Standart funktsiyalar - Mapleda nomli va nomsiz buyruqlar bajartirilishining ikki XIL o`suli Standart funktsiyalar

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Mapleda nomli va nomsiz buyruqlar bajartirilishining ikki XIL o`suli Standart funktsiyalar
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bet | 2/2 | Sana | 29.11.2023 | Hajmi | 52,59 Kb. | | #107803 |
Bog'liq Maple muhitida hisoblashlarStandart funktsiyalar.
Maple da standart funktsiyalarning ayrimlarini ro’yxatini keltiramiz:
N
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funktsiya
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Maple da
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N
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funktsiya
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Maple da
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1
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exp(x)
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12
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cosecx
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cosec(x)
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2
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lnx
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ln(x)
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13
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arcsinx
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arcsin(x)
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3
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lgx
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lg10(x)
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14
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arccosx
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arcos(x)
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4
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log[a](x)
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15
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arctgx
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arctg(x)
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5
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sqrt(x)
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16
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arcctgx
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arcctg(x)
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6
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abs(x)
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17
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shx
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sh(x)
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7
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sinx
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sin(x)
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18
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chx
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ch(x)
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8
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cosx
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cos(x)
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19
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thx
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th(x)
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9
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tgx
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tg(x)
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20
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cthx
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cth(x)
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10
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ctgx
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ctg(x)
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21
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-Dirak funktsiyasi
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Dirac(x)
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11
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secx
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sec(x)
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22
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-Xevisayd funktsiyasi
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Heaviside(x)
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Maple ga juda katta miqdorda maxsus funktsiyalar ham kiritilgan. Ular Bessel, Eylerning beta-, gamma-funktsiyalari, xatoliklar integrali, elliptik integrallar, har xil ortogonal ko’phadlar va hokazo. Eyler soni ye=2.718281828…. exp(x) orqali quyidagicha hisoblanadi: exp(1).
Topshiriq №1.3.
1. Matnli rejimda Amaliy topshiriq №2 deb yozing.
2. ni hisoblang.\\(t.10-2-58;j:0;1;-1;0.5;-0.5)
Komandani 1-to’g’ri o`sul bilan bajaramiz:
> a:=cos(12*Pi*(log[2](0.25)+log[0.25](2))/5);\\a:=1.
3. ifodani hisoblang.
Komandani smart o`sul (o’ngdagi jadval kontekst menyu)bilan bajaramiz:
>b:=(sin(Pi/8))^2+(cos(3*Pi/8))^2+(sin(5*Pi/8))^2+(cos(7*Pi/8))^2;
> R3 := evalf[5]( sin(1/8*Pi)^2+cos(3/8*Pi)^2 +sin(3/8*Pi)^2+cos(1/8*Pi)^2 ); \\R3:=2.0000
Komandani to’g’ri o`sul bilan tekshirib ko’ramiz:
> simplify(b); \\2
Ayrim ko’p uchraydigan buyruqlar va ularga doir misollar keltiramiz.
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Komanda
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Ma’nosi
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Parametrlaning ma’nosi
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1
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expand(eq)
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Qavslarni ochib yoyish
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eq-ifoda
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2
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fastor(eq)
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Ko’phadni ko’paytuvchilarga ajratish
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3
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normal(eq)
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Kasrni normal ko’rinishga keltirish
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4
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collect(eq, var)
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O’xshash hadlarni ixchamlash
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var-o’zgaruvchi
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5
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simplify(eq {,option})
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Ifodalarni soddalashtirish
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option-parametr
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6
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combine(eq, param)
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Darajalarni birlashtirish yoki trigonometrik ifodalarni darajalarini pasaytirish
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param=trig,
param=power,
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7
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radnormal(eq)
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Ildiz, darajali ifodalarni soddalashtirish
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8
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convert(eq,param)
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Ifoda param tipli ifodaga almashtiriladi
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param- tip parametr
param=sincos, param=tan,
param=vector, param=string,
param=termin
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9
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subs(g(x)=t, f)
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f(x) da g(x)=t deb o’zgaruvchini almashtirish
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Topshiriq 1.4.
1. Qavslarni ochib yoyish.
>eq:=(x+1)*(x-1)*(x^2-x+1)*( x^2+x+1); \\ >expand(eq); \\x^6-1
2. Ko’phadni ko’paytuvchilarga ajratish (99-10-7)
> p:=a^5+a^4-2*a^3-2*a^2+a+1; \\
>p:=factor(a^5+a^4-2*a^3-2*a^2+a+1);\\
3. Kasrni normal ko’rinishga keltirish (96-3-74)
> q:=(x^3+2*x^2+x)/(x+1)^2; \\
> normal(%); \\ x
4. Ifodalarni soddalashtirish
> simplify((a^3-b^3)/(a^2+a*b+b^2)); \\a-b
> expand((a+b)*(a^2-a*b+b^2)); \\
> normal(y/x+1/x^2); \\
> collect(x^2+3*x^2+4*x+4*x+y,x); \\
> simplify(2*a/sqrt(a^2),assume(a<0)); \\-2
> combine((x^(1/2))*x^(3/2)); \\
5. Irratsional ifodalarni ratsionallashtirib soddalashtirish
> f:=((sqrt(x)+1)/(x*sqrt(x)+x+sqrt(x)))*(x^2-sqrt(x));
> g:=subs(sqrt(x)=a,x^2=a^4,x^(3/2)=a^3,x=a^2,f);
> R2 := simplify( (a+1)*(a^4-a)/(a^3+a^2+a), 'assume=real' );
Oldingi o’zgaruvchiga qaytib x-1 javobni olamiz.
6. Trigonometrik ifodalarni soddalashtirish
> simplify(cos(x)^2+sin(x)^2); \\1
> expand(cos(x+y)); \\cos(x)cos(y)-sin(x)sin(y)
> expand(cos(2*x)); \\
> expand(sin(2*x)); \\ 2sin(x)cos(x)
> combine(4*cos(x)^3); \\ cos(3x)+3cos(x)
> combine(8*sin(x)^4); \\ 3+cos(4x)-4cos(2x)
> expand(cos(5*x)); \\
>combine(4*sin(x)^3,trig); \\-sin(3x)+3sin(x)
7. Ildiz, darajali ifodalarni soddalashtirish
> a:=sqrt(3+sqrt(3)+(10+6*sqrt(3))^(1/3)):
> a1:=radnormal(a);\\
8.> b:=(m^2-(2+m^4)/(m^2-1))/((m^2+2)/(m-1)):
> b1:=simplify(b);\\b1:=-1/(m+1).
9. > c:=(a^(3/2)-b^(3/2))/(a^(1/2)-b^(1/2))-(a^(3/2)+b^(3/2))/(a^(1/2)+b^(1/2));
> c1:=simplify(c); \\
> a:=8*sqrt(2):b:=4*sqrt(2):
> c1:=simplify(c); \\c1:=16
10. > a:=(sqrt(192)-sqrt(108)+sqrt(243)/3);\\ (99-6-36)
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