 00:14:40,620
+المعادلة هذه امانات يبقى هذه واحد ناقص I في من في
+
+144
+00:14:40,620 --> 00:14:46,840
+ال X واحد ناقص اتنين X اتنين بده يساوي Zero صف
+
+145
+00:14:46,840 --> 00:14:52,420
+الأول في العمول الأول بعدها X واحد كمان وهذه
+
+146
+00:14:52,420 --> 00:14:59,160
+يخليها ناقص يبقى ناقص I زائد واحد في ال X اتنين
+
+147
+00:14:59,160 --> 00:15:08,220
+بده يساوي من بده يساوي Zeroمعادلتين شكلا مختلفات
+
+148
+00:15:08,220 --> 00:15:14,340
+عن بعض تماما لكن انا بعتقد ان الاتنين نفس الشيء
+
+149
+00:15:17,140 --> 00:15:21,360
+بدي أضرب هنا في مين؟ واحد ناقص I يبقى بيصير واحد
+
+150
+00:15:21,360 --> 00:15:27,000
+ناقص I في I واحد هيو بدي أجينا هنا واحد ناقص I
+
+151
+00:15:27,000 --> 00:15:33,020
+وعندي ناقص بيصير I ناقص واحد صح؟ وبيطير السالي بعد
+
+152
+00:15:33,020 --> 00:15:36,560
+راحة ويصير I ناقص واحد في I زايد واحد اللي هو
+
+153
+00:15:36,560 --> 00:15:41,640
+الفرق بين المربعين يعني I تربية ناقص واحد طب I
+
+154
+00:15:41,640 --> 00:15:45,580
+تربية بناقص واحد وناقص واحد يبقى بناقص اتنين هي
+
+155
+00:15:46,030 --> 00:15:51,810
+يبقى هدول اتنين كمان نفس الشيء يبقى بعدي بقوله
+
+156
+00:15:51,810 --> 00:16:01,840
+these two equations are the sameيبقى هدول التنتين
+
+157
+00:16:01,840 --> 00:16:09,620
+نفس الشيء يبقى هذا معناه ان ال X واحد بدها تساوي I
+
+158
+00:16:09,620 --> 00:16:15,200
+زائد واحد في مين في ال X اتنين يبقى باجي بقوله لو
+
+159
+00:16:15,200 --> 00:16:24,940
+كانتالـ X2 بده يساوي ايه ثم X1 بده يساوي I زائد
+
+160
+00:16:24,940 --> 00:16:31,280
+واحد في مين في ايه يبقى هنا الشهر The Eigen
+
+161
+00:16:31,280 --> 00:16:37,360
+vectors Corresponding
+
+162
+00:16:44,790 --> 00:16:56,630
+cross bonding to the land يساوي السلب I are in the
+
+163
+00:16:56,630 --> 00:17:05,670
+formيبقى في الشكل التالي اللي هو X1 X2 بده يساوي
+
+164
+00:17:05,670 --> 00:17:14,630
+الآن ال X1 طلعت هنا ب I زائد واحد في ال A و X2 A ب
+
+165
+00:17:14,630 --> 00:17:22,210
+A اللي بقدر اقول A في I plus one وهنا واحد بالشكل
+
+166
+00:17:22,210 --> 00:17:23,390
+اللي عندنا هذا
+
+167
+00:17:29,220 --> 00:17:35,390
+نذهب الآن لمثال آخريبقى هذا مثال عمل يابانات على
+
+168
+00:17:35,390 --> 00:17:39,930
+ال eigenvectors اللي هو ممكن يطلعوا complex
+
+169
+00:17:39,930 --> 00:17:44,290
+numbers إذا أخدنا الآن مثالين مثال المرة الماضية
+
+170
+00:17:44,290 --> 00:17:49,030
+ومثال هذه المرة المثال الماضي كانت land a real
+
+171
+00:17:49,030 --> 00:17:53,830
+numbers والمرة هذه land كانت complex numbers لكن
+
+172
+00:17:53,830 --> 00:17:57,850
+كلا المثالين كانوا عندها مصوفة مربع نظام هاتنين في
+
+173
+00:17:57,850 --> 00:18:03,910
+اتنين أو مصوفة من الدرجة الثانيةنأخد مثال ثالث بس
+
+174
+00:18:03,910 --> 00:18:13,690
+نخل المصوفة من الدرجة الثالثة يبقى example 3 سؤال
+
+175
+00:18:13,690 --> 00:18:24,120
+عشرة من الكتاب بيقول خدلي المصوفة إيه تساوي؟1 2 3
+
+176
+00:18:24,120 --> 00:18:39,820
+-1 4 3 1-2-1 المطلوب الأول لمرة A find the
+
+177
+00:18:39,820 --> 00:18:46,020
+eigenvalues of
+
+178
+00:18:46,020 --> 00:19:00,800
+the matrix Aنمر بي find the eigen vectors of the
+
+179
+00:19:00,800 --> 00:19:14,420
+matrix A نمر سي بيقول find a basis for
+
+180
+00:19:14,420 --> 00:19:15,340
+the corresponding
+
+181
+00:19:29,990 --> 00:19:36,470
+Eigenspace of the
+
+182
+00:19:36,470 --> 00:19:40,070
+eigenvectors
+
+183
+00:19:40,070 --> 00:19:44,090
+يعني
+
+184
+00:19:44,090 --> 00:19:49,010
+لو قلناإن الـ eigenvectors كوّنولي vector space
+
+185
+00:19:49,010 --> 00:19:54,290
+بدي أعرف قداش ال basis لل vector space عظيم شافة
+
+186
+00:19:54,290 --> 00:19:59,610
+يا بنات لو جيت للحالة الأولى بنقدر نقول إن عندي
+
+187
+00:19:59,610 --> 00:20:03,960
+basis لل vector space الأول مين هوالو ال vector
+
+188
+00:20:03,960 --> 00:20:09,080
+واحد ناقص I وهنا واحد وبالتالي طبعا هذا linearly
+
+189
+00:20:09,080 --> 00:20:13,960
+independent لانه لحاله مافيش غيره مستقل تمام غير
+
+190
+00:20:13,960 --> 00:20:18,980
+ثابع لأي أحد يبقى بناء انا عليه بقول في هذه الحالة
+
+191
+00:20:18,980 --> 00:20:24,160
+ال basis في element واحد وبالتالي ال dimension إيه
+
+192
+00:20:24,160 --> 00:20:31,040
+جداش؟تمام في الحالة التانية نفس القصة ال basis هو
+
+193
+00:20:31,040 --> 00:20:34,180
+عبارة عن ال vector اللي عندنا هذا وبالتالي ال
+
+194
+00:20:34,180 --> 00:20:38,720
+dimension له يسوى جداش يسوى واحد صحيح طيب ماعلينا
+
+195
+00:20:38,720 --> 00:20:42,620
+نيجي للسؤال اللي عندنا عشان اجيب ال eigen value و
+
+196
+00:20:42,620 --> 00:20:46,740
+ال eigen vector بدي مباشرة اروح على النقطة الأولى
+
+197
+00:20:46,740 --> 00:20:52,420
+وهي حساب المصوفة lambda I ناقص ال A يبقى باجي
+
+198
+00:20:52,420 --> 00:21:00,760
+بقوله solutionبتدرج لاندا اي ناقص ال a وتساوي
+
+199
+00:21:00,760 --> 00:21:09,980
+لاندا اي اللي هي لاندا زيرو زيرو لاندا زيرو زيرو
+
+200
+00:21:09,980 --> 00:21:16,240
+لاندا اي لاندا اي ناقص المصفوفة a بده نزلها كما هي
+
+201
+00:21:16,240 --> 00:21:23,690
+واحد اتنين تلاتةنقص واحد اربعة تلاتة واحد ناقص
+
+202
+00:21:23,690 --> 00:21:30,930
+اتنين ناقص واحد ويساوي المصوف التالي لاندا ناقص
+
+203
+00:21:30,930 --> 00:21:37,610
+واحد ناقص اتنين ناقص تلاتة اللي بعدها ناقص ناقص
+
+204
+00:21:37,610 --> 00:21:43,850
+واحد اللي هي ابواحد بعدها لاندا ناقص اربعةبعدها
+
+205
+00:21:43,850 --> 00:21:50,290
+Zero ناقص ثلاثة يبقى بناقص ثلاثة اللي بعدها ناقص
+
+206
+00:21:50,290 --> 00:21:56,230
+واحد وهنا اتنين وهنا Lambda زائد واحد بالشكل اللي
+
+207
+00:21:56,230 --> 00:21:57,270
+عندنا هنا
+
+208
+00:22:14,290 --> 00:22:22,450
+طيب نحسب قيمة لاندا عن طريق المعادلة اللى عندنا
+
+209
+00:22:22,450 --> 00:22:29,190
+هذه يبقى بدي اجي اخد ال determinant للاندا I ناقص
+
+210
+00:22:29,190 --> 00:22:36,040
+ال A يبقى هي المحددlanda plus one ناقص اتنين ناقص
+
+211
+00:22:36,040 --> 00:22:42,940
+تلاتة واحد landa ناقص اربعة و هنا ناقص تلاتة ناقص
+
+212
+00:22:42,940 --> 00:22:49,600
+واحد اتنين landa plus one بهذا الشكل يبقى بدي اروح
+
+213
+00:22:49,600 --> 00:22:54,460
+افكر المحدد هذا باستخدام عناصر الصفر
+
+214
+00:23:00,730 --> 00:23:07,390
+أول لندن ناقص واحد اه هذه لندن ناقص واحد صحيح هذه
+
+215
+00:23:07,390 --> 00:23:12,030
+لندن ناقص اه هي كتبناها لندن ناقص واحد يبقى هنا
+
+216
+00:23:12,030 --> 00:23:16,330
+واحد لندن ناقص اربعة ناقص ثلاث مية المية تمام يبقى
+
+217
+00:23:16,330 --> 00:23:21,610
+بدي افكر المحدد هذا باستخدام عناصر الصف الأول مثلا
+
+218
+00:23:21,610 --> 00:23:27,250
+يبقى هذا المحدد بده يساوي هاي لندن ناقص واحد
+
+219
+00:23:27,640 --> 00:23:31,900
+فاهمين؟ في المحدد الأصغر موضوع اللي قشط بالصف هذا
+
+220
+00:23:31,900 --> 00:23:37,660
+وهذا بيصير lambda minus four في lambda plus one
+
+221
+00:23:37,660 --> 00:23:43,980
+هذا الرئيسي ناقص مع ناقص بيصير زائد ستة هذا ال
+
+222
+00:23:43,980 --> 00:23:47,920
+term الأول ال term التاني حسب قاعدة الإشارات شرطه
+
+223
+00:23:47,920 --> 00:23:54,010
+سلب وهو سلب بيصير موجةوشطبي برضه الصف تبعه و
+
+224
+00:23:54,010 --> 00:24:02,110
+العمود بصير lambda زائد واحد ناقص تلاتة يبقى هنا
+
+225
+00:24:02,110 --> 00:24:07,550
+ناقص تلاتة اللي بعده حسب قادة الشرط الشرط موجبة
+
+226
+00:24:07,550 --> 00:24:14,110
+وهو سالب فبظل سالببنجي نشطة بصفه وعموده بصير اتنين
+
+227
+00:24:14,110 --> 00:24:22,350
+ناقص مع ناقص بصير زائد يبقى لندن ناقص اربعة بالشكل
+
+228
+00:24:22,350 --> 00:24:27,350
+هذا وهذا كله اللي هو بيساوي مين؟ بيساوي ال zero
+
+229
+00:24:27,350 --> 00:24:31,490
+يبقى ال determinant بده يساوي zero طيب تعالى نشوف
+
+230
+00:24:31,490 --> 00:24:36,950
+هذه اللي وين بدها توصلنا يبقى هذا الكلام لندن ناقص
+
+231
+00:24:36,950 --> 00:24:42,720
+واحدهذه المناطق بتدفكها يبقى لاندا تربيع عندك ناقص
+
+232
+00:24:42,720 --> 00:24:48,740
+أربع لاندا وزائد لاندا بيظل ناقص تلاتة لاندا وهنا
+
+233
+00:24:48,740 --> 00:24:57,560
+عندنا قداش ناقص أربعةوعندك هنا اللي هو زائد ستة
+
+234
+00:24:57,560 --> 00:25:03,500
+الشكل لأن هذا هو هذا زائد اتنين فلاندا ناقص اتنين
+
+235
+00:25:03,500 --> 00:25:08,540
+وانا ناقص تلاندا فلاندا ناقص اتنين كله بده يساوي
+
+236
+00:25:08,540 --> 00:25:14,330
+zeroيبقى فكّت التربيع هذا هايقوا قدامك بالكامل هذا
+
+237
+00:25:14,330 --> 00:25:18,310
+واحد و سالب تلاتة بسالب اتنين هنا اتنين و سالب
+
+238
+00:25:18,310 --> 00:25:24,090
+اربعة بسالب اتنين يبقى هذا الكلام بده يساوي اللي
+
+239
+00:25:24,090 --> 00:25:31,110
+هو مين لاندا ناقص واحد في لاندا تربيع ناقص تلاتة
+
+240
+00:25:31,110 --> 00:25:39,180
+لاندا زائد اتنين هذه مش هي هذه يا بناتهذا المقدار
+
+241
+00:25:39,180 --> 00:25:42,880
+مش هو نفس المقدار هذا لاندا ناقص اتنين يبقى هنا
+
+242
+00:25:42,880 --> 00:25:47,440
+اتنين وهنا سالب تلاتة بيظل القداش سالب لاندا ناقص
+
+243
+00:25:47,440 --> 00:25:54,720
+اتنين يبقى هذا سالب لاندا ناقص اتنين كل هذا الكلام
+
+244
+00:25:54,720 --> 00:25:57,720
+بيساوي مين؟ بيساوي زر
+
+245
+00:26:00,680 --> 00:26:06,980
+وصلت إلى الـ determinant لـ lambda I ناقص الـ A
+
+246
+00:26:06,980 --> 00:26:07,960
+بده يساوي
+
+247
+00:26:11,430 --> 00:26:15,190
+هذه بنقدر نحللها اللي هي لاندا ناقص واحد في لاندا
+
+248
+00:26:15,190 --> 00:26:22,030
+ناقص اتنين يبقى هذه لاندا ناقص واحد في لاندا ناقص
+
+249
+00:26:22,030 --> 00:26:28,390
+اتنين وعنا هنا ناقص لاندا ناقص اتنين كله بده يستوي
+
+250
+00:26:28,390 --> 00:26:34,790
+zero بقدر اخد اعمال لاندا ناقص اتنين عامل مشترك من
+
+251
+00:26:34,790 --> 00:26:42,100
+الطرفينبظل كده؟ بظل land ناقص واحد لكل تربيع ناقص
+
+252
+00:26:42,100 --> 00:26:46,900
+واحد بده يساوي من zero يبقى من الاتنين هدولة خط
+
+253
+00:26:46,900 --> 00:26:51,660
+land ناقص اتنين بظل الجثة ده هو نفسه تربيع وهنا
+
+254
+00:26:51,660 --> 00:26:58,640
+بظل كده؟ ناقص واحديبقى هذا الكلام لاندا ناقص اتنين
+
+255
+00:26:58,640 --> 00:27:05,680
+هذا لو جيت فكته بيصير لاندا تربيع ناقص اتنين لاندا
+
+256
+00:27:05,680 --> 00:27:11,970
+زائد واحد وناقص واحد كله بده يساوي زيرونقص واحد
+
+257
+00:27:11,970 --> 00:27:16,770
+وزايد واحد مع السلامة يبقى آلة المسألة إلى لاندا
+
+258
+00:27:16,770 --> 00:27:22,530
+ناقص اتنين في لاندا تربية ناقص اتنين لاندا يسوى
+
+259
+00:27:22,530 --> 00:27:29,730
+كده؟ Zero اظن هذا بقدر اقول كتالي لاندا ناقص اتنين
+
+260
+00:27:30,050 --> 00:27:34,670
+وهذا بقدر اخد لاندا عامل مشترك بضال قداش لاندا
+
+261
+00:27:34,670 --> 00:27:41,150
+ناقص اتنين بده يساوي zero ومنها لاندا في لاندا
+
+262
+00:27:41,150 --> 00:27:48,170
+ناقص اتنين يساوي من يساوي zero يبقى هذا نتيجة من
+
+263
+00:27:48,170 --> 00:27:56,520
+فكل محدد بناء عليه لاندا complex ولا realهي قدامك
+
+264
+00:27:56,520 --> 00:28:02,600
+قداش real numbers يبقى بناء عليا اما lambda او
+
+265
+00:28:02,600 --> 00:28:10,240
+باجي بقوله هنا the eigen vectors the eigen values
+
+266
+00:28:10,240 --> 00:28:18,520
+are lambda تساوي zero او lambda تساوي قداش اتنين
+
+267
+00:28:18,520 --> 00:28:22,700
+يبقى في عندي قيمتين هنا لمين ل lambda
+
+268
+00:28:25,840 --> 00:28:30,060
+لاندا في لاندا تربيع هذه تربيعة منها لأن هذا الجثة
+
+269
+00:28:30,060 --> 00:28:34,360
+مضروف في بعض يبقى لاندا تربيع يبقى معناته الجثة
+
+270
+00:28:34,360 --> 00:28:38,080
+الأولى يساوي zero والجثة التانية يساوي zero يبقى
+
+271
+00:28:38,080 --> 00:28:43,080
+هذا لايعطني إلا قيمتين فقط للاندا ماهياش تلاتة
+
+272
+00:28:43,080 --> 00:28:46,440
+طبعا الجثة التانية لما أقول تربيع معناته في قيمتين
+
+273
+00:28:46,440 --> 00:28:50,560
+والقيمتين ماعنهم مكررات كل واحدة فيهم تساوي كده
+
+274
+00:28:50,560 --> 00:28:55,120
+إتنين يعني في الحقيقة ماعنديش إلا قيمتين وليست
+
+275
+00:29:00,210 --> 00:29:05,830
+أحنا فكرنا أن الضرر ناقصلأ ضرب هذه كلها عام
+
+276
+00:29:05,830 --> 00:29:12,210
+المشترك هي هذا نقطة لماذا؟ لأن تحليل أخذت لاندا من
+
+277
+00:29:12,210 --> 00:29:15,790
+القوس هذا عام المشترك يبقى لدي لاندا ناقص اتنين
+
+278
+00:29:15,790 --> 00:29:19,230
+لما أخد لاندا برا يبقى سار القوس لاندا في لاندا
+
+279
+00:29:19,230 --> 00:29:24,190
+ناقص اتنين لكل square يبقى كم؟ Zero يبقى لدي لاندا
+
+280
+00:29:24,190 --> 00:29:28,070
+تسوى Zero لاندا minus two لكل square يسوى Zeroلو
+
+281
+00:29:28,070 --> 00:29:32,310
+اختلها الجدر بيصير لاندا ناقص اتنين يساوي زيرو إذا
+
+282
+00:29:32,310 --> 00:29:36,950
+لاندا يساوي اتنين صحيح إن هذه معادلة من الدرجة
+
+283
+00:29:36,950 --> 00:29:42,130
+الثانية بس بتعطيني قيمتين مكررات يعني نفس القيمة
+
+284
+00:29:42,130 --> 00:29:46,030
+اللي هيقداش اتنين والتانية كمان اتنين يبقى في
+
+285
+00:29:46,030 --> 00:29:50,950
+الحقيقة ماعنديش إلا قيمتين وليست ثلاثيبقى باجي
+
+286
+00:29:50,950 --> 00:29:53,930
+بقول صاروا ال eigen values هو لاندا تساوي زيرو
+
+287
+00:29:53,930 --> 00:29:59,710
+لاندا تساوي اتنين إذا بدي أجي أخد الحالة الأولى لو
+
+288
+00:29:59,710 --> 00:30:04,630
+كانت لاندا تساوي زيرو then يبقى بدي أرجع على
+
+289
+00:30:04,630 --> 00:30:10,030
+المعادلة الأساسية اللي عندنا هنا و أجي أحط بدالها
+
+290
+00:30:10,030 --> 00:30:16,670
+لاندا بقداش بزيرو يبقى بدي أصير المعادلة لاندا I
+
+291
+00:30:16,790 --> 00:30:23,030
+ناقص ال a في ال x بدها تساوي zero has the form
+
+292
+00:30:23,030 --> 00:30:28,610
+يبقى بدها تاخد الشكل التالي هذا lambda I ناقص ال a
+
+293
+00:30:28,610 --> 00:30:32,890
+يبقى بده أشيل lambda و أحط مكانها جداش zero بصير
+
+294
+00:30:32,890 --> 00:30:38,250
+عند هنا مين ناقص واحد ناقص اتنين ناقص تلاتة واحد
+
+295
+00:30:38,250 --> 00:30:46,320
+ناقص اربعة ناقص تلاتة ناقص واحد اتنين واحدبالشكل
+
+296
+00:30:46,320 --> 00:30:50,420
+اللي عندنا ده يبقى شيلت لاندا وحطيت مكانها zero
+
+297
+00:30:50,420 --> 00:30:57,760
+وهنا X واحد X اتنين X تلاتة بده يساوي zero zero
+
+298
+00:30:57,760 --> 00:31:04,510
+zeroإذاً هذا بدي يقودني إلى الشكل التالي بدي أضرب
+
+299
+00:31:04,510 --> 00:31:14,070
+المصففين هدول في بعض يبقى ناقص X1 ناقص 2 X2 ناقص 3
+
+300
+00:31:14,070 --> 00:31:26,430
+X3 الصفر الثاني يبقى X1 ناقص 4 X2 ناقص 4 X2 ناقص 3
+
+301
+00:31:26,430 --> 00:31:37,150
+X3الصف التالت يبقى ناقص X1 زائد 2 X2 زائد X3 كل
+
+302
+00:31:37,150 --> 00:31:43,270
+هذا الكلام بده يساوي Zero و Zero و Zero إذا أصبحت
+
+303
+00:31:43,270 --> 00:31:48,310
+المعادلات التلاتة عندي على الشكل التالي سالب X1
+
+304
+00:31:48,310 --> 00:31:56,600
+سالب 2 X2 سالب 3 X3 بده تساوي Zeroالمعادلة التانية
+
+305
+00:31:56,600 --> 00:32:00,720
+x1-4x2
+
+306
+00:32:00,720 --> 00:32:14,180
+-3x3 بده يساوي 0-x1 زيدي 2x2 زيدي x3 بده يساوي 0
+
+307
+00:32:14,770 --> 00:32:19,570
+خلّينا نتأكد ان ال system هذا سليم 100% حتى نواصل
+
+308
+00:32:19,570 --> 00:32:26,110
+يبقى جيبنا ال lambda و راحنا عوضنا بال zero لما
+
+309
+00:32:26,110 --> 00:32:31,850
+عوضنا بال zero طلعت عندنا المعادلة ناقص x1 ناقص 2
+
+310
+00:32:31,850 --> 00:32:38,730
+x2 ناقص 3 x3 بده يسوي zero و x1 ناقص 4 x2 ناقص 3
+
+311
+00:32:38,730 --> 00:32:46,030
+x3 بده يسوي zero و هذه ناقص x1 زائد 2 x2زائد X
+
+312
+00:32:46,030 --> 00:32:52,770
+ثلاثة كله بيساوي Zero مطبوط مية المية طيب ايش رايك
+
+313
+00:32:52,770 --> 00:32:58,490
+لو جينا على المعادلات اللي عندنا هذه بدي احاول
+
+314
+00:32:58,490 --> 00:33:03,950
+اشوف ايش علاقتها مع بعضها لو جيت للمعادلات اللي
+
+315
+00:33:03,950 --> 00:33:10,030
+عندى الأولى و الثالثة المعادلات اللي اتنين هدوة
+
+316
+00:33:10,030 --> 00:33:17,740
+يعني هذه ههه وهذهجيت جمعت الاتنين مع بعض يبقى هذه
+
+317
+00:33:17,740 --> 00:33:24,100
+هتروح مع من؟ مع هذه بظل عندي قداش ناقص اتنين X
+
+318
+00:33:24,100 --> 00:33:31,200
+واحد ناقص اتنين X واحد ناقص اتنين X تلاتة يسوي
+
+319
+00:33:31,200 --> 00:33:38,860
+قداش Zero يعني هذا بده يعطينا ان X واحد زي X تلاتة
+
+320
+00:33:38,860 --> 00:33:44,880
+بده يسوي Zero هذا بده يعطينا ان X واحديساوي سالب
+
+321
+00:33:44,880 --> 00:33:55,660
+X3 طيب لو جينا جمعنا المعادلة هذه والمعادلة هذه
+
+322
+00:33:55,660 --> 00:34:00,460
+تين تين مع بعض ايش بده يعطينا هدول بيروحوا مع بعض
+
+323
+00:34:01,350 --> 00:34:05,950
+مظبوط بيظل ناقص
+
+324
+00:34:05,950 --> 00:34:12,890
+اتنين اكس اتنين او ناقص اتنين اكس تلاتة بده يساوي
+
+325
+00:34:12,890 --> 00:34:18,030
+زيرو يبقى هذا بده يعطينا انه اكس اتنين زايد اكس
+
+326
+00:34:18,030 --> 00:34:22,370
+تلاتة بده يساوي زيرو هذا بده يعطينا انه اكس اتنين
+
+327
+00:34:22,370 --> 00:34:31,050
+يساوي سالب اكس تلاتة اذا لو كانتالـ X ثلاثة بدها
+
+328
+00:34:31,050 --> 00:34:34,190
+تساوي من؟ بدها تساوي الـ A
+
+329
+00:34:46,100 --> 00:34:51,600
+بناء عليه بقدر أجيب له من المطلوب التاني جليهات
+
+330
+00:34:51,600 --> 00:34:55,620
+للـEigenvectors المطلوب الأول جيبناله
+
+331
+00:34:55,620 --> 00:35:00,840
+الـEigenvalues يبقى من هنا بدأ المطلوب الأول اللي
+
+332
+00:35:00,840 --> 00:35:07,960
+هو A وانتهى هنالما جيبنا اللانت من هنا بدنا نبدأ
+
+333
+00:35:07,960 --> 00:35:17,860
+نمرى بيه يبقى الآن بناء عليه بقوله the eigenvalues
+
+334
+00:35:17,860 --> 00:35:26,620
+the eigenvectors the eigenvectors corresponding
+
+335
+00:35:31,160 --> 00:35:42,280
+corresponding to لاندا بده يساوي zero are in the
+
+336
+00:35:42,280 --> 00:35:45,720
+form على الشكل التالي
+
+337
+00:35:48,930 --> 00:35:58,490
+اكس اتنين اكس تلاتة بده يساوي اكس واحد بناقص
+
+338
+00:35:58,490 --> 00:36:07,770
+a و اكس اتنين بناقص a و اكس تلاتة بناقص a و اكس
+
+339
+00:36:07,770 --> 00:36:12,110
+تلاتة بناقص
+
+340
+00:36:12,110 --> 00:36:18,270
+aإذا خلصنا من المطلوب نمر بي تبع من؟ تبع
+
+341
+00:36:18,270 --> 00:36:25,610
+الـEigenvectors المناظرة اللي لديها تساوي 0 لم يلأ
+
+342
+00:36:25,610 --> 00:36:31,030
+نقطة من نقطة C جاليهات ليه؟ اللي هو الـBases for
+
+343
+00:36:31,030 --> 00:36:37,830
+the corresponding Eigen spaceالان مش هذه تمثلي ال
+
+344
+00:36:37,830 --> 00:36:42,830
+space او ال vector space تبع ال eigen vectors يبقى
+
+345
+00:36:42,830 --> 00:36:48,390
+هذا شو يعتبر basis اللي هو طلبه يبقى هذا بده
+
+346
+00:36:48,390 --> 00:36:53,110
+يعطينا مين يبقى هذا النقطة بي و سي يا بنات مع بعض
+
+347
+00:36:53,110 --> 00:36:57,430
+اتنين مع بعض في اي نوع يبقى باجي بيقول هذا بده
+
+348
+00:36:57,430 --> 00:37:03,710
+يعطينا the basis of the
+
+349
+00:37:15,300 --> 00:37:20,160
+السطر اللي عندنا هذه اللي هو على شكل سالب واحد
+
+350
+00:37:20,160 --> 00:37:27,580
+سالب واحد واحد بالشكل اللي عندنا هنا كيف
+
+351
+00:37:27,580 --> 00:37:29,320
+مش سانة
+
+352
+00:37:33,000 --> 00:37:37,240
+Eigenvectors لاندا خلصناها من الأول يبقى هذه الان
+
+353
+00:37:37,240 --> 00:37:41,380
+اللي جيبناه لمين للنقطة الأولى لاندا تساوي Zero
+
+354
+00:37:41,380 --> 00:37:45,380
+اللي عملناه للاندا تساوي Zero بدنا نروح نكرره من
+
+355
+00:37:45,380 --> 00:37:51,040
+جديد للاندا تساوي اتنين طبعا الشطرة الأولى من
+
+356
+00:37:51,040 --> 00:37:57,460
+السؤال هذا انتهينا منه يبقى بدي اروح اجيب له بي و
+
+357
+00:37:57,460 --> 00:38:00,440
+سي لمين للاندا التانية
+
+358
+00:38:07,460 --> 00:38:16,300
+يبقى باجي بقوله لو كانت لاندا تساوي اتنين then
+
+359
+00:38:16,300 --> 00:38:26,120
+اللاندا I ناقص ال A في ال X بدي يساوي zero has the
+
+360
+00:38:26,120 --> 00:38:29,600
+form تبقى على الشكل التالي
+
+361
+00:38:35,100 --> 00:38:40,320
+ماذا كانت المعادلة؟ كانت أنها مناطق احنا مسحناها
+
+362
+00:38:40,320 --> 00:38:45,960
+بس خلينا نذكر بها كانت المعادلة اللي عندنا على
+
+363
+00:38:45,960 --> 00:38:52,180
+الشكل التالي اللي هي مين؟ المصوفة كانت اللي هو
+
+364
+00:38:52,180 --> 00:38:58,550
+بلندن أقص واحدوهنا ناقص اتنين ناقص تلاتة واحد
+
+365
+00:38:58,550 --> 00:39:06,190
+لاندا ناقص اربعة ناقص تلاتة هنا ناقص واحد اتنين
+
+366
+00:39:06,190 --> 00:39:11,310
+لاندا plus one يبقى هذه المصروفة اللي كانت عندنا
+
+367
+00:39:11,310 --> 00:39:16,410
+قبل قليل مكتوبة معاكي تمام؟ الآن بدي اعوض فيها على
+
+368
+00:39:16,410 --> 00:39:21,930
+لاندا بجداش باتنينبصير اتنين ناقص واحد يبقى هذا
+
+369
+00:39:21,930 --> 00:39:27,370
+اتنين ناقص واحد و عندك هنا ناقص اتنين ناقص تلاتة و
+
+370
+00:39:27,370 --> 00:39:34,470
+هنا واحد و هنا اتنين ناقص اربع و هنا ناقص تلاتة و
+
+371
+00:39:34,470 --> 00:39:42,890
+هنا ناقص واحد اتنين و هنا اتنين زائد واحد كله في X
+
+372
+00:39:42,890 --> 00:39:52,910
+واحد X اتنين X تلاتةبتساوي 000 هذا معناه ما يأتي
+
+373
+00:39:52,910 --> 00:39:58,210
+هذا بيصير المصفوف اتنين ناقص واحد يلو بواحد ناقص
+
+374
+00:39:58,210 --> 00:40:03,250
+اتنين ناقص تلاتة وهنا واحد وهنا ناقص اتنين وهنا
+
+375
+00:40:03,250 --> 00:40:10,750
+ناقص تلاتة وهنا سالب واحدهنا اتنين وهنا تلاتة اكس
+
+376
+00:40:10,750 --> 00:40:18,230
+واحد اكس اتنين اكس تلاتة بده يساوي زيرو زيرو زيرو
+
+377
+00:40:22,460 --> 00:40:27,600
+أنا جيت على المعادلة الأصلية لان دا اي ناقص ا كله
+
+378
+00:40:27,600 --> 00:40:32,400
+في اكس بده يسوى زيرو و كتبتها في شكل المصوفات ا
+
+379
+00:40:32,400 --> 00:40:35,780
+التالية اللي عندنا هنا يبقى بده اروح اضرب
+
+380
+00:40:35,780 --> 00:40:40,290
+المصوفتين هدول في بعضلو ضربت المصففين الاتنين هذا
+
+381
+00:40:40,290 --> 00:40:48,050
+الفواعد ياخدوني الشكل التالي يبقى هذا x1-2x2
+
+382
+00:40:48,050 --> 00:41:00,610
+-3x3 الصف التاني اللي هو x1-2x2-3x3 الصف الثالث
+
+383
+00:41:00,610 --> 00:41:10,120
+ناقص x1زائد اتنين X2 زائد تلاتة X3 كل هذا الكلام
+
+384
+00:41:10,120 --> 00:41:17,620
+بده يساوي Zero Zero Zero يبقى هذا بده يساوي من
+
+385
+00:41:17,620 --> 00:41:25,410
+Zero Zero Zeroلو قررنا العناصر المتنظرة في كل من
+
+386
+00:41:25,410 --> 00:41:36,790
+المصففاتين نحصل على ما يأتي x1-2x2-3x3 يساوي 0 x1
+
+387
+00:41:36,790 --> 00:41:47,810
+-2x2-x3 يساوي 0 x1-x2-x3
+
+388
+00:41:47,810 --> 00:41:57,800
+يساوي 0هذا الكم معادلة؟ كده؟ معادلتين؟ انا بقول
+
+389
+00:41:57,800 --> 00:42:02,820
+واحدة اضرب الصف التالت او المعادلة التالتة في سالب
+
+390
+00:42:02,820 --> 00:42:07,620
+واحد تطلع لمنا و فوق يبقى هدول مش تلت معادلات
+
+391
+00:42:07,620 --> 00:42:15,660
+وانما في الحقيقة معادلة واحدة يبقى هذه بقوله this
+
+392
+00:42:15,660 --> 00:42:17,680
+system
+
+393
+00:42:19,620 --> 00:42:22,080
+هذا الـ system is
+
+394
+00:42:25,210 --> 00:42:32,270
+one question only يبقى هذا معادلة واحدة فقط ل X
+
+395
+00:42:32,270 --> 00:42:37,890
+واحد ناقص اتنين X اتنين ناقص تلاتة X تلاتة يساوي
+
+396
+00:42:37,890 --> 00:42:42,190
+Zero ليش؟ لأن المعادلة التالتة لو ضربتها في سالب
+
+397
+00:42:42,190 --> 00:42:46,550
+واحد بتطلع المعادلة التانية او المعادلة الأولى
+
+398
+00:42:46,550 --> 00:42:50,630
+لاتنين are the same يبقى انا عندي معادلة واحدة في
+
+399
+00:42:50,630 --> 00:42:57,050
+كام مجهولةفي ثلاثة مجاهيل فيش إمكانية للحل اللي
+
+400
+00:42:57,050 --> 00:43:01,070
+أحط مجهولين من عندي و أروح أجيب قيمة المجهول
+
+401
+00:43:01,070 --> 00:43:07,590
+التالت بدلالة الاتنين هذول يبقى مثلا لو جيت قولتله
+
+402
+00:43:07,590 --> 00:43:20,250
+if ال X2 بدر ساوي A andالـ X تلاتة بده يساوي B ثم
+
+403
+00:43:20,250 --> 00:43:27,690
+X واحد جداش بده يساوي 2A زي التلاتة B يعني انا
+
+404
+00:43:27,690 --> 00:43:33,190
+بقوله مع الشجة التانية بصي X واحد يساوي 2A زي
+
+405
+00:43:33,190 --> 00:43:39,010
+التلاتة B إذن بقدر أجيب شكل الـEigenvectors يبقى
+
+406
+00:43:39,010 --> 00:43:43,710
+باجي بقوله هنا The Eigen
+
+407
+00:43:47,230 --> 00:43:53,370
+Vectors Corresponding المناظرة
+
+408
+00:43:53,370 --> 00:43:59,510
+to land يبقى في
+
+409
+00:43:59,510 --> 00:44:03,750
+الشكل
+
+410
+00:44:03,750 --> 00:44:06,930
+التالي X1
+
+411
+00:44:07,910 --> 00:44:22,610
+و X2 و X3 بده يساوي X1 ب 2A زي 3B X2 ب A و X3 ب B
+
+412
+00:44:27,060 --> 00:44:33,440
+طب ايش رأيك احط هادول على شكل مجموع مصوفتين يبقى
+
+413
+00:44:33,440 --> 00:44:43,360
+بقدر اقول هذا الكلام بده يساوي 2A و A و 0 زائد 3B
+
+414
+00:44:43,360 --> 00:44:55,000
+و 0 و B بنفعبنفع اقول ايه كذلك عامل مشترك بيضل 2 1
+
+415
+00:44:55,000 --> 00:45:03,280
+0 زائد بيعمل مشترك بيضل 3 0 1
+
+416
+00:45:05,790 --> 00:45:09,910
+يبقى هاي اللي جيبته الـEigenvectors تمام؟ كل
+
+417
+00:45:09,910 --> 00:45:13,850
+الـVectors اللي على الشكل اللي عندنا هذا او مجموعة
+
+418
+00:45:13,850 --> 00:45:17,410
+الـTwo Vectors هدول المطلوب التالت جاليهات
+
+419
+00:45:17,410 --> 00:45:23,450
+للـBases للـEigenspace بقوله كويس هدول
+
+420
+00:45:23,450 --> 00:45:27,470
+الـEigenvectors يبقى اي اي Eigenvector في
+
+421
+00:45:27,470 --> 00:45:31,190
+الـVector Space في الـEigenspace بدي اقدر اكتب
+
+422
+00:45:31,190 --> 00:45:36,090
+الشكل هذا إذا كانالاتنين هدول are linearly
+
+423
+00:45:36,090 --> 00:45:40,530
+independent
+
+424
+00:45:40,530 --> 00:45:44,630
+ممتاز جدا يبقى السؤال هو هل هدول linearly
+
+425
+00:45:44,630 --> 00:45:51,170
+dependent ولا linearly independent independent لأن
+
+426
+00:45:51,170 --> 00:46:01,830
+ولا واحد فيهم مضاعفات الآخر يبقى the two vectors
+
+427
+00:46:03,410 --> 00:46:12,890
+منهم اتنين واحد زيرو and اللي هو تلاتة زيرو واحد
+
+428
+00:46:12,890 --> 00:46:24,470
+are linearly independent because any one of them
+
+429
+00:46:24,470 --> 00:46:27,930
+is
+
+430
+00:46:27,930 --> 00:46:32,310
+not a multiple
+
+431
+00:46:35,060 --> 00:46:44,520
+of multiple of the other هذا
+
+432
+00:46:44,520 --> 00:46:47,880
+بدي اعطيك ان ال basis المطلوب
+
+433
+00:46:49,640 --> 00:46:57,560
+is the set يبقى هو عبارة عن المجموعة بحط فيها ال
+
+434
+00:46:57,560 --> 00:47:03,120
+vector الأول اتنين واحد زيرو و بروح بحط ال vector
+
+435
+00:47:03,120 --> 00:47:08,700
+التاني تلاتة زيرو واحد الشكل اللي عندنا هنا
+
+436
+00:47:14,930 --> 00:47:20,530
+حد فيكوا لايه تساؤل هنا؟ يعني كل أندعها بيقابلها
+
+437
+00:47:20,530 --> 00:47:26,450
+vector space خاص بها، يبقى كأنه فيها two vector أو
+
+438
+00:47:26,450 --> 00:47:31,490
+two eigenspaces، حد فيكوا لايه تساؤل؟ طيب أعطيكوا
+
+439
+00:47:31,490 --> 00:47:31,890
+العافية
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/v0cHtZxEtkI.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/v0cHtZxEtkI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..57f3c86b34f60bbf1150d63f33deddf141b906fe
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/v0cHtZxEtkI.srt
@@ -0,0 +1,1431 @@
+1
+00:00:19,490 --> 00:00:23,750
+بسم الله الرحمن الرحيم المرة اللي فاتت بدأنا في
+
+2
+00:00:23,750 --> 00:00:28,150
+موضوع ال vector spaces الفضاءات الاتجاهية أعطينا 
+
+3
+00:00:28,150 --> 00:00:32,090
+تعريف وإذا لو عندي 6 V وحطينا عليها عملية جمع
+
+4
+00:00:32,090 --> 00:00:37,970
+وعملية ضرب نعرفها بأي طريقة أنشأنا فهذا بيكون لـ V
+
+5
+00:00:37,970 --> 00:00:43,490
+مع الضرب مع الجمع vector space إذا تحققت عشر خواص
+
+6
+00:00:43,490 --> 00:00:48,580
+وذكرنا هذه الخواص وأخذنا على ذلك بدل المثال 4 وهنا
+
+7
+00:00:48,580 --> 00:00:56,100
+نكمل الأمثلة على نفس الموضوع يفترض أن V هو عبارة
+
+8
+00:00:56,100 --> 00:01:00,880
+عن set of all ordered pairs X1 و X2 بعد X1 و X2
+
+9
+00:01:00,880 --> 00:01:05,240
+موجودة في R نعرف عملية الجمع وعملية الضرب على V
+
+10
+00:01:05,240 --> 00:01:10,110
+بالتاليلو جمعت two elements يبقى المُركّبة الأولى
+
+11
+00:01:10,110 --> 00:01:14,430
+زائد المُركّبة الأولى والمُركّبة الثانية ناقص
+
+12
+00:01:14,430 --> 00:01:18,390
+المُركّبة الثانية يعني عرفت عملية الجمع بهذه
+
+13
+00:01:18,390 --> 00:01:24,090
+الطريقة وعملية الضرب component-wise عادي جدا ما في
+
+14
+00:01:24,090 --> 00:01:31,230
+مشكلة بسأل هل ال V هذا vector space ولا لأ بقوله
+
+15
+00:01:31,230 --> 00:01:37,050
+كويس من ضمن من ضمن البنود تبعات المرة اللي فاتت و
+
+16
+00:01:37,050 --> 00:01:42,330
+أعتقد كان البند الثاني أنه عندك U زائد V بيكون V
+
+17
+00:01:42,330 --> 00:01:47,590
+زائد U يعني عملية الجمع عملية إبدالية بنشوف هل
+
+18
+00:01:47,590 --> 00:01:52,150
+عملية الجمع اللي عرفنا بها بهذه الطريقة عملية إبدالية
+
+19
+00:01:52,150 --> 00:01:58,520
+ولا لأ فلو جهة goals له هنا solution يبقى أنا بدي
+
+20
+00:01:58,520 --> 00:02:04,300
+آخذ ال U زائد ال V وأشوف إيش بتعطينا يبقى ال U
+
+21
+00:02:04,300 --> 00:02:15,240
+زائد ال V تساوي الآن يعني X1 و X2 زائد Y1 و Y2
+
+22
+00:02:15,240 --> 00:02:24,410
+يساوي حسب التعريف إلى x1 زائد y1 و x2 ناقص y2 لو
+
+23
+00:02:24,410 --> 00:02:36,670
+جئت قلت ال V زائد ال U يبقى y1 و y2 زائد x1 و x2
+
+24
+00:02:36,670 --> 00:02:46,700
+و يساوي y1 زائد x1 و y2 ناقص x2 ما هو رأيك في
+
+25
+00:02:46,700 --> 00:02:53,540
+العملتين هذين؟ هل النتيجة هي نفس النتيجة؟ لأ ال term
+
+26
+00:02:53,540 --> 00:02:57,360
+الأول صحيح هو ال term الأول بس ال term الثاني هذا
+
+27
+00:02:57,360 --> 00:03:02,680
+ماهواش ال term هذا هذا نفسه بس بإشارة إيه مخالفة
+
+28
+00:03:02,680 --> 00:03:11,820
+يبقى هدول ما همش بعض يبقى هنا ال V is not a vector
+
+29
+00:03:11,820 --> 00:03:14,620
+space because
+
+30
+00:03:16,680 --> 00:03:23,920
+إن الـ U زائد الـ V لا يساوي الـ V زائد الـ U يبقى
+
+31
+00:03:23,920 --> 00:03:28,800
+سقطت إحدى الخواص وبالتالي هذا ليس vector space
+
+32
+00:03:28,800 --> 00:03:30,420
+example 6
+
+33
+00:03:36,230 --> 00:03:43,450
+بقول let V تساوي let V تساوي the set of all
+
+34
+00:03:43,450 --> 00:03:50,650
+elements X وY وZ بحيث
+
+35
+00:03:50,650 --> 00:03:58,830
+أن X وY وZ كلهم أعداد حقيقية موجودة في R define
+
+36
+00:03:58,830 --> 00:04:01,690
+addition
+
+37
+00:04:04,550 --> 00:04:15,110
+and multiplication on
+
+38
+00:04:15,110 --> 00:04:24,410
+V by X
+
+39
+00:04:24,410 --> 00:04:31,070
+واحد و Y واحد و Z واحد زائد
+
+40
+00:04:54,750 --> 00:04:56,150
+Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2Y2
+
+41
+00:04:57,890 --> 00:05:07,570
+الـ a ال x و ال y و ال z بده يساوي x و 1 و z
+
+42
+00:05:07,570 --> 00:05:19,470
+السؤال هو is V a vector space هل هذا عبارة عن V a
+
+43
+00:05:19,470 --> 00:05:21,370
+vector space أم لا؟
+
+44
+00:05:29,690 --> 00:05:31,950
+هل هذا vector of space هو الله موهاش vector of
+
+45
+00:05:31,950 --> 00:05:39,590
+space بنقول الله أعلم نيجي لل solution لو
+
+46
+00:05:39,590 --> 00:05:47,270
+جئت على بعض الخواص مثلا و جئت قلت خديلي a في u
+
+47
+00:05:47,270 --> 00:05:55,730
+زائد v بنشوف إيش بتعطينا يعني هذا الكلام a v u زائد
+
+48
+00:05:55,730 --> 00:06:02,730
+ال v اللي هو x واحد و y واحد و z واحد زائد اللي هو
+
+49
+00:06:02,730 --> 00:06:11,280
+x اتنين و y اتنين و z اتنين هذا كله كلام يساوي يبقى
+
+50
+00:06:11,280 --> 00:06:24,660
+يساوي إيه في نيجي X1 زائد X2 Y1 زائد Y2 Z1 زائد Z2
+
+51
+00:06:24,660 --> 00:06:31,230
+يساوي يبقى صار عندي scalar a في element موجود في ال
+
+52
+00:06:31,230 --> 00:06:35,730
+vector space حسب الضرب اللي عندها بقول لو تضرب a
+
+53
+00:06:35,730 --> 00:06:39,490
+في ال element بضل ال element زي ما هم عدا اللي في
+
+54
+00:06:39,490 --> 00:06:44,870
+النص مصير جداش واحد صحيح يبقى هذا الكلام بدي يساوي
+
+55
+00:06:44,870 --> 00:06:52,880
+x واحد زي x اتنين و واحد و y واحد زي y اتنين طب لو
+
+56
+00:06:52,880 --> 00:06:59,340
+جئت أخذت ال A في ال U زائد ال A في ال V يبقى ال A
+
+57
+00:06:59,340 --> 00:07:07,520
+X واحد و Y واحد و Z واحد زائد A في X اتنين و Y
+
+58
+00:07:07,520 --> 00:07:14,270
+اتنين و Z اتنين و Y ساوي حسب تعريف الضرب يبقى هذا
+
+59
+00:07:14,270 --> 00:07:22,270
+شو بدي يعطينا X واحد وواحد صحيح وزد واحد زائد برضه
+
+60
+00:07:22,270 --> 00:07:30,350
+هذا X اتنين واحد وزد اتنين الآن حسب تعريف الجمع
+
+61
+00:07:30,350 --> 00:07:35,710
+يبقى الجمع component wise يبقى X واحد زائد X
+
+62
+00:07:35,710 --> 00:07:43,850
+اتنين واحد زائد واحد يسوي كده اتنين وزد واحد زائد
+
+63
+00:07:43,850 --> 00:07:48,770
+زد اتنين إيش رأيكوا في هذه النتيجة هذه موجودة في
+
+64
+00:07:48,770 --> 00:07:55,130
+V؟ لأ يبقى هذه does not belong to V السبب أن هذا
+
+65
+00:07:55,130 --> 00:08:00,550
+اتنين وليس واحد صحيح معناته ال V هذا ماله is not a
+
+66
+00:08:00,550 --> 00:08:10,790
+vector space يبقى هنا V is not a vector space
+
+67
+00:08:15,820 --> 00:08:20,400
+Need some properties
+
+68
+00:08:20,400 --> 00:08:25,280
+of
+
+69
+00:08:25,280 --> 00:08:35,380
+a vector space Let
+
+70
+00:08:35,380 --> 00:08:45,120
+V be a vector space
+
+71
+00:08:46,570 --> 00:08:56,590
+and ال U موجودة في V and
+
+72
+00:08:56,590 --> 00:09:05,550
+let ال
+
+73
+00:09:05,550 --> 00:09:13,290
+U موجودة في V and ال A موجودة في R
+
+74
+00:09:17,060 --> 00:09:26,940
+النقطة الأولى Zero في you يساوي ال zero النقطة
+
+75
+00:09:26,940 --> 00:09:35,840
+الثانية ال a في ال zero بده يساوي ال zero النقطة
+
+76
+00:09:35,840 --> 00:09:43,520
+الثالثة سالب واحد في ال you يساوي سالب you
+
+77
+00:09:43,520 --> 00:09:46,040
+exercises
+
+78
+00:09:47,820 --> 00:09:57,220
+ثلاثة واحد المسائل اثنين خمسة ستة ثمانية تسعة عشر
+
+79
+00:09:57,220 --> 00:10:03,940
+ثلاث عشرة خمس عشرة سبع عشرة ثمان عشرة
+
+80
+00:10:47,910 --> 00:10:52,310
+نرجع للخواص اللي قدامنا هذه يبقى عندنا some
+
+81
+00:10:52,310 --> 00:10:56,170
+properties of a vector space يبقى بعض الخواص
+
+82
+00:10:56,170 --> 00:10:59,830
+المتعلقة بال vector space فبجي بقول لو كان ال V هو
+
+83
+00:10:59,830 --> 00:11:06,410
+vector space واخت vector U موجود في V and A scalar
+
+84
+00:11:06,410 --> 00:11:11,310
+موجود في R then الـ zero scalar في ال U ك vector
+
+85
+00:11:25,560 --> 00:11:29,800
+بعد ذلك لو ضربت ال scalar a في ال zero vector برضه
+
+86
+00:11:29,800 --> 00:11:34,580
+بدي يعطيني main ال zero vector سالب واحد لو ضربته
+
+87
+00:11:34,580 --> 00:11:39,660
+في u بدي يعطيني main ال u تماما طيب ما هو السبب
+
+88
+00:11:39,660 --> 00:11:43,360
+لأن احنا قولنا الخاصية العاشرة واحد في u بدي
+
+89
+00:11:43,360 --> 00:11:47,940
+يعطيني ال u تماما ومن ضمن التعريف في البداية قلنا لو
+
+90
+00:11:47,940 --> 00:11:53,840
+أخذت a scalar من R وضربته في عنصر من V فال A في ال
+
+91
+00:11:53,840 --> 00:11:58,880
+U بيكون موجود في V ومن هنا سالب واحد في U بيكون
+
+92
+00:11:58,880 --> 00:12:04,760
+سالب U وهو موجود أيضا في ال V طب ننتقل الآن إلى
+
+93
+00:12:04,760 --> 00:12:10,360
+الموضوع الثاني وهو موضوع ال subspaces يبقى بدنا
+
+94
+00:12:10,360 --> 00:12:16,660
+نيجي ل section تلاتة اتنين اللي هو subspaces
+
+95
+00:12:16,660 --> 00:12:24,020
+الفضاءات الجزئية نعطي تعريف لل subspace وبعد هيك
+
+96
+00:12:24,020 --> 00:12:32,600
+بنروح ناخد أمثلة عليه يبقى definition a
+
+97
+00:12:32,600 --> 00:12:37,640
+subspace a subspace
+
+98
+00:12:37,640 --> 00:12:55,910
+u of a vector space V is called a subspace is a
+
+99
+00:12:55,910 --> 00:13:05,850
+subset وليس subset a subset U of a vector space V
+
+100
+00:13:05,850 --> 00:13:07,790
+is called
+
+101
+00:13:10,410 --> 00:13:18,730
+A subspace of
+
+102
+00:13:18,730 --> 00:13:23,450
+VFLU
+
+103
+00:13:23,450 --> 00:13:32,130
+is itself
+
+104
+00:13:32,130 --> 00:13:34,750
+a vector space
+
+105
+00:13:41,100 --> 00:13:47,680
+vector space under the
+
+106
+00:13:47,680 --> 00:13:57,320
+same operations of
+
+107
+00:13:57,320 --> 00:14:08,460
+اللي هو V firearm let
+
+108
+00:14:08,460 --> 00:14:22,680
+ال V be a vector space be a vector space and let
+
+109
+00:14:22,680 --> 00:14:31,640
+اليوم be a subset
+
+110
+00:14:31,640 --> 00:14:40,180
+of V then اليوم
+
+111
+00:14:41,970 --> 00:14:53,650
+is a subspace of the if and only if النقطة الأولى
+
+112
+00:14:53,650 --> 00:15:06,850
+الـ U is non-empty النقطة الثانية if الـ C موجود في
+
+113
+00:15:06,850 --> 00:15:08,930
+R and
+
+114
+00:15:11,520 --> 00:15:21,440
+الـ V موجود في اليوم then الـ C في الـ V موجود في
+
+115
+00:15:21,440 --> 00:15:32,160
+اليوم النقطة الثالثة if V1 وV2 موجودات في اليوم
+
+116
+00:15:32,160 --> 00:15:38,980
+then V1 زائد V2 موجودات في اليوم
+
+117
+00:15:42,380 --> 00:15:47,240
+example one let
+
+118
+00:15:47,240 --> 00:15:57,920
+ال V بدأ تساوي R تكيب اللي هي set of قلم X واحد و
+
+119
+00:15:57,920 --> 00:16:05,760
+X اتنين و X تلاتة such that X واحد و X اتنين و X
+
+120
+00:16:05,760 --> 00:16:10,640
+تلاتة موجودة في set of real number بي
+
+121
+00:16:14,270 --> 00:16:23,050
+Vector Vector Space Under
+
+122
+00:16:23,050 --> 00:16:26,950
+The
+
+123
+00:16:26,950 --> 00:16:32,670
+Usual Addition
+
+124
+00:16:32,670 --> 00:16:36,850
+And Multiplication
+
+125
+00:16:42,120 --> 00:16:49,680
+and multiplication let ال
+
+126
+00:16:49,680 --> 00:16:56,320
+U بدسة with a set of all element X و Zero و Zero
+
+127
+00:16:56,320 --> 00:17:09,760
+بحيث ال X موجودة في R السؤال هو is U a subspace
+
+128
+00:17:12,290 --> 00:17:14,910
+of a أم لأ
+
+129
+00:17:49,720 --> 00:17:50,820
+مش كفاية
+
+130
+00:18:18,210 --> 00:18:21,950
+بنروح الكلام اللي احنا كتبناه هذا يبقى احنا في ال
+
+131
+00:18:21,950 --> 00:18:25,770
+section الماضي جئنا نتحدث عن ال vector space اللي
+
+132
+00:18:25,770 --> 00:18:29,210
+هم بيروحوا ياخذوا مجموعة جزئية من هذا ال vector
+
+133
+00:18:29,210 --> 00:18:34,250
+space هذه المجموعة قد تكون vector space وقد لا
+
+134
+00:18:34,250 --> 00:18:39,310
+تكون vector space بيجينا نشوف ما هو الشرط أن
+
+135
+00:18:39,310 --> 00:18:43,630
+المجموعة هذه لو أخذتها تبقى vector space فمثلا لو
+
+136
+00:18:43,630 --> 00:18:46,350
+قلت كل البنات اللي موجودة في القاع هدول vector
+
+137
+00:18:46,350 --> 00:18:51,710
+space بتاخذ المجموعة هذه هل المجموعة هذه في حد
+
+138
+00:18:51,710 --> 00:18:55,350
+ذاتها بتكون vector space ولا .. طبعا هذه مجموعة
+
+139
+00:18:55,350 --> 00:18:59,630
+جزئية من مين؟ من المجموعة الكبيرة فهل هذه المجموعة
+
+140
+00:18:59,630 --> 00:19:04,300
+الجزئية بتكون subspace أم لا هذا السؤال التعريف
+
+141
+00:19:04,300 --> 00:19:08,520
+بيقول الـ subset U of a vector space V يبقى احنا
+
+142
+00:19:08,520 --> 00:19:12,280
+أخذنا مجموعة جزئية من ال vector space V هذه is
+
+143
+00:19:12,280 --> 00:19:18,600
+called a subspace بسميها فضاء اتجاهي جزئي of V إذا
+
+144
+00:19:18,600 --> 00:19:23,100
+كان الـ U نفسها عبارة عن vector space under the
+
+145
+00:19:23,100 --> 00:19:28,060
+same operations of V يبقى بنات القاعة كلها vector
+
+146
+00:19:28,060 --> 00:19:32,120
+space عليها عملية جمع عليها عملية ضرب أخذت مجموعة
+
+147
+00:19:32,120 --> 00:19:36,280
+منهم إذا و الله هذه المجموعة اللي أخذتها لقيتها
+
+148
+00:19:36,280 --> 00:19:40,840
+vector space جديد تحت نفسه العمليتين بتاعة ال
+
+149
+00:19:40,840 --> 00:19:45,740
+vector space الأصلي يبقى بقول هذه subspace طب
+
+150
+00:19:45,740 --> 00:19:50,360
+هتقولي واحدة طب واحنا كل مرة بدنا نيجي نطبق العشر
+
+151
+00:19:50,360 --> 00:19:54,500
+خواص على هذه المجموعة الجزئية هذه قصة طويلة فرح
+
+152
+00:19:54,500 --> 00:19:58,700
+العلماء جلسوا مع بعض ودرسوا الموضوع واستطاعوا أنهم
+
+153
+00:19:58,700 --> 00:20:04,760
+يختصروا هذه العشرة بنود في ثلاثة بنود فقط لا غير
+
+154
+00:20:04,760 --> 00:20:09,800
+ما هي البنود الثلاثة انحطت بصيغة النظرية التالية
+
+155
+00:20:09,930 --> 00:20:14,650
+لتكن V بـ vector space و U عبارة عن subset من V
+
+156
+00:20:14,650 --> 00:20:19,090
+يبقى الـ U بقول أنها subspace if and only if يعني
+
+157
+00:20:19,090 --> 00:20:23,650
+لو تحققت الشروط الثلاثة بيكون الـ U subspace ولا
+
+158
+00:20:23,650 --> 00:20:29,030
+عكس لو كان U subspace يجب أن تتحقق من الشروط
+
+159
+00:20:29,030 --> 00:20:32,890
+الثلاثة يبقى لو أعطاني اجمعية جزئية من vector space
+
+160
+00:20:32,890 --> 00:20:37,410
+وقال لي شوف هل هي subspace ولا لأ بقوله بدي أشوف
+
+161
+00:20:37,410 --> 00:20:41,870
+هل ال set هذه non-empty ولا لأ على الأقل بدي أثبت
+
+162
+00:20:41,870 --> 00:20:47,230
+أن فيها ولو عنصر واحد فقط تمام يعني أساس ما تبقاش
+
+163
+00:20:47,230 --> 00:20:50,850
+non-empty فيها ولو عنصر واحد إن شاء الله يكون
+
+164
+00:20:50,850 --> 00:20:57,190
+العنصر الصفري اثنين لو أخذت أي element من R يعني
+
+165
+00:20:57,190 --> 00:21:01,930
+أي real number أو scalar وأخذت أي vector space من
+
+166
+00:21:01,930 --> 00:21:06,490
+ال U هذه من ال subset وضربت اثنين اللي جئته في U
+
+167
+00:21:06,490 --> 00:21:10,390
+يبقى تحقق ال condition الثاني أروح لل condition
+
+168
+00:21:10,390 --> 00:21:16,350
+الثالث لو أخذت أي عنصر من U ولجأت حاصل الجمع
+
+169
+00:21:16,350 --> 00:21:20,450
+اللي موجود في U إذا ال U هذا على طول الخط سيكون
+
+170
+00:21:20,450 --> 00:21:25,910
+ماله subspace يكفيني للحكم على subset اللي بأخده
+
+171
+00:21:25,910 --> 00:21:29,750
+لأن subspace ثلاثة شر وإن الـ subset اللي أخذتها
+
+172
+00:21:29,750 --> 00:21:34,410
+الـ non-empty بمعنى على الأقل بدي أثبت إن فيها ولو
+
+173
+00:21:34,410 --> 00:21:40,770
+عنصر واحد فقط اثنين لو أخذت scalar و vector من ال
+
+174
+00:21:40,770 --> 00:21:45,150
+U ضربت اثنين مع بعض جئته في U ثلاثة لو أخذت two
+
+175
+00:21:45,150 --> 00:21:49,110
+vectors من هذه ال U جمعتهم لجئنا الناتج في U وليس
+
+176
+00:21:49,110 --> 00:21:52,930
+خارج U automatic ال U بقدر أقول عليها ما لها
+
+177
+00:21:52,930 --> 00:21:58,950
+subspace من V نبدأ بأخذ الأمثلة قال ياخذ الـ vector
+
+178
+00:21:58,950 --> 00:22:04,210
+space اللي هو R تكعيب أو R تلاتة اللي هو the set
+
+179
+00:22:04,210 --> 00:22:07,430
+of all three tuples بحيث X واحد و X اتنين و X
+
+180
+00:22:07,430 --> 00:22:11,450
+تلاتة كلها موجودة في R بدنا نعرف عليهم عملية الجمع
+
+181
+00:22:11,450 --> 00:22:15,950
+والضرب العادية إيش يعني عملية الجمع العادية يعني
+
+182
+00:22:15,950 --> 00:22:19,150
+الجمع ال component و ايزي والضرب لو ضربت scalar
+
+183
+00:22:19,150 --> 00:22:22,890
+في ال components بدي أضربه في كل component من هذه
+
+184
+00:22:22,890 --> 00:22:29,580
+ال components لما سميت ضرب العادي والجمع
+
+201
+00:24:01,930 --> 00:24:06,350
+عليهاش قيود قد تكون صفر وقد لا تكون صفر، القيود على 
+
+202
+00:24:06,350 --> 00:24:10,370
+الـ two components الأخرى يبقى خلصنا النقطة الأولى 
+
+203
+00:24:10,370 --> 00:24:16,290
+النقطة الثانية بيقول لي لو أخدت أي element من R و
+
+204
+00:24:16,290 --> 00:24:21,910
+أي element موجود في V يبقى بالضبط أقول له let C
+
+205
+00:24:21,910 --> 00:24:30,830
+موجود في R and الـ U بيكون X و 0 و 0 موجود في U
+
+206
+00:24:33,240 --> 00:24:40,600
+بتاخد أمانات C في الـ U إذا هذه بدأت تساوي C في X
+
+207
+00:24:40,600 --> 00:24:47,120
+و Zero بـ Zero قلت ضرب ضرب عادي يبقى هذيش بتعطينا C
+
+208
+00:24:47,120 --> 00:24:52,670
+X و C في Zero بـ Zero موجودة في U ولا لا؟ هذه
+
+209
+00:24:52,670 --> 00:24:57,450
+المركبتين تنتهي بـ 0 وهذه مين ما كانت it تكون يبقى
+
+210
+00:24:57,450 --> 00:25:01,010
+معانا مشكلة إذا تحقق مين ال condition التاني؟
+
+211
+00:25:01,010 --> 00:25:04,290
+بتروح على ال condition التالت يبقى بدي أجي لـ الـ
+
+212
+00:25:04,290 --> 00:25:14,150
+condition الثالث يبقى بدي أقوله let مثلا الـ U و الـ
+
+213
+00:25:14,150 --> 00:25:26,980
+V let الـ U تساوي X و Zero و Zero و V تساوي Y و Zero
+
+214
+00:25:26,980 --> 00:25:34,160
+و Zero موجودة في الـ U موجودة في الـ U ولا لأ لأن
+
+215
+00:25:34,160 --> 00:25:38,000
+المركبة التانية هي كلها فقداش بـ Zero و الأولى مين 
+
+216
+00:25:38,000 --> 00:25:44,670
+ما كانت تكون then بدي أخد الجامع تبعهم يبقى بدي أخد
+
+217
+00:25:44,670 --> 00:25:51,070
+الـ U زائد الـ V يبقى الـ X و Zero و Zero زائد Y و
+
+218
+00:25:51,070 --> 00:25:55,530
+Zero و Zero يساوي جالي جامع عادي يبقى الجامع
+
+219
+00:25:55,530 --> 00:26:01,750
+العادي هو الـ component Y's يبقى X زائد Y و Zero و
+
+220
+00:26:01,750 --> 00:26:06,020
+Zero موجود في الـ U ولا لا يا ابني يبقى تحققت
+
+221
+00:26:06,020 --> 00:26:10,120
+ثلاثة شروط ولا لأ؟ خلصت يبقى إذا الـ U هو عبارة عن 
+
+222
+00:26:10,120 --> 00:26:20,340
+subspace يبقى هنا الساعة الـ U is a subspace of V
+
+223
+00:26:20,340 --> 00:26:22,420
+وأنت هنا من المثلة
+
+224
+00:26:28,240 --> 00:26:33,580
+مين ما تيجي تحط تحط ما عنديش قيود على X أنا بقول لك
+
+225
+00:26:33,580 --> 00:26:37,100
+بدك تجيب لي ولو عنصر واحد فستبينوا أن ها الـ none
+
+226
+00:26:37,100 --> 00:26:40,300
+empty يعني مش القرآن نزل من السماء لازم يكون عنصر
+
+227
+00:26:40,300 --> 00:26:44,170
+الـ صفر لأ لأ ليس بضرورة أي عنصر بيعني يكون موجود
+
+228
+00:26:44,170 --> 00:26:47,650
+حقيقيا يعني لو قلت أنا شيلت زيرو و حطيت بدله مية
+
+229
+00:26:47,650 --> 00:26:51,470
+حدله كلام عندي المية موجودة في R ولا لأ موجودة
+
+230
+00:26:51,470 --> 00:26:55,090
+يبقى أنا متقيل بالـ definition يبقى مية و زيرو و
+
+231
+00:26:55,090 --> 00:27:02,670
+زيرو موجودة في R في الـ U إذا الـ U is non-empty طيب
+
+232
+00:27:02,670 --> 00:27:04,410
+example two
+
+233
+00:27:11,930 --> 00:27:16,850
+Example 2 هذا سؤال اتنين من الكتاب كذلك بقول let
+
+234
+00:27:16,850 --> 00:27:23,690
+الـ V تساوي R2 اللي هي the set of all elements X و
+
+235
+00:27:23,690 --> 00:27:27,710
+Y بحيث الـ X و الـ Y موجودة في الـ set of real
+
+236
+00:27:27,710 --> 00:27:34,340
+numbers قال لي let الـ U بدها تساوي الـ set of all
+
+237
+00:27:34,340 --> 00:27:40,400
+elements واحد و Y such that الـ Y موجودة في R
+
+238
+00:27:40,400 --> 00:27:49,060
+السؤال هو is الـ U a
+
+239
+00:27:49,060 --> 00:27:57,160
+subspace of V أم
+
+240
+00:27:57,160 --> 00:27:57,820
+لأ؟
+
+241
+00:28:06,370 --> 00:28:11,550
+بمجرد النظر يا بنات لما أقول الـ U بالشكل اللي 
+
+242
+00:28:11,550 --> 00:28:15,490
+عندنا هذا يبقى ال condition الأول متحقق طبيعي ولا
+
+243
+00:28:15,490 --> 00:28:25,890
+لا بدورش عليه الأمر الثاني شرط التاني متحقق؟ لأ مش
+
+244
+00:28:25,890 --> 00:28:32,380
+متحقق طب التالت؟ يبقى لشرط التاني و لشرط التالت
+
+245
+00:28:32,380 --> 00:28:36,080
+متحقق يبقى أنا باهمني الشرط التاني باهمني بس واحد
+
+246
+00:28:36,080 --> 00:28:40,120
+فيهم لو أثبتت أن واحد الـ three conditions is not
+
+247
+00:28:40,120 --> 00:28:44,080
+satisfied يبقى على طول الخط بطل يحصل هذا الـ
+
+248
+00:28:44,080 --> 00:28:54,080
+subspace solution الـ U is not a subspace because
+
+249
+00:28:54,080 --> 00:29:05,150
+السبب if واحد و واي واحد و واحد و واي اتنين موجودات
+
+250
+00:29:05,150 --> 00:29:12,550
+فيه then واحد و واي واحد زائد واحد و واي اتنين
+
+251
+00:29:12,550 --> 00:29:18,150
+يساوي اتنين و واي واحد زائد واي اتنين و هذا does
+
+252
+00:29:18,150 --> 00:29:23,650
+not belong to U لذلك الـ U is not a subspace of
+
+253
+00:29:23,650 --> 00:29:23,910
+me
+
+254
+00:29:39,180 --> 00:29:48,940
+Example 3 let
+
+255
+00:29:48,940 --> 00:30:01,050
+V تساوي the set of all elements a و b و c و d بحيث
+
+256
+00:30:01,050 --> 00:30:08,930
+الـ a و الـ b و الـ c و الـ d كلها أعداد حقيقية موجودة
+
+257
+00:30:08,930 --> 00:30:09,630
+في R
+
+258
+00:30:13,120 --> 00:30:25,040
+كل المصفوفات اللي على الشكل خمسة a b c d بحيث الـ a
+
+259
+00:30:25,040 --> 00:30:31,400
+و الـ b و الـ c و الـ d موجودة في set of real numbers
+
+260
+00:30:31,400 --> 00:30:37,000
+بقول prove or
+
+261
+00:30:37,000 --> 00:30:42,520
+disprove that
+
+262
+00:30:45,040 --> 00:30:52,300
+الـ U is a subspace of V
+
+263
+00:31:22,620 --> 00:31:28,400
+كل واحدة علمتك بقى اسمها قاضي تعالى، خد اللي حاجة
+
+264
+00:31:28,400 --> 00:31:32,180
+يبقى 
+
+265
+00:31:32,180 --> 00:31:36,300
+بقى أصلا باري على الشخص أن هذا مرة ثانية بقول افترض
+
+266
+00:31:36,300 --> 00:31:41,820
+بيه كل المصوفات لنظامها اتنين في اتنين والعناصر الـ
+
+267
+00:31:41,820 --> 00:31:46,000
+interest الـ A والـ B والـ C والـ D كلهم are real numbers
+
+268
+00:31:46,000 --> 00:31:51,360
+قال يخودي الـ U برضه مصوفة نظامها اتنين في اتنين بس
+
+269
+00:31:51,360 --> 00:31:56,060
+العنصر الأول فيها هو مضاعفات العنصر الأول في مين
+
+270
+00:31:56,060 --> 00:32:01,730
+في V بيقول لي هل هذي بيكون subspace ولا ماهواش 
+
+271
+00:32:01,730 --> 00:32:05,770
+subspace يعني prove or disprove إذا بتقدر تثبت أنه
+
+272
+00:32:05,770 --> 00:32:09,670
+vector space كان بيها بتقدر تثبت أنه ماهواش vector
+
+273
+00:32:09,670 --> 00:32:13,290
+space ماهواش subspace كان بيها إيه بيها اللي تقدر
+
+274
+00:32:13,290 --> 00:32:19,250
+عليه اللي تقدر عليه بقوله كويس الآن أنا أدعي أن الـ
+
+275
+00:32:19,250 --> 00:32:25,700
+U هذي is non-empty صح؟ لأن على الأقل المصفوفة
+
+276
+00:32:25,700 --> 00:32:30,300
+الصفرية موجودة في الـ space اللي عندنا هنا يبقى هنا
+
+277
+00:32:30,300 --> 00:32:38,780
+النقطة الأولى الـ U is non-empty تمام؟ non-empty
+
+278
+00:32:38,780 --> 00:32:45,520
+ليش؟ since لو أخدت المصفوفة الصفرية يا بنات مش 
+
+279
+00:32:45,520 --> 00:32:53,420
+بقدر أكتبها خمسة في zero و zero و zero صح ولا لأ؟
+
+280
+00:32:53,420 --> 00:32:58,940
+يبقى هذه موجودة في وين؟ موجودة فيه طيب، بدأ نجي
+
+281
+00:32:58,940 --> 00:33:06,580
+للنقطة الثانية بدأ أخد أي element if الـ K موجود في
+
+282
+00:33:06,580 --> 00:33:10,700
+الـ A then
+
+283
+00:33:10,700 --> 00:33:17,680
+لو أخدت الـ .. بدأ أخد كمان element موجود في الـ U
+
+284
+00:33:17,680 --> 00:33:19,060
+and
+
+285
+00:33:20,930 --> 00:33:29,770
+الـ A تساوي الخمسة A,B,C,D موجودة في الـ U
+
+286
+00:33:38,010 --> 00:33:42,750
+مش الـ K في الـ A تعتبر مضروبة في كل عنصر من عناصر
+
+287
+00:33:42,750 --> 00:33:52,690
+المصفوفة يبقى بقدر أقول هذه خمسة A K خمسة B خمسة C
+
+288
+00:33:52,690 --> 00:34:05,980
+خمسة K خمسة .. لا ك بي ولا بي ك بي ك هنا سي ك هنا
+
+289
+00:34:05,980 --> 00:34:13,390
+دي ك بالشكل اللي عندنا هنا موجودة في U ولا لا؟ هذا
+
+290
+00:34:13,390 --> 00:34:18,770
+عنصر و هذا عنصر و هذا عنصر و الخمسة مضروبة في
+
+291
+00:34:18,770 --> 00:34:24,070
+العنصر إذا موجودة ولا لا يبقى كافة هذه موجودة في
+
+292
+00:34:24,070 --> 00:34:29,750
+الـ U بدي أروح لل condition الثالث بدي أخد two
+
+293
+00:34:29,750 --> 00:34:41,230
+elements الـ A يساوي خمسة A و هنا بي و هنا سي و دي
+
+294
+00:34:41,230 --> 00:34:49,910
+و بي تساوي اللي همين خمسة A one و B one و C one و
+
+295
+00:34:49,910 --> 00:34:55,070
+D one then بتاخد 
+
+296
+00:34:55,070 --> 00:35:03,220
+الـ A زي دي الـ B الـ A زائد الـ B يبقى الجامع خمسة A
+
+297
+00:35:03,220 --> 00:35:08,780
+زائد خمسة A1 الجامع على الأنصفات component-wise
+
+298
+00:35:08,780 --> 00:35:20,520
+وبعد ذلك B زائد B1 و C زائد C1 و D زائد D1 يساوي
+
+299
+00:35:20,520 --> 00:35:26,080
+أظن بقدر أخد خمسة عامل مشترك منهم يبقى هذا بيعطيني
+
+300
+00:35:26,080 --> 00:35:37,000
+خمسة في A زائد A1 B زائد B1 C زائد C1 D زائد D1
+
+301
+00:35:37,000 --> 00:35:41,350
+موجودة في الـ U ولا يا بنات؟ يبقى تحققت الشروط
+
+302
+00:35:41,350 --> 00:35:46,530
+اختلقتها ولا لا يبقى معناته الـ U دي is a subspace
+
+303
+00:35:46,530 --> 00:35:57,570
+يبقى باجي بقوله بص وهكذا اللي هو الـ U is a
+
+304
+00:35:57,570 --> 00:36:04,370
+subspace of
+
+305
+00:36:04,370 --> 00:36:11,170
+V يعني احنا بنحاول نحقق الشروط التلاتة إذا حققناها
+
+306
+00:36:11,170 --> 00:36:26,570
+كان بيها طيب نيجي ناخد كمان مثال example 4 بيقول
+
+307
+00:36:26,570 --> 00:36:36,670
+لـ let أبطل V يساوي RN مين الـ RN؟ The set of all X1
+
+308
+00:36:36,670 --> 00:36:48,910
+و X2 و XN بحيث أن X1 و X2 و XN كله موجود في الـ set of
+
+309
+00:36:48,910 --> 00:36:54,050
+real numbers Let الـ A
+
+310
+00:37:00,870 --> 00:37:13,510
+مصفوفة مربعة let U be the set of all solutions
+
+311
+00:37:13,510 --> 00:37:20,110
+of
+
+312
+00:37:20,110 --> 00:37:23,750
+the system
+
+313
+00:37:25,230 --> 00:37:37,990
+اكس بدي ساوي زيرو show that show that show that أن
+
+314
+00:37:37,990 --> 00:37:45,990
+الـ U is a subspace of RN
+
+315
+00:38:16,970 --> 00:38:24,450
+مرة تانية السؤال بيقول ما يعني افترضي أن عندي الـ 
+
+316
+00:38:24,450 --> 00:38:29,290
+vector space V the set of all innitube pairs X1 و
+
+317
+00:38:29,290 --> 00:38:33,170
+X2 و XN بحيث كل الـ X هذه موجودة في R
+
+318
+00:38:38,140 --> 00:38:43,200
+افترض الـ U هو كل الحلول للـ system الهوموجينية
+
+319
+00:38:43,200 --> 00:38:49,200
+قال يبيني أن الـ U عبارة عن subspace من مين؟ من R
+
+320
+00:38:49,200 --> 00:38:54,570
+نرجع بالذاكرة إلى الوراء لما أقول عندي homogeneous
+
+321
+00:38:54,570 --> 00:39:00,790
+system يبقى في عندي إما حل واحد فقط وهو الحل
+
+322
+00:39:00,790 --> 00:39:06,410
+الصفري أو عندي عدد لنهائي من الحلول والعدد إن هي
+
+323
+00:39:06,410 --> 00:39:11,710
+يجتمل على الحل الصفري إذا في عندي حل ولا مافيش حل
+
+324
+00:39:12,300 --> 00:39:16,880
+يبقى الـ set هذه لا يمكن أن تكون empty يبقى non
+
+325
+00:39:16,880 --> 00:39:22,820
+-empty لأن على الأقل فيها الحل الصفري تمام فبعدين
+
+326
+00:39:22,820 --> 00:39:27,900
+بقول solution the 
+
+327
+00:39:27,900 --> 00:39:39,880
+set U is non-empty because is
+
+328
+00:39:39,880 --> 00:39:50,650
+zero اللي هو بده يساوي Zero و Zero و Zero is the
+
+329
+00:39:50,650 --> 00:39:55,550
+trivial solution
+
+330
+00:39:55,550 --> 00:40:08,780
+of الـ AX بده يساوي Zero Because Zero هذا موجود U is
+
+331
+00:40:08,780 --> 00:40:14,140
+the trivial solution of M يبقى بناء عليه الـ U هذه
+
+332
+00:40:14,140 --> 00:40:20,180
+مالها is non-empty يبقى تحقق من ال condition الأول
+
+333
+00:40:20,180 --> 00:40:23,940
+يبقى هذا ال condition الأول بالداخل ال condition
+
+334
+00:40:23,940 --> 00:40:33,940
+الثاني بدي أخد element موجود في R يبقى هنا fc موجود
+
+335
+00:40:33,940 --> 00:40:49,280
+في الـ R and x1 مثلا is a solution of
+
+336
+00:41:02,640 --> 00:41:11,670
+X1 موجود في الـ U ماذا أثبت؟ أثبت أن الـ CX1 موجود
+
+337
+00:41:11,670 --> 00:41:17,130
+في الـ U بمعنى آخر أثبت أن الـ CX1 هو عبارة عن حل
+
+338
+00:41:17,130 --> 00:41:22,370
+لمن؟ للـ homogeneous system صح ولا لا؟ مرة ثانية
+
+339
+00:41:22,370 --> 00:41:26,380
+بقول أنا أخدت ال condition التاني في حالة الـ
+
+340
+00:41:26,380 --> 00:41:31,300
+subspace بقول لو أخدت element من R كسكلر و vector
+
+341
+00:41:31,300 --> 00:41:36,420
+من U و ضربت اتنين في بعض بد النتج يكون وين في U
+
+342
+00:41:36,420 --> 00:41:41,540
+بمعنى آخر لما أخدت x واحد عبارة عن حل وجبت constant
+
+343
+00:41:41,540 --> 00:41:49,020
+C من R بدي C في X1 يكون حل يعني إيش بدي يكون موجود
+
+344
+00:41:49,020 --> 00:41:56,060
+فيه بمعنى آخر إنه C X1 لما أضرب فيه الـ A بديه يساوي
+
+345
+00:41:56,060 --> 00:42:01,780
+كده؟ بديه يساوي Zero إن كان هيك بصير هذا هو حل طيب
+
+346
+00:42:01,780 --> 00:42:06,380
+تمام بقول لك كويس إذا بدي أجي أقول لك consider
+
+347
+00:42:09,300 --> 00:42:18,760
+أو قبل قبل consider يبقى هنا since بما أن x1 a
+
+348
+00:42:18,760 --> 00:42:32,950
+solution of AX بده يساوي zero we have الـ A X1 يبقى
+
+349
+00:42:32,950 --> 00:42:43,370
+كذلك بالنسبة لنا
+
+350
+00:42:46,330 --> 00:42:52,630
+إن طلع هذا الناتج يساوي Zero بيكون فعلا CX1 هو
+
+351
+00:42:52,630 --> 00:42:56,350
+عبارة عن حل لـ هموجينيا الـ system بقوله كويس هذه
+
+352
+00:42:56,350 --> 00:43:00,570
+الآن scalar الـ scalar أخدنا من اسم الـ vector بقدر
+
+353
+00:43:00,570 --> 00:43:04,830
+أخليها جوا وبقدر أطلعها برا من القواس يبقى بقدر 
+
+354
+00:43:04,830 --> 00:43:09,230
+أقول هذا الكلام يساوي CX1
+
+355
+00:43:15,530 --> 00:43:20,350
+يبقى الـ Zero Vector Scalar في Zero Vector بيعطي
+
+356
+00:43:20,350 --> 00:43:26,510
+لمين الـ Zero Vector شو معنى هذا الكلام أن الـ CX1
+
+357
+00:43:26,510 --> 00:43:31,770
+عبارة عن حل للـ homogeneous system يبقى هذا معناته 
+
+358
+00:43:31,770 --> 00:43:43,560
+أن الـ CX1 is a solution of The homogenous
+
+359
+00:43:43,560 --> 00:43:57,120
+system AX == 0 هذا معناه أن CX1 موجود في U
+
+360
+00:44:00,330 --> 00:44:07,070
+افترض عندي حلين موجودات في الـ U يبقى هنا بدأ أقول
+
+361
+00:44:07,070 --> 00:44:17,130
+له let x1 و x2 موجودات في الـ U يبقى مش
+
+362
+00:44:17,130 --> 00:44:23,530
+معنا x1 و x2 عبارة عن إيه؟ حلين لمن؟ للـ
+
+363
+00:44:23,530 --> 00:44:26,990
+homogeneous system يبقى then
+
+364
+00:44:29,570 --> 00:44:42,490
+x1 and x2 are two solutions of the homogeneous
+
+365
+00:44:42,490 --> 00:44:54,630
+system A x بيساوي 0 هذا معناه أن A x1 بيساوي 0 and
+
+366
+00:44:56,270 --> 00:45:04,750
+الـ A X2 بده يساوي 0 طب أنا إيش بدي أثبت؟ بدي أثبت
+
+367
+00:45:04,750 --> 00:45:10,070
+أن مجموعهم بده يكون حل للـ Homogeneous System
+
+368
+00:45:10,070 --> 00:45:16,610
+بمعنى آخر، إذا كنت أثبت إن A X1 زي X2 بده يعطينا
+
+369
+00:45:16,610 --> 00:45:22,940
+0، بتم المطلوب، صح؟ يبقى باجي بقوله هنا الآن بدي 
+
+370
+00:45:22,940 --> 00:45:33,100
+أخد الـ A في x1 زائد x2 بدي أساوي بدي أفك هذا يبقى
+
+371
+00:45:33,100 --> 00:45:44,560
+هذا A x1 زائد A x2 طب A x1 يبقى كده؟ و A x2 يبقى
+
+372
+00:45:44,560 --> 00:45:56,160
+ناتج كده؟ يبقى هذا معناه أن الـ x1 زائد x2 هي حلول
+
+373
+00:45:58,010 --> 00:46:06,590
+الـ AX بدي يساوي 0 هذا معناه أن الـ x1 زيدي الـ x2
+
+374
+00:46:06,590 --> 00:46:23,590
+م
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/x6ZZjvJCeB8.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/x6ZZjvJCeB8.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4c59a2543f75313413ee0bfae3e77a582057a667
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/x6ZZjvJCeB8.srt
@@ -0,0 +1,1703 @@
+1
+00:00:20,670 --> 00:00:25,350
+بسم الله الرحمن الرحيم بالعودة إلى section 2.9
+
+2
+00:00:25,350 --> 00:00:29,530
+الذي ابتدأناه في المرة الماضية كان هذا الـ section
+
+3
+00:00:29,530 --> 00:00:35,110
+يتحدث عن خواص المحددات اللي هو الـ properties of
+
+4
+00:00:35,110 --> 00:00:41,430
+determinants خواص المحددات واخدنا ثمانية خواص لهذه
+
+5
+00:00:41,430 --> 00:00:47,770
+المحددات والآن بنحاول نستخدم هذه الخواص ما أمكن
+
+6
+00:00:47,770 --> 00:00:52,080
+ذلك، نعطي أول مثال على هذا الموضوع، بيقول evaluate
+
+7
+00:00:52,080 --> 00:00:57,320
+the determinant احسب هذا المحدد، وزي ما أنت شايفه 
+
+8
+00:00:57,320 --> 00:01:03,160
+هذا محدد من الرتبة الرابعة، يبقى أربعة صفوف وأربعة 
+
+9
+00:01:03,160 --> 00:01:08,260
+أعمدة، مش هفك بالطريقة المطولة بتاعت الثانوية وإنما
+
+10
+00:01:08,260 --> 00:01:13,560
+هفك باستخدام هذه الخواص، بمعنى آخر، إذا قررت أخد 
+
+11
+00:01:13,560 --> 00:01:19,780
+محدد لمصفوفة قطرية، آخر ملاحظة مكتوبة معكم المرة
+
+12
+00:01:19,780 --> 00:01:24,500
+اللي فاتت، آخر سطر مكتوب معكم المرة الماضية لو 
+
+13
+00:01:24,500 --> 00:01:28,320
+كانت عندي الـ triangle matrix سواء كانت upper
+
+14
+00:01:28,320 --> 00:01:32,440
+triangle ولا lower triangle فإن قيمة هذا المحدد
+
+15
+00:01:32,440 --> 00:01:39,060
+تساوي حاصل ضرب عناصر القطر الرئيسي، مصبوط a11, a22,
+
+16
+00:01:39,460 --> 00:01:46,650
+a33 لغاية ann، لذلك أنا هحاول أحل أو أوجد قيمة هذا 
+
+17
+00:01:46,650 --> 00:01:51,990
+المحدد باستخدام هذه الخاصية، بمعنى آخر يعني بدي 
+
+18
+00:01:51,990 --> 00:01:57,530
+أحول هذا المحدد إلى محدد لمصفوفة مثلثة عليا أو
+
+19
+00:01:57,530 --> 00:02:03,130
+مثلثة سفلى أي منهما، وبالتالي بروح بجيب حاصل ضرب
+
+20
+00:02:03,130 --> 00:02:08,450
+عناصر قَطْر الرئيسي بتكون هي قيمة المحدد المطلوبة.
+
+21
+00:02:09,120 --> 00:02:15,080
+بدنا نبدأ نشتغل في قيمة هذا المحدد، فباقي بقوله هذا
+
+22
+00:02:15,080 --> 00:02:18,400
+المحدد كتالي، يبقى هي solution
+
+23
+00:02:20,790 --> 00:02:27,330
+بالدرجة المحددة اللي احنا كاتبينه اللي هو 6 2 8 0
+
+24
+00:02:27,330 --> 00:02:43,210
+1 3 5 2 2 1 0 3 2 -5 -2 -7 هذا المحدد يساوي
+
+25
+00:02:45,660 --> 00:02:49,940
+أظن بنفع من إحدى الخواص، نقول: لو ضربنا المحدد في
+
+26
+00:02:49,940 --> 00:02:54,440
+مقدار ثابت بضربه في أحد الصفوف أو أحد الأعمدة، إذا 
+
+27
+00:02:54,440 --> 00:02:58,800
+أنا هنا لو في عندي عامل مشترك في أحد الصفوف أو أحد
+
+28
+00:02:58,800 --> 00:03:03,720
+الأعمدة، بقدر أقوله: "شرفنا برا"، يبقى بقدر أخد هذه 
+
+29
+00:03:03,720 --> 00:03:08,840
+الصف الأول، فيه اثنين في الثاني لا ما فيش، يبقى باجي
+
+30
+00:03:08,840 --> 00:03:15,020
+بقوله: هذا المحدد يساوي اثنين، وهنا بداجي أعمل matrix.
+
+31
+00:03:15,020 --> 00:03:21,360
+بيظل عندي ثلاثة وهنا واحد وهنا أربعة وهنا زيرو هنا 
+
+32
+00:03:21,360 --> 00:03:27,500
+عندنا واحد وهي ثلاثة وهي خمسة اثنين اثنين واحد 
+
+33
+00:03:27,500 --> 00:03:33,920
+زيرو سالب ثلاثة اثنين سالب خمسة سالب اثنين سالب
+
+34
+00:03:33,920 --> 00:03:41,830
+سبعة، بالشكل اللي عندنا، هذا المحدد يساوي هذه الاثنين 
+
+35
+00:03:41,830 --> 00:03:47,290
+وهذه المحدد، شو رأيكم يا بنات لو بدلت الصف الأول 
+
+36
+00:03:47,290 --> 00:03:57,490
+والثاني مع بعض، هل تتغير قيمة المحدد بالمرة؟
+
+37
+00:03:57,490 --> 00:04:02,870
+من خلاص، لو بدلنا صف مكان صف أو عمود مكان عمود
+
+38
+00:04:02,870 --> 00:04:08,580
+تبقى قيمة المحدد كما هي، إشارة A مخالفة، يعني لو بدلت
+
+39
+00:04:08,580 --> 00:04:12,780
+صف مكان صف بدي أحط إشارة إيه؟ إشارة سالب، يبقى هذا 
+
+40
+00:04:12,780 --> 00:04:18,200
+المحدد يساوي سالب اثنين، يبقى هاي سالب.. شو اللي
+
+41
+00:04:18,200 --> 00:04:23,620
+بدي أبدله؟ بدي أبدل الصف الأول والثاني، يبقى 
+
+42
+00:04:23,620 --> 00:04:32,490
+replace اللي هو R1 and R2 بدي أبدل R1 و R2 مع بعض
+
+43
+00:04:32,490 --> 00:04:37,610
+ليش؟ بدي أخلي الواحد في البداية عندي هنا، يبقى بقدر 
+
+44
+00:04:37,610 --> 00:04:45,570
+أقول هي واحد ثلاثة خمسة اثنين ثلاثة واحد أربعة زيرو
+
+45
+00:04:45,860 --> 00:04:52,540
+وهنا ثلاثة واحد أربعة زيرو وهنا اثنين واحد زيرو 
+
+46
+00:04:52,540 --> 00:05:01,330
+سالب ثلاثة اثنين ناقص خمسة ناقص اثنين ناقص سبعة، طب
+
+47
+00:05:01,330 --> 00:05:06,450
+الآن بدي أعمل بعض العمليات بحيث بدي أخليها upper
+
+48
+00:05:06,450 --> 00:05:11,330
+triangle matrix مصفوفة مثلثة عالية، يبقى بدي أخلي 
+
+49
+00:05:11,330 --> 00:05:16,770
+العناصر أسفل القطر الرئيسي أصفار، يبقى بدي أخلي هنا 
+
+50
+00:05:16,770 --> 00:05:23,330
+صفر وهنا صفر وهنا صفر، من ضمن خواص المحددات لو ضربت 
+
+51
+00:05:23,330 --> 00:05:28,370
+أي صف أو أي عمود في مقدار ثابت وأضفته لعناصر صف
+
+52
+00:05:28,370 --> 00:05:32,170
+أو عمود ثاني لا تتغير قيمة المحدد، مكتوبة الخاصية هذه
+
+53
+00:05:32,170 --> 00:05:36,210
+معكم المرة الماضية، صحيح؟ يبقى أنا بادعي أضرب الصف 
+
+54
+00:05:36,210 --> 00:05:41,370
+الأول في سالب ثلاثة وأضيفه للصف الثاني، وأضربه في
+
+55
+00:05:41,370 --> 00:05:46,790
+سالب اثنين وأضيفه للصف الثالث وللصف الرابع، يبقى
+
+56
+00:05:46,790 --> 00:05:54,050
+بقدر أقول هذا الكلام يساوي تمام هذا السالب اثنين 
+
+57
+00:05:54,050 --> 00:05:58,450
+اللي عندنا وهذا المحدد وبدي أشوف شو اللي بدي يصير
+
+58
+00:05:58,450 --> 00:06:07,050
+يبقى هنا بدي أضيف سالب ثلاثة R1 to R2 للصف الثاني
+
+59
+00:06:07,050 --> 00:06:21,190
+and اللي هو سالب اثنين R1 to R3 and R4 يبقى الصف 
+
+60
+00:06:21,190 --> 00:06:27,070
+الأول كما هو يبقى هاي واحد وهي ثلاثة وهي خمسة وهي 
+
+61
+00:06:27,070 --> 00:06:31,990
+اثنين وهي جفالة بالدالي للصف الثاني ضربته في سالب
+
+62
+00:06:31,990 --> 00:06:36,770
+ثلاثة وأضافته له يبقى Zero سالب تسعة واحد بيصير 
+
+63
+00:06:36,770 --> 00:06:43,760
+كده؟ سالب ثمانية هنا سالب ثلاثة بيصير سالب خمسة عشر
+
+64
+00:06:43,760 --> 00:06:49,320
+سالب خمسة عشر اللي بيظهر سالب أحد عشر هنا سالب ثلاثة
+
+65
+00:06:49,320 --> 00:06:56,840
+بيصير سالب ستة سالب ستة كما هو، بعد ذلك طلبنا في
+
+66
+00:06:56,840 --> 00:07:02,580
+سالب اثنين بيصير عندي Zero سالب ستة واحد بيصير 
+
+67
+00:07:02,580 --> 00:07:09,700
+سالب خمسة سالب عشرة و Zero بسالب عشرة كما هو وهنا
+
+68
+00:07:09,700 --> 00:07:15,500
+سالب أربعة وسالب ثلاثة بيصير سالب سبعة هنا كمان 
+
+69
+00:07:15,500 --> 00:07:22,780
+Zero هنا سالب ستة وسالب خمسة بسالب أحد عشر يبقى
+
+70
+00:07:22,780 --> 00:07:27,900
+سالب
+
+71
+00:07:27,900 --> 00:07:32,920
+عشر أو سالب اثنين بسالب اثنا عشر يبقى سالب أربعة أو
+
+72
+00:07:32,920 --> 00:07:39,620
+سالب سبعة بسالب أحد عشر بالشكل اللي عندنا في ناقص 
+
+73
+00:07:39,620 --> 00:07:43,640
+كثير يعني، يبقى ممكن أخد من هنا شر السالب واحد ومن
+
+74
+00:07:43,640 --> 00:07:47,400
+هنا شر السالب واحد ومن هنا شر السالب واحد، صح ولا
+
+75
+00:07:47,400 --> 00:07:51,880
+لا، يعني كعامل مشترك من الكل بيصير سالب واحد في سالب 
+
+76
+00:07:51,880 --> 00:07:56,400
+واحد في سالب واحد في سالب واحد في سالب واحد في 
+
+77
+00:07:56,400 --> 00:08:00,750
+سالب واحد، بموجب يبقى بضيع الإشارة اللي جوا والإشارة 
+
+78
+00:08:00,750 --> 00:08:05,810
+اللي برا، يبقى المحدد هيصبح على الشكل التالي، هاي
+
+79
+00:08:05,810 --> 00:08:11,350
+يساوي وهذا اثنين اللي برا، تمام؟ أو لسهولة خليه مش 
+
+80
+00:08:11,350 --> 00:08:16,830
+تبقى واضحة يساوي هاي سالب اثنين زي ما هو، واخد كمان
+
+81
+00:08:16,830 --> 00:08:22,210
+سالب واحد في سالب واحد في سالب واحد وهي المحدد حتى 
+
+82
+00:08:22,210 --> 00:08:26,340
+لما تروحي تراجعي تعرفي كيف جات هذه، يبقى هاي واحد 
+
+83
+00:08:26,340 --> 00:08:34,720
+ثلاثة اثنين خمسة اثنين خمسة اثنين، الصف الثاني Zero
+
+84
+00:08:34,720 --> 00:08:42,820
+ثمانية أحد عشر وهنا ستة وهنا Zero وهنا خمسة عشر 
+
+85
+00:08:42,820 --> 00:08:51,280
+سبعة وهنا Zero أحد عشر وهنا اثنا عشر وهنا أحد عشر
+
+86
+00:08:51,280 --> 00:08:54,420
+بالشكل اللي عندنا، طيب 
+
+87
+00:08:55,490 --> 00:09:01,870
+أريد أن أحاول أن أجعل هذا الرقم واحد، صحيح؟ لكي أجعل
+
+88
+00:09:01,870 --> 00:09:06,090
+هنا تحته أصفار، لكي أجعل واحد صحيح، لكي أقسم كله
+
+89
+00:09:06,090 --> 00:09:12,350
+عالميا على ثمانية، يبقى كأنه أريد أن آخذ ثمانية
+
+90
+00:09:12,350 --> 00:09:18,130
+بره عامل مشترك، يبقى هذه تساوي هذه الاثنين اللي بره
+
+91
+00:09:18,130 --> 00:09:27,530
+وهذه الثمانية، وصار عندي هذا المحدد 1 3 5 2 وهنا 0
+
+92
+00:09:27,530 --> 00:09:38,220
+وهنا 1 وهنا 11 على 8 وهنا 6 على 8 يعني 3 على 4 وهنا 
+
+93
+00:09:38,220 --> 00:09:45,240
+zero زي ما هو وهنا خمسة وهنا عشرة وهنا سبعة وهنا 
+
+94
+00:09:45,240 --> 00:09:52,140
+zero وهنا أحد عشر وهنا اثنا عشر وهنا أحد عشر بالشكل
+
+95
+00:09:52,140 --> 00:09:57,780
+اللي عندنا هنا، الآن هذا الكلام بده يساوي الـ 16 
+
+96
+00:09:57,780 --> 00:10:03,660
+اثنين في ثمانية، 16 ولخاطر المحدد هذا أضربه 
+
+97
+00:10:03,660 --> 00:10:09,020
+في سالب خمسة وأضيفه للصف الثاني، وأقلل الثالث، و
+
+98
+00:10:09,020 --> 00:10:14,280
+أضربه في سالب أحد عشر وأضيفه للصف الرابع، يبقى هذا
+
+99
+00:10:14,280 --> 00:10:19,940
+الكلام بده يساوي أحد
+
+100
+00:10:19,940 --> 00:10:23,100
+عشر على ثمانية وهذا ثلاثة على أربعة
+
+101
+00:10:32,020 --> 00:10:36,600
+أخدنا ثمانية عامل مشترك، اثنين في ثمانية وليس اثنين
+
+102
+00:10:36,600 --> 00:10:40,100
+على ثمانية، أنا أخدت ثمانية عامل مشترك، على حين هذه 
+
+103
+00:10:40,100 --> 00:10:42,760
+الثمانية لو بدي أدخلها جوا بيصير ثمانية في Zero
+
+104
+00:10:42,760 --> 00:10:47,900
+بـ Zero هنا ثمانية هنا أحد عشر هنا اللي هو ستة 
+
+105
+00:10:50,500 --> 00:10:58,200
+اللي بدي أعمله الآن بداجي أخد سالب خمسة R2 
+
+106
+00:10:58,200 --> 00:11:05,740
+to R3 وبدي أخد سالب أحد عشر R2  سالب
+
+107
+00:11:05,740 --> 00:11:14,500
+أحد عشر R2 إلى to R4 تصبح بالشكل
+
+108
+00:11:14,500 --> 00:11:21,910
+التالي، الآن أنا عندي اثنين في ثمانية هذا اللي هو 16
+
+109
+00:11:21,910 --> 00:11:27,210
+ستة عشر، هذا الـ 16 وهذا المحدد أصبح على الشكل
+
+110
+00:11:27,210 --> 00:11:34,810
+التالي واحد ثلاثة خمسة اثنين وهنا عندك اللي هو 
+
+111
+00:11:34,810 --> 00:11:41,990
+Zero وهنا واحد وهنا أحد عشر على ثمانية كما هي وهنا 
+
+112
+00:11:41,990 --> 00:11:46,690
+ثلاثة على أربعة كما هي الحين هنا Zero وهنا Zero
+
+113
+00:11:46,690 --> 00:11:51,390
+ليش؟ لأنه ضارب سالب خمسة هذه، Zero اللي ما هو سالب 
+
+114
+00:11:51,390 --> 00:11:56,590
+خمسة وخمسة Zero نجي هذه سالب خمسة في أحد عشر بسالب
+
+115
+00:11:56,590 --> 00:12:02,050
+خمسة وخمسين على ثمانية، يبقى هذه سالب خمسة وخمسين
+
+116
+00:12:02,050 --> 00:12:05,670
+على ثمانية، سالب خمسة وخمسين على ثمانية يبقى أضيفه
+
+117
+00:12:05,670 --> 00:12:11,990
+لمين؟ لعشرة، يبقى باجي بقوله: زائد عشرة، النتيجة تساوي 
+
+118
+00:12:11,990 --> 00:12:17,730
+ثمانين بدي أشيل منها خمسة وخمسين، مضل قداش؟ خمسة و
+
+119
+00:12:17,730 --> 00:12:22,330
+عشرين على ثمانية، يبقى النتيجة خمسة وعشرين على
+
+120
+00:12:22,330 --> 00:12:28,270
+ثمانية بالموجب، إذا هذه بدها تصير خمسة وعشرين على
+
+121
+00:12:28,270 --> 00:12:35,290
+ثمانية بالموجب، أنا ضربت هنا في قداش؟ في سالب خمسة
+
+122
+00:12:35,290 --> 00:12:41,050
+بيصير سالب خمسة عشر على أربعة، يبقى سالب خمسة عشر على
+
+123
+00:12:41,050 --> 00:12:48,170
+أربعة بتضيف لمن؟ بتضيف لسبعة، يبقى زائد سبعة، وسبعة 
+
+124
+00:12:48,170 --> 00:12:53,590
+في أربعة، ثمانية وعشرين، بتشيل منهم خمسة عشر بظل 
+
+125
+00:12:53,590 --> 00:13:01,200
+قداش؟ ثلاثة عشر على أربعة، يبقى هنا 13 على 4، نجي للصفة 
+
+126
+00:13:01,200 --> 00:13:07,900
+الرابعة 00 ليش؟ نضربه في سالب 11 ونضيفه هنا، بيصير سالب
+
+127
+00:13:07,900 --> 00:13:18,700
+11، سالب 11 في 11 بسالب 121، 121 على 8 تمام؟ بدي أضيفه 
+
+128
+00:13:18,700 --> 00:13:25,700
+لمين؟ للـ 12 يبقى زائد 12، مظبوط هيك يا بنات؟ بتضيف
+
+129
+00:13:25,700 --> 00:13:32,180
+للـ 12، طبعاً ثمانية في 12، 96، أربعة 
+
+130
+00:13:32,180 --> 00:13:37,240
+واحد وعشرين يعني خمسة وعشرين، بس بالسالم سالم
+
+131
+00:13:37,240 --> 00:13:42,600
+خمسة وعشرين على ثمانية، يبقى سالم خمسة وعشرين على 
+
+132
+00:13:42,600 --> 00:13:48,920
+مهم على ثمانية، الآن بدي أضربه كمان مرة في سالب 11
+
+133
+00:13:48,920 --> 00:13:59,620
+بيصير سالب 33 يبقى سالب 33 على 4، سالب 33 على 4 زائد
+
+134
+00:13:59,620 --> 00:14:05,580
+11 زائد 11 اللي هو 44 بدي أشيل منهم 
+
+135
+00:14:05,580 --> 00:14:16,900
+بظل 11 مظبوط 44 - 33 يبقى 11 على 4، يبقى هذا 11 على 4
+
+136
+00:14:16,900 --> 00:14:23,100
+بالشكل اللي عندنا، كويس؟ طب الآن بقدر أضيف الصف 
+
+137
+00:14:23,100 --> 00:14:29,060
+الثالث إلى الصف الرابع مرة واحدة، يبقى هذا الكلام
+
+138
+00:14:29,060 --> 00:14:38,960
+بده يساوي بده R3 to R4 مباشرة، يبقى بيصير 
+
+139
+00:14:38,960 --> 00:14:44,980
+هي الـ 16 بره وهي المحدد هي واحد ثلاثة خمسة
+
+140
+00:14:44,980 --> 00:15:06,340
+اثنين وهنا 0 1 11 على 8 3 على 4 0 0 25 على 8 13 على 4 بقى الصف الرابع 
+
+141
+00:15:06,340 --> 00:15:12,980
+0 0 0 يبقى هذا أضفته إلى هذا مباشرة، يبقى بدي أضيف هذا
+
+142
+00:15:12,980 --> 00:15:18,420
+إلى هذا مباشرة، ثلاثة عشر وأحد عشر، أربعة وعشرين على
+
+143
+00:15:18,420 --> 00:15:25,120
+أربعة فيها ستة تمام؟ إذا أنا بدي قيمة هذا المحدد
+
+144
+00:15:25,120 --> 00:15:30,600
+يبقى قيمته هي الـ 16 اللي برة في مين؟ في واحد في
+
+145
+00:15:30,600 --> 00:15:38,340
+كمان واحد في خمسة وعشرين على ثمانية في ستة، يبقى
+
+146
+00:15:38,340 --> 00:15:42,800
+هذا الكلام يساوي ثمانية مع 16 فيها اثنين، اثنين
+
+147
+00:15:42,800 --> 00:15:47,260
+في خمسة وعشرين، 50، خمسة في ستة، 30، يبقى
+
+148
+00:15:47,260 --> 00:15:53,020
+300، إذا قيمة هذا المحدد يساوي 300 بدون 
+
+149
+00:15:53,020 --> 00:15:58,570
+ملجأ لفكه، يبقى أنا استخدمت الخاصية الشهيرة أن
+
+150
+00:15:58,570 --> 00:16:04,690
+إضافة أي  أو ضرب أي صف في أي رقم ثم اضافته إلى
+
+151
+00:16:04,690 --> 00:16:10,490
+صف آخر لا يغير من قيمة المحدد، أخد كمان خاصية
+
+152
+00:16:10,490 --> 00:16:14,450
+ثانية إذا في عندي مقدار ثابت موجود في أحد الصفوف أو 
+
+153
+00:16:14,450 --> 00:16:18,670
+في أحد الأعمدة مشترك بين جميع العناصر بقدر أخدها
+
+154
+00:16:18,670 --> 00:16:25,390
+برا المحدد، يعني هنا احنا اشتغلنا عدد خواص لهذا
+
+155
+00:16:25,390 --> 00:16:29,630
+المحدد، ولغاية ما جينا لآخر ملاحظة كانت أن في المرة
+
+156
+00:16:29,630 --> 00:16:36,170
+الماضية أصبح عندي محدد لمصفوفة مثلثة عليا كل
+
+157
+00:16:36,170 --> 00:16:40,850
+العناصر أسفل القطر الرئيسي أصفار، إذا قيمة هذا
+
+158
+00:16:40,850 --> 00:16:46,020
+المحدد يساوي حاصل ضرب عناصر القطر الرئيسي، يبقى آخر 
+
+159
+00:16:46,020 --> 00:16:49,760
+سطر كتبناه المرة الماضية هذا اللي طبقته هنا
+
+160
+00:16:49,760 --> 00:16:53,880
+وبالتالي طلعت قيمة المحدد مضبوط، روح أفك وأحسب 
+
+161
+00:16:53,880 --> 00:16:59,400
+حسابات تمام؟ يبقى هذا المثال الأول، في حدا فيكم 
+
+162
+00:16:59,400 --> 00:17:02,840
+بتحب تسأل أي سؤال هنا؟ في أي نقطة من الكلام اللي
+
+163
+00:17:02,840 --> 00:17:06,540
+قدامنا على اللوح؟ أيوة، أنا دايماً أرجع لفكرة اللي
+
+164
+00:17:06,540 --> 00:17:12,650
+هيمثلثة العالية؟ ولا في إيش؟ بينفك، لا بتقدر تفكي
+
+165
+00:17:12,650 --> 00:17:16,150
+فك عادي، كمان بيسألني، ل
+
+201
+00:20:51,340 --> 00:20:58,010
+يبقى قيمة هذا حاصل الضرب يساوي خمسة وسبعين يبقى
+
+202
+00:20:58,010 --> 00:21:05,610
+استطاعنا الحصول على محددات هذه المصفوفات دون معرفة
+
+203
+00:21:05,610 --> 00:21:11,270
+شكل هذه المصفوفات ولكن عن طريق استخدام خواص
+
+204
+00:21:11,270 --> 00:21:14,310
+المحددات المختلفة
+
+205
+00:21:22,140 --> 00:21:25,900
+في عندكوا أكثر من سؤال في التمرين؟ الأسئلة دي
+
+206
+00:21:25,900 --> 00:21:37,480
+جمعتهم في مثال واحد في عندي مثال ثلاثي بيقول
+
+207
+00:21:37,480 --> 00:21:47,700
+لي نمرة A F  الـ A تربيع بديه يساوي مصفوفة الوحدة
+
+208
+00:21:47,700 --> 00:21:57,910
+show that بين لأن الـ determinant للـ A بيكون زائد 
+
+209
+00:21:57,910 --> 00:22:06,810
+أو ناقص واحد نمر يا بيه لو كان الـ A transpose في
+
+210
+00:22:06,810 --> 00:22:12,830
+الـ A يساوي الـ I برضه show that أن الـ
+
+211
+00:22:12,830 --> 00:22:20,540
+determinant للـ A بيكون زائد أو ناقص واحد الآن نمري
+
+212
+00:22:20,540 --> 00:22:33,480
+الـ C F الـ A تربيع بده يساوي الـ A what can
+
+213
+00:22:33,480 --> 00:22:44,120
+you say about determinant
+
+214
+00:22:44,120 --> 00:22:45,520
+للـ A
+
+215
+00:22:51,330 --> 00:22:56,170
+يبقى عندنا الآن مطروح ثلاثة أسئلة بدنا نحاول نجاوب 
+
+216
+00:22:56,170 --> 00:23:01,330
+على كل سؤال من هذه الأسئلة الثلاثة إجابة علمية
+
+217
+00:23:01,330 --> 00:23:06,190
+دقيقة من خلال اللي هو المحددات أو من خلال خواص
+
+218
+00:23:06,190 --> 00:23:12,790
+المحددات التي درست في المحاضرة الماضية الآن بداجي
+
+219
+00:23:12,790 --> 00:23:15,430
+للحل يبقى solution
+
+220
+00:23:19,290 --> 00:23:25,110
+احنا عنا الـA تربيع تساوي مصفوفة الوحدة هذا كلام 
+
+221
+00:23:25,110 --> 00:23:31,290
+مُعطى طيب إيش المطلوب؟ الـdeterminant لـA إذا بدي 
+
+222
+00:23:31,290 --> 00:23:34,610
+أجيب الـdeterminant للـtwo matrices اللي عندنا 
+
+223
+00:23:34,610 --> 00:23:39,370
+يبقى مدام المصوفتين نفس بعض يبقى الـdeterminant
+
+224
+00:23:39,370 --> 00:23:45,790
+للـA تربيع هو نفس الـdeterminant للـI الـidentity
+
+225
+00:23:45,790 --> 00:23:51,430
+صحيح ولا لأ؟ طيب الحين لما أقول هذه determinant ليه 
+
+226
+00:23:51,430 --> 00:23:56,770
+تربيع مش عبارة عن A مضروبة في A يبقى هذه كأنها 
+
+227
+00:23:56,770 --> 00:24:04,290
+determinant للمصفوف A مضروبة في المصفوف الوحدة
+
+228
+00:24:04,460 --> 00:24:08,720
+مصفوفة الوحدة جميع عناصرها أصفار ما عدا عناصر القطر 
+
+229
+00:24:08,720 --> 00:24:13,480
+الرئيسي 1 1 1 طبق الآخر سطر خدناه المرة الماضية
+
+230
+00:24:13,480 --> 00:24:18,560
+يبقى حصل determinant للـ matrix اللي هو 1 في 1 في 1
+
+231
+00:24:18,560 --> 00:24:23,740
+جد ما يكون يبقى النتيجة جداش؟ 1 من دائما وأبدا 
+
+232
+00:24:23,740 --> 00:24:29,310
+قيمة محددة لمصفوفة الوحدة هو بواحد صحيح طيب، هذا يا
+
+233
+00:24:29,310 --> 00:24:33,730
+بنات القيمة في نفسها مش عبارة عن الـdeterminant 
+
+234
+00:24:33,730 --> 00:24:39,890
+للـA لكل تربيع يساوي واحد؟ طيب، خلينا ناخد الجذر
+
+235
+00:24:39,890 --> 00:24:44,830
+التربيعي للطرفين يبقى لو أخذنا الـdeterminant
+
+236
+00:24:44,830 --> 00:24:50,890
+للـA، بدها تعطينا هذا زائد أو ناقص واحد، اللي هو 
+
+237
+00:24:50,890 --> 00:24:55,080
+الجذر التربيعي للطرفين، أظن وهو المطلوب؟ خلصنا منه
+
+238
+00:24:55,080 --> 00:25:00,660
+نجي لنمرة B من المثال بجهدي كانت نمرة A بدي اجي 
+
+239
+00:25:00,660 --> 00:25:05,920
+لنمرة B بنفس التكتيك أنا عندي A transpose في ال A
+
+240
+00:25:05,920 --> 00:25:11,220
+بده يساوي ال I يعني لو ضربت مدور المصفوفة في المصفوفة 
+
+241
+00:25:11,220 --> 00:25:16,730
+وطلع الناتج هو مصفوفة الوحدة يبقى بناءً عليه بدي 
+
+242
+00:25:16,730 --> 00:25:22,310
+أروح أخد الـ Determinant للـ A Transpose في الـ A
+
+243
+00:25:22,310 --> 00:25:29,520
+بدي أساوي Determinant لمصفوفة الوحدة حسب الخواص يبقى
+
+244
+00:25:29,520 --> 00:25:34,100
+هذا الـ determinant للـ A transpose في الـ
+
+245
+00:25:34,100 --> 00:25:40,480
+determinant للـ A بده يساوي قد ايش واحد صحيح طب ال
+
+246
+00:25:40,480 --> 00:25:44,760
+determinant للـ A transpose هو determinant لـ A
+
+247
+00:25:44,760 --> 00:25:50,290
+اللي هي أول خاصية من خواص المحددات هذا معناه أن
+
+248
+00:25:50,290 --> 00:25:55,690
+الـ determinant للـ A في الـ determinant للـ A 
+
+249
+00:25:55,690 --> 00:26:01,670
+بيكون 1 هذا معناه أن الـ determinant للـ A لكل 
+
+250
+00:26:01,670 --> 00:26:07,110
+تربيع بيكون جداش 1 لو أخذنا الجذر التربيعي إلى
+
+251
+00:26:07,110 --> 00:26:12,810
+الطرفين يبقى الـ determinant للـ A بيكون جداش زائد
+
+252
+00:26:12,810 --> 00:26:19,340
+أو ناقص 1 طيب يبقى أظن ما هو المطلوب؟ وهو المطلوب 
+
+253
+00:26:19,340 --> 00:26:24,680
+نجي للنقطة الثالثة اللي هي نمرة الـC نمرة الـC
+
+254
+00:26:24,680 --> 00:26:30,930
+يعطيني أن الـA تربيع تساوي الـA بيقول لي ماذا
+
+255
+00:26:30,930 --> 00:26:36,510
+تستطيع أن تقول عن ال determinant للـA يعني
+
+256
+00:26:36,510 --> 00:26:41,050
+ما يعطينيها دي بنسميها في لغة الجبر العنصر ما نسميه 
+
+257
+00:26:41,050 --> 00:26:46,050
+idempotent idempotent لو كان مربع العنصر بيعطيني
+
+258
+00:26:46,050 --> 00:26:51,010
+نفس العنصر A تربيع تساوي A معناته ال matrix دي 
+
+259
+00:26:51,010 --> 00:26:57,370
+بنسميها idempotent انسى الباقي كله بس مجرد معلومة 
+
+260
+00:26:57,370 --> 00:27:00,930
+للتذكير أو لو مرت عليك في يوم من الأيام تكوني على
+
+261
+00:27:00,930 --> 00:27:04,150
+علم ودراية بها يعني معنى أن مش هذا الموضوع
+
+262
+00:27:04,150 --> 00:27:08,810
+يبقى أنا عندي مربع لـ A مصفوفة بيعطيني نفس المصفوفة 
+
+263
+00:27:08,810 --> 00:27:16,680
+بيقول لي ماذا يمكن أن تقول عن محدد المصفوفة A؟ بقوله
+
+264
+00:27:16,680 --> 00:27:20,360
+تعالى نجيب المحدد وبعدين بيصير خير نتفهم عن 
+
+265
+00:27:20,360 --> 00:27:25,880
+الموضوع يبقى باجي بقول له خذ المحدد بيصير ال
+
+266
+00:27:25,880 --> 00:27:32,480
+determinant لل A تربيع يساوي ال determinant لمن؟ لل 
+
+267
+00:27:32,480 --> 00:27:39,060
+A أو إن شئتم فقولوا يبقى ال determinant لل A في ال
+
+268
+00:27:39,060 --> 00:27:46,360
+A يساوي ال determinant لل A أو ال determinant للـ A
+
+269
+00:27:46,360 --> 00:27:52,900
+في الـ determinant للـ A ناقص الـ determinant للـ
+
+270
+00:27:52,900 --> 00:27:58,960
+A بده يساوي Zero فكيت هذه كحاصل ضرب two determinants
+
+271
+00:27:58,960 --> 00:28:03,580
+و أضفت سالب determinant A ليها للطرفين فحصلت على 
+
+272
+00:28:03,580 --> 00:28:08,960
+هذه المعادلة وكأنه أنا عندي معادلة من الدرجة 
+
+273
+00:28:08,960 --> 00:28:13,520
+الثانية بالنسبة لـ determinant A و بده حل هذه
+
+274
+00:28:13,520 --> 00:28:17,500
+المعادلة إيه ده حلها؟ خلاص أنا كنت هنا من هذه
+
+275
+00:28:17,500 --> 00:28:22,760
+الشغلة أظن بقدر أقول هذا ممكن اخذ determinant
+
+276
+00:28:22,760 --> 00:28:29,000
+للـA عامل مشترك بيظل determinant للـA ناقص واحد 
+
+277
+00:28:29,000 --> 00:28:33,720
+يساوي Zero مظبوط؟
+
+278
+00:28:33,720 --> 00:28:38,540
+إذا يا إما ال term الأول هو اللي بيساوي Zero يا
+
+279
+00:28:38,540 --> 00:28:43,740
+إما ال term الثاني بده يساوي Zero وقد يكون كلاهما
+
+280
+00:28:43,740 --> 00:28:50,240
+مثلاً الله أعلم يبقى باجي بقول هذا معناه أن ال
+
+281
+00:28:50,240 --> 00:28:55,980
+determinant لل A بده يساوي 0 أو ال determinant لل
+
+282
+00:28:55,980 --> 00:29:01,840
+A minus ال 1 هو اللي بده يساوي 0 هذا معناه أن ال
+
+283
+00:29:01,840 --> 00:29:08,720
+determinant لل A بده يساوي 0 أو ال determinant لل
+
+284
+00:29:08,720 --> 00:29:14,280
+A بده يساوي قد ايش 1 يبقى هذا كل اللي بنستطيع نقوله 
+
+285
+00:29:14,280 --> 00:29:19,230
+عن ال determinant لل A يا إما محدد هذه المصفوفة
+
+286
+00:29:19,230 --> 00:29:23,930
+يساوي الصفر، يا إما محدد هذه المصفوفة يساوي كده؟
+
+287
+00:29:23,930 --> 00:29:27,730
+يساوي واحد، حق صحيح هذا كل اللي بنقدر نقوله عن
+
+288
+00:29:27,730 --> 00:29:32,570
+القصة هذه، تمام؟ لحد هنا، stop، انتهى هذا ال
+
+289
+00:29:32,570 --> 00:29:38,130
+section، ولا ننسى أرقام المسائل، يبقى بداجي ل
+
+290
+00:29:38,130 --> 00:29:38,910
+exercises
+
+291
+00:29:41,390 --> 00:29:47,990
+اثنين وتسعة المسائل التالية السؤال الرابع والسؤال
+
+292
+00:29:47,990 --> 00:29:58,630
+الخامس B والسؤال السادس A والسؤال السابع وبعد ذلك
+
+293
+00:29:58,630 --> 00:30:04,050
+من تسعة لغاية اثني عشر من تسعة لغاية اثني عشر
+
+294
+00:30:29,610 --> 00:30:35,490
+ننتقل الآن إلى ال section الذي يليه وهو section
+
+295
+00:30:35,490 --> 00:30:41,410
+الـ cofactors يعني العوامل المرافقة
+
+296
+00:30:47,110 --> 00:30:54,590
+لغاية هذه النقطة هذه هي الامتحان لغاية نهاية 2 تسعة 
+
+297
+00:30:54,590 --> 00:31:00,830
+طبعاً الامتحان يوم الثلاثاء القادم يوم 12 ثلاثة إن 
+
+298
+00:31:00,830 --> 00:31:05,030
+شاء الله تعالى على أي حال يبقى بدنا نيجي لل
+
+299
+00:31:05,030 --> 00:31:09,810
+section الجديد اللي هو ال section 210 اللي هو
+
+300
+00:31:09,810 --> 00:31:11,730
+cofactors
+
+301
+00:31:13,630 --> 00:31:22,490
+العوامل المرافقة نعطي بعض التعريفات Definition let
+
+302
+00:31:22,490 --> 00:31:33,930
+A be an m×n matrix then
+
+303
+00:31:33,930 --> 00:31:35,350
+a submatrix
+
+304
+00:31:41,780 --> 00:31:50,680
+مصفوفة جزئية is a matrix is a matrix هي عبارة عن
+
+305
+00:31:50,680 --> 00:31:56,840
+مصفوفة obtained from
+
+306
+00:31:56,840 --> 00:32:10,800
+A من المصوفة A by deleting وليس adding
+
+307
+00:32:14,900 --> 00:32:20,660
+by deleting rows or
+
+308
+00:32:20,660 --> 00:32:25,180
+columns or
+
+309
+00:32:25,180 --> 00:32:39,920
+columns of A or both أو كلهما definition ثاني if
+
+310
+00:32:42,730 --> 00:32:57,410
+الـ A is a square matrix مصفوفة مربعة order N من 
+
+311
+00:32:57,410 --> 00:33:06,090
+الرتبة النونية then the minor of 
+
+312
+00:33:06,090 --> 00:33:11,530
+the
+
+313
+00:33:15,270 --> 00:33:22,830
+Element The minor of the element AIK
+
+314
+00:33:22,830 --> 00:33:25,850
+AIK
+
+315
+00:33:25,850 --> 00:33:33,890
+is the determinant is the determinant
+
+316
+00:33:33,890 --> 00:33:38,670
+of
+
+317
+00:33:38,670 --> 00:33:41,350
+the determinant
+
+318
+00:33:43,820 --> 00:33:49,760
+of a submatrix
+
+319
+00:33:49,760 --> 00:34:07,760
+of A of order n minus one that obtained واللي 
+
+320
+00:34:07,760 --> 00:34:10,560
+حصلنا عليه by deleting
+
+321
+00:34:16,960 --> 00:34:24,600
+by deleting the I row the
+
+322
+00:34:24,600 --> 00:34:39,780
+I row and the  
+
+323
+00:34:39,780 --> 00:34:50,840
+of A I column English يعني the row and
+
+324
+00:34:50,840 --> 00:34:57,180
+the
+
+325
+00:34:57,180 --> 00:35:00,600
+column
+
+326
+00:35:00,600 --> 00:35:10,620
+of
+
+327
+00:35:10,620 --> 00:35:12,800
+aik
+
+328
+00:35:16,440 --> 00:35:22,800
+this minor this
+
+329
+00:35:22,800 --> 00:35:34,840
+minor is denoted by mik
+
+330
+00:35:34,840 --> 00:35:41,780
+command
+
+331
+00:35:41,780 --> 00:35:42,420
+definition
+
+332
+00:35:49,700 --> 00:35:56,180
+مع الـ square matrix
+
+333
+00:35:56,180 --> 00:36:10,280
+of order n ندفع
+
+334
+00:36:15,250 --> 00:36:22,070
+The Cofactor The 
+
+335
+00:36:22,070 --> 00:36:32,890
+Cofactor Of The Element Cofactor
+
+336
+00:36:32,890 --> 00:36:36,970
+Of The
+
+337
+00:36:36,970 --> 00:36:40,290
+Element AIK
+
+338
+00:36:42,490 --> 00:36:53,070
+aik to be the number to be the number وعبارة عن 
+
+339
+00:36:53,070 --> 00:36:57,570
+الرقم aik
+
+340
+00:36:57,570 --> 00:37:06,950
+واللي هو اللي بده يساوي سالب واحد أس i زائد k م
+
+341
+00:37:06,950 --> 00:37:10,270
+اي ك
+
+342
+00:37:43,380 --> 00:37:49,760
+example let A تساوي
+
+343
+00:37:49,760 --> 00:37:59,720
+واحد تلاتة اثنين ناقص اثنين ناقص واحد أربعة ناقص 
+
+344
+00:37:59,720 --> 00:38:13,630
+ثلاثة خمسة zero المطلب الأول نمرة a find the minor
+
+345
+00:38:13,630 --> 00:38:18,930
+of the
+
+346
+00:38:18,930 --> 00:38:32,550
+elements of the element خمسة and zero نمرة b Find
+
+347
+00:38:32,550 --> 00:38:38,550
+the cofactors 
+
+348
+00:38:38,550 --> 00:38:44,330
+of the elements خمسة and زيرو 
+
+349
+00:39:36,670 --> 00:39:41,610
+نرجع لكلام اللي احنا كاتبينه الـ cofactors العوامل
+
+350
+00:39:41,610 --> 00:39:48,110
+المرافقة نعطيه ثلاثة تعريفات ومن ثم نذهب إلى
+
+351
+00:39:48,110 --> 00:39:53,190
+استخدام هذه التعريفات بالمثال بيقول لك الـ A بي ان m 
+
+352
+00:39:53,190 --> 00:39:57,450
+by n matrix then a submatrix is a matrix obtained
+
+353
+00:39:57,450 --> 00:40:02,410
+from A by deleting rows or columns or both يعني
+
+354
+00:40:02,410 --> 00:40:07,750
+هنا بتتكلم على مصفوفة جزئية sub matrix يعني مصفوفة
+
+355
+00:40:07,750 --> 00:40:14,890
+جزئية إذا احنا من مصفوفة عندنا بدنا بدنا نجيب 
+
+356
+00:40:14,890 --> 00:40:19,150
+مصفوفة جزئية مثال وذلك لو اعتبرت يا بنات اللي
+
+357
+00:40:19,150 --> 00:40:23,470
+قاعدة دول في الشجرة هذه كلهم matrix دول جينا
+
+358
+00:40:23,470 --> 00:40:27,930
+جلنا للصف الأول يلا جم من هنا يبقى ما بيصير لهم sub
+
+359
+00:40:27,930 --> 00:40:31,990
+matrix اللي بياخد منهم ال sub matrix أو جلنا للصف
+
+360
+00:40:31,990 --> 00:40:35,940
+هذا كله يلا أنتِ جلعتِ الشجرة الثانية يبقى الباقية هنا
+
+361
+00:40:35,940 --> 00:40:41,160
+sub matrix من ال matrix الأصلية ويمكن أقول الصف
+
+362
+00:40:41,160 --> 00:40:44,840
+هذا والصف هذا يلا مع السلامة الصف والعمود يعني
+
+363
+00:40:44,840 --> 00:40:48,180
+يلا أنتِ جلعي للشجرة الثانية يبقى الباقية ده كله
+
+364
+00:40:48,180 --> 00:40:53,560
+مالها sub matrix يبقى هنا إذا شطبت صف من صفوف
+
+365
+00:40:53,560 --> 00:41:00,730
+المصفوفة أو أكثر أو شطبت عمود أو أكثر أو شطبت صف و
+
+366
+00:41:00,730 --> 00:41:06,890
+عمود في أي واحد or both كلهم صف وعمود يبقى
+
+367
+00:41:06,890 --> 00:41:12,810
+المصفوفة المتبقية بنسميها sub matrix مصفوفة جزئية
+
+368
+00:41:12,810 --> 00:41:18,250
+من مين؟ من المصفوفة الأولى تمام؟ يبقى هذا ال
+
+369
+00:41:18,250 --> 00:41:23,250
+definition الأول أظن بسيط جدا بتدوا الشغلة ال
+
+370
+00:41:23,250 --> 00:41:27,330
+Definition الثانية بقول لو كانت الـ A مصفوفة مربعة
+
+371
+00:41:27,330 --> 00:41:32,390
+الرتب تبعها N يبقى The Minor The Minor يبقى لغتنا 
+
+372
+00:41:32,390 --> 00:41:38,590
+العربية بسميه المحدد أو المحدد الأصغر يعني إذا
+
+373
+00:41:38,590 --> 00:41:43,330
+عندي مصفوفة أصلية A هه ها دي بقول المحدد تبع
+
+374
+00:41:43,330 --> 00:41:47,530
+المصفوفة A إذا شطبت منها صفوف أو أعمدة وجئت أحسب 
+
+375
+00:41:47,530 --> 00:41:51,770
+إيه المحدد ها دي بقى يسميه المحدد الأصغر أو 
+
+376
+00:41:51,770 --> 00:42:01,150
+المحدد يبقى الـ minor هو المحدد الأصغر أو المحدد
+
+377
+00:42:01,150 --> 00:42:06,850
+المناظر لمين أو المأخوذ من ليه الـ sub matrix من من 
+
+378
+00:42:06,850 --> 00:42:12,570
+من الـ matrix الأصلية فبقول F ليها is a square
+
+379
+00:42:12,570 --> 00:42:18,210
+matrix of order N يبقى هذه المصفوفة N من الصفوف و N 
+
+380
+00:42:18,210 --> 00:42:23,740
+من الأعمدة الـ Minor then the minor of the element 
+
+381
+00:42:23,740 --> 00:42:31,760
+AIK يب
+
+401
+00:44:21,150 --> 00:44:27,090
+العمود اللي فيه المتبقي هي مصفوفة مربعة نقص صف و
+
+402
+00:44:27,090 --> 00:44:31,230
+نقص عمود يبقى بدل ما كانت من الرتبة انصرت من
+
+403
+00:44:31,230 --> 00:44:36,110
+الرتبة ناقص واحد يبقى هاي المقصود بهذا التعريف
+
+404
+00:44:36,410 --> 00:44:42,630
+that obtained by deleting يعني كيف حصلنا على هذا
+
+405
+00:44:42,630 --> 00:44:48,650
+by obtaining by deleting the i-th row and كذا يعني
+
+406
+00:44:48,650 --> 00:44:55,750
+بالشطب الصف رقم I والعمود رقم K العنصر يقع في الصف
+
+407
+00:44:55,750 --> 00:44:59,370
+الفلاني نشطب صفه ويقع في العمود الفلاني يبقى منه نشطب
+
+408
+00:44:59,370 --> 00:45:03,690
+عموده زي ما قلنا الأخت هذه اللي موجودة نشطب
+
+409
+00:45:03,690 --> 00:45:08,170
+الصف التي تقع فيه ونشطب العمود التي تقع فيه
+
+410
+00:45:08,170 --> 00:45:15,170
+المتبقي هو المحدد الأصغر المناظر لهذه الأخت بس 
+
+411
+00:45:15,170 --> 00:45:16,010
+صعب؟
+
+412
+00:45:18,440 --> 00:45:23,160
+هي نجي حطيت بينجوسين ذره and the column of a k
+
+413
+00:45:23,160 --> 00:45:28,120
+يعني الصف و العمود اللي يقع فيه العنصر a i k طيب
+
+414
+00:45:28,120 --> 00:45:33,400
+خلاص لما نقصت مين اللي هو المحدد الأصغر ال minor
+
+415
+00:45:33,400 --> 00:45:37,860
+بدنا نجي لـ الموضوع اللي احنا بدنا ياه و احنا رفعينه
+
+416
+00:45:37,860 --> 00:45:41,760
+ال cofactor بس قبل ال factor ال minor هذا هدله رمز
+
+417
+00:45:41,760 --> 00:45:51,610
+m i k يبقى m i k عنصر ولا محددمحدد أصغر يبقى MIK
+
+418
+00:46:00,750 --> 00:46:05,650
+الآن بدنا نيجي لمين؟ for the square matrix للمصفوفة
+
+419
+00:46:05,650 --> 00:46:13,350
+المربع of order n we define the cofactor العملي
+
+420
+00:46:13,350 --> 00:46:19,290
+المرافق لل element ik to be the number aik مين هو
+
+421
+00:46:19,290 --> 00:46:25,290
+aik؟ يبقى سالب واحد أس i زائد k في ال MIK
+
+422
+00:46:26,140 --> 00:46:29,340
+فاكرين لما كنا المحدد بيجينا و بيقول اللي بنفكه
+
+423
+00:46:29,340 --> 00:46:32,860
+باستخدام عناصر أي صف و أي عمود؟ معمرات، قاعدة
+
+424
+00:46:32,860 --> 00:46:37,700
+الإشارات، هذه قاعدة الإشارات، ليس إلا أنا ماخد
+
+425
+00:46:37,700 --> 00:46:43,280
+العنصر في الصف الأول و العمود الثاني يبقى بدأ أقول
+
+426
+00:46:43,280 --> 00:46:48,220
+سالب واحد أس واحد زائد اثنين يعني أس ثلاثة بإشارة
+
+427
+00:46:48,220 --> 00:46:53,580
+سالب بصير العنصر هذا بإشارة سالب هذه كنا سميها قبل
+
+428
+00:46:53,580 --> 00:46:59,340
+ذلك قاعدة الإشارات يبقى بحصل على ال cofactor إذا
+
+429
+00:46:59,340 --> 00:47:03,940
+حصلت على ال minor و ال minor هذا قد يكون بإشارة
+
+430
+00:47:03,940 --> 00:47:09,130
+سالبة أو بإشارة موجبة حسب جمع I زائد K إن كان عددا
+
+431
+00:47:09,130 --> 00:47:13,570
+فرديا فالإشارة بالسالب وإن كان عددا زوجيا فالإشارة
+
+432
+00:47:13,570 --> 00:47:18,270
+بالموجب كما سنرى عظيم واضح هذا الكلام طيب ناخد
+
+433
+00:47:18,270 --> 00:47:22,700
+مثال عملي على الكلام اللي بنقوله هنأعطيني مصفوفة
+
+434
+00:47:22,700 --> 00:47:27,080
+نظامها ثلاثة في ثلاثة وقال لي هات لل minor لل
+
+435
+00:47:27,080 --> 00:47:32,820
+elements اللي هو خمسة وزي هيك تمام باجي بقوله كويس
+
+436
+00:47:32,820 --> 00:47:38,520
+يبقى أنا ال minor بديله الرمز مين يا بنات M I K
+
+437
+00:47:38,520 --> 00:47:44,990
+الآن العنصر خمسة هي خمسة ما فيش غيره هذا جاي وين في
+
+438
+00:47:44,990 --> 00:47:54,810
+الصف الثالث والعمودي الثاني يبقى هنا the minor of
+
+439
+00:47:54,810 --> 00:48:03,210
+خمسة is M ثلاثة اثنين من وين جبته ثلاثة اثنين لأن
+
+440
+00:48:03,210 --> 00:48:10,370
+العنصر خمسة يقع في الصف الثالث والعمود الثاني تمام
+
+441
+00:48:10,370 --> 00:48:15,230
+طيب هذا ال M ثلاثة اثنين يساوي المحدد بدنا نشطب
+
+442
+00:48:15,230 --> 00:48:21,450
+الصف تبعه والعمود تبعه واللي بيظل بيكون هو قيمة ال
+
+443
+00:48:21,450 --> 00:48:27,550
+minor وهنا صفه وعموده بيظل عند هنا جذاش اثنين
+
+444
+00:48:27,550 --> 00:48:33,720
+أربعة هذا لو جيت فاكته يبقى أربعة زائد أربعة يساوي
+
+445
+00:48:33,720 --> 00:48:38,800
+كدهش؟ يساوي ثمانية يبقى ال minor للخمسة هو ثمانية
+
+446
+00:48:38,800 --> 00:48:43,800
+يبقى هو قيمة المحدد الأصغر المناظر لمين؟ للخمسة
+
+447
+00:48:43,800 --> 00:48:47,300
+بالمثل بدنا نروح نجيب ال minor ل صفر مش يتروح
+
+448
+00:48:47,300 --> 00:48:51,560
+الجودة ال minor ل صفر ب صفر لا ما لهش دعوة فبجي
+
+449
+00:48:51,560 --> 00:48:58,900
+بقوله هنا the minor of zero is باجي على ال صفر هي
+
+450
+00:48:58,900 --> 00:49:04,560
+ال صفر واقع في الصف الثالث والعمود الثالث يبقى
+
+451
+00:49:04,560 --> 00:49:10,940
+باجي بقوله M ثلاثة ثلاثة ويساوي المحدد تبعه الأصم
+
+452
+00:49:10,940 --> 00:49:16,700
+نظر بشطه بصف وعمود بيضل واحد ثلاثة ناقص اثنين ناقص
+
+453
+00:49:16,700 --> 00:49:24,710
+واحد يبقى هذه النتيجة بناقص واحد زائد ستة تجدد ايوه
+
+454
+00:49:24,710 --> 00:49:28,950
+يبقى ال minor ل صفر طلع خمسة مش صفر يبقى أنا
+
+455
+00:49:28,950 --> 00:49:33,050
+بأخدهش أنا بأخد المحدد تبعه مش بأخد العنصر تمام
+
+456
+00:49:33,050 --> 00:49:37,110
+يبقى هذا ال minor خلاصة المطلوب الأول مطلوب الثاني
+
+457
+00:49:37,110 --> 00:49:43,370
+جالي هات لل cofactor لكل منها تمام يبقى بداجي على
+
+458
+00:49:43,370 --> 00:49:49,590
+ال cofactor بداجي لل cofactor الأول الآن نمر بـ The
+
+459
+00:49:49,590 --> 00:50:01,250
+cofactor of خمسة is ثلاثة اثنين يعني سالب واحد
+
+460
+00:50:01,250 --> 00:50:08,110
+ثلاثة زائد اثنين في المحدد الأصغر المناظر اللي هو
+
+461
+00:50:08,110 --> 00:50:15,540
+جبناه فوق ما تغيرش ناقص اثنين أربعة الحين هذا سالب
+
+462
+00:50:15,540 --> 00:50:20,220
+واحد أس ثلاثة يعني سالب واحد أس قداش الأس فر دي
+
+463
+00:50:20,220 --> 00:50:26,000
+يبقى الإشارة بالسالب يبقى هذا الكلام بيساوي سالب
+
+464
+00:50:26,000 --> 00:50:32,880
+ثمانية الآن بدنا نروح نجيب ال cofactor of zero is
+
+465
+00:50:32,880 --> 00:50:40,080
+اييه ثلاثة ثلاثة بدي أساوي سالب واحد أس ثلاثة زائد
+
+466
+00:50:40,080 --> 00:50:45,380
+ثلاثة في المحدد الأصغر المناظر له اللي هو واحد
+
+467
+00:50:45,380 --> 00:50:50,460
+ثلاثة سالب اثنين سالب واحد و اللي هو بيصير عندنا
+
+468
+00:50:50,460 --> 00:50:57,000
+كده؟ خمسة كذلك لأن هذه السالب واحد أس ستة الأس
+
+469
+00:50:57,000 --> 00:51:00,880
+زوجي بيطلع بالموجة، بيضل يشيل قيمة المحدد، قيمة
+
+470
+00:51:00,880 --> 00:51:06,570
+المحدد يتساوي خمسة من أعلى يبقى هذا الفرق ما بين ال
+
+471
+00:51:06,570 --> 00:51:11,070
+minor و ال cofactor و زي ما تشوفي ال cofactor
+
+472
+00:51:11,070 --> 00:51:16,030
+يعتمد على من؟ على ال minor و هذا ده كنت بتذكر و
+
+473
+00:51:16,030 --> 00:51:21,050
+بجينا بقول انفك المحدد هذا بنجي بنفكه باستخدام
+
+474
+00:51:21,050 --> 00:51:24,430
+عناصر أو صف أو عمود فبجي بقول مثلا بالصف الثالث
+
+475
+00:51:24,430 --> 00:51:28,790
+يبقى العنصر هذا نشطب بصف و عمود و بضل المحدد هذا
+
+476
+00:51:29,200 --> 00:51:33,380
+حسب قاعدة الإشارات الإشارة هذه اتبعته بالسالب وهيها
+
+477
+00:51:33,380 --> 00:51:38,220
+طلعت عندنا بمين بالسالب تمام يبقى بروح بشطب صفه
+
+478
+00:51:38,220 --> 00:51:41,940
+عموده المحدد اللي بضل بضربه في الخمسة اللي بعده
+
+479
+00:51:41,940 --> 00:51:45,600
+ما هو ال صفر في محدده يبقى بصفر طيّعنا من هنا
+
+480
+00:51:45,600 --> 00:51:49,540
+تمام؟ بنكمل المرة القادمة إن شاء الله تعالى
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_postprocess.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f9cb51253f2227c4fe2af6725ceef8b179add8db
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_postprocess.srt
@@ -0,0 +1,1520 @@
+1
+00:00:20,320 --> 00:00:24,720
+بسم الله الرحمن الرحيم في المحاضرة الماضية اتحدثنا
+
+2
+00:00:24,720 --> 00:00:29,220
+في chapter واحد section اتنين اللي هو separable
+
+3
+00:00:29,220 --> 00:00:34,000
+equations و هي المعادلات التي فصلنا فيها المتغيرات
+
+4
+00:00:34,000 --> 00:00:38,520
+بين ال X في ناحية و ال Y في ناحية ثم أكملنا الحل
+
+5
+00:00:38,520 --> 00:00:42,580
+بواسطة ال integration يبقى أكملنا الطرفين حصلنا
+
+6
+00:00:42,580 --> 00:00:50,000
+على شكل حل المعادلةالان ننتقل للنوع الثاني وهو الـ
+
+7
+00:00:50,000 --> 00:00:55,260
+Homogeneous equations المعادلات المتجانسة الان
+
+8
+00:00:55,260 --> 00:01:01,620
+نحكم كيف المعادلة المتجانسة فنعطيها تعريف التاني
+
+9
+00:01:02,130 --> 00:01:04,210
+فبقى اللي بفهمه بجهة بقول الـ differential
+
+10
+00:01:04,210 --> 00:01:08,230
+equation dy by dx يسوى f of x y is called
+
+11
+00:01:08,230 --> 00:01:12,770
+homogeneous هذه اختصار لكلمة homogeneous اللي فوق
+
+12
+00:01:12,770 --> 00:01:17,810
+عند الـ g هعطينا نقطة if it can be written as إذا
+
+13
+00:01:17,810 --> 00:01:22,570
+جدوا أنه نكتبه على الصيغة dy على dx يسوى capital F
+
+14
+00:01:22,570 --> 00:01:27,390
+اللي فوق small f واللي تحت capital Fas a function
+
+15
+00:01:27,390 --> 00:01:32,470
+of y على x يعني إذا قدرنا نكتب المعادلة على شكل y
+
+16
+00:01:32,470 --> 00:01:38,950
+على x بقدر أسميها دالة متجلسة دالة معادلة متجلسة
+
+17
+00:01:38,950 --> 00:01:44,250
+طبعا هذا منابط مش ممكن يحصل إلا إذا كان عندي بسط و
+
+18
+00:01:44,250 --> 00:01:50,410
+مقام يعني dy على dx يساوي بسط على مقام لإن في هذه
+
+19
+00:01:50,410 --> 00:01:55,030
+الحالة بقدر أكتب ربما نقدر و ربما نقدرشنكتب
+
+20
+00:01:55,030 --> 00:02:00,630
+المعادلة كلها بدلالة Y على X لكن constant على X
+
+21
+00:02:00,630 --> 00:02:04,470
+ولا constant على Y ممنوع بس constant لحاله مافي
+
+22
+00:02:04,470 --> 00:02:08,710
+مشكلة يعني لو جينا جسمنا على X على Y إلى آخره
+
+23
+00:02:08,710 --> 00:02:13,630
+وصارت في عندي طلع زائد 3 على X هل هذه homogeneous؟
+
+24
+00:02:13,630 --> 00:02:19,430
+لأ طبعاً بديها تبقى Y على X أو مقدار ثابت خالي من
+
+25
+00:02:19,430 --> 00:02:25,440
+كل من X وY كما سنراه من خلال الأمثلة بعد قليلالان
+
+26
+00:02:25,440 --> 00:02:32,120
+بدنا نحل المعادلة التفاضلية المتجنسة يبقى
+
+27
+00:02:32,120 --> 00:02:35,660
+المعادلات التفاضلية المتجنسة لها تكتيك واحد في
+
+28
+00:02:35,660 --> 00:02:37,460
+الحل وهو كالتالي
+
+29
+00:02:47,050 --> 00:02:54,010
+المتغير V يساوي Y على X لو جاءت ضرب، ضرب التبادل
+
+30
+00:02:54,010 --> 00:02:57,970
+يساوي
+
+31
+00:02:57,970 --> 00:03:06,560
+X في Vالان لو جيت اشتقت يبقى الـ dy by dx يساوي
+
+32
+00:03:06,560 --> 00:03:15,340
+هذا يعتبر مشتقت حاصل ضرب دالتين يبقى v زائد x في
+
+33
+00:03:15,340 --> 00:03:22,320
+dv على dxالأولى في مشتقة التانية هيها زي دالة
+
+34
+00:03:22,320 --> 00:03:28,300
+التانية في مشتقة الأولى زيها الان انا عندى y على x
+
+35
+00:03:28,300 --> 00:03:32,600
+ممكن اشيله و اكتب بدلها v و dy على dx بدي اشيله و
+
+36
+00:03:32,600 --> 00:03:38,740
+اكتب بدلها v زي x في dv على dx نمسك المعلومات هذه
+
+37
+00:03:38,740 --> 00:03:44,300
+و نرجع نعوض في المعادلة رقم star بنحصل على ما يأتي
+
+38
+00:03:44,740 --> 00:03:52,840
+Vزاد X في الـDV على DX يساوي capital F as a
+
+39
+00:03:52,840 --> 00:03:58,720
+function of V لأن شيلت Y على X وحطيت مكان امين V
+
+40
+00:03:59,400 --> 00:04:04,560
+الان ممكن اجيب V وين؟ على الناحية الثانية يبقى او
+
+41
+00:04:04,560 --> 00:04:12,040
+اضفنا سلب V للطرفين يبقى X في الـDV على DX يسوي
+
+42
+00:04:12,040 --> 00:04:18,620
+capital F of V نقص الـV ايش رايك؟ بقدر افصل
+
+43
+00:04:18,620 --> 00:04:24,670
+المتغيرات الآن؟بتخلّي ال V's في شجة و ال X's في
+
+44
+00:04:24,670 --> 00:04:28,450
+شجة تانية يبقى بناء عليه هذا بيصير
+
+45
+00:04:53,840 --> 00:05:06,960
+differential equation that can be solved as before
+
+46
+00:05:06,960 --> 00:05:11,860
+زي ما كنا بنحل قبل بنقدر نروح نحلي المعادلة اللي
+
+47
+00:05:11,860 --> 00:05:18,900
+عندنا هذه طب كويس لاحظوا قبل قليلقلت لكم إن
+
+48
+00:05:18,900 --> 00:05:22,680
+المعادلة هذه بقدر اكتبها بالشكل هذا لو كانت
+
+49
+00:05:22,680 --> 00:05:27,560
+rational function الطرف اليمين يعني بسط على مقام
+
+50
+00:05:27,560 --> 00:05:32,320
+طب افترضي ماكانش عندي بسط على مقام كانت دالة عادية
+
+51
+00:05:32,320 --> 00:05:36,360
+دي واي على دي اكس سوى اكس واي تربية زي اتنين اكس
+
+52
+00:05:36,360 --> 00:05:41,170
+واي زي التلاتة مثلا تمامطب كيف بنعمل في هذه
+
+53
+00:05:41,170 --> 00:05:47,770
+الحالة؟ في عندي طريقة أخرى للحكم على هذه المعادلة
+
+54
+00:05:47,770 --> 00:05:53,530
+هل هي معادلة متجانسة ام لا شو هذه الطريقة هنحطها
+
+55
+00:05:53,530 --> 00:05:57,990
+لك في ال definition التالي يبقى بدنا نروح نعطي
+
+56
+00:05:57,990 --> 00:06:05,990
+definition جديد يبقى بداجي definition هقسمه
+
+57
+00:06:05,990 --> 00:06:08,630
+إلى نقطتين النقطة الأولى
+
+58
+00:06:11,240 --> 00:06:19,180
+differential equation الـ differential equation dy
+
+59
+00:06:19,180 --> 00:06:30,000
+by dx بده يساوي f of x y is called homogeneous is
+
+60
+00:06:30,000 --> 00:06:35,300
+called homogeneous
+
+61
+00:06:35,300 --> 00:06:46,780
+if and only ifF and only F فالـ
+
+62
+00:06:46,780 --> 00:07:00,800
+F of T X و T Y بدي يسوى من F of X Y for all T
+
+63
+00:07:00,800 --> 00:07:04,060
+النقطة
+
+64
+00:07:04,060 --> 00:07:17,840
+الثانية A functionf of x و y is called homogeneous
+
+65
+00:07:17,840 --> 00:07:24,100
+of degree
+
+66
+00:07:24,100 --> 00:07:35,360
+mf
+
+67
+00:07:37,650 --> 00:07:47,390
+الـ F of T X و T Y بديوا يساوي T to the power M في
+
+68
+00:07:47,390 --> 00:07:57,530
+ال F of X Y فالـ
+
+69
+00:07:57,530 --> 00:08:04,450
+F of T X و T Y بديوا يساوي ال F of X Y
+
+70
+00:08:07,930 --> 00:08:18,330
+a homogeneous equation of degree الله أعلم
+
+71
+00:08:32,640 --> 00:08:37,080
+نرجع الآن للـ two definitions اللي احنا كتبينهم
+
+72
+00:08:37,080 --> 00:08:41,940
+نفهم كل واحد من ال two definitions هذا طبعا التان
+
+73
+00:08:41,940 --> 00:08:45,900
+اللي هما علاقة ببعض علاقة قوية جدا و اللي هما
+
+74
+00:08:45,900 --> 00:08:50,690
+علاقة بال definition الأولالدفينيشن الأولاني هذا
+
+75
+00:08:50,690 --> 00:08:54,370
+بيقول الـ differential equation dy by dx يسوي f of
+
+76
+00:08:54,370 --> 00:08:59,390
+x y is called homogeneous فقلنا homogeneous إذا
+
+77
+00:08:59,390 --> 00:09:02,830
+قدرنا نكتبها على الشكل اللي عندنا هذا هنا بقول
+
+78
+00:09:02,830 --> 00:09:09,610
+homogeneous f and all f ال f of t x and و t y
+
+79
+00:09:09,610 --> 00:09:16,060
+بيبقى يسوي f of x y لأي t نحطهابيقول بتيجي على
+
+80
+00:09:16,060 --> 00:09:22,000
+المعادلة لو شيلت كل X و حطيت مكانها TX و جيت على Y
+
+81
+00:09:22,000 --> 00:09:27,320
+و شيلت و حطيت مكانها TY تبقى المعادلة كما هي إن
+
+82
+00:09:27,320 --> 00:09:31,280
+بقيت كما هي بقول هذه homogeneous differential
+
+83
+00:09:31,280 --> 00:09:36,100
+equation طب أنا هنا لو جيت و حطيت يا بنات TY على
+
+84
+00:09:36,100 --> 00:09:43,180
+TX مش بتظلها Y على Xومن هنا باختصر T مع T بالضل Y
+
+85
+00:09:43,180 --> 00:09:47,360
+علي X ومن هنا هذا ال definition يكافئ هذا ال
+
+86
+00:09:47,360 --> 00:09:52,970
+definition تمامالما أقول هذي homogeneous اللي هو
+
+87
+00:09:52,970 --> 00:09:57,550
+differential equation ممكن يكونها درجة ما تعالى
+
+88
+00:09:57,550 --> 00:10:01,790
+نشوف إيش اللي بقول هنا بقول دالة F of X Y بقول
+
+89
+00:10:01,790 --> 00:10:07,030
+عنها homogeneous of degree M دالة متجانسة من
+
+90
+00:10:07,030 --> 00:10:13,210
+الدرجة رقم M طبعا M عدد صحيح موجب أو صفر ماعناه
+
+91
+00:10:13,210 --> 00:10:19,790
+مشكلة بس ليس كثير ليس سالباوهنا ايه فاصلة وقليل
+
+92
+00:10:19,790 --> 00:10:30,670
+الام greater than or equal to zero والام is an
+
+93
+00:10:30,670 --> 00:10:34,930
+integer يبقى
+
+94
+00:10:34,930 --> 00:10:35,810
+عدد صحيح
+
+95
+00:10:38,550 --> 00:10:43,830
+أنا جيت على X شيلتها و حاطيت مكانها TX جيت على Y
+
+96
+00:10:43,830 --> 00:10:48,230
+شيلتها و حاطيت مكانها TY لاجيت انها تجميش زي اللي
+
+97
+00:10:48,230 --> 00:10:53,310
+فوق يسوي F of XY لاجيت يسوي T to the power M في F
+
+98
+00:10:53,310 --> 00:10:59,550
+of XY بقول إن حدث ذلك يبقى الدالة اللي عنها دي
+
+99
+00:10:59,550 --> 00:11:06,450
+بقول عنها homogeneous من الدرجة رقم M تمام؟يبقى
+
+100
+00:11:06,450 --> 00:11:12,790
+هذا degree M هوموجينيس من degree M طيب يبقى بناء
+
+101
+00:11:12,790 --> 00:11:18,950
+عليه الدالة الأولى هذه في عندي هنا T ماعنديش يعني
+
+102
+00:11:18,950 --> 00:11:25,030
+كانت T أو Zero يبقى هذه بالهوموجينيس of degree
+
+103
+00:11:25,030 --> 00:11:31,870
+Zero تمام degree Zero يبقى هذه متجانسة من الدرجة
+
+104
+00:11:31,870 --> 00:11:36,680
+الصفريةالان بدنا نروح كيف بدنا نفهم ال two
+
+105
+00:11:36,680 --> 00:11:41,280
+definitions هدول بدنا ناخد بعض الأمثلة يبقى
+
+106
+00:11:41,280 --> 00:11:48,340
+example one بقول
+
+107
+00:11:48,340 --> 00:11:54,100
+determine determine
+
+108
+00:11:54,100 --> 00:12:00,300
+whether the following
+
+109
+00:12:03,040 --> 00:12:07,920
+determine whether the following functions are
+
+110
+00:12:07,920 --> 00:12:18,200
+homogeneous or not if
+
+111
+00:12:18,200 --> 00:12:30,080
+itHomogeneous لو كانت homogenous state its degree
+
+112
+00:12:30,080 --> 00:12:36,100
+بدي أعرف قداش الدرجة بتبعتها النقطة الأولى
+
+113
+00:12:51,130 --> 00:13:03,950
+النقطة الثانيةالـ F of X و Y بدها تساوي XY Cos Y
+
+114
+00:13:03,950 --> 00:13:08,690
+على X زائد X تربيع
+
+115
+00:13:14,510 --> 00:13:19,270
+السؤال بيقول لي شوف لمين من الدول التالية بتبقى
+
+116
+00:13:19,270 --> 00:13:22,890
+homogenous ومين ماهياش homogenous وإذا كانت
+
+117
+00:13:22,890 --> 00:13:27,450
+homogenous بدي أعرف الـ M هذه قداش قيمته يعني قداش
+
+118
+00:13:27,450 --> 00:13:34,290
+درجة هذه المعادلة بقوله كويس بيداجي ال solution هو
+
+119
+00:13:34,290 --> 00:13:41,310
+بيداجي للنقطة الأولى اللي هي رقم I رقم I بدي أشيل
+
+120
+00:13:41,310 --> 00:13:48,050
+كل X و أحط مكانهاوشيل كل Y وحط مكانها TY يبقى
+
+121
+00:13:48,050 --> 00:13:57,310
+بالداجي اقوله هنا G of TX وTY بده يساوي اتنين TX
+
+122
+00:13:57,310 --> 00:14:07,800
+لكل تربية زائد تلاتة TY لكل تربية زائد اربعةيعني
+
+123
+00:14:07,800 --> 00:14:14,560
+هذه بقدر اقول اللي هي اتنين T تربيع X تربيع زائد
+
+124
+00:14:14,560 --> 00:14:24,720
+تلاتة T تربيع Y تربيع زائد اربعة الـ G is a non
+
+125
+00:14:24,720 --> 00:14:31,020
+homogeneous function
+
+126
+00:14:31,020 --> 00:14:35,660
+يبقى هذه ليست homogeneous function
+
+127
+00:14:46,190 --> 00:14:51,590
+نأتي للمعادلة التانية او للـ function التانية ناخد
+
+128
+00:14:51,590 --> 00:15:01,730
+النقطة التانية لـ F of TX و TY يساوي يبقى هنا TX
+
+129
+00:15:01,730 --> 00:15:14,190
+مضروبة في TY TX في TY في Cosتي واي عالى تي اكس
+
+130
+00:15:14,190 --> 00:15:24,010
+زائد تي اكس لكل تربيع هذه لو جيت ضربتها بنات بيصير
+
+131
+00:15:24,010 --> 00:15:31,250
+تي تربيع اكس واي وهنا لو اختصرت تي مع تي بيظل
+
+132
+00:15:31,250 --> 00:15:38,130
+cosine واي عالى اكس وهذه زائد تي تربيع اكس تربيع
+
+133
+00:15:39,380 --> 00:15:44,000
+أظن ممكن من المعادلة هذه أخد T تربيع عمل مشترك إذا
+
+134
+00:15:44,000 --> 00:15:51,580
+لو أخدنا T تربيع عمل مشترك بيظل لإن X Y Cos Y على
+
+135
+00:15:51,580 --> 00:15:57,820
+X زائد X تربيع اللي بين Cos أليس T F of X وY
+
+136
+00:15:57,820 --> 00:16:05,280
+الأصلية يبقى هذا الكلام بدي ساوي T تربيع في F of X
+
+137
+00:16:05,280 --> 00:16:14,840
+وYيبقى هذا معناه ايه؟ ف ال f of x و y is a
+
+138
+00:16:14,840 --> 00:16:19,820
+homogeneous function
+
+139
+00:16:19,820 --> 00:16:31,880
+of degree اتنين طيب انت هنا روح ناخد مثاليبقى هذا
+
+140
+00:16:31,880 --> 00:16:36,720
+المثال على آخر التعريفين بدنا نروح ناخد مثال على
+
+141
+00:16:36,720 --> 00:16:41,020
+التعريف الأول لل homogenous differential equation
+
+142
+00:16:41,020 --> 00:16:49,320
+يبقى example two بيقول
+
+143
+00:16:49,320 --> 00:16:57,800
+solve the following differential
+
+144
+00:16:59,520 --> 00:17:05,540
+Equations حل المعادلات التفاضلية التالية أول
+
+145
+00:17:05,540 --> 00:17:12,440
+معادلة من هذه المعادلات التي هي رقم A بيقول XYY'
+
+146
+00:17:13,280 --> 00:17:19,520
+يساوي 2Y تربيع ناقص X تربيع
+
+147
+00:17:44,670 --> 00:17:49,890
+أول شي بتبحث هل هي homogeneous ماهياش homogeneous
+
+148
+00:17:49,890 --> 00:17:56,980
+نقدر نفصل متغيرات هل نقدر عليهلما كان موضوعنا
+
+149
+00:17:56,980 --> 00:18:00,180
+موضوع الـ homogeneous إذا أنا أول شغل بدي أختبرها
+
+150
+00:18:00,180 --> 00:18:02,940
+هل هي homogeneous أم لا إذا ما طلعتش homogeneous
+
+151
+00:18:02,940 --> 00:18:08,080
+بروح بدور main, separable أو غيره طب الآن أنا بدي
+
+152
+00:18:08,080 --> 00:18:14,100
+Y' لحالة يبقى بروح أجسم الطرفين على XY يبقى لو
+
+153
+00:18:14,100 --> 00:18:20,860
+قسمت الطرفين على XY بصير المعادلة يساوي 2Y على X
+
+154
+00:18:21,350 --> 00:18:25,870
+والله بلاش نقولك كيف هاد أجت بدي أعملها لك على
+
+155
+00:18:25,870 --> 00:18:30,970
+خطوط اللي لو جسمت على x y بظهر y prime يبقى 2y
+
+156
+00:18:30,970 --> 00:18:39,130
+تربيع على x y ناقص x تربيع على x في y بالشكل هذا
+
+157
+00:18:39,130 --> 00:18:44,730
+هذه كلها اللي هي main y primeإذا هذه المعادلة يا
+
+158
+00:18:44,730 --> 00:18:51,090
+بنات قدرت الأصلية أكتبها على الشكل الجديد هذا شو
+
+159
+00:18:51,090 --> 00:18:56,860
+رأيك في الشكل الجديد؟هموجينيوس ولا لأ يبجى هذه
+
+160
+00:18:56,860 --> 00:19:01,200
+هموجينيوس اللي قدرت اكتبها على شكل y على x بدون ما
+
+161
+00:19:01,200 --> 00:19:05,880
+يكون ثابت لحاله او بدون ما يكون عدد على x او عدد
+
+162
+00:19:05,880 --> 00:19:13,560
+على ماين على y يبجى هذه this is a homogeneous
+
+163
+00:19:13,560 --> 00:19:21,850
+differential equationبدنا نحلها إذا بنروح نتابع
+
+164
+00:19:21,850 --> 00:19:27,370
+التكتيك اللي ابتدأناه في الجزء النظري قبل قليل شو
+
+165
+00:19:27,370 --> 00:19:35,460
+بدنا نعمل؟ بنقول له put ال V تساوي Y على Xأضرب ضرب
+
+166
+00:19:35,460 --> 00:19:40,580
+تبادل يبقى الـ
+
+167
+00:19:40,580 --> 00:19:47,040
+y تساوي x في v اشتق طرفين بالنسبة إلى x يبقى dy
+
+168
+00:19:47,040 --> 00:19:57,850
+على dx يساوي v زائد x في dv على dxنعوض الأن
+
+169
+00:19:57,850 --> 00:20:07,870
+بالمعلومات اللي عندنا في المعادلة المستاطيلة في
+
+170
+00:20:07,870 --> 00:20:10,250
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+171
+00:20:10,250 --> 00:20:10,370
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+172
+00:20:10,370 --> 00:20:10,490
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+173
+00:20:10,490 --> 00:20:11,150
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+174
+00:20:11,150 --> 00:20:11,170
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+175
+00:20:11,170 --> 00:20:14,390
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+176
+00:20:14,390 --> 00:20:24,290
+المعادلة المستاطيلة في المعادلة
+
+177
+00:20:24,290 --> 00:20:33,320
+المستاطيلطب ايش رايك؟ بدي اضيف سالب V للطرفين يبقى
+
+178
+00:20:33,320 --> 00:20:41,040
+هذه ايش بتعطينا؟تعطينا ان X في الـDV على DX يسوى V
+
+179
+00:20:41,040 --> 00:20:49,400
+ناقص واحد على V او ان شئتنا فقلنا X في الـDV على
+
+180
+00:20:49,400 --> 00:20:55,560
+DX يسوى V تربية ناقص واحد كله على V وحتى المقامات
+
+181
+00:20:55,560 --> 00:21:00,480
+للطرف اليمين طب ايش رأيك و بقدر افصل المتغيرات ولا
+
+182
+00:21:00,480 --> 00:21:02,940
+لا نقدر
+
+183
+00:21:04,340 --> 00:21:10,800
+يبقى بقدر أقول هذه V على V تربيع ناقص واحد في
+
+184
+00:21:10,800 --> 00:21:18,560
+الـDV بده يساوي DX على X يبقى الـV's صاروا في شجة
+
+185
+00:21:18,560 --> 00:21:22,640
+و الـX's صاروا في شجة واحدة يبقى هذه شو اسمها؟
+
+186
+00:21:22,640 --> 00:21:26,500
+Separable يبقى حولت الـHomogeneous Differential
+
+187
+00:21:26,500 --> 00:21:33,080
+Equation إلى Separable Equation يبقى هذه Separable
+
+188
+00:21:35,010 --> 00:21:38,850
+Equation زي ما قلنا في الجزء الناضري أول مبتعدين
+
+189
+00:21:38,850 --> 00:21:42,270
+التعريف الأول قلنا بشأن حلها بتشيل ال Y على X و
+
+190
+00:21:42,270 --> 00:21:47,170
+بتحط مكانها V و اشتقنا و عوضنا و فاصلنا المتغيرات
+
+191
+00:21:47,170 --> 00:21:50,890
+فصارت ال V في شجة و ال X في شجة فقلنا ها دي
+
+192
+00:21:50,890 --> 00:21:53,910
+separable equation يبقى هيها صارت separable
+
+193
+00:21:53,910 --> 00:21:59,190
+equation بده حلها ايش بنعمل؟بنكمل طيب الطرف اليمين
+
+194
+00:21:59,190 --> 00:22:05,110
+أظن سهل طيب و الطرف الشمال بقول بس لو فيه اتنين في
+
+195
+00:22:05,110 --> 00:22:09,370
+ال bus اللي أصبح ال bus تفاضل المقام إذا بنضرب في
+
+196
+00:22:09,370 --> 00:22:14,490
+اتنين و بنقسم على اتنين يعني هذه كأنها النص في
+
+197
+00:22:14,490 --> 00:22:22,410
+اتنين V على V تربية ناقص واحد كله في DV بده يساوي
+
+198
+00:22:22,410 --> 00:22:30,330
+DX على Xصار البسطة فضل مقام يبقى بالتكامل ايش بصير
+
+199
+00:22:30,330 --> 00:22:37,090
+عندنا مص لن absolute value ل V تربيع ناقص واحد
+
+200
+00:22:37,090 --> 00:22:45,060
+يسوى لن absolute value ل X زائد C1 مثلاًطب لو
+
+201
+00:22:45,060 --> 00:22:51,500
+ضربنا في اتنين بصير الـLin هذه يا بنات كأنها ايه؟
+
+202
+00:22:51,500 --> 00:22:57,840
+كأنها الـLin الـV تربيع ناقص واحد يساوي الـLin
+
+203
+00:22:57,840 --> 00:23:03,700
+absolute value لل X تربيع أظن سواء كتبنا الـLin و
+
+204
+00:23:03,700 --> 00:23:11,280
+الله ما كتبناش بتفرجش عندنا تمام؟ هها زائد اتنين
+
+205
+00:23:11,280 --> 00:23:19,570
+C1أنا بدي اشيل لن هذه برفع اتنين كأس للعداد ايه
+
+206
+00:23:19,570 --> 00:23:24,530
+يبقاش بيصير عند هنا absolute value لل V تربيع ناقص
+
+207
+00:23:24,530 --> 00:23:32,570
+واحد يساوي E أس لن اللي هو ال X تربيع لإن ال X
+
+208
+00:23:32,570 --> 00:23:38,530
+تربيع زائد اتنين C1 كونه كمية مربعة حطيت ال
+
+209
+00:23:38,530 --> 00:23:43,000
+absolute والله شيلته بتفرجش عندنايبقى هذه يا بنات
+
+210
+00:23:43,000 --> 00:23:50,480
+اللي هي بتتساوي قداش X تربيع في E أس اتنين C1 E أس
+
+211
+00:23:50,480 --> 00:23:56,640
+لين X تربيع و E أس اتنين C1 تمام ال E و ال L عكس
+
+212
+00:23:56,640 --> 00:24:02,020
+بعض بصير X تربيع في من في C1 طب إيش رأيك هذه عمرها
+
+213
+00:24:02,020 --> 00:24:07,680
+تصير قيمة سالبة يبقى ال absolute value هذا لا معنى
+
+214
+00:24:07,680 --> 00:24:13,190
+له موجب دايما و أبدايبقى بناءً عليه بقدر أقول إذا
+
+215
+00:24:13,190 --> 00:24:21,410
+الـV تربيع ناقص واحد يساوي C في X تربيع والـC بدي
+
+216
+00:24:21,410 --> 00:24:27,010
+يساوي E أس اتنين C1 هذا مقدار ثابت بدل ما هم كانوا
+
+217
+00:24:27,010 --> 00:24:31,150
+بديوا يحطوا مداله C التفلي بس في الكتاب مقدار ثابت
+
+218
+00:24:31,150 --> 00:24:37,410
+جد ما يكون يكونطيب الواحد هذا بقدر أنقله اين؟ على
+
+219
+00:24:37,410 --> 00:24:44,570
+الشجرة التانية يبقى بصير ال V تربيع بده يساوي CX
+
+220
+00:24:44,570 --> 00:24:51,190
+تربيع زائد واحدطب ال V تربية هذه مش عبارة عن Y على
+
+221
+00:24:51,190 --> 00:24:57,730
+X لكل تربية صح نضرب الطرفين في X تربية بصير عندنا
+
+222
+00:24:57,730 --> 00:25:05,970
+هنا Y تربية يساوي X تربية في C X تربية زائد واحد
+
+223
+00:25:06,560 --> 00:25:13,160
+ناخد الجذر التربيعي للطرفين يبقى بصير Y يساوي
+
+224
+00:25:13,160 --> 00:25:19,180
+الزائد أو ناقص اللي هو main اللي هو absolute value
+
+225
+00:25:19,180 --> 00:25:25,780
+لل X في main في الجذر التربيعي ل CX تربيع زائد
+
+226
+00:25:25,780 --> 00:25:35,150
+واحد يبقى هذا هو الحل تبع المثلة اللي عندناتمام؟
+
+227
+00:25:35,150 --> 00:25:39,150
+حد إلها أي تساؤل هنا قبل أن نذهب إلى المثال الذي
+
+228
+00:25:39,150 --> 00:25:45,750
+يليه .. آه أيوة اتفضلي مافيش
+
+229
+00:25:45,750 --> 00:25:50,310
+رأيك تيجي هنا؟ تعالي يالا يا بنات أخدنا طال الوقت
+
+230
+00:25:50,310 --> 00:25:54,570
+four example كمثال مشان اللي مش مخدمة تاخد بالها
+
+231
+00:25:54,570 --> 00:26:00,410
+تسألي هنا اللي بدكية هنا يجب أن تعمل E أسنين extra
+
+232
+00:26:00,410 --> 00:26:06,160
+B زي اتنين C one مش هي الاتنين C one بحالهالأ ماشي
+
+233
+00:26:06,160 --> 00:26:14,620
+لكن هذا كله كأسل العدد E هذا كله أسل العدد E E أسل
+
+234
+00:26:14,620 --> 00:26:20,080
+يساوي E أس المقدر هذا كله مظبوط ولا لأ يبقى بيصير
+
+235
+00:26:20,080 --> 00:26:29,150
+E أسل X تربيع E أسل X تربيع في E أس اتنين C1هي
+
+236
+00:26:29,150 --> 00:26:33,290
+وزنها مظبوط هيك عند ضرب تجمع الأسس فصارت مجموعة
+
+237
+00:26:33,290 --> 00:26:37,890
+بهذا الشكل الـE والإنعكس بعض بضل X تربيعها دي حطيت
+
+238
+00:26:37,890 --> 00:26:42,790
+بدلة مقدار ثابت لإن 2 و7 من 10 أس مقدار ثابت هيك
+
+239
+00:26:42,790 --> 00:26:47,110
+كنت بدك تسألي ولا بطلتي نفس السؤال في حاب تسأل
+
+240
+00:26:47,110 --> 00:26:54,250
+تاني يا بنات خلاص نذهب إلى السلمثال الذي يليه
+
+241
+00:27:10,480 --> 00:27:15,160
+نمر بـ X
+
+242
+00:27:15,160 --> 00:27:27,980
+تربية Y' ناقص XY X تربية زائد Y تربية في 10
+
+243
+00:27:27,980 --> 00:27:36,040
+inverse Y على X نحل المعادلة التفاضلية اللي قدامنا
+
+244
+00:27:36,040 --> 00:27:44,090
+هذه بسيطة جدايبقى الخطوة الأولى بدي أخلّي Y' لحالة
+
+245
+00:27:44,090 --> 00:27:51,130
+يبقى إيش نعمل؟ نكسب على X ربيع صحيح ولا لا؟ يبقى
+
+246
+00:27:51,130 --> 00:27:58,490
+باجي بقوله solutionأجسم المعادلة كلها على X تربية
+
+247
+00:27:58,490 --> 00:28:05,090
+لو جسمت على X تربية هنا يقدرش بيطلع Y' لو جسمت على
+
+248
+00:28:05,090 --> 00:28:13,110
+X تربية بيظل يقدرش Y على X يبدو يساوي 1 زائد Y على
+
+249
+00:28:13,110 --> 00:28:19,550
+X لكل تربية تان Inverse Y على X
+
+250
+00:28:23,140 --> 00:28:27,480
+بعد ذلك الان صارت هذه homogenous differential
+
+251
+00:28:27,480 --> 00:28:34,840
+equation يبقى هذه homogenous differential
+
+252
+00:28:34,840 --> 00:28:38,980
+equation مادام homogenous إذا بنحلها بالطريقة اللي
+
+253
+00:28:38,980 --> 00:28:45,450
+حلناها بالمثال قبل قليل يبقى باجي بقوله podحط لي v
+
+254
+00:28:45,450 --> 00:28:52,430
+تساوي y على x هذا معناه ان y يساوي xv هذا معناه ان
+
+255
+00:28:52,430 --> 00:29:01,930
+dy by dx يساوي v زائد x في dv على dx اذا بدنا نمسك
+
+256
+00:29:01,930 --> 00:29:05,050
+المعلومات اللي حصلنا عليها و نرجع نعوضها بقى في
+
+257
+00:29:05,050 --> 00:29:12,180
+المعادلة أعلىيبقى الـY' يا بنات اللي هي V زائد X
+
+258
+00:29:12,180 --> 00:29:21,640
+في الـDV على DX نقص الـV يسوى 1 زائد V ترابيع في
+
+259
+00:29:21,640 --> 00:29:30,860
+10 inverse Vأظن سالب V وموجة V مع السلامة يبقى
+
+260
+00:29:30,860 --> 00:29:39,140
+تقول المثل إلى X في الـDV على DX 1 زائد V تربيع في
+
+261
+00:29:39,140 --> 00:29:47,460
+Tan inverse Vنفصل المتغيرات بيدخل ال V في الشجة
+
+262
+00:29:47,460 --> 00:29:54,340
+الشمال وال X في الشجة اليمين يبقى دي بيصير DV على
+
+263
+00:29:54,340 --> 00:30:02,600
+واحد زائد V تربيع في turn inverse V يسوى DX على X
+
+264
+00:30:02,600 --> 00:30:07,520
+وهذه C Parabol equation
+
+265
+00:30:08,420 --> 00:30:14,100
+يبقى هذه معادلة فيها المتغيرات مفصولة إذا المعادلة
+
+266
+00:30:14,100 --> 00:30:20,160
+اللى كانت homogeneous حولناها إلى separable ومن ثم
+
+267
+00:30:20,160 --> 00:30:25,800
+مش ضايل علينا إلا نكامل هذه المعادلة بيكون حصلنا
+
+268
+00:30:25,800 --> 00:30:33,540
+على الحل المطلوب السؤال هو هذه very easy طب و هذه
+
+269
+00:30:33,540 --> 00:30:41,000
+very easy كمانمش تقت الـ tan inverse كده؟ 1 لا 1
+
+270
+00:30:41,000 --> 00:30:47,900
+زائد V تربيع إذا هذه كلها هي مش تقت من؟ tan
+
+271
+00:30:47,900 --> 00:30:54,580
+inverse يبقى المثل بقدر أقول هي D ل tan inverse V
+
+272
+00:30:54,580 --> 00:31:02,400
+على tan inverse V بده يسوى DX على X إذا رحت كتبت
+
+273
+00:31:02,400 --> 00:31:07,790
+المعادلة اللي عندي بصياغة جديدةطب البسط هو تفاضل
+
+274
+00:31:07,790 --> 00:31:13,430
+المقام يبقى الجواب لين absolute value للمقام يبقى
+
+275
+00:31:13,430 --> 00:31:19,430
+هذا بدي يعطينا بالتكامل لين absolute value ل 10
+
+276
+00:31:19,430 --> 00:31:25,990
+inverse V بدي سوى لين absolute value ل X زائد
+
+277
+00:31:25,990 --> 00:31:33,990
+constant C1 طيب شو رايك؟ناخد الـ exponential
+
+278
+00:31:33,990 --> 00:31:40,110
+للطرفين يبقى لها رافعت اتنين كأس للعدد E بصير عندي
+
+279
+00:31:40,110 --> 00:31:46,890
+absolute value ل 10 inverse V بيصير E أسلن
+
+280
+00:31:46,890 --> 00:31:55,570
+absolute value ل X زائد C1 شو اسمك انت والله؟ مش
+
+281
+00:31:55,570 --> 00:32:02,670
+سامعأخوك نرمي توسيع سالة السؤال اللي بعضكوا كانت
+
+282
+00:32:02,670 --> 00:32:08,550
+خجلانة تسألك نشجعها على ذلك ونذهب نذكر تذكير بما
+
+283
+00:32:08,550 --> 00:32:15,170
+كنا نصنعه في Calculus B يبقى هذه E أس لين absolute
+
+284
+00:32:15,170 --> 00:32:25,300
+value ل X في E أس C1 تمام؟ هذا الكلام بده يساويأو
+
+285
+00:32:25,300 --> 00:32:29,760
+هذا الكلام هو اللي ان عكس بعض يبقى absolute value
+
+286
+00:32:29,760 --> 00:32:38,440
+ل X في C والـ C بده يساوي E on C1 مشان أضيع الكلكة
+
+287
+00:32:38,440 --> 00:32:44,620
+مخليش عندي كلكعة كتيرة طيب شو رايك؟ بده أخد الآن
+
+288
+00:32:44,620 --> 00:32:55,200
+10 للطرفينيبقى V تساوي 10 C absolute value ل X
+
+289
+00:32:58,220 --> 00:33:06,300
+Y على X يبقى هذا معناه ان Y على X يساوي 10 ل C
+
+290
+00:33:06,300 --> 00:33:11,100
+absolute value ل X يبقى الحل اللي عندنا لو نضرب
+
+291
+00:33:11,100 --> 00:33:18,740
+الطرفين في X بيصير Y يساوي X في 10C absolute value
+
+292
+00:33:18,740 --> 00:33:23,480
+ل X هذا هو حل المعادلة المعطاة
+
+293
+00:33:28,600 --> 00:33:36,820
+هذا كله بيظبط يكون Y على X ممكن
+
+294
+00:33:36,820 --> 00:33:40,880
+ما يظبطش ولما ماظبطش بدنا نروح لل C Parable أو
+
+295
+00:33:40,880 --> 00:33:46,670
+لبعض الطرق الأخرى اللتي لم ندرسها بعديعني احنا
+
+296
+00:33:46,670 --> 00:33:52,730
+بالاخر ممكن نجيبلك تمرين عام بعد كله تحل على أي
+
+297
+00:33:52,730 --> 00:33:56,730
+طريقة بس تجرب الطريقة اللي تعجبك بس ال Y على X
+
+298
+00:33:56,730 --> 00:34:01,990
+بتقدر تطلع فيها بمجرد النظر يعني انا لو جسمت على X
+
+299
+00:34:01,990 --> 00:34:06,030
+و لا على X تربيها هل بطلع Y على X و X على Y ولا لأ
+
+300
+00:34:06,030 --> 00:34:09,350
+اذا طلع خلاص هموجينة قبل ما تشتغلولها بمجرد ما
+
+301
+00:34:09,350 --> 00:34:13,580
+تطلع فيهاتمام او اذا قررت افصل بقدر افصل المتغير
+
+302
+00:34:13,580 --> 00:34:19,040
+يبقى ياسي برامول و هكذا لسه لازال عندنا بعض انواع
+
+303
+00:34:19,040 --> 00:34:24,080
+اخرى من ال first order differential equation طيب
+
+304
+00:34:24,080 --> 00:34:34,420
+نعطيكي ملاحظة remark to
+
+305
+00:34:34,420 --> 00:34:35,280
+solve
+
+306
+00:34:39,910 --> 00:34:48,770
+لأ differential equation لحل المعادلة التفاضلية a1
+
+307
+00:34:48,770 --> 00:34:59,830
+x1 b1 y1 زائد c1 كل هذا مضروب في ال y prime بيساوي
+
+308
+00:34:59,830 --> 00:35:15,500
+a2 x زائد a2 xA1X يا ابناتو B1X يساو as A2X زائد
+
+309
+00:35:15,500 --> 00:35:30,340
+B2Y زائد C2 و examine the following بدنا نختبر ما
+
+310
+00:35:30,340 --> 00:35:34,280
+يأتي النقطة
+
+311
+00:35:34,280 --> 00:35:34,660
+الأولى
+
+312
+00:35:37,390 --> 00:35:51,310
+إذا الـ A1 في الـ B2 بتسوي A2 في الـ B1 نحل بالروح
+
+313
+00:35:51,310 --> 00:36:02,110
+نحل نحل بالروح نحل as the final example
+
+314
+00:36:03,880 --> 00:36:14,260
+as a final example in section واحد اتنين نقطة
+
+315
+00:36:14,260 --> 00:36:26,980
+ثانية if ال a1 b2 لا يسوى ال a2 في ال b1 we use
+
+316
+00:36:26,980 --> 00:36:31,620
+the transform
+
+317
+00:36:34,360 --> 00:36:43,440
+و نستخدم الـ transform اللي هو X يسوى X كابتل زائد
+
+318
+00:36:43,440 --> 00:36:56,380
+P و Y يسوى Y كابتل زائد Q حيث
+
+319
+00:36:56,380 --> 00:37:01,220
+ال P و ال Q هي الحل
+
+320
+00:37:07,180 --> 00:37:15,540
+is the solution of the system
+
+321
+00:37:15,540 --> 00:37:20,440
+of equations
+
+322
+00:37:20,440 --> 00:37:24,020
+a1p
+
+323
+00:37:24,020 --> 00:37:37,900
+زائد b1q زائد c1 يساوي zero و a2pزائد بيتو اكيو
+
+324
+00:37:37,900 --> 00:37:46,700
+بيتو اكيو زائد C2 بده يساوي مين؟ بده يساوي Zero
+
+325
+00:38:33,240 --> 00:38:39,670
+Y' يسوى المقدار هذا على المقدار هذاأو ضربنا
+
+326
+00:38:39,670 --> 00:38:43,270
+الطرفين في المقام فصرت على الشكل اللي قدامي هذا
+
+327
+00:38:43,270 --> 00:38:48,250
+يبقى الشكل اللي قدامي هذا او y prime يساوي هذا على
+
+328
+00:38:48,250 --> 00:38:52,510
+الجثة سيان كل واحد طيب انا عندي معادلة بشكل لأن
+
+329
+00:38:52,510 --> 00:38:57,450
+انا بداجي احل هذه المعادلةيا بنات في عند المعادلة
+
+330
+00:38:57,450 --> 00:39:02,650
+أحيانا بتكونش homogeneous لكن أنا بقدر بطريقة ما
+
+331
+00:39:02,650 --> 00:39:06,710
+أحولها إلى homogeneous differential equation وإذا
+
+332
+00:39:06,710 --> 00:39:09,970
+حولتها بقدر أحلها بالطريقة اللي حلناها بالمثالين
+
+333
+00:39:09,970 --> 00:39:15,070
+السابقين قبل قليل طبعا يبقى إذا عندي مثلة من هذا
+
+334
+00:39:15,070 --> 00:39:19,850
+القبيل وهذه ليست homogeneous بده أطلع على شغلين
+
+335
+00:39:19,850 --> 00:39:29,140
+الشغل الأولى هل a1 في ال b2مع الـ A2 في الـ B1 هل
+
+336
+00:39:29,140 --> 00:39:33,740
+هدول بيساووا بعض؟ والله بيساووش والله إذا كان هدول
+
+337
+00:39:33,740 --> 00:39:38,140
+بيساووا بعض بنروح أنحل المعادلة هذه زي آخر مثال
+
+338
+00:39:38,140 --> 00:39:42,160
+أخدناه في المحاضرة الماضية بصير عندي جوس كله
+
+339
+00:39:42,160 --> 00:39:47,600
+بعتبره variable جديد جوس بيحتوي على X و Y بشيله
+
+340
+00:39:47,600 --> 00:39:52,500
+بحطه variable وليكن V وبالتالي بصير عندي separable
+
+341
+00:39:52,500 --> 00:39:56,700
+differential equationوإذا ما كانش وفي الغالب ما
+
+342
+00:39:56,700 --> 00:40:01,940
+بيكونش وإذا ما كانش بنجي للنقطة الثانية يعني فباجي
+
+343
+00:40:01,940 --> 00:40:06,600
+بقول لو كان ال a1 في ال b2 لا يسوى ال a2 في ال b1
+
+344
+00:40:06,600 --> 00:40:13,030
+شو بنعمل؟ we use the transfer بنعمل تحويلة جديدةشو
+
+345
+00:40:13,030 --> 00:40:20,210
+التحويل الجديد هذه؟ بحط x small اللي عندى هذه او x
+
+346
+00:40:20,210 --> 00:40:26,450
+هذه بx capital زائد رقم و ال y small بy capital
+
+347
+00:40:26,450 --> 00:40:32,240
+زائد رقممين هو الرقم هذا ا؟ باجي على المعادلة هذه
+
+348
+00:40:32,240 --> 00:40:37,380
+و بسويها بالصفر بعد ما اشيل ال X و احط مكانها بيه
+
+349
+00:40:37,380 --> 00:40:41,900
+و اشيل ال Y و احط مكانها لكيو و باجي على المعادلة
+
+350
+00:40:41,900 --> 00:40:46,500
+هذه كمان و بسويها بمين بالصفر يبقى انا المثل
+
+351
+00:40:46,500 --> 00:40:53,440
+بمتغير جديد بده اسمي X كابتل زائد ال Pوالـ Y أسمه
+
+352
+00:40:53,440 --> 00:40:58,020
+اللي بدي أسميه Y كابتل زائد Q اللي طالع تاندي بعد
+
+353
+00:40:58,020 --> 00:41:03,760
+هيك بدي أشيل كل X و أحط مكانها X زائد P في
+
+354
+00:41:03,760 --> 00:41:08,820
+المعادلة هذه و هذا بدي أحط Y كابتل زائد Q والتاني
+
+355
+00:41:08,820 --> 00:41:12,820
+هذي زيها لما أعمل هيك عارفين إيش بعمل لما أعمل
+
+356
+00:41:12,820 --> 00:41:18,710
+هذا؟بطير الثابت اللى عندى C2 وC1 بتخلص من الثوابت
+
+357
+00:41:18,710 --> 00:41:23,950
+اللى بسببه للمشكلة لأن وجودهم لو جسمت على X و لو
+
+358
+00:41:23,950 --> 00:41:27,890
+جسمت على Y بتبطل الصيرة homogeneous لكن لما حط
+
+359
+00:41:27,890 --> 00:41:31,470
+التعويض هذه بطيروا الثابت لو ما طروش الثوابت
+
+360
+00:41:31,470 --> 00:41:35,730
+معناته في شغل غلط عندك الغلط في حساب ال P و ال Q
+
+361
+00:41:35,730 --> 00:41:40,440
+أو في التعويض عندكيبقى بعد ذلك تتحول إلى
+
+362
+00:41:40,440 --> 00:41:45,320
+homogeneous differential equation يعني فائدة هذه
+
+363
+00:41:45,320 --> 00:41:51,220
+التحولة اتحول المعادلة من non homogeneous إلى
+
+364
+00:41:51,220 --> 00:41:55,260
+homogeneous differential equation وبالتالي بنروح
+
+365
+00:41:55,260 --> 00:42:01,160
+نحلها زي ما كنا بنحل المثالين قبل قليل واضح كلامي؟
+
+366
+00:42:01,440 --> 00:42:07,620
+يعني هذه الملاحظة أو هذا النوع من المسائل بنلجأ له
+
+367
+00:42:07,620 --> 00:42:11,620
+إذا طلعت المعادلة اللى عندي ماهياش متجنسة زى ما
+
+368
+00:42:11,620 --> 00:42:16,560
+سألتي قبلها قلت يمكن ماتطلعش متجنسة بقولك في طرق
+
+369
+00:42:16,560 --> 00:42:20,680
+أخرى أو في معادلة أخرى بروح أختبرها إيش أخدناه
+
+370
+00:42:20,680 --> 00:42:24,920
+وإيش ماخدناهوش هذا .. هذا احنا أخدناهاإن المعادلة
+
+371
+00:42:24,920 --> 00:42:30,860
+هذه ممكن أحولها إلى معادلة متجنسة كيف؟ بالطريقة
+
+372
+00:42:30,860 --> 00:42:36,220
+التالية بمسك كل معادلة من المعادلتين هدول و بسويها
+
+373
+00:42:36,220 --> 00:42:41,900
+بالصفر و بحلف تنتين و بجيب قيمة x و y بعد هيكبكتب
+
+374
+00:42:41,900 --> 00:42:49,980
+المعادلة بدلالة variable جديد XY X أساسي بحط X
+
+375
+00:42:49,980 --> 00:42:53,980
+كابتل زائد الرقم اللي طالع عندي و Y أساسي بحط Y
+
+376
+00:42:53,980 --> 00:42:56,980
+كابتل زائد الرقم اللي طالع عندي وبعوض في المعادلة
+
+377
+00:42:56,980 --> 00:43:01,020
+الأصليه اوتوماتيك لازم تنقلب الى homogeneous
+
+378
+00:43:01,020 --> 00:43:04,380
+differential equation اذا ما طلعتش homogeneous
+
+379
+00:43:04,380 --> 00:43:07,660
+differential equation بدك تراجع حسابتك معناته غلط
+
+380
+00:43:07,660 --> 00:43:09,040
+في شغلة تمام
+
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_raw.json b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..57d956d656ab68657914c8f08f5e27a9411a652c
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_raw.json
@@ -0,0 +1 @@
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هذه", "probability": 0.5810546875}, {"start": 682.53, "end": 683.75, "word": " بالهوموجينيس", "probability": 0.7642996651785714}, {"start": 683.75, "end": 684.29, "word": " of", "probability": 0.7158203125}, {"start": 684.29, "end": 685.03, "word": " degree", "probability": 0.974609375}, {"start": 685.03, "end": 686.35, "word": " Zero", "probability": 0.7724609375}, {"start": 686.35, "end": 687.49, "word": " تمام", "probability": 0.84228515625}, {"start": 687.49, "end": 688.71, "word": " degree", "probability": 0.875}, {"start": 688.71, "end": 689.25, "word": " Zero", "probability": 0.919921875}, {"start": 689.25, "end": 689.69, "word": " يبقى", "probability": 0.9722900390625}, {"start": 689.69, "end": 689.99, "word": " هذه", "probability": 0.96044921875}, {"start": 689.99, "end": 690.93, "word": " متجانسة", "probability": 0.95791015625}, {"start": 690.93, "end": 691.11, "word": " من", "probability": 0.99169921875}, {"start": 691.11, "end": 691.87, "word": " الدرجة", "probability": 0.9638671875}, {"start": 691.87, "end": 692.87, "word": " الصفرية", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 29, "seek": 72030, "start": 693.56, "end": 720.3, "text": "الان بدنا نروح كيف بدنا نفهم ال two definitions هدول بدنا ناخد بعض الأمثلة يبقى example one بقول determine determine whether the following", "tokens": [6027, 7649, 47525, 8315, 8717, 32887, 5016, 9122, 33911, 47525, 8315, 8717, 5172, 16095, 2423, 732, 21988, 8032, 3215, 12610, 47525, 8315, 8717, 47283, 3215, 45030, 11242, 16247, 2304, 12984, 37977, 7251, 3555, 4587, 7578, 1365, 472, 4724, 39648, 6997, 6997, 1968, 264, 3480], "avg_logprob": -0.20034721692403157, "compression_ratio": 1.3402777777777777, "no_speech_prob": 0.0, "words": [{"start": 693.56, "end": 694.08, "word": "الان", "probability": 0.7177734375}, {"start": 694.08, "end": 694.46, "word": " بدنا", "probability": 0.7183837890625}, {"start": 694.46, "end": 695.28, "word": " نروح", "probability": 0.7972819010416666}, {"start": 695.28, "end": 695.7, "word": " كيف", "probability": 0.856689453125}, {"start": 695.7, "end": 695.98, "word": " بدنا", "probability": 0.837890625}, {"start": 695.98, "end": 696.36, "word": " نفهم", "probability": 0.99072265625}, {"start": 696.36, "end": 696.56, "word": " ال", "probability": 0.8759765625}, {"start": 696.56, "end": 696.68, "word": " two", "probability": 0.4736328125}, {"start": 696.68, "end": 697.34, "word": " definitions", "probability": 0.90576171875}, {"start": 697.34, "end": 698.0, "word": " هدول", "probability": 0.8136393229166666}, {"start": 698.0, "end": 698.36, "word": " بدنا", "probability": 0.875244140625}, {"start": 698.36, "end": 698.76, "word": " ناخد", "probability": 0.9884440104166666}, {"start": 698.76, "end": 699.32, "word": " بعض", "probability": 0.98046875}, {"start": 699.32, "end": 700.32, "word": " الأمثلة", "probability": 0.941162109375}, {"start": 700.32, "end": 701.28, "word": " يبقى", "probability": 0.922119140625}, {"start": 701.28, "end": 701.84, "word": " example", "probability": 0.90966796875}, {"start": 701.84, "end": 702.54, "word": " one", "probability": 0.6826171875}, {"start": 702.54, "end": 708.34, "word": " بقول", "probability": 0.799072265625}, {"start": 708.34, "end": 709.4, "word": " determine", "probability": 0.2099609375}, {"start": 709.4, "end": 714.1, "word": " determine", "probability": 0.7822265625}, {"start": 714.1, "end": 715.66, "word": " whether", "probability": 0.84619140625}, {"start": 715.66, "end": 718.62, "word": " the", "probability": 0.88525390625}, {"start": 718.62, "end": 720.3, "word": " following", "probability": 0.88330078125}], "temperature": 1.0}, {"id": 30, "seek": 74022, "start": 723.04, "end": 740.22, "text": "determine whether the following functions are homogeneous or not if it", "tokens": [49136, 533, 1968, 264, 3480, 6828, 366, 42632, 420, 406, 498, 309], "avg_logprob": -0.3419471245545607, "compression_ratio": 1.09375, "no_speech_prob": 0.0, "words": [{"start": 723.04, "end": 723.8, "word": "determine", "probability": 0.5223388671875}, {"start": 723.8, "end": 724.08, "word": " whether", "probability": 0.75}, {"start": 724.08, "end": 724.4, "word": " the", "probability": 0.900390625}, {"start": 724.4, "end": 724.84, "word": " following", "probability": 0.90087890625}, {"start": 724.84, "end": 725.96, "word": " functions", "probability": 0.8837890625}, {"start": 725.96, "end": 727.92, "word": " are", "probability": 0.93603515625}, {"start": 727.92, "end": 730.2, "word": " homogeneous", "probability": 0.79443359375}, {"start": 730.2, "end": 733.12, "word": " or", "probability": 0.94580078125}, {"start": 733.12, "end": 733.64, "word": " not", "probability": 0.9404296875}, {"start": 733.64, "end": 738.2, "word": " if", "probability": 0.82861328125}, {"start": 738.2, "end": 740.22, "word": " it", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 31, "seek": 75610, "start": 741.06, "end": 756.1, "text": "Homogeneous لو كانت homogenous state its degree بدي أعرف قداش الدرجة بتبعتها النقطة الأولى", "tokens": [39, 298, 31112, 45164, 25961, 2655, 3655, 45519, 1785, 1080, 4314, 4724, 16254, 5551, 3615, 28480, 12174, 3215, 33599, 32748, 47341, 3660, 39894, 3555, 34268, 11296, 28239, 47432, 3660, 16247, 12610, 7578], "avg_logprob": -0.3084753787878788, "compression_ratio": 1.1282051282051282, "no_speech_prob": 0.0, "words": [{"start": 741.06, "end": 742.34, "word": "Homogeneous", "probability": 0.5975748697916666}, {"start": 742.34, "end": 743.58, "word": " لو", "probability": 0.64208984375}, {"start": 743.58, "end": 744.14, "word": " كانت", "probability": 0.945068359375}, {"start": 744.14, "end": 745.02, "word": " homogenous", "probability": 0.40478515625}, {"start": 745.02, "end": 746.48, "word": " state", "probability": 0.34228515625}, {"start": 746.48, "end": 749.42, "word": " its", "probability": 0.6630859375}, {"start": 749.42, "end": 750.08, "word": " degree", "probability": 0.9833984375}, {"start": 750.08, "end": 751.22, "word": " بدي", 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1.0}, {"id": 33, "seek": 78869, "start": 774.61, "end": 788.69, "text": "الـ F of X و Y بدها تساوي XY Cos Y على X زائد X تربيع", "tokens": [6027, 39184, 479, 295, 1783, 4032, 398, 47525, 11296, 6055, 3794, 995, 45865, 48826, 15855, 398, 15844, 1783, 30767, 16373, 3215, 1783, 6055, 2288, 21292, 3615], "avg_logprob": -0.33391204807493424, "compression_ratio": 0.9512195121951219, "no_speech_prob": 0.0, "words": [{"start": 774.61, "end": 775.09, "word": "الـ", "probability": 0.6453857421875}, {"start": 775.09, "end": 775.51, "word": " F", "probability": 0.5341796875}, {"start": 775.51, "end": 776.09, "word": " of", "probability": 0.366455078125}, {"start": 776.09, "end": 776.67, "word": " X", "probability": 0.71826171875}, {"start": 776.67, "end": 777.03, "word": " و", "probability": 0.564453125}, {"start": 777.03, "end": 777.47, "word": " Y", "probability": 0.52783203125}, {"start": 777.47, "end": 778.45, "word": " بدها", "probability": 0.6500244140625}, {"start": 778.45, "end": 779.07, 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اللي هي رقم I رقم I بدي أشيل كل X و أحط مكانها", "tokens": [6027, 3794, 33604, 6027, 4724, 1829, 39648, 32239, 13412, 38688, 32767, 9957, 9154, 32748, 12610, 16712, 6027, 10632, 39894, 3555, 4587, 7578, 3655, 45519, 4032, 2304, 9957, 19446, 3224, 1829, 33599, 3655, 45519, 4032, 28814, 15730, 25961, 2655, 3655, 45519, 4724, 16254, 5551, 3615, 28480, 2423, 39184, 376, 29538, 12174, 3215, 33599, 12174, 32640, 47395, 37495, 22653, 12174, 3215, 33599, 11778, 47341, 3660, 29538, 9673, 3615, 18513, 37977, 4724, 39648, 3224, 9122, 45865, 3794, 4724, 25708, 26108, 1829, 2423, 3827, 31439, 4724, 25708, 26108, 1829, 24976, 1863, 47432, 3660, 16247, 12610, 7578, 13672, 1829, 39896, 12602, 4587, 2304, 286, 12602, 4587, 2304, 286, 4724, 16254, 5551, 8592, 26895, 28242, 1783, 4032, 5551, 5016, 9566, 3714, 41361, 11296], "avg_logprob": -0.20127118921886056, "compression_ratio": 1.7736625514403292, "no_speech_prob": 0.0, "words": [{"start": 794.51, "end": 795.07, "word": "السؤال", "probability": 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"probability": 0.9860026041666666}, {"start": 816.17, "end": 816.33, "word": " اللي", "probability": 0.8671875}, {"start": 816.33, "end": 816.61, "word": " هي", "probability": 0.95654296875}, {"start": 816.61, "end": 817.39, "word": " رقم", "probability": 0.9814453125}, {"start": 817.39, "end": 817.91, "word": " I", "probability": 0.89794921875}, {"start": 817.91, "end": 820.07, "word": " رقم", "probability": 0.9860026041666666}, {"start": 820.07, "end": 820.29, "word": " I", "probability": 0.9912109375}, {"start": 820.29, "end": 820.67, "word": " بدي", "probability": 0.751953125}, {"start": 820.67, "end": 821.31, "word": " أشيل", "probability": 0.9070638020833334}, {"start": 821.31, "end": 821.89, "word": " كل", "probability": 0.98291015625}, {"start": 821.89, "end": 822.37, "word": " X", "probability": 0.92529296875}, {"start": 822.37, "end": 822.55, "word": " و", "probability": 0.86669921875}, {"start": 822.55, "end": 822.79, "word": " أحط", "probability": 0.90380859375}, {"start": 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1017.8, "text": "يبقى هذا المثال على آخر التعريفين بدنا نروح ناخد مثال على التعريف الأول لل homogenous differential equation يبقى example two بيقول solve the following differential", "tokens": [1829, 3555, 4587, 7578, 23758, 9673, 12984, 6027, 15844, 19753, 34740, 16712, 3615, 16572, 5172, 9957, 47525, 8315, 8717, 32887, 5016, 8717, 47283, 3215, 50113, 6027, 15844, 16712, 3615, 16572, 5172, 16247, 12610, 24976, 3655, 45519, 15756, 5367, 7251, 3555, 4587, 7578, 1365, 732, 4724, 1829, 39648, 5039, 264, 3480, 15756], "avg_logprob": -0.1912560142003573, "compression_ratio": 1.4654088050314464, "no_speech_prob": 0.0, "words": [{"start": 990.92, "end": 991.54, "word": "يبقى", "probability": 0.84716796875}, {"start": 991.54, "end": 991.88, "word": " هذا", "probability": 0.88427734375}, {"start": 991.88, "end": 992.52, "word": " المثال", "probability": 0.9514973958333334}, {"start": 992.52, "end": 992.86, "word": " على", "probability": 0.93017578125}, {"start": 992.86, "end": 993.6, "word": " 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equation", "probability": 0.931640625}, {"start": 1001.02, "end": 1002.38, "word": " يبقى", "probability": 0.946044921875}, {"start": 1002.38, "end": 1003.06, "word": " example", "probability": 0.7724609375}, {"start": 1003.06, "end": 1004.08, "word": " two", "probability": 0.50537109375}, {"start": 1004.08, "end": 1009.32, "word": " بيقول", "probability": 0.9078776041666666}, {"start": 1009.32, "end": 1010.46, "word": " solve", "probability": 0.468994140625}, {"start": 1010.46, "end": 1012.74, "word": " the", "probability": 0.84130859375}, {"start": 1012.74, "end": 1014.7, "word": " following", "probability": 0.884765625}, {"start": 1014.7, "end": 1017.8, "word": " differential", "probability": 0.8681640625}], "temperature": 1.0}, {"id": 42, "seek": 103952, "start": 1019.52, "end": 1039.52, "text": "Equations حل المعادلات التفاضلية التالية أول معادلة من هذه المعادلات التي هي رقم A بيقول XYY' يساوي 2Y تربيع ناقص X تربيع", "tokens": [36, 358, 763, 11331, 1211, 9673, 3615, 18513, 1211, 9307, 16712, 5172, 46958, 1211, 10632, 16712, 6027, 10632, 5551, 12610, 20449, 18513, 37977, 9154, 29538, 9673, 3615, 18513, 1211, 9307, 38392, 39896, 12602, 4587, 2304, 316, 4724, 1829, 39648, 48826, 56, 6, 7251, 3794, 995, 45865, 568, 56, 6055, 2288, 21292, 3615, 8717, 995, 4587, 9381, 1783, 6055, 2288, 21292, 3615], "avg_logprob": -0.16141633064516128, "compression_ratio": 1.4676258992805755, "no_speech_prob": 0.0, "words": [{"start": 1019.52, "end": 1020.88, "word": "Equations", "probability": 0.7737630208333334}, {"start": 1020.88, "end": 1022.12, "word": " حل", "probability": 0.771728515625}, {"start": 1022.12, "end": 1022.84, "word": " المعادلات", "probability": 0.9607421875}, {"start": 1022.84, "end": 1023.78, "word": " التفاضلية", "probability": 0.925}, {"start": 1023.78, "end": 1024.48, "word": " التالية", "probability": 0.9833984375}, {"start": 1024.48, "end": 1025.54, "word": " أول", "probability": 0.787109375}, {"start": 1025.54, "end": 1026.32, "word": " معادلة", "probability": 0.9739583333333334}, {"start": 1026.32, "end": 1026.6, "word": " من", "probability": 0.962890625}, {"start": 1026.6, "end": 1026.96, "word": " هذه", "probability": 0.96142578125}, {"start": 1026.96, "end": 1027.86, "word": " المعادلات", "probability": 0.98984375}, {"start": 1027.86, "end": 1028.04, "word": " التي", "probability": 0.2296142578125}, {"start": 1028.04, "end": 1028.26, "word": " هي", "probability": 0.8876953125}, {"start": 1028.26, "end": 1028.94, "word": " رقم", "probability": 0.9182942708333334}, {"start": 1028.94, "end": 1029.44, "word": " A", "probability": 0.58203125}, {"start": 1029.44, "end": 1030.56, "word": " بيقول", "probability": 0.8359375}, {"start": 1030.56, "end": 1032.44, "word": " XYY'", "probability": 0.4302978515625}, {"start": 1033.28, "end": 1034.76, "word": " يساوي", "probability": 0.642852783203125}, {"start": 1034.76, "end": 1035.92, "word": " 2Y", "probability": 0.849365234375}, {"start": 1035.92, "end": 1036.96, "word": " تربيع", "probability": 0.86962890625}, {"start": 1036.96, "end": 1038.52, "word": " ناقص", "probability": 0.9312744140625}, {"start": 1038.52, "end": 1038.94, "word": " X", "probability": 0.98388671875}, {"start": 1038.94, "end": 1039.52, "word": " تربيع", "probability": 0.962890625}], "temperature": 1.0}, {"id": 43, "seek": 107436, "start": 1064.67, "end": 1074.37, "text": "أول شي بتبحث هل هي homogeneous ماهياش homogeneous نقدر نفصل متغيرات هل نقدر عليه", "tokens": [10721, 12610, 44049, 39894, 49628, 12984, 8032, 1211, 39896, 42632, 19446, 3224, 1829, 33599, 42632, 8717, 28543, 2288, 8717, 5172, 36520, 44650, 17082, 13546, 9307, 8032, 1211, 8717, 28543, 2288, 47356], "avg_logprob": -0.27856444008648396, "compression_ratio": 1.2376237623762376, "no_speech_prob": 0.0, "words": [{"start": 1064.67, "end": 1065.95, "word": "أول", "probability": 0.775634765625}, {"start": 1065.95, "end": 1066.15, "word": " شي", "probability": 0.64013671875}, {"start": 1066.15, "end": 1066.91, "word": " بتبحث", 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"seek": 110085, "start": 1075.68, "end": 1100.86, "text": "لما كان موضوعنا موضوع الـ homogeneous إذا أنا أول شغل بدي أختبرها هل هي homogeneous أم لا إذا ما طلعتش homogeneous بروح بدور main, separable أو غيره طب الآن أنا بدي Y' لحالة يبقى بروح أجسم الطرفين على XY يبقى لو قسمت الطرفين على XY بصير المعادلة يساوي 2Y على X", "tokens": [1211, 15042, 25961, 3714, 2407, 11242, 45367, 8315, 3714, 2407, 11242, 45367, 2423, 39184, 42632, 11933, 15730, 41850, 5551, 12610, 13412, 17082, 1211, 4724, 16254, 5551, 46456, 26890, 11296, 8032, 1211, 39896, 42632, 5551, 2304, 20193, 11933, 15730, 19446, 23032, 1211, 34268, 8592, 42632, 4724, 32887, 5016, 47525, 13063, 2135, 11, 3128, 712, 34051, 32771, 13546, 3224, 23032, 3555, 6024, 48506, 41850, 4724, 16254, 398, 6, 5296, 5016, 6027, 3660, 7251, 3555, 4587, 7578, 4724, 32887, 5016, 5551, 7435, 38251, 41950, 28480, 9957, 15844, 48826, 7251, 3555, 4587, 7578, 45164, 12174, 38251, 2655, 41950, 28480, 9957, 15844, 48826, 4724, 9381, 13546, 9673, 3615, 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1097.94, "word": " المعادلة", "probability": 0.970947265625}, {"start": 1097.94, "end": 1098.8, "word": " يساوي", "probability": 0.8736572265625}, {"start": 1098.8, "end": 1100.26, "word": " 2Y", "probability": 0.8525390625}, {"start": 1100.26, "end": 1100.54, "word": " على", "probability": 0.471435546875}, {"start": 1100.54, "end": 1100.86, "word": " X", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 45, "seek": 112260, "start": 1101.35, "end": 1122.61, "text": "والله بلاش نقولك كيف هاد أجت بدي أعملها لك على خطوط اللي لو جسمت على x y بظهر y prime يبقى 2y تربيع على x y ناقص x تربيع على x في y بالشكل هذا هذه كلها اللي هي main y prime", "tokens": [2407, 6027, 43761, 4724, 1211, 33599, 8717, 39648, 4117, 9122, 33911, 8032, 18513, 5551, 7435, 2655, 4724, 16254, 5551, 25957, 1211, 11296, 5296, 4117, 15844, 16490, 9566, 2407, 9566, 13672, 1829, 45164, 10874, 38251, 2655, 15844, 2031, 288, 4724, 19913, 3224, 2288, 288, 5835, 7251, 3555, 4587, 7578, 568, 88, 6055, 2288, 21292, 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"probability": 0.9642333984375}, {"start": 1110.03, "end": 1110.97, "word": " 2y", "probability": 0.72509765625}, {"start": 1110.97, "end": 1112.05, "word": " تربيع", "probability": 0.72686767578125}, {"start": 1112.05, "end": 1112.53, "word": " على", "probability": 0.74365234375}, {"start": 1112.53, "end": 1113.11, "word": " x", "probability": 0.9521484375}, {"start": 1113.11, "end": 1113.63, "word": " y", "probability": 0.533203125}, {"start": 1113.63, "end": 1114.63, "word": " ناقص", "probability": 0.8709716796875}, {"start": 1114.63, "end": 1115.03, "word": " x", "probability": 0.953125}, {"start": 1115.03, "end": 1115.79, "word": " تربيع", "probability": 0.9676513671875}, {"start": 1115.79, "end": 1116.25, "word": " على", "probability": 0.85302734375}, {"start": 1116.25, "end": 1116.75, "word": " x", "probability": 0.97900390625}, {"start": 1116.75, "end": 1116.99, "word": " في", "probability": 0.9697265625}, {"start": 1116.99, "end": 1117.31, "word": " y", "probability": 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إلى x يبقى dy على dx يساوي v زائد x في dv على dx", "tokens": [10721, 11242, 25513, 48812, 25513, 6055, 3555, 18513, 1211, 7251, 3555, 4587, 7578, 2423, 39184, 288, 6055, 3794, 995, 45865, 2031, 8978, 371, 1975, 8592, 2655, 4587, 23032, 28480, 9957, 20666, 1863, 35457, 3660, 30731, 2031, 7251, 3555, 4587, 7578, 14584, 15844, 30017, 7251, 3794, 995, 45865, 371, 30767, 16373, 3215, 2031, 8978, 274, 85, 15844, 30017], "avg_logprob": -0.22184806342782645, "compression_ratio": 1.4827586206896552, "no_speech_prob": 0.0, "words": [{"start": 1174.5, "end": 1175.1, "word": "أضرب", "probability": 0.644775390625}, {"start": 1175.1, "end": 1175.46, "word": " ضرب", "probability": 0.945556640625}, {"start": 1175.46, "end": 1176.28, "word": " تبادل", "probability": 0.8897705078125}, {"start": 1176.28, "end": 1177.4, "word": " يبقى", "probability": 0.80303955078125}, {"start": 1177.4, "end": 1180.58, "word": " الـ", "probability": 0.40081787109375}, {"start": 1180.58, "end": 1180.6, "word": " y", 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"probability": 0.94873046875}, {"start": 2092.39, "end": 2093.69, "word": " زائد", "probability": 0.6844075520833334}, {"start": 2093.69, "end": 2094.65, "word": " c1", "probability": 0.940185546875}, {"start": 2094.65, "end": 2095.53, "word": " كل", "probability": 0.7666015625}, {"start": 2095.53, "end": 2096.03, "word": " هذا", "probability": 0.91162109375}, {"start": 2096.03, "end": 2096.77, "word": " مضروب", "probability": 0.925048828125}, {"start": 2096.77, "end": 2096.97, "word": " في", "probability": 0.94140625}, {"start": 2096.97, "end": 2097.17, "word": " ال", "probability": 0.580078125}, {"start": 2097.17, "end": 2097.51, "word": " y", "probability": 0.270751953125}, {"start": 2097.51, "end": 2098.21, "word": " prime", "probability": 0.49169921875}, {"start": 2098.21, "end": 2099.83, "word": " بيساوي", "probability": 0.58701171875}, {"start": 2099.83, "end": 2101.55, "word": " a2", "probability": 0.9140625}, {"start": 2101.55, "end": 2102.31, "word": " x", "probability": 0.54931640625}, {"start": 2102.31, "end": 2103.89, "word": " زائد", "probability": 0.9254557291666666}, {"start": 2103.89, "end": 2105.35, "word": " a2", "probability": 0.9853515625}, {"start": 2105.35, "end": 2106.31, "word": " x", "probability": 0.9306640625}], "temperature": 1.0}, {"id": 87, "seek": 213466, "start": 2108.16, "end": 2134.66, "text": "A1X يا ابناتو B1X يساو as A2X زائد B2Y زائد C2 و examine the following بدنا نختبر ما يأتي النقطة الأولى", "tokens": [32, 16, 55, 35186, 48127, 1863, 9307, 2407, 363, 16, 55, 7251, 3794, 995, 2407, 382, 316, 17, 55, 30767, 16373, 3215, 363, 17, 56, 30767, 16373, 3215, 383, 17, 4032, 17496, 264, 3480, 47525, 8315, 8717, 46456, 26890, 19446, 7251, 10721, 31371, 28239, 47432, 3660, 16247, 12610, 7578], "avg_logprob": -0.3170312631130219, "compression_ratio": 1.1526717557251909, "no_speech_prob": 0.0, "words": [{"start": 2108.16, "end": 2109.56, "word": "A1X", "probability": 0.612060546875}, {"start": 2109.56, "end": 2109.78, "word": " يا", "probability": 0.124755859375}, {"start": 2109.78, "end": 2110.26, "word": " ابناتو", "probability": 0.435455322265625}, {"start": 2110.26, "end": 2111.7, "word": " B1X", "probability": 0.7638346354166666}, {"start": 2111.7, "end": 2112.92, "word": " يساو", "probability": 0.82275390625}, {"start": 2112.92, "end": 2113.14, "word": " as", "probability": 0.185791015625}, {"start": 2113.14, "end": 2114.42, "word": " A2X", "probability": 0.93017578125}, {"start": 2114.42, "end": 2115.5, "word": " زائد", "probability": 0.644775390625}, {"start": 2115.5, "end": 2117.3, "word": " B2Y", "probability": 0.9794921875}, {"start": 2117.3, "end": 2118.5, "word": " زائد", "probability": 0.9602864583333334}, {"start": 2118.5, "end": 2119.8, "word": " C2", "probability": 0.985595703125}, {"start": 2119.8, "end": 2121.52, "word": " و", "probability": 0.42578125}, {"start": 2121.52, "end": 2124.14, "word": " examine", "probability": 0.1448974609375}, {"start": 2124.14, "end": 2126.64, "word": " the", "probability": 0.83349609375}, {"start": 2126.64, "end": 2127.52, "word": " following", "probability": 0.90234375}, {"start": 2127.52, "end": 2129.14, "word": " بدنا", "probability": 0.859375}, {"start": 2129.14, "end": 2129.96, "word": " نختبر", "probability": 0.9860026041666666}, {"start": 2129.96, "end": 2130.34, "word": " ما", "probability": 0.9462890625}, {"start": 2130.34, "end": 2131.24, "word": " يأتي", "probability": 0.9397786458333334}, {"start": 2131.24, "end": 2134.28, "word": " النقطة", "probability": 0.9392903645833334}, {"start": 2134.28, "end": 2134.66, "word": " الأولى", "probability": 0.9684244791666666}], "temperature": 1.0}, {"id": 88, "seek": 216211, "start": 2137.39, "end": 2162.11, "text": "إذا الـ A1 في الـ B2 بتسوي A2 في الـ B1 نحل بالروح نحل نحل بالروح نحل as the final example", "tokens": [28814, 15730, 2423, 39184, 316, 16, 8978, 2423, 39184, 363, 17, 39894, 3794, 45865, 316, 17, 8978, 2423, 39184, 363, 16, 8717, 5016, 1211, 20666, 32887, 5016, 8717, 5016, 1211, 8717, 5016, 1211, 20666, 32887, 5016, 8717, 5016, 1211, 382, 264, 2572, 1365], "avg_logprob": -0.3945312560959296, "compression_ratio": 1.4673913043478262, "no_speech_prob": 0.0, "words": [{"start": 2137.39, "end": 2138.03, "word": "إذا", "probability": 0.60498046875}, {"start": 2138.03, "end": 2140.13, "word": " الـ", "probability": 0.52838134765625}, {"start": 2140.13, "end": 2140.85, "word": " A1", "probability": 0.72607421875}, {"start": 2140.85, "end": 2141.41, "word": " في", "probability": 0.67724609375}, {"start": 2141.41, "end": 2141.61, "word": " الـ", "probability": 0.85302734375}, {"start": 2141.61, "end": 2142.35, "word": " B2", "probability": 0.908447265625}, {"start": 2142.35, "end": 2143.55, "word": " بتسوي", "probability": 0.531982421875}, {"start": 2143.55, "end": 2144.69, "word": " A2", "probability": 0.896728515625}, {"start": 2144.69, "end": 2144.97, "word": " في", "probability": 0.9677734375}, {"start": 2144.97, "end": 2145.19, "word": " الـ", "probability": 0.781982421875}, {"start": 2145.19, "end": 2145.85, "word": " B1", "probability": 0.85205078125}, {"start": 2145.85, "end": 2147.93, "word": " نحل", "probability": 0.6180013020833334}, {"start": 2147.93, "end": 2151.31, "word": " بالروح", "probability": 0.7201334635416666}, {"start": 2151.31, "end": 2152.31, "word": " نحل", "probability": 0.8181966145833334}, {"start": 2152.31, "end": 2153.85, "word": " نحل", "probability": 0.7989908854166666}, {"start": 2153.85, "end": 2156.31, "word": " بالروح", "probability": 0.6290079752604166}, {"start": 2156.31, "end": 2156.31, "word": " نحل", "probability": 0.9083658854166666}, {"start": 2156.31, "end": 2156.31, "word": " as", "probability": 0.1966552734375}, {"start": 2156.31, "end": 2158.15, "word": " the", "probability": 0.802734375}, {"start": 2158.15, "end": 2160.01, "word": " final", "probability": 0.93798828125}, {"start": 2160.01, "end": 2162.11, "word": " example", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 89, "seek": 219162, "start": 2163.88, "end": 2191.62, "text": "as a final example in section واحد اتنين نقطة ثانية if ال a1 b2 لا يسوى ال a2 في ال b1 we use the transform", "tokens": [296, 257, 2572, 1365, 294, 3541, 36764, 24401, 1975, 2655, 1863, 9957, 8717, 47432, 3660, 38637, 7649, 10632, 498, 2423, 257, 16, 272, 17, 20193, 7251, 3794, 2407, 7578, 2423, 257, 17, 8978, 2423, 272, 16, 321, 764, 264, 4088], "avg_logprob": -0.29058689024390244, "compression_ratio": 1.139344262295082, "no_speech_prob": 0.0, "words": [{"start": 2163.88, "end": 2164.26, "word": "as", "probability": 0.07391357421875}, {"start": 2164.26, "end": 2164.48, "word": " a", "probability": 0.9228515625}, {"start": 2164.48, "end": 2164.84, "word": " final", "probability": 0.91748046875}, {"start": 2164.84, "end": 2165.68, "word": " example", "probability": 0.97607421875}, {"start": 2165.68, "end": 2166.88, "word": " in", "probability": 0.69140625}, {"start": 2166.88, "end": 2168.98, "word": " section", "probability": 0.701171875}, {"start": 2168.98, "end": 2171.18, "word": " واحد", "probability": 0.60662841796875}, {"start": 2171.18, "end": 2172.34, "word": " اتنين", "probability": 0.943359375}, {"start": 2172.34, "end": 2174.26, "word": " نقطة", "probability": 0.8846028645833334}, {"start": 2174.26, "end": 2174.94, "word": " ثانية", "probability": 0.9391276041666666}, {"start": 2174.94, "end": 2176.4, "word": " if", "probability": 0.69921875}, {"start": 2176.4, "end": 2177.46, "word": " ال", "probability": 0.63623046875}, {"start": 2177.46, "end": 2178.36, "word": " a1", "probability": 0.4365234375}, {"start": 2178.36, "end": 2180.32, "word": " b2", "probability": 0.65234375}, {"start": 2180.32, "end": 2181.26, "word": " لا", "probability": 0.8583984375}, {"start": 2181.26, "end": 2181.98, "word": " يسوى", "probability": 0.7847900390625}, {"start": 2181.98, "end": 2182.18, "word": " ال", "probability": 0.9072265625}, {"start": 2182.18, "end": 2182.8, "word": " a2", "probability": 0.979248046875}, {"start": 2182.8, "end": 2183.0, "word": " في", "probability": 0.84326171875}, {"start": 2183.0, "end": 2183.14, "word": " ال", "probability": 0.916015625}, {"start": 2183.14, "end": 2183.7, "word": " b1", "probability": 0.955810546875}, {"start": 2183.7, "end": 2186.04, "word": " we", "probability": 0.701171875}, {"start": 2186.04, "end": 2186.98, "word": " use", "probability": 0.896484375}, {"start": 2186.98, "end": 2189.5, "word": " the", "probability": 0.701171875}, {"start": 2189.5, "end": 2191.62, "word": " transform", "probability": 0.94970703125}], "temperature": 1.0}, {"id": 90, "seek": 222121, "start": 2194.36, "end": 2221.22, "text": "و نستخدم الـ transform اللي هو X يسوى X كابتل زائد P و Y يسوى Y كابتل زائد Q حيث ال P و ال Q هي الحل", "tokens": [2407, 8717, 14851, 9778, 40448, 2423, 39184, 4088, 13672, 1829, 31439, 1783, 7251, 3794, 2407, 7578, 1783, 9122, 16758, 2655, 1211, 30767, 16373, 3215, 430, 4032, 398, 7251, 3794, 2407, 7578, 398, 9122, 16758, 2655, 1211, 30767, 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"probability": 0.839111328125}, {"start": 2201.74, "end": 2203.44, "word": " زائد", "probability": 0.8723958333333334}, {"start": 2203.44, "end": 2204.0, "word": " P", "probability": 0.98046875}, {"start": 2204.0, "end": 2205.56, "word": " و", "probability": 0.77099609375}, {"start": 2205.56, "end": 2207.44, "word": " Y", "probability": 0.67138671875}, {"start": 2207.44, "end": 2208.94, "word": " يسوى", "probability": 0.956298828125}, {"start": 2208.94, "end": 2209.38, "word": " Y", "probability": 0.96826171875}, {"start": 2209.38, "end": 2210.36, "word": " كابتل", "probability": 0.988037109375}, {"start": 2210.36, "end": 2211.88, "word": " زائد", "probability": 0.9768880208333334}, {"start": 2211.88, "end": 2212.4, "word": " Q", "probability": 0.9638671875}, {"start": 2212.4, "end": 2216.38, "word": " حيث", "probability": 0.777587890625}, {"start": 2216.38, "end": 2217.44, "word": " ال", "probability": 0.53369140625}, {"start": 2217.44, "end": 2217.94, "word": " P", "probability": 0.72412109375}, {"start": 2217.94, "end": 2218.74, "word": " و", "probability": 0.78173828125}, {"start": 2218.74, "end": 2218.84, "word": " ال", "probability": 0.56396484375}, {"start": 2218.84, "end": 2219.36, "word": " Q", "probability": 0.869140625}, {"start": 2219.36, "end": 2220.74, "word": " هي", "probability": 0.869140625}, {"start": 2220.74, "end": 2221.22, "word": " الحل", "probability": 0.583740234375}], "temperature": 1.0}, {"id": 91, "seek": 225388, "start": 2227.18, "end": 2253.88, "text": "is the solution of the system of equations a1p زائد b1q زائد c1 يساوي zero و a2p", "tokens": [271, 264, 3827, 295, 264, 1185, 295, 11787, 257, 16, 79, 30767, 16373, 3215, 272, 16, 80, 30767, 16373, 3215, 269, 16, 7251, 3794, 995, 45865, 4018, 4032, 257, 17, 79], "avg_logprob": -0.26293945498764515, "compression_ratio": 1.0804597701149425, "no_speech_prob": 0.0, "words": [{"start": 2227.18, "end": 2227.56, "word": "is", "probability": 0.1583251953125}, {"start": 2227.56, "end": 2227.8, "word": " the", "probability": 0.802734375}, {"start": 2227.8, "end": 2228.78, "word": " solution", "probability": 0.95849609375}, {"start": 2228.78, "end": 2230.76, "word": " of", "probability": 0.943359375}, {"start": 2230.76, "end": 2231.0, "word": " the", "probability": 0.8037109375}, {"start": 2231.0, "end": 2235.54, "word": " system", "probability": 0.9384765625}, {"start": 2235.54, "end": 2237.24, "word": " of", "probability": 0.89404296875}, {"start": 2237.24, "end": 2240.44, "word": " equations", "probability": 0.90234375}, {"start": 2240.44, "end": 2244.02, "word": " a1p", "probability": 0.75}, {"start": 2244.02, "end": 2245.7, "word": " زائد", "probability": 0.5872650146484375}, {"start": 2245.7, "end": 2247.54, "word": " b1q", "probability": 0.9602864583333334}, {"start": 2247.54, "end": 2248.78, "word": " زائد", "probability": 0.962890625}, {"start": 2248.78, "end": 2249.46, "word": " c1", "probability": 0.982666015625}, {"start": 2249.46, "end": 2250.1, "word": " يساوي", "probability": 0.79986572265625}, {"start": 2250.1, "end": 2250.58, "word": " zero", "probability": 0.3193359375}, {"start": 2250.58, "end": 2251.64, "word": " و", "probability": 0.5673828125}, {"start": 2251.64, "end": 2253.88, "word": " a2p", "probability": 0.8649088541666666}], "temperature": 1.0}, {"id": 92, "seek": 226669, "start": 2254.5, "end": 2266.7, "text": "زائد بيتو اكيو بيتو اكيو زائد C2 بده يساوي مين؟ بده يساوي Zero", "tokens": [11622, 16373, 3215, 4724, 36081, 2407, 1975, 4117, 1829, 2407, 4724, 36081, 2407, 1975, 4117, 1829, 2407, 30767, 16373, 3215, 383, 17, 47525, 3224, 7251, 3794, 995, 45865, 3714, 9957, 22807, 47525, 3224, 7251, 3794, 995, 45865, 17182], "avg_logprob": -0.3052884584818131, "compression_ratio": 1.4722222222222223, "no_speech_prob": 0.0, "words": [{"start": 2254.5, "end": 2255.4, "word": "زائد", "probability": 0.5788981119791666}, {"start": 2255.4, "end": 2256.68, "word": " بيتو", "probability": 0.5767415364583334}, {"start": 2256.68, "end": 2257.9, "word": " اكيو", "probability": 0.850341796875}, {"start": 2257.9, "end": 2259.62, "word": " بيتو", "probability": 0.7403971354166666}, {"start": 2259.62, "end": 2260.78, "word": " اكيو", "probability": 0.9871826171875}, {"start": 2260.78, "end": 2262.22, "word": " زائد", "probability": 0.8756510416666666}, {"start": 2262.22, "end": 2263.28, "word": " C2", "probability": 0.37762451171875}, {"start": 2263.28, "end": 2263.9, "word": " بده", "probability": 0.55078125}, {"start": 2263.9, "end": 2264.36, "word": " يساوي", "probability": 0.93798828125}, {"start": 2264.36, "end": 2265.04, "word": " مين؟", "probability": 0.6661783854166666}, {"start": 2265.04, "end": 2265.4, "word": " بده", "probability": 0.9365234375}, {"start": 2265.4, "end": 2266.1, "word": " يساوي", "probability": 0.9864501953125}, {"start": 2266.1, "end": 2266.7, "word": " Zero", "probability": 0.59228515625}], "temperature": 1.0}, {"id": 93, "seek": 231784, "start": 2313.24, "end": 2317.84, "text": "Y' يسوى المقدار هذا على المقدار هذا", "tokens": [56, 6, 7251, 3794, 2407, 7578, 9673, 28543, 9640, 23758, 15844, 9673, 28543, 9640, 23758], "avg_logprob": -0.24731445126235485, "compression_ratio": 1.2156862745098038, "no_speech_prob": 0.0, "words": [{"start": 2313.2400000000002, "end": 2314.28, "word": "Y'", "probability": 0.1976318359375}, {"start": 2314.84, "end": 2315.32, "word": " يسوى", "probability": 0.64971923828125}, {"start": 2315.32, "end": 2315.94, "word": " المقدار", "probability": 0.9518229166666666}, {"start": 2315.94, "end": 2316.36, "word": " هذا", "probability": 0.6591796875}, {"start": 2316.36, "end": 2316.68, "word": " على", "probability": 0.8525390625}, {"start": 2316.68, "end": 2317.46, "word": " المقدار", "probability": 0.96435546875}, {"start": 2317.46, "end": 2317.84, "word": " هذا", "probability": 0.93408203125}], "temperature": 1.0}, {"id": 94, "seek": 233563, "start": 2318.07, "end": 2335.63, "text": "أو ضربنا الطرفين في المقام فصرت على الشكل اللي قدامي هذا يبقى الشكل اللي قدامي هذا او y prime يساوي هذا على الجثة سيان كل واحد طيب انا عندي معادلة بشكل لأن انا بداجي احل هذه المعادلة", "tokens": [10721, 2407, 48812, 25513, 8315, 41950, 28480, 9957, 8978, 9673, 4587, 10943, 6156, 9381, 43500, 15844, 25124, 28820, 13672, 1829, 12174, 3215, 10943, 1829, 23758, 7251, 3555, 4587, 7578, 25124, 28820, 13672, 1829, 12174, 3215, 10943, 1829, 23758, 1975, 2407, 288, 5835, 7251, 3794, 995, 45865, 23758, 15844, 25724, 12984, 3660, 8608, 1829, 7649, 28242, 36764, 24401, 23032, 1829, 3555, 1975, 8315, 18871, 16254, 20449, 18513, 37977, 4724, 8592, 28820, 5296, 33456, 1975, 8315, 4724, 28259, 7435, 1829, 1975, 5016, 1211, 29538, 9673, 3615, 18513, 37977], "avg_logprob": -0.20420258415156398, "compression_ratio": 1.861271676300578, "no_speech_prob": 0.0, "words": [{"start": 2318.07, "end": 2318.59, "word": "أو", "probability": 0.81396484375}, {"start": 2318.59, "end": 2319.67, "word": " ضربنا", "probability": 0.726806640625}, {"start": 2319.67, "end": 2320.33, "word": " 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قدامي", "probability": 0.9920654296875}, {"start": 2325.15, "end": 2325.49, "word": " هذا", "probability": 0.97021484375}, {"start": 2325.49, "end": 2326.07, "word": " او", "probability": 0.674560546875}, {"start": 2326.07, "end": 2326.67, "word": " y", "probability": 0.63720703125}, {"start": 2326.67, "end": 2327.13, "word": " prime", "probability": 0.257080078125}, {"start": 2327.13, "end": 2327.65, "word": " يساوي", "probability": 0.8426513671875}, {"start": 2327.65, "end": 2327.97, "word": " هذا", "probability": 0.9111328125}, {"start": 2327.97, "end": 2328.25, "word": " على", "probability": 0.9560546875}, {"start": 2328.25, "end": 2329.01, "word": " الجثة", "probability": 0.9055989583333334}, {"start": 2329.01, "end": 2329.55, "word": " سيان", "probability": 0.676025390625}, {"start": 2329.55, "end": 2329.83, "word": " كل", "probability": 0.9580078125}, {"start": 2329.83, "end": 2330.21, "word": " واحد", "probability": 0.89697265625}, {"start": 2330.21, "end": 2330.69, "word": " طيب", "probability": 0.89794921875}, {"start": 2330.69, "end": 2330.97, "word": " انا", "probability": 0.790771484375}, {"start": 2330.97, "end": 2331.23, "word": " عندي", "probability": 0.87744140625}, {"start": 2331.23, "end": 2331.75, "word": " معادلة", "probability": 0.9910481770833334}, {"start": 2331.75, "end": 2332.21, "word": " بشكل", "probability": 0.943359375}, {"start": 2332.21, "end": 2332.51, "word": " لأن", "probability": 0.3125}, {"start": 2332.51, "end": 2332.71, "word": " انا", "probability": 0.6715087890625}, {"start": 2332.71, "end": 2333.75, "word": " بداجي", "probability": 0.58306884765625}, {"start": 2333.75, "end": 2334.31, "word": " احل", "probability": 0.88134765625}, {"start": 2334.31, "end": 2334.85, "word": " هذه", "probability": 0.9794921875}, {"start": 2334.85, "end": 2335.63, "word": " المعادلة", "probability": 0.9835205078125}], "temperature": 1.0}, {"id": 95, "seek": 236467, "start": 2335.97, "end": 2364.67, "text": "يا بنات في عند المعادلة أحيانا بتكونش homogeneous لكن أنا بقدر بطريقة ما أحولها إلى homogeneous differential equation وإذا حولتها بقدر أحلها بالطريقة اللي حلناها بالمثالين السابقين قبل قليل طبعا يبقى إذا عندي مثلة من هذا القبيل وهذه ليست homogeneous بده أطلع على شغلين الشغل الأولى هل a1 في ال b2", "tokens": [25528, 4724, 8315, 2655, 8978, 43242, 9673, 3615, 18513, 37977, 5551, 5016, 1829, 7649, 995, 39894, 30544, 8592, 42632, 44381, 41850, 4724, 28543, 2288, 4724, 9566, 16572, 28671, 19446, 5551, 5016, 12610, 11296, 30731, 42632, 15756, 5367, 4032, 28814, 15730, 11331, 12610, 2655, 11296, 4724, 28543, 2288, 5551, 5016, 1211, 11296, 20666, 9566, 16572, 28671, 13672, 1829, 11331, 1211, 8315, 11296, 20666, 2304, 12984, 6027, 9957, 21136, 16758, 4587, 9957, 12174, 36150, 12174, 20292, 1211, 23032, 3555, 3615, 995, 7251, 3555, 4587, 7578, 11933, 15730, 18871, 16254, 50113, 37977, 9154, 23758, 25062, 21292, 1211, 37037, 24192, 32239, 14851, 42632, 47525, 3224, 5551, 9566, 1211, 3615, 15844, 13412, 17082, 1211, 9957, 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0.94091796875}, {"start": 2353.93, "end": 2354.45, "word": " مثلة", "probability": 0.8896484375}, {"start": 2354.45, "end": 2354.67, "word": " من", "probability": 0.99169921875}, {"start": 2354.67, "end": 2355.07, "word": " هذا", "probability": 0.9736328125}, {"start": 2355.07, "end": 2356.11, "word": " القبيل", "probability": 0.90576171875}, {"start": 2356.11, "end": 2356.81, "word": " وهذه", "probability": 0.886474609375}, {"start": 2356.81, "end": 2357.53, "word": " ليست", "probability": 0.9755859375}, {"start": 2357.53, "end": 2358.09, "word": " homogeneous", "probability": 0.91748046875}, {"start": 2358.09, "end": 2358.69, "word": " بده", "probability": 0.464599609375}, {"start": 2358.69, "end": 2359.05, "word": " أطلع", "probability": 0.7703857421875}, {"start": 2359.05, "end": 2359.25, "word": " على", "probability": 0.206298828125}, {"start": 2359.25, "end": 2359.85, "word": " شغلين", "probability": 0.8857421875}, {"start": 2359.85, "end": 2361.15, "word": " الشغل", "probability": 0.8722330729166666}, {"start": 2361.15, "end": 2361.63, "word": " الأولى", "probability": 0.783447265625}, {"start": 2361.63, "end": 2362.09, "word": " هل", "probability": 0.845703125}, {"start": 2362.09, "end": 2363.29, "word": " a1", "probability": 0.667724609375}, {"start": 2363.29, "end": 2363.79, "word": " في", "probability": 0.80029296875}, {"start": 2363.79, "end": 2363.97, "word": " ال", "probability": 0.8583984375}, {"start": 2363.97, "end": 2364.67, "word": " b2", "probability": 0.728759765625}], "temperature": 1.0}, {"id": 96, "seek": 239398, "start": 2365.4, "end": 2393.98, "text": "مع الـ A2 في الـ B1 هل هدول بيساووا بعض؟ والله بيساووش والله إذا كان هدول بيساووا بعض بنروح أنحل المعادلة هذه زي آخر مثال أخدناه في المحاضرة الماضية بصير عندي جوس كله بعتبره variable جديد جوس بيحتوي على X و Y بشيله بحطه variable وليكن V وبالتالي بصير عندي separable differential equation", "tokens": [2304, 3615, 2423, 39184, 316, 17, 8978, 2423, 39184, 363, 16, 8032, 1211, 8032, 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" الـ", "probability": 0.6907958984375}, {"start": 2366.86, "end": 2367.82, "word": " A2", "probability": 0.4952392578125}, {"start": 2367.82, "end": 2368.2, "word": " في", "probability": 0.751953125}, {"start": 2368.2, "end": 2368.36, "word": " الـ", "probability": 0.8984375}, {"start": 2368.36, "end": 2368.78, "word": " B1", "probability": 0.8701171875}, {"start": 2368.78, "end": 2369.14, "word": " هل", "probability": 0.88818359375}, {"start": 2369.14, "end": 2369.54, "word": " هدول", "probability": 0.7368977864583334}, {"start": 2369.54, "end": 2370.08, "word": " بيساووا", "probability": 0.759033203125}, {"start": 2370.08, "end": 2370.44, "word": " بعض؟", "probability": 0.75732421875}, {"start": 2370.44, "end": 2370.68, "word": " والله", "probability": 0.722412109375}, {"start": 2370.68, "end": 2371.34, "word": " بيساووش", "probability": 0.8722795758928571}, {"start": 2371.34, "end": 2372.48, "word": " والله", "probability": 0.667236328125}, {"start": 2372.48, "end": 2372.84, "word": " إذا", "probability": 0.871826171875}, {"start": 2372.84, "end": 2373.24, "word": " كان", "probability": 0.953125}, {"start": 2373.24, "end": 2373.74, "word": " هدول", "probability": 0.9912109375}, {"start": 2373.74, "end": 2374.5, "word": " بيساووا", "probability": 0.9579264322916666}, {"start": 2374.5, "end": 2374.92, "word": " بعض", "probability": 0.993408203125}, {"start": 2374.92, "end": 2375.72, "word": " بنروح", "probability": 0.7777506510416666}, {"start": 2375.72, "end": 2376.16, "word": " أنحل", "probability": 0.647216796875}, {"start": 2376.16, "end": 2376.74, "word": " المعادلة", "probability": 0.966064453125}, {"start": 2376.74, "end": 2377.02, "word": " هذه", "probability": 0.763671875}, {"start": 2377.02, "end": 2377.32, "word": " زي", "probability": 0.912841796875}, {"start": 2377.32, "end": 2377.74, "word": " آخر", "probability": 0.802978515625}, {"start": 2377.74, "end": 2378.14, "word": " مثال", "probability": 0.983154296875}, {"start": 2378.14, "end": 2378.64, "word": " أخدناه", "probability": 0.93408203125}, {"start": 2378.64, "end": 2378.72, "word": " في", "probability": 0.97509765625}, {"start": 2378.72, "end": 2379.5, "word": " المحاضرة", "probability": 0.9232177734375}, {"start": 2379.5, "end": 2380.5, "word": " الماضية", "probability": 0.9588216145833334}, {"start": 2380.5, "end": 2380.88, "word": " بصير", "probability": 0.923828125}, {"start": 2380.88, "end": 2381.28, "word": " عندي", "probability": 0.83740234375}, {"start": 2381.28, "end": 2381.76, "word": " جوس", "probability": 0.3763427734375}, {"start": 2381.76, "end": 2382.16, "word": " كله", "probability": 0.89501953125}, {"start": 2382.16, "end": 2382.76, "word": " بعتبره", "probability": 0.906494140625}, {"start": 2382.76, "end": 2383.2, "word": " variable", "probability": 0.7861328125}, {"start": 2383.2, "end": 2383.92, "word": " جديد", "probability": 0.9269205729166666}, {"start": 2383.92, "end": 2384.72, "word": " جوس", "probability": 0.90478515625}, {"start": 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-0.19029707084467382, "compression_ratio": 1.7721518987341771, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2544.02, "end": 2544.36, "word": "إن", "probability": 0.6123046875}, {"start": 2544.36, "end": 2544.92, "word": " المعادلة", "probability": 0.9412841796875}, {"start": 2544.92, "end": 2545.34, "word": " هذه", "probability": 0.72607421875}, {"start": 2545.34, "end": 2546.36, "word": " ممكن", "probability": 0.97802734375}, {"start": 2546.36, "end": 2547.5, "word": " أحولها", "probability": 0.922119140625}, {"start": 2547.5, "end": 2548.04, "word": " إلى", "probability": 0.88671875}, {"start": 2548.04, "end": 2548.66, "word": " معادلة", "probability": 0.9886067708333334}, {"start": 2548.66, "end": 2549.5, "word": " متجنسة", "probability": 0.9830078125}, {"start": 2549.5, "end": 2550.26, "word": " كيف؟", "probability": 0.619873046875}, {"start": 2550.26, "end": 2550.86, "word": " بالطريقة", "probability": 0.917724609375}, {"start": 2550.86, "end": 2551.24, "word": " التالية", "probability": 0.9625651041666666}, {"start": 2551.24, "end": 2552.1, "word": " بمسك", "probability": 0.8687744140625}, {"start": 2552.1, "end": 2552.78, "word": " كل", "probability": 0.9375}, {"start": 2552.78, "end": 2553.74, "word": " معادلة", "probability": 0.9873046875}, {"start": 2553.74, "end": 2554.2, "word": " من", "probability": 0.9677734375}, {"start": 2554.2, "end": 2555.12, "word": " المعادلتين", "probability": 0.9561360677083334}, {"start": 2555.12, "end": 2555.52, "word": " هدول", "probability": 0.8043619791666666}, {"start": 2555.52, "end": 2555.64, "word": " و", "probability": 0.480224609375}, {"start": 2555.64, "end": 2556.22, "word": " بسويها", "probability": 0.8858642578125}, {"start": 2556.22, "end": 2556.9, "word": " بالصفر", "probability": 0.82183837890625}, {"start": 2556.9, "end": 2557.34, "word": " و", "probability": 0.63720703125}, {"start": 2557.34, "end": 2557.86, "word": " بحلف", "probability": 0.7997233072916666}, {"start": 2557.86, "end": 2558.36, "word": " تنتين", "probability": 0.7394205729166666}, {"start": 2558.36, "end": 2558.46, "word": " و", "probability": 0.415283203125}, {"start": 2558.46, "end": 2558.86, "word": " بجيب", "probability": 0.9881591796875}, {"start": 2558.86, "end": 2559.34, "word": " قيمة", "probability": 0.9879557291666666}, {"start": 2559.34, "end": 2559.68, "word": " x", "probability": 0.46435546875}, {"start": 2559.68, "end": 2559.92, "word": " و", "probability": 0.837890625}, {"start": 2559.92, "end": 2560.08, "word": " y", "probability": 0.6005859375}, {"start": 2560.08, "end": 2560.58, "word": " بعد", "probability": 0.71826171875}, {"start": 2560.58, "end": 2560.98, "word": " هيك", "probability": 0.662109375}], "temperature": 1.0}, {"id": 105, "seek": 258904, "start": 2561.2, "end": 2589.04, "text": "بكتب المعادلة بدلالة variable جديد XY X أساسي بحط X كابتل زائد الرقم اللي طالع عندي و Y أساسي بحط Y كابتل زائد الرقم اللي طالع عندي وبعوض في المعادلة الأصليه اوتوماتيك لازم تنقلب الى homogeneous differential equation اذا ما طلعتش homogeneous differential equation بدك تراجع حسابتك معناته غلط في شغلة تمام", "tokens": [3555, 4117, 2655, 3555, 9673, 3615, 18513, 37977, 47525, 1211, 6027, 3660, 7006, 10874, 16254, 3215, 1783, 56, 1783, 5551, 3794, 32277, 1829, 4724, 5016, 9566, 1783, 9122, 16758, 2655, 1211, 30767, 16373, 3215, 34892, 4587, 2304, 13672, 1829, 23032, 6027, 3615, 18871, 16254, 4032, 398, 5551, 3794, 32277, 1829, 4724, 5016, 9566, 398, 9122, 16758, 2655, 1211, 30767, 16373, 3215, 34892, 4587, 2304, 13672, 1829, 23032, 6027, 3615, 18871, 16254, 46599, 3615, 2407, 11242, 8978, 9673, 3615, 18513, 37977, 16247, 9381, 20292, 3224, 1975, 35473, 20498, 9307, 1829, 4117, 5296, 31377, 2304, 6055, 1863, 4587, 46152, 2423, 7578, 42632, 15756, 5367, 1975, 15730, 19446, 23032, 1211, 34268, 8592, 42632, 15756, 5367, 47525, 4117, 6055, 2288, 26108, 3615, 11331, 3794, 16758, 2655, 4117, 20449, 8315, 47395, 32771, 1211, 9566, 8978, 13412, 17082, 37977, 46811, 10943], "avg_logprob": -0.23713235359858065, "compression_ratio": 1.939516129032258, "no_speech_prob": 0.0, "words": [{"start": 2561.2, "end": 2561.9, "word": "بكتب", "probability": 0.8638916015625}, {"start": 2561.9, "end": 2562.44, "word": " المعادلة", "probability": 0.966796875}, {"start": 2562.44, "end": 2563.12, "word": " بدلالة", "probability": 0.911865234375}, {"start": 2563.12, "end": 2563.84, "word": " variable", "probability": 0.552734375}, {"start": 2563.84, "end": 2564.66, "word": " جديد", "probability": 0.9366861979166666}, {"start": 2564.66, "end": 2566.14, "word": " XY", "probability": 0.48779296875}, {"start": 2566.14, "end": 2567.66, "word": " X", "probability": 0.495361328125}, {"start": 2567.66, "end": 2569.1, "word": " أساسي", "probability": 0.6006927490234375}, {"start": 2569.1, "end": 2569.56, "word": " بحط", "probability": 0.6507161458333334}, {"start": 2569.56, "end": 2569.98, "word": " X", "probability": 0.6865234375}, {"start": 2569.98, "end": 2570.46, "word": " كابتل", "probability": 0.629852294921875}, {"start": 2570.46, "end": 2570.82, "word": " زائد", "probability": 0.8365885416666666}, {"start": 2570.82, "end": 2571.26, "word": " الرقم", "probability": 0.9583333333333334}, {"start": 2571.26, "end": 2571.42, "word": " اللي", "probability": 0.776123046875}, {"start": 2571.42, "end": 2571.72, "word": " طالع", "probability": 0.8177083333333334}, {"start": 2571.72, "end": 2572.08, "word": " عندي", "probability": 0.85498046875}, {"start": 2572.08, "end": 2572.74, "word": " و", "probability": 0.51806640625}, {"start": 2572.74, "end": 2573.06, "word": " Y", "probability": 0.48486328125}, {"start": 2573.06, "end": 2573.38, "word": " أساسي", "probability": 0.7933349609375}, {"start": 2573.38, "end": 2573.76, "word": " بحط", "probability": 0.9606119791666666}, {"start": 2573.76, "end": 2573.98, "word": " Y", "probability": 0.84130859375}, {"start": 2573.98, "end": 2574.42, "word": " كابتل", "probability": 0.98388671875}, {"start": 2574.42, "end": 2574.86, "word": " زائد", "probability": 0.9658203125}, {"start": 2574.86, "end": 2575.28, "word": " الرقم", "probability": 0.9811197916666666}, {"start": 2575.28, "end": 2575.44, "word": " اللي", "probability": 0.986572265625}, {"start": 2575.44, "end": 2575.72, "word": " طالع", "probability": 0.9835611979166666}, {"start": 2575.72, "end": 2575.96, "word": " عندي", "probability": 0.964599609375}, {"start": 2575.96, "end": 2576.5, "word": " وبعوض", "probability": 0.739288330078125}, {"start": 2576.5, "end": 2576.64, "word": " في", "probability": 0.91064453125}, {"start": 2576.64, "end": 2576.98, "word": " المعادلة", "probability": 0.9910888671875}, {"start": 2576.98, "end": 2577.36, "word": " الأصليه", "probability": 0.62567138671875}, {"start": 2577.36, "end": 2578.26, "word": " اوتوماتيك", "probability": 0.7717692057291666}, {"start": 2578.26, "end": 2578.78, "word": " لازم", "probability": 0.9806315104166666}, {"start": 2578.78, "end": 2579.52, "word": " تنقلب", "probability": 0.9849853515625}, {"start": 2579.52, "end": 2580.28, "word": " الى", "probability": 0.7213134765625}, {"start": 2580.28, "end": 2581.02, "word": " homogeneous", "probability": 0.77392578125}, {"start": 2581.02, "end": 2582.18, "word": " differential", "probability": 0.9453125}, {"start": 2582.18, "end": 2582.8, "word": " equation", "probability": 0.93310546875}, {"start": 2582.8, "end": 2583.5, "word": " اذا", "probability": 0.689697265625}, {"start": 2583.5, "end": 2583.62, "word": " ما", "probability": 0.80615234375}, {"start": 2583.62, "end": 2584.12, "word": " طلعتش", "probability": 0.8837890625}, {"start": 2584.12, "end": 2584.38, "word": " homogeneous", "probability": 0.8310546875}, {"start": 2584.38, "end": 2584.88, "word": " differential", "probability": 0.9482421875}, {"start": 2584.88, "end": 2585.02, "word": " equation", "probability": 0.58837890625}, {"start": 2585.02, "end": 2585.44, "word": " بدك", "probability": 0.662841796875}, {"start": 2585.44, "end": 2586.04, "word": " تراجع", "probability": 0.842529296875}, {"start": 2586.04, "end": 2586.68, "word": " حسابتك", "probability": 0.96904296875}, {"start": 2586.68, "end": 2587.2, "word": " معناته", "probability": 0.861328125}, {"start": 2587.2, "end": 2587.66, "word": " غلط", "probability": 0.97119140625}, {"start": 2587.66, "end": 2587.86, "word": " في", "probability": 0.869140625}, {"start": 2587.86, "end": 2588.38, "word": " شغلة", "probability": 0.6704915364583334}, {"start": 2588.38, "end": 2589.04, "word": " تمام", "probability": 0.865966796875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2589.95375, "duration_after_vad": 2430.022499999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_raw.srt b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8a3f8d8ff257427f6ab54c544ebef33b12450588
--- /dev/null
+++ b/PL9fwy3NUQKwYaToDpbPxaOdkUX3PS_VKf/xaphhldfua0_raw.srt
@@ -0,0 +1,1532 @@
+1
+00:00:20,320 --> 00:00:24,720
+بسم الله الرحمن الرحيم في المحاضرة الماضية اتحدثنا
+
+2
+00:00:24,720 --> 00:00:29,220
+في chapter واحد section اتنين اللي هو separable
+
+3
+00:00:29,220 --> 00:00:34,000
+equations و هي المعادلات التي فصلنا فيها المتغيرات
+
+4
+00:00:34,000 --> 00:00:38,520
+بين ال X في ناحية و ال Y في ناحية ثم أكملنا الحل
+
+5
+00:00:38,520 --> 00:00:42,580
+بواسطة ال integration يبقى أكملنا الطرفين حصلنا
+
+6
+00:00:42,580 --> 00:00:50,000
+على شكل حل المعادلةالان ننتقل للنوع الثاني وهو الـ
+
+7
+00:00:50,000 --> 00:00:55,260
+Homogeneous equations المعادلات المتجانسة الان
+
+8
+00:00:55,260 --> 00:01:01,620
+نحكم كيف المعادلة المتجانسة فنعطيها تعريف التاني
+
+9
+00:01:02,130 --> 00:01:04,210
+فبقى اللي بفهمه بجهة بقول الـ differential
+
+10
+00:01:04,210 --> 00:01:08,230
+equation dy by dx يسوى f of x y is called
+
+11
+00:01:08,230 --> 00:01:12,770
+homogeneous هذه اختصار لكلمة homogeneous اللي فوق
+
+12
+00:01:12,770 --> 00:01:17,810
+عند الـ g هعطينا نقطة if it can be written as إذا
+
+13
+00:01:17,810 --> 00:01:22,570
+جدوا أنه نكتبه على الصيغة dy على dx يسوى capital F
+
+14
+00:01:22,570 --> 00:01:27,390
+اللي فوق small f واللي تحت capital Fas a function
+
+15
+00:01:27,390 --> 00:01:32,470
+of y على x يعني إذا قدرنا نكتب المعادلة على شكل y
+
+16
+00:01:32,470 --> 00:01:38,950
+على x بقدر أسميها دالة متجلسة دالة معادلة متجلسة
+
+17
+00:01:38,950 --> 00:01:44,250
+طبعا هذا منابط مش ممكن يحصل إلا إذا كان عندي بسط و
+
+18
+00:01:44,250 --> 00:01:50,410
+مقام يعني dy على dx يساوي بسط على مقام لإن في هذه
+
+19
+00:01:50,410 --> 00:01:55,030
+الحالة بقدر أكتب ربما نقدر و ربما نقدرشنكتب
+
+20
+00:01:55,030 --> 00:02:00,630
+المعادلة كلها بدلالة Y على X لكن constant على X
+
+21
+00:02:00,630 --> 00:02:04,470
+ولا constant على Y ممنوع بس constant لحاله مافي
+
+22
+00:02:04,470 --> 00:02:08,710
+مشكلة يعني لو جينا جسمنا على X على Y إلى آخره
+
+23
+00:02:08,710 --> 00:02:13,630
+وصارت في عندي طلع زائد 3 على X هل هذه homogeneous؟
+
+24
+00:02:13,630 --> 00:02:19,430
+لأ طبعاً بديها تبقى Y على X أو مقدار ثابت خالي من
+
+25
+00:02:19,430 --> 00:02:25,440
+كل من X وY كما سنراه من خلال الأمثلة بعد قليلالان
+
+26
+00:02:25,440 --> 00:02:32,120
+بدنا نحل المعادلة التفاضلية المتجنسة يبقى
+
+27
+00:02:32,120 --> 00:02:35,660
+المعادلات التفاضلية المتجنسة لها تكتيك واحد في
+
+28
+00:02:35,660 --> 00:02:37,460
+الحل وهو كالتالي
+
+29
+00:02:47,050 --> 00:02:54,010
+المتغير V يساوي Y على X لو جاءت ضرب، ضرب التبادل
+
+30
+00:02:54,010 --> 00:02:57,970
+يساوي
+
+31
+00:02:57,970 --> 00:03:06,560
+X في Vالان لو جيت اشتقت يبقى الـ dy by dx يساوي
+
+32
+00:03:06,560 --> 00:03:15,340
+هذا يعتبر مشتقت حاصل ضرب دالتين يبقى v زائد x في
+
+33
+00:03:15,340 --> 00:03:22,320
+dv على dxالأولى في مشتقة التانية هيها زي دالة
+
+34
+00:03:22,320 --> 00:03:28,300
+التانية في مشتقة الأولى زيها الان انا عندى y على x
+
+35
+00:03:28,300 --> 00:03:32,600
+ممكن اشيله و اكتب بدلها v و dy على dx بدي اشيله و
+
+36
+00:03:32,600 --> 00:03:38,740
+اكتب بدلها v زي x في dv على dx نمسك المعلومات هذه
+
+37
+00:03:38,740 --> 00:03:44,300
+و نرجع نعوض في المعادلة رقم star بنحصل على ما يأتي
+
+38
+00:03:44,740 --> 00:03:52,840
+Vزاد X في الـDV على DX يساوي capital F as a
+
+39
+00:03:52,840 --> 00:03:58,720
+function of V لأن شيلت Y على X وحطيت مكان امين V
+
+40
+00:03:59,400 --> 00:04:04,560
+الان ممكن اجيب V وين؟ على الناحية الثانية يبقى او
+
+41
+00:04:04,560 --> 00:04:12,040
+اضفنا سلب V للطرفين يبقى X في الـDV على DX يسوي
+
+42
+00:04:12,040 --> 00:04:18,620
+capital F of V نقص الـV ايش رايك؟ بقدر افصل
+
+43
+00:04:18,620 --> 00:04:24,670
+المتغيرات الآن؟بتخلّي ال V's في شجة و ال X's في
+
+44
+00:04:24,670 --> 00:04:28,450
+شجة تانية يبقى بناء عليه هذا بيصير
+
+45
+00:04:53,840 --> 00:05:06,960
+differential equation that can be solved as before
+
+46
+00:05:06,960 --> 00:05:11,860
+زي ما كنا بنحل قبل بنقدر نروح نحلي المعادلة اللي
+
+47
+00:05:11,860 --> 00:05:18,900
+عندنا هذه طب كويس لاحظوا قبل قليلقلت لكم إن
+
+48
+00:05:18,900 --> 00:05:22,680
+المعادلة هذه بقدر اكتبها بالشكل هذا لو كانت
+
+49
+00:05:22,680 --> 00:05:27,560
+rational function الطرف اليمين يعني بسط على مقام
+
+50
+00:05:27,560 --> 00:05:32,320
+طب افترضي ماكانش عندي بسط على مقام كانت دالة عادية
+
+51
+00:05:32,320 --> 00:05:36,360
+دي واي على دي اكس سوى اكس واي تربية زي اتنين اكس
+
+52
+00:05:36,360 --> 00:05:41,170
+واي زي التلاتة مثلا تمامطب كيف بنعمل في هذه
+
+53
+00:05:41,170 --> 00:05:47,770
+الحالة؟ في عندي طريقة أخرى للحكم على هذه المعادلة
+
+54
+00:05:47,770 --> 00:05:53,530
+هل هي معادلة متجانسة ام لا شو هذه الطريقة هنحطها
+
+55
+00:05:53,530 --> 00:05:57,990
+لك في ال definition التالي يبقى بدنا نروح نعطي
+
+56
+00:05:57,990 --> 00:06:05,990
+definition جديد يبقى بداجي definition هقسمه
+
+57
+00:06:05,990 --> 00:06:08,630
+إلى نقطتين النقطة الأولى
+
+58
+00:06:11,240 --> 00:06:19,180
+differential equation الـ differential equation dy
+
+59
+00:06:19,180 --> 00:06:30,000
+by dx بده يساوي f of x y is called homogeneous is
+
+60
+00:06:30,000 --> 00:06:35,300
+called homogeneous
+
+61
+00:06:35,300 --> 00:06:46,780
+if and only ifF and only F فالـ
+
+62
+00:06:46,780 --> 00:07:00,800
+F of T X و T Y بدي يسوى من F of X Y for all T
+
+63
+00:07:00,800 --> 00:07:04,060
+النقطة
+
+64
+00:07:04,060 --> 00:07:17,840
+الثانية A functionf of x و y is called homogeneous
+
+65
+00:07:17,840 --> 00:07:24,100
+of degree
+
+66
+00:07:24,100 --> 00:07:35,360
+mf
+
+67
+00:07:37,650 --> 00:07:47,390
+الـ F of T X و T Y بديوا يساوي T to the power M في
+
+68
+00:07:47,390 --> 00:07:57,530
+ال F of X Y فالـ
+
+69
+00:07:57,530 --> 00:08:04,450
+F of T X و T Y بديوا يساوي ال F of X Y
+
+70
+00:08:07,930 --> 00:08:18,330
+a homogeneous equation of degree الله أعلم
+
+71
+00:08:32,640 --> 00:08:37,080
+نرجع الآن للـ two definitions اللي احنا كتبينهم
+
+72
+00:08:37,080 --> 00:08:41,940
+نفهم كل واحد من ال two definitions هذا طبعا التان
+
+73
+00:08:41,940 --> 00:08:45,900
+اللي هما علاقة ببعض علاقة قوية جدا و اللي هما
+
+74
+00:08:45,900 --> 00:08:50,690
+علاقة بال definition الأولالدفينيشن الأولاني هذا
+
+75
+00:08:50,690 --> 00:08:54,370
+بيقول الـ differential equation dy by dx يسوي f of
+
+76
+00:08:54,370 --> 00:08:59,390
+x y is called homogeneous فقلنا homogeneous إذا
+
+77
+00:08:59,390 --> 00:09:02,830
+قدرنا نكتبها على الشكل اللي عندنا هذا هنا بقول
+
+78
+00:09:02,830 --> 00:09:09,610
+homogeneous f and all f ال f of t x and و t y
+
+79
+00:09:09,610 --> 00:09:16,060
+بيبقى يسوي f of x y لأي t نحطهابيقول بتيجي على
+
+80
+00:09:16,060 --> 00:09:22,000
+المعادلة لو شيلت كل X و حطيت مكانها TX و جيت على Y
+
+81
+00:09:22,000 --> 00:09:27,320
+و شيلت و حطيت مكانها TY تبقى المعادلة كما هي إن
+
+82
+00:09:27,320 --> 00:09:31,280
+بقيت كما هي بقول هذه homogeneous differential
+
+83
+00:09:31,280 --> 00:09:36,100
+equation طب أنا هنا لو جيت و حطيت يا بنات TY على
+
+84
+00:09:36,100 --> 00:09:43,180
+TX مش بتظلها Y على Xومن هنا باختصر T مع T بالضل Y
+
+85
+00:09:43,180 --> 00:09:47,360
+علي X ومن هنا هذا ال definition يكافئ هذا ال
+
+86
+00:09:47,360 --> 00:09:52,970
+definition تمامالما أقول هذي homogeneous اللي هو
+
+87
+00:09:52,970 --> 00:09:57,550
+differential equation ممكن يكونها درجة ما تعالى
+
+88
+00:09:57,550 --> 00:10:01,790
+نشوف إيش اللي بقول هنا بقول دالة F of X Y بقول
+
+89
+00:10:01,790 --> 00:10:07,030
+عنها homogeneous of degree M دالة متجانسة من
+
+90
+00:10:07,030 --> 00:10:13,210
+الدرجة رقم M طبعا M عدد صحيح موجب أو صفر ماعناه
+
+91
+00:10:13,210 --> 00:10:19,790
+مشكلة بس ليس كثير ليس سالباوهنا ايه فاصلة وقليل
+
+92
+00:10:19,790 --> 00:10:30,670
+الام greater than or equal to zero والام is an
+
+93
+00:10:30,670 --> 00:10:34,930
+integer يبقى
+
+94
+00:10:34,930 --> 00:10:35,810
+عدد صحيح
+
+95
+00:10:38,550 --> 00:10:43,830
+أنا جيت على X شيلتها و حاطيت مكانها TX جيت على Y
+
+96
+00:10:43,830 --> 00:10:48,230
+شيلتها و حاطيت مكانها TY لاجيت انها تجميش زي اللي
+
+97
+00:10:48,230 --> 00:10:53,310
+فوق يسوي F of XY لاجيت يسوي T to the power M في F
+
+98
+00:10:53,310 --> 00:10:59,550
+of XY بقول إن حدث ذلك يبقى الدالة اللي عنها دي
+
+99
+00:10:59,550 --> 00:11:06,450
+بقول عنها homogeneous من الدرجة رقم M تمام؟يبقى
+
+100
+00:11:06,450 --> 00:11:12,790
+هذا degree M هوموجينيس من degree M طيب يبقى بناء
+
+101
+00:11:12,790 --> 00:11:18,950
+عليه الدالة الأولى هذه في عندي هنا T ماعنديش يعني
+
+102
+00:11:18,950 --> 00:11:25,030
+كانت T أو Zero يبقى هذه بالهوموجينيس of degree
+
+103
+00:11:25,030 --> 00:11:31,870
+Zero تمام degree Zero يبقى هذه متجانسة من الدرجة
+
+104
+00:11:31,870 --> 00:11:36,680
+الصفريةالان بدنا نروح كيف بدنا نفهم ال two
+
+105
+00:11:36,680 --> 00:11:41,280
+definitions هدول بدنا ناخد بعض الأمثلة يبقى
+
+106
+00:11:41,280 --> 00:11:48,340
+example one بقول
+
+107
+00:11:48,340 --> 00:11:54,100
+determine determine
+
+108
+00:11:54,100 --> 00:12:00,300
+whether the following
+
+109
+00:12:03,040 --> 00:12:07,920
+determine whether the following functions are
+
+110
+00:12:07,920 --> 00:12:18,200
+homogeneous or not if
+
+111
+00:12:18,200 --> 00:12:30,080
+itHomogeneous لو كانت homogenous state its degree
+
+112
+00:12:30,080 --> 00:12:36,100
+بدي أعرف قداش الدرجة بتبعتها النقطة الأولى
+
+113
+00:12:51,130 --> 00:13:03,950
+النقطة الثانيةالـ F of X و Y بدها تساوي XY Cos Y
+
+114
+00:13:03,950 --> 00:13:08,690
+على X زائد X تربيع
+
+115
+00:13:14,510 --> 00:13:19,270
+السؤال بيقول لي شوف لمين من الدول التالية بتبقى
+
+116
+00:13:19,270 --> 00:13:22,890
+homogenous ومين ماهياش homogenous وإذا كانت
+
+117
+00:13:22,890 --> 00:13:27,450
+homogenous بدي أعرف الـ M هذه قداش قيمته يعني قداش
+
+118
+00:13:27,450 --> 00:13:34,290
+درجة هذه المعادلة بقوله كويس بيداجي ال solution هو
+
+119
+00:13:34,290 --> 00:13:41,310
+بيداجي للنقطة الأولى اللي هي رقم I رقم I بدي أشيل
+
+120
+00:13:41,310 --> 00:13:48,050
+كل X و أحط مكانهاوشيل كل Y وحط مكانها TY يبقى
+
+121
+00:13:48,050 --> 00:13:57,310
+بالداجي اقوله هنا G of TX وTY بده يساوي اتنين TX
+
+122
+00:13:57,310 --> 00:14:07,800
+لكل تربية زائد تلاتة TY لكل تربية زائد اربعةيعني
+
+123
+00:14:07,800 --> 00:14:14,560
+هذه بقدر اقول اللي هي اتنين T تربيع X تربيع زائد
+
+124
+00:14:14,560 --> 00:14:24,720
+تلاتة T تربيع Y تربيع زائد اربعة الـ G is a non
+
+125
+00:14:24,720 --> 00:14:31,020
+homogeneous function
+
+126
+00:14:31,020 --> 00:14:35,660
+يبقى هذه ليست homogeneous function
+
+127
+00:14:46,190 --> 00:14:51,590
+نأتي للمعادلة التانية او للـ function التانية ناخد
+
+128
+00:14:51,590 --> 00:15:01,730
+النقطة التانية لـ F of TX و TY يساوي يبقى هنا TX
+
+129
+00:15:01,730 --> 00:15:14,190
+مضروبة في TY TX في TY في Cosتي واي عالى تي اكس
+
+130
+00:15:14,190 --> 00:15:24,010
+زائد تي اكس لكل تربيع هذه لو جيت ضربتها بنات بيصير
+
+131
+00:15:24,010 --> 00:15:31,250
+تي تربيع اكس واي وهنا لو اختصرت تي مع تي بيظل
+
+132
+00:15:31,250 --> 00:15:38,130
+cosine واي عالى اكس وهذه زائد تي تربيع اكس تربيع
+
+133
+00:15:39,380 --> 00:15:44,000
+أظن ممكن من المعادلة هذه أخد T تربيع عمل مشترك إذا
+
+134
+00:15:44,000 --> 00:15:51,580
+لو أخدنا T تربيع عمل مشترك بيظل لإن X Y Cos Y على
+
+135
+00:15:51,580 --> 00:15:57,820
+X زائد X تربيع اللي بين Cos أليس T F of X وY
+
+136
+00:15:57,820 --> 00:16:05,280
+الأصلية يبقى هذا الكلام بدي ساوي T تربيع في F of X
+
+137
+00:16:05,280 --> 00:16:14,840
+وYيبقى هذا معناه ايه؟ ف ال f of x و y is a
+
+138
+00:16:14,840 --> 00:16:19,820
+homogeneous function
+
+139
+00:16:19,820 --> 00:16:31,880
+of degree اتنين طيب انت هنا روح ناخد مثاليبقى هذا
+
+140
+00:16:31,880 --> 00:16:36,720
+المثال على آخر التعريفين بدنا نروح ناخد مثال على
+
+141
+00:16:36,720 --> 00:16:41,020
+التعريف الأول لل homogenous differential equation
+
+142
+00:16:41,020 --> 00:16:49,320
+يبقى example two بيقول
+
+143
+00:16:49,320 --> 00:16:57,800
+solve the following differential
+
+144
+00:16:59,520 --> 00:17:05,540
+Equations حل المعادلات التفاضلية التالية أول
+
+145
+00:17:05,540 --> 00:17:12,440
+معادلة من هذه المعادلات التي هي رقم A بيقول XYY'
+
+146
+00:17:13,280 --> 00:17:19,520
+يساوي 2Y تربيع ناقص X تربيع
+
+147
+00:17:44,670 --> 00:17:49,890
+أول شي بتبحث هل هي homogeneous ماهياش homogeneous
+
+148
+00:17:49,890 --> 00:17:56,980
+نقدر نفصل متغيرات هل نقدر عليهلما كان موضوعنا
+
+149
+00:17:56,980 --> 00:18:00,180
+موضوع الـ homogeneous إذا أنا أول شغل بدي أختبرها
+
+150
+00:18:00,180 --> 00:18:02,940
+هل هي homogeneous أم لا إذا ما طلعتش homogeneous
+
+151
+00:18:02,940 --> 00:18:08,080
+بروح بدور main, separable أو غيره طب الآن أنا بدي
+
+152
+00:18:08,080 --> 00:18:14,100
+Y' لحالة يبقى بروح أجسم الطرفين على XY يبقى لو
+
+153
+00:18:14,100 --> 00:18:20,860
+قسمت الطرفين على XY بصير المعادلة يساوي 2Y على X
+
+154
+00:18:21,350 --> 00:18:25,870
+والله بلاش نقولك كيف هاد أجت بدي أعملها لك على
+
+155
+00:18:25,870 --> 00:18:30,970
+خطوط اللي لو جسمت على x y بظهر y prime يبقى 2y
+
+156
+00:18:30,970 --> 00:18:39,130
+تربيع على x y ناقص x تربيع على x في y بالشكل هذا
+
+157
+00:18:39,130 --> 00:18:44,730
+هذه كلها اللي هي main y primeإذا هذه المعادلة يا
+
+158
+00:18:44,730 --> 00:18:51,090
+بنات قدرت الأصلية أكتبها على الشكل الجديد هذا شو
+
+159
+00:18:51,090 --> 00:18:56,860
+رأيك في الشكل الجديد؟هموجينيوس ولا لأ يبجى هذه
+
+160
+00:18:56,860 --> 00:19:01,200
+هموجينيوس اللي قدرت اكتبها على شكل y على x بدون ما
+
+161
+00:19:01,200 --> 00:19:05,880
+يكون ثابت لحاله او بدون ما يكون عدد على x او عدد
+
+162
+00:19:05,880 --> 00:19:13,560
+على ماين على y يبجى هذه this is a homogeneous
+
+163
+00:19:13,560 --> 00:19:21,850
+differential equationبدنا نحلها إذا بنروح نتابع
+
+164
+00:19:21,850 --> 00:19:27,370
+التكتيك اللي ابتدأناه في الجزء النظري قبل قليل شو
+
+165
+00:19:27,370 --> 00:19:35,460
+بدنا نعمل؟ بنقول له put ال V تساوي Y على Xأضرب ضرب
+
+166
+00:19:35,460 --> 00:19:40,580
+تبادل يبقى الـ
+
+167
+00:19:40,580 --> 00:19:47,040
+y تساوي x في v اشتق طرفين بالنسبة إلى x يبقى dy
+
+168
+00:19:47,040 --> 00:19:57,850
+على dx يساوي v زائد x في dv على dxنعوض الأن
+
+169
+00:19:57,850 --> 00:20:07,870
+بالمعلومات اللي عندنا في المعادلة المستاطيلة في
+
+170
+00:20:07,870 --> 00:20:10,250
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+171
+00:20:10,250 --> 00:20:10,250
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+172
+00:20:10,250 --> 00:20:10,370
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+173
+00:20:10,370 --> 00:20:10,490
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+174
+00:20:10,490 --> 00:20:11,150
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+175
+00:20:11,150 --> 00:20:11,150
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+176
+00:20:11,150 --> 00:20:11,150
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+177
+00:20:11,150 --> 00:20:11,170
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+178
+00:20:11,170 --> 00:20:14,390
+المعادلة المستاطيلة في المعادلة المستاطيلة في
+
+179
+00:20:14,390 --> 00:20:24,290
+المعادلة المستاطيلة في المعادلة
+
+180
+00:20:24,290 --> 00:20:33,320
+المستاطيلطب ايش رايك؟ بدي اضيف سالب V للطرفين يبقى
+
+181
+00:20:33,320 --> 00:20:41,040
+هذه ايش بتعطينا؟تعطينا ان X في الـDV على DX يسوى V
+
+182
+00:20:41,040 --> 00:20:49,400
+ناقص واحد على V او ان شئتنا فقلنا X في الـDV على
+
+183
+00:20:49,400 --> 00:20:55,560
+DX يسوى V تربية ناقص واحد كله على V وحتى المقامات
+
+184
+00:20:55,560 --> 00:21:00,480
+للطرف اليمين طب ايش رأيك و بقدر افصل المتغيرات ولا
+
+185
+00:21:00,480 --> 00:21:02,940
+لا نقدر
+
+186
+00:21:04,340 --> 00:21:10,800
+يبقى بقدر أقول هذه V على V تربيع ناقص واحد في
+
+187
+00:21:10,800 --> 00:21:18,560
+الـDV بده يساوي DX على X يبقى الـV's صاروا في شجة
+
+188
+00:21:18,560 --> 00:21:22,640
+و الـX's صاروا في شجة واحدة يبقى هذه شو اسمها؟
+
+189
+00:21:22,640 --> 00:21:26,500
+Separable يبقى حولت الـHomogeneous Differential
+
+190
+00:21:26,500 --> 00:21:33,080
+Equation إلى Separable Equation يبقى هذه Separable
+
+191
+00:21:35,010 --> 00:21:38,850
+Equation زي ما قلنا في الجزء الناضري أول مبتعدين
+
+192
+00:21:38,850 --> 00:21:42,270
+التعريف الأول قلنا بشأن حلها بتشيل ال Y على X و
+
+193
+00:21:42,270 --> 00:21:47,170
+بتحط مكانها V و اشتقنا و عوضنا و فاصلنا المتغيرات
+
+194
+00:21:47,170 --> 00:21:50,890
+فصارت ال V في شجة و ال X في شجة فقلنا ها دي
+
+195
+00:21:50,890 --> 00:21:53,910
+separable equation يبقى هيها صارت separable
+
+196
+00:21:53,910 --> 00:21:59,190
+equation بده حلها ايش بنعمل؟بنكمل طيب الطرف اليمين
+
+197
+00:21:59,190 --> 00:22:05,110
+أظن سهل طيب و الطرف الشمال بقول بس لو فيه اتنين في
+
+198
+00:22:05,110 --> 00:22:09,370
+ال bus اللي أصبح ال bus تفاضل المقام إذا بنضرب في
+
+199
+00:22:09,370 --> 00:22:14,490
+اتنين و بنقسم على اتنين يعني هذه كأنها النص في
+
+200
+00:22:14,490 --> 00:22:22,410
+اتنين V على V تربية ناقص واحد كله في DV بده يساوي
+
+201
+00:22:22,410 --> 00:22:30,330
+DX على Xصار البسطة فضل مقام يبقى بالتكامل ايش بصير
+
+202
+00:22:30,330 --> 00:22:37,090
+عندنا مص لن absolute value ل V تربيع ناقص واحد
+
+203
+00:22:37,090 --> 00:22:45,060
+يسوى لن absolute value ل X زائد C1 مثلاًطب لو
+
+204
+00:22:45,060 --> 00:22:51,500
+ضربنا في اتنين بصير الـLin هذه يا بنات كأنها ايه؟
+
+205
+00:22:51,500 --> 00:22:57,840
+كأنها الـLin الـV تربيع ناقص واحد يساوي الـLin
+
+206
+00:22:57,840 --> 00:23:03,700
+absolute value لل X تربيع أظن سواء كتبنا الـLin و
+
+207
+00:23:03,700 --> 00:23:11,280
+الله ما كتبناش بتفرجش عندنا تمام؟ هها زائد اتنين
+
+208
+00:23:11,280 --> 00:23:19,570
+C1أنا بدي اشيل لن هذه برفع اتنين كأس للعداد ايه
+
+209
+00:23:19,570 --> 00:23:24,530
+يبقاش بيصير عند هنا absolute value لل V تربيع ناقص
+
+210
+00:23:24,530 --> 00:23:32,570
+واحد يساوي E أس لن اللي هو ال X تربيع لإن ال X
+
+211
+00:23:32,570 --> 00:23:38,530
+تربيع زائد اتنين C1 كونه كمية مربعة حطيت ال
+
+212
+00:23:38,530 --> 00:23:43,000
+absolute والله شيلته بتفرجش عندنايبقى هذه يا بنات
+
+213
+00:23:43,000 --> 00:23:50,480
+اللي هي بتتساوي قداش X تربيع في E أس اتنين C1 E أس
+
+214
+00:23:50,480 --> 00:23:56,640
+لين X تربيع و E أس اتنين C1 تمام ال E و ال L عكس
+
+215
+00:23:56,640 --> 00:24:02,020
+بعض بصير X تربيع في من في C1 طب إيش رأيك هذه عمرها
+
+216
+00:24:02,020 --> 00:24:07,680
+تصير قيمة سالبة يبقى ال absolute value هذا لا معنى
+
+217
+00:24:07,680 --> 00:24:13,190
+له موجب دايما و أبدايبقى بناءً عليه بقدر أقول إذا
+
+218
+00:24:13,190 --> 00:24:21,410
+الـV تربيع ناقص واحد يساوي C في X تربيع والـC بدي
+
+219
+00:24:21,410 --> 00:24:27,010
+يساوي E أس اتنين C1 هذا مقدار ثابت بدل ما هم كانوا
+
+220
+00:24:27,010 --> 00:24:31,150
+بديوا يحطوا مداله C التفلي بس في الكتاب مقدار ثابت
+
+221
+00:24:31,150 --> 00:24:37,410
+جد ما يكون يكونطيب الواحد هذا بقدر أنقله اين؟ على
+
+222
+00:24:37,410 --> 00:24:44,570
+الشجرة التانية يبقى بصير ال V تربيع بده يساوي CX
+
+223
+00:24:44,570 --> 00:24:51,190
+تربيع زائد واحدطب ال V تربية هذه مش عبارة عن Y على
+
+224
+00:24:51,190 --> 00:24:57,730
+X لكل تربية صح نضرب الطرفين في X تربية بصير عندنا
+
+225
+00:24:57,730 --> 00:25:05,970
+هنا Y تربية يساوي X تربية في C X تربية زائد واحد
+
+226
+00:25:06,560 --> 00:25:13,160
+ناخد الجذر التربيعي للطرفين يبقى بصير Y يساوي
+
+227
+00:25:13,160 --> 00:25:19,180
+الزائد أو ناقص اللي هو main اللي هو absolute value
+
+228
+00:25:19,180 --> 00:25:25,780
+لل X في main في الجذر التربيعي ل CX تربيع زائد
+
+229
+00:25:25,780 --> 00:25:35,150
+واحد يبقى هذا هو الحل تبع المثلة اللي عندناتمام؟
+
+230
+00:25:35,150 --> 00:25:39,150
+حد إلها أي تساؤل هنا قبل أن نذهب إلى المثال الذي
+
+231
+00:25:39,150 --> 00:25:45,750
+يليه .. آه أيوة اتفضلي مافيش
+
+232
+00:25:45,750 --> 00:25:50,310
+رأيك تيجي هنا؟ تعالي يالا يا بنات أخدنا طال الوقت
+
+233
+00:25:50,310 --> 00:25:54,570
+four example كمثال مشان اللي مش مخدمة تاخد بالها
+
+234
+00:25:54,570 --> 00:26:00,410
+تسألي هنا اللي بدكية هنا يجب أن تعمل E أسنين extra
+
+235
+00:26:00,410 --> 00:26:06,160
+B زي اتنين C one مش هي الاتنين C one بحالهالأ ماشي
+
+236
+00:26:06,160 --> 00:26:14,620
+لكن هذا كله كأسل العدد E هذا كله أسل العدد E E أسل
+
+237
+00:26:14,620 --> 00:26:20,080
+يساوي E أس المقدر هذا كله مظبوط ولا لأ يبقى بيصير
+
+238
+00:26:20,080 --> 00:26:29,150
+E أسل X تربيع E أسل X تربيع في E أس اتنين C1هي
+
+239
+00:26:29,150 --> 00:26:33,290
+وزنها مظبوط هيك عند ضرب تجمع الأسس فصارت مجموعة
+
+240
+00:26:33,290 --> 00:26:37,890
+بهذا الشكل الـE والإنعكس بعض بضل X تربيعها دي حطيت
+
+241
+00:26:37,890 --> 00:26:42,790
+بدلة مقدار ثابت لإن 2 و7 من 10 أس مقدار ثابت هيك
+
+242
+00:26:42,790 --> 00:26:47,110
+كنت بدك تسألي ولا بطلتي نفس السؤال في حاب تسأل
+
+243
+00:26:47,110 --> 00:26:54,250
+تاني يا بنات خلاص نذهب إلى السلمثال الذي يليه
+
+244
+00:27:10,480 --> 00:27:15,160
+نمر بـ X
+
+245
+00:27:15,160 --> 00:27:27,980
+تربية Y' ناقص XY X تربية زائد Y تربية في 10
+
+246
+00:27:27,980 --> 00:27:36,040
+inverse Y على X نحل المعادلة التفاضلية اللي قدامنا
+
+247
+00:27:36,040 --> 00:27:44,090
+هذه بسيطة جدايبقى الخطوة الأولى بدي أخلّي Y' لحالة
+
+248
+00:27:44,090 --> 00:27:51,130
+يبقى إيش نعمل؟ نكسب على X ربيع صحيح ولا لا؟ يبقى
+
+249
+00:27:51,130 --> 00:27:58,490
+باجي بقوله solutionأجسم المعادلة كلها على X تربية
+
+250
+00:27:58,490 --> 00:28:05,090
+لو جسمت على X تربية هنا يقدرش بيطلع Y' لو جسمت على
+
+251
+00:28:05,090 --> 00:28:13,110
+X تربية بيظل يقدرش Y على X يبدو يساوي 1 زائد Y على
+
+252
+00:28:13,110 --> 00:28:19,550
+X لكل تربية تان Inverse Y على X
+
+253
+00:28:23,140 --> 00:28:27,480
+بعد ذلك الان صارت هذه homogenous differential
+
+254
+00:28:27,480 --> 00:28:34,840
+equation يبقى هذه homogenous differential
+
+255
+00:28:34,840 --> 00:28:38,980
+equation مادام homogenous إذا بنحلها بالطريقة اللي
+
+256
+00:28:38,980 --> 00:28:45,450
+حلناها بالمثال قبل قليل يبقى باجي بقوله podحط لي v
+
+257
+00:28:45,450 --> 00:28:52,430
+تساوي y على x هذا معناه ان y يساوي xv هذا معناه ان
+
+258
+00:28:52,430 --> 00:29:01,930
+dy by dx يساوي v زائد x في dv على dx اذا بدنا نمسك
+
+259
+00:29:01,930 --> 00:29:05,050
+المعلومات اللي حصلنا عليها و نرجع نعوضها بقى في
+
+260
+00:29:05,050 --> 00:29:12,180
+المعادلة أعلىيبقى الـY' يا بنات اللي هي V زائد X
+
+261
+00:29:12,180 --> 00:29:21,640
+في الـDV على DX نقص الـV يسوى 1 زائد V ترابيع في
+
+262
+00:29:21,640 --> 00:29:30,860
+10 inverse Vأظن سالب V وموجة V مع السلامة يبقى
+
+263
+00:29:30,860 --> 00:29:39,140
+تقول المثل إلى X في الـDV على DX 1 زائد V تربيع في
+
+264
+00:29:39,140 --> 00:29:47,460
+Tan inverse Vنفصل المتغيرات بيدخل ال V في الشجة
+
+265
+00:29:47,460 --> 00:29:54,340
+الشمال وال X في الشجة اليمين يبقى دي بيصير DV على
+
+266
+00:29:54,340 --> 00:30:02,600
+واحد زائد V تربيع في turn inverse V يسوى DX على X
+
+267
+00:30:02,600 --> 00:30:07,520
+وهذه C Parabol equation
+
+268
+00:30:08,420 --> 00:30:14,100
+يبقى هذه معادلة فيها المتغيرات مفصولة إذا المعادلة
+
+269
+00:30:14,100 --> 00:30:20,160
+اللى كانت homogeneous حولناها إلى separable ومن ثم
+
+270
+00:30:20,160 --> 00:30:25,800
+مش ضايل علينا إلا نكامل هذه المعادلة بيكون حصلنا
+
+271
+00:30:25,800 --> 00:30:33,540
+على الحل المطلوب السؤال هو هذه very easy طب و هذه
+
+272
+00:30:33,540 --> 00:30:41,000
+very easy كمانمش تقت الـ tan inverse كده؟ 1 لا 1
+
+273
+00:30:41,000 --> 00:30:47,900
+زائد V تربيع إذا هذه كلها هي مش تقت من؟ tan
+
+274
+00:30:47,900 --> 00:30:54,580
+inverse يبقى المثل بقدر أقول هي D ل tan inverse V
+
+275
+00:30:54,580 --> 00:31:02,400
+على tan inverse V بده يسوى DX على X إذا رحت كتبت
+
+276
+00:31:02,400 --> 00:31:07,790
+المعادلة اللي عندي بصياغة جديدةطب البسط هو تفاضل
+
+277
+00:31:07,790 --> 00:31:13,430
+المقام يبقى الجواب لين absolute value للمقام يبقى
+
+278
+00:31:13,430 --> 00:31:19,430
+هذا بدي يعطينا بالتكامل لين absolute value ل 10
+
+279
+00:31:19,430 --> 00:31:25,990
+inverse V بدي سوى لين absolute value ل X زائد
+
+280
+00:31:25,990 --> 00:31:33,990
+constant C1 طيب شو رايك؟ناخد الـ exponential
+
+281
+00:31:33,990 --> 00:31:40,110
+للطرفين يبقى لها رافعت اتنين كأس للعدد E بصير عندي
+
+282
+00:31:40,110 --> 00:31:46,890
+absolute value ل 10 inverse V بيصير E أسلن
+
+283
+00:31:46,890 --> 00:31:55,570
+absolute value ل X زائد C1 شو اسمك انت والله؟ مش
+
+284
+00:31:55,570 --> 00:32:02,670
+سامعأخوك نرمي توسيع سالة السؤال اللي بعضكوا كانت
+
+285
+00:32:02,670 --> 00:32:08,550
+خجلانة تسألك نشجعها على ذلك ونذهب نذكر تذكير بما
+
+286
+00:32:08,550 --> 00:32:15,170
+كنا نصنعه في Calculus B يبقى هذه E أس لين absolute
+
+287
+00:32:15,170 --> 00:32:25,300
+value ل X في E أس C1 تمام؟ هذا الكلام بده يساويأو
+
+288
+00:32:25,300 --> 00:32:29,760
+هذا الكلام هو اللي ان عكس بعض يبقى absolute value
+
+289
+00:32:29,760 --> 00:32:38,440
+ل X في C والـ C بده يساوي E on C1 مشان أضيع الكلكة
+
+290
+00:32:38,440 --> 00:32:44,620
+مخليش عندي كلكعة كتيرة طيب شو رايك؟ بده أخد الآن
+
+291
+00:32:44,620 --> 00:32:55,200
+10 للطرفينيبقى V تساوي 10 C absolute value ل X
+
+292
+00:32:58,220 --> 00:33:06,300
+Y على X يبقى هذا معناه ان Y على X يساوي 10 ل C
+
+293
+00:33:06,300 --> 00:33:11,100
+absolute value ل X يبقى الحل اللي عندنا لو نضرب
+
+294
+00:33:11,100 --> 00:33:18,740
+الطرفين في X بيصير Y يساوي X في 10C absolute value
+
+295
+00:33:18,740 --> 00:33:23,480
+ل X هذا هو حل المعادلة المعطاة
+
+296
+00:33:28,600 --> 00:33:36,820
+هذا كله بيظبط يكون Y على X ممكن
+
+297
+00:33:36,820 --> 00:33:40,880
+ما يظبطش ولما ماظبطش بدنا نروح لل C Parable أو
+
+298
+00:33:40,880 --> 00:33:46,670
+لبعض الطرق الأخرى اللتي لم ندرسها بعديعني احنا
+
+299
+00:33:46,670 --> 00:33:52,730
+بالاخر ممكن نجيبلك تمرين عام بعد كله تحل على أي
+
+300
+00:33:52,730 --> 00:33:56,730
+طريقة بس تجرب الطريقة اللي تعجبك بس ال Y على X
+
+301
+00:33:56,730 --> 00:34:01,990
+بتقدر تطلع فيها بمجرد النظر يعني انا لو جسمت على X
+
+302
+00:34:01,990 --> 00:34:06,030
+و لا على X تربيها هل بطلع Y على X و X على Y ولا لأ
+
+303
+00:34:06,030 --> 00:34:09,350
+اذا طلع خلاص هموجينة قبل ما تشتغلولها بمجرد ما
+
+304
+00:34:09,350 --> 00:34:13,580
+تطلع فيهاتمام او اذا قررت افصل بقدر افصل المتغير
+
+305
+00:34:13,580 --> 00:34:19,040
+يبقى ياسي برامول و هكذا لسه لازال عندنا بعض انواع
+
+306
+00:34:19,040 --> 00:34:24,080
+اخرى من ال first order differential equation طيب
+
+307
+00:34:24,080 --> 00:34:34,420
+نعطيكي ملاحظة remark to
+
+308
+00:34:34,420 --> 00:34:35,280
+solve
+
+309
+00:34:39,910 --> 00:34:48,770
+لأ differential equation لحل المعادلة التفاضلية a1
+
+310
+00:34:48,770 --> 00:34:59,830
+x1 b1 y1 زائد c1 كل هذا مضروب في ال y prime بيساوي
+
+311
+00:34:59,830 --> 00:35:15,500
+a2 x زائد a2 xA1X يا ابناتو B1X يساو as A2X زائد
+
+312
+00:35:15,500 --> 00:35:30,340
+B2Y زائد C2 و examine the following بدنا نختبر ما
+
+313
+00:35:30,340 --> 00:35:34,280
+يأتي النقطة
+
+314
+00:35:34,280 --> 00:35:34,660
+الأولى
+
+315
+00:35:37,390 --> 00:35:51,310
+إذا الـ A1 في الـ B2 بتسوي A2 في الـ B1 نحل بالروح
+
+316
+00:35:51,310 --> 00:36:02,110
+نحل نحل بالروح نحل as the final example
+
+317
+00:36:03,880 --> 00:36:14,260
+as a final example in section واحد اتنين نقطة
+
+318
+00:36:14,260 --> 00:36:26,980
+ثانية if ال a1 b2 لا يسوى ال a2 في ال b1 we use
+
+319
+00:36:26,980 --> 00:36:31,620
+the transform
+
+320
+00:36:34,360 --> 00:36:43,440
+و نستخدم الـ transform اللي هو X يسوى X كابتل زائد
+
+321
+00:36:43,440 --> 00:36:56,380
+P و Y يسوى Y كابتل زائد Q حيث
+
+322
+00:36:56,380 --> 00:37:01,220
+ال P و ال Q هي الحل
+
+323
+00:37:07,180 --> 00:37:15,540
+is the solution of the system
+
+324
+00:37:15,540 --> 00:37:20,440
+of equations
+
+325
+00:37:20,440 --> 00:37:24,020
+a1p
+
+326
+00:37:24,020 --> 00:37:37,900
+زائد b1q زائد c1 يساوي zero و a2pزائد بيتو اكيو
+
+327
+00:37:37,900 --> 00:37:46,700
+بيتو اكيو زائد C2 بده يساوي مين؟ بده يساوي Zero
+
+328
+00:38:33,240 --> 00:38:39,670
+Y' يسوى المقدار هذا على المقدار هذاأو ضربنا
+
+329
+00:38:39,670 --> 00:38:43,270
+الطرفين في المقام فصرت على الشكل اللي قدامي هذا
+
+330
+00:38:43,270 --> 00:38:48,250
+يبقى الشكل اللي قدامي هذا او y prime يساوي هذا على
+
+331
+00:38:48,250 --> 00:38:52,510
+الجثة سيان كل واحد طيب انا عندي معادلة بشكل لأن
+
+332
+00:38:52,510 --> 00:38:57,450
+انا بداجي احل هذه المعادلةيا بنات في عند المعادلة
+
+333
+00:38:57,450 --> 00:39:02,650
+أحيانا بتكونش homogeneous لكن أنا بقدر بطريقة ما
+
+334
+00:39:02,650 --> 00:39:06,710
+أحولها إلى homogeneous differential equation وإذا
+
+335
+00:39:06,710 --> 00:39:09,970
+حولتها بقدر أحلها بالطريقة اللي حلناها بالمثالين
+
+336
+00:39:09,970 --> 00:39:15,070
+السابقين قبل قليل طبعا يبقى إذا عندي مثلة من هذا
+
+337
+00:39:15,070 --> 00:39:19,850
+القبيل وهذه ليست homogeneous بده أطلع على شغلين
+
+338
+00:39:19,850 --> 00:39:29,140
+الشغل الأولى هل a1 في ال b2مع الـ A2 في الـ B1 هل
+
+339
+00:39:29,140 --> 00:39:33,740
+هدول بيساووا بعض؟ والله بيساووش والله إذا كان هدول
+
+340
+00:39:33,740 --> 00:39:38,140
+بيساووا بعض بنروح أنحل المعادلة هذه زي آخر مثال
+
+341
+00:39:38,140 --> 00:39:42,160
+أخدناه في المحاضرة الماضية بصير عندي جوس كله
+
+342
+00:39:42,160 --> 00:39:47,600
+بعتبره variable جديد جوس بيحتوي على X و Y بشيله
+
+343
+00:39:47,600 --> 00:39:52,500
+بحطه variable وليكن V وبالتالي بصير عندي separable
+
+344
+00:39:52,500 --> 00:39:56,700
+differential equationوإذا ما كانش وفي الغالب ما
+
+345
+00:39:56,700 --> 00:40:01,940
+بيكونش وإذا ما كانش بنجي للنقطة الثانية يعني فباجي
+
+346
+00:40:01,940 --> 00:40:06,600
+بقول لو كان ال a1 في ال b2 لا يسوى ال a2 في ال b1
+
+347
+00:40:06,600 --> 00:40:13,030
+شو بنعمل؟ we use the transfer بنعمل تحويلة جديدةشو
+
+348
+00:40:13,030 --> 00:40:20,210
+التحويل الجديد هذه؟ بحط x small اللي عندى هذه او x
+
+349
+00:40:20,210 --> 00:40:26,450
+هذه بx capital زائد رقم و ال y small بy capital
+
+350
+00:40:26,450 --> 00:40:32,240
+زائد رقممين هو الرقم هذا ا؟ باجي على المعادلة هذه
+
+351
+00:40:32,240 --> 00:40:37,380
+و بسويها بالصفر بعد ما اشيل ال X و احط مكانها بيه
+
+352
+00:40:37,380 --> 00:40:41,900
+و اشيل ال Y و احط مكانها لكيو و باجي على المعادلة
+
+353
+00:40:41,900 --> 00:40:46,500
+هذه كمان و بسويها بمين بالصفر يبقى انا المثل
+
+354
+00:40:46,500 --> 00:40:53,440
+بمتغير جديد بده اسمي X كابتل زائد ال Pوالـ Y أسمه
+
+355
+00:40:53,440 --> 00:40:58,020
+اللي بدي أسميه Y كابتل زائد Q اللي طالع تاندي بعد
+
+356
+00:40:58,020 --> 00:41:03,760
+هيك بدي أشيل كل X و أحط مكانها X زائد P في
+
+357
+00:41:03,760 --> 00:41:08,820
+المعادلة هذه و هذا بدي أحط Y كابتل زائد Q والتاني
+
+358
+00:41:08,820 --> 00:41:12,820
+هذي زيها لما أعمل هيك عارفين إيش بعمل لما أعمل
+
+359
+00:41:12,820 --> 00:41:18,710
+هذا؟بطير الثابت اللى عندى C2 وC1 بتخلص من الثوابت
+
+360
+00:41:18,710 --> 00:41:23,950
+اللى بسببه للمشكلة لأن وجودهم لو جسمت على X و لو
+
+361
+00:41:23,950 --> 00:41:27,890
+جسمت على Y بتبطل الصيرة homogeneous لكن لما حط
+
+362
+00:41:27,890 --> 00:41:31,470
+التعويض هذه بطيروا الثابت لو ما طروش الثوابت
+
+363
+00:41:31,470 --> 00:41:35,730
+معناته في شغل غلط عندك الغلط في حساب ال P و ال Q
+
+364
+00:41:35,730 --> 00:41:40,440
+أو في التعويض عندكيبقى بعد ذلك تتحول إلى
+
+365
+00:41:40,440 --> 00:41:45,320
+homogeneous differential equation يعني فائدة هذه
+
+366
+00:41:45,320 --> 00:41:51,220
+التحولة اتحول المعادلة من non homogeneous إلى
+
+367
+00:41:51,220 --> 00:41:55,260
+homogeneous differential equation وبالتالي بنروح
+
+368
+00:41:55,260 --> 00:42:01,160
+نحلها زي ما كنا بنحل المثالين قبل قليل واضح كلامي؟
+
+369
+00:42:01,440 --> 00:42:07,620
+يعني هذه الملاحظة أو هذا النوع من المسائل بنلجأ له
+
+370
+00:42:07,620 --> 00:42:11,620
+إذا طلعت المعادلة اللى عندي ماهياش متجنسة زى ما
+
+371
+00:42:11,620 --> 00:42:16,560
+سألتي قبلها قلت يمكن ماتطلعش متجنسة بقولك في طرق
+
+372
+00:42:16,560 --> 00:42:20,680
+أخرى أو في معادلة أخرى بروح أختبرها إيش أخدناه
+
+373
+00:42:20,680 --> 00:42:24,920
+وإيش ماخدناهوش هذا .. هذا احنا أخدناهاإن المعادلة
+
+374
+00:42:24,920 --> 00:42:30,860
+هذه ممكن أحولها إلى معادلة متجنسة كيف؟ بالطريقة
+
+375
+00:42:30,860 --> 00:42:36,220
+التالية بمسك كل معادلة من المعادلتين هدول و بسويها
+
+376
+00:42:36,220 --> 00:42:41,900
+بالصفر و بحلف تنتين و بجيب قيمة x و y بعد هيكبكتب
+
+377
+00:42:41,900 --> 00:42:49,980
+المعادلة بدلالة variable جديد XY X أساسي بحط X
+
+378
+00:42:49,980 --> 00:42:53,980
+كابتل زائد الرقم اللي طالع عندي و Y أساسي بحط Y
+
+379
+00:42:53,980 --> 00:42:56,980
+كابتل زائد الرقم اللي طالع عندي وبعوض في المعادلة
+
+380
+00:42:56,980 --> 00:43:01,020
+الأصليه اوتوماتيك لازم تنقلب الى homogeneous
+
+381
+00:43:01,020 --> 00:43:04,380
+differential equation اذا ما طلعتش homogeneous
+
+382
+00:43:04,380 --> 00:43:07,660
+differential equation بدك تراجع حسابتك معناته غلط
+
+383
+00:43:07,660 --> 00:43:09,040
+في شغلة تمام
+