Best online resource to help with Calculus III? - Page 1
Forum section: electronics / general

author: trilerian
author_rank: Regular Contributor
timestamp: September 30, 2024, 03:37:49 am
content: A little back story here. I think I made a horrible decision... I got into designing electronics a year and a half ago. Lots of research, yada, yada. I came to the conclusion that my knowledge was fundamentally lacking and figured school would be the best place to go. So at almost 50 years old I decide to go back to school for my EE degree. I got my associates a long time ago, lol and I got into IT right after getting it, so using calculus is not really part of my job. Now, I got As in both calc I and II, but I am seriously suffering from CRS as it pertains to calculus and am having an awful time with calc III.I work a full time job, run a side business on top of that, and am taking 9 credit hours this semester. My other 2 classes are engineering classes, and are going ok. Ok, so I took my first exam last week and got a B-. I started studying for this exam in week 1, and I found a way to study at least 20 hours a week for it, yet I still got a B-. There is just too much stuff I am trying to cram into my head and I forget steps and just struggle trying to remember how to do something. Not to mention I am awful at the quadric surfaces and such.So that is behind me, now I am getting into partial derivatives and double integrals, and well, I'm in over my head. I want to quit every day. If I can't pass calc III there is no point in going any farther since both calc III and IV are required for an EE degree.School resources are difficult for me to use since I have a fulltime job, my instructor, well I can't understand her. My hearing isn't what it used to be either (getting hearing aids in a couple of months, but everything moves slowly for those around here), but my instructor has an accent that I have difficulty with. Now the TA who does recitation is great, but I only get 2 hours a week with him, so...Anyway, I'm looking for a really good online resource to help me with Calc III. I have found some good Youtube instructors, The Organic Chemistry Tutor is one. Khan Academy pops up on some stuff I search as well, and ChatGPT has been great. I never actually used it before this class, lol. But at least it gives me all the steps to a problem, and is mostly right... I've been making do with this combination, but I am really hoping there is a better solution out there.

author: Smokey
author_rank: Super Contributor
timestamp: September 30, 2024, 03:54:19 am
content: Quote from: trilerian on September 30, 2024, 03:37:49 amwelcome to an engineering degree programGreat job getting at it!my 2c. You want a real live human 1 on 1 tutor to target exactly what you are having issues with, not generic online stuff. Go talk to the math department. There will be someone (probably a grad student) willing to do some by the hour tutoring around your schedule.

author: 5U4GB
author_rank: Super Contributor
timestamp: September 30, 2024, 07:24:36 am
content: Another resource I could highly recommend is Silvanus Thompson's "Calculus Made Easy", which is a significant improvement over anything written since. It's freely available online astextoran audiobook, although you really want the printed/written form for the diagrams and notation. You can also get it for a few dollars from any source of secondhand books.I'd also recommend getting one that hasn't been updated for current usage, it's kinda cool reading a text written by someone who was a contemporary of Lord Kelvin.

author: coppercone2
author_rank: Super Contributor
timestamp: September 30, 2024, 08:35:02 am
content: have you considered really small binoculars?what would be interesting is if they made some realistic problems about something with electronics related to it. then it might be possible to pay attention and have learned something useful.

author: 10101
author_rank: Contributor
timestamp: September 30, 2024, 09:25:03 am
content: These are the ones that i saw were some of the most helpful (besides the ones you said)Written resource:https://tutorial.math.lamar.edu/Video resources:https://www.youtube.com/@ProfessorLeonard/featuredhttp://www.ilectureonline.com/lectures/subject/MATH/22Good luck

author: EPAIII
author_rank: Super Contributor
timestamp: October 04, 2024, 09:18:46 am
content: Small binoculars?I guess I'm dense. I don't get it. I'm not even sure which post it refers to.If you want to see problems about electronics you will need to go to the EE department. And the ME department for mechanical engineering problems. Etc. The math guys are going to teach generic math and have their hands full at that.Quote from: coppercone2 on September 30, 2024, 08:35:02 am

author: rstofer
author_rank: Super Contributor
timestamp: October 04, 2024, 05:34:38 pm
content: <removed link to Khan Academy>It costs money but Calc Workshop is VERY goodhttps://calcworkshop.com/calculus-3/Then there's MATLAB which does everything but eat (DEBE). Free to students, cheap for personal license.https://www.mathworks.com/help/matlab/ref/integral2.htmlSymbolab for solving:https://www.symbolab.com/solverDesmos for graphing (now integrated with symbolab)https://www.desmos.com/

author: SteveThackery
author_rank: Super Contributor
timestamp: October 07, 2024, 11:33:48 pm
content: My question: do any EEs here actually use Calc III to do their work?

author: HuronKing
author_rank: Frequent Contributor
timestamp: October 08, 2024, 12:06:20 am
content: Quote from: SteveThackery on October 07, 2024, 11:33:48 pmI guess it depends on what type of work you end up doing - but I can tell you that I have.One cannot understand Maxwell's Eqns without Calc III - they're all partial differential/integral vector equations.And when I was on a path towards designing conical spiral and patch antennas for micro-satellites, I used HFSS from Ansys to simulate their performance for my supervisor. One would have no hope of understanding how to use the Fields Calculator in the software if one didn't have a foundational knowledge of calculus of vector fields. The Fields Calculator will do the math for you, but you have to know what equation and boundary conditions to feed it for analysis:The EE who will spend their career calculating residential power consumption and affixing their PE stamp to a set of drawings for permitting purposes on a home probably/definitely has no daily need for Calc III... whereas the EE who wants to simulate the performance of an antenna absolutely needs to know Calc III just to use the software.Besides, from a purely philosophical point of view its important to make EEs learn Calc 3 since its the calculus of 3-dimensional space and we live in a 3-dimensional world.@The OPFirst off, you deserve kudos for doing something INCREDIBLY difficult - trying to get an EE degree. It's not easy. I have sometimes taught students who were much like you (trying to get their degree well into their careers) and it's even harder than it is for students in their 20s for all the reasons you know.Second, a lot of the resources that have been posted here I'd recommend as well. When I was a student I volunteered in the math department tutoring center (it got me on a list that went out to the school district so I could charge big money for private tutoring). Your school probably has a similar center.Third, from a purely approach point of view, if you conquered Calc 1 and Calc 2, Calc 3 is just those but for 3-dimensional space.

author: BILLPOD
author_rank: Frequent Contributor
timestamp: October 08, 2024, 07:29:30 pm
content: Has it been determined how the small binoculars will help

author: Bicurico
author_rank: Super Contributor
timestamp: October 09, 2024, 08:03:11 am
content: As a student in my 18-24 age, I had to learn incredibly difficult to understand concepts, which I then never used again. Part of this is to make sure an engineer is able to overcome his limitations.If you had straight A's in Calc 1+2, a B- should not be a deterrent at all. You cannot excel always. Congratulations for having done so much already.Just openly discuss your issues with your math teacher and see what options can be offered to you.And if you dedicate 20h/week, you can be sure you work much more than most of your younger student colleagues.

author: jonpaul
author_rank: Super Contributor
timestamp: October 09, 2024, 09:22:43 am
content: FIND AND READ A BOOKOnline and videos WILL NOT teach you.Learning takes time and effort there is no shortcutj

author: DimitriP
author_rank: Super Contributor
timestamp: October 09, 2024, 09:38:33 am
content: QuoteYou should get A+ for perseverance. I've walked out of conference presentations when incomprehensible accents were involved.I don't mind accents. I don't mind strong accents. But there is a limit.One of the reasons why courses have a "last day to drop the class with a refund" !

author: coppercone2
author_rank: Super Contributor
timestamp: October 09, 2024, 10:56:23 am
content: Quote from: DimitriP on October 09, 2024, 09:38:33 amthat comes in hand 1% of the time, usually if you make the slightest of deviations it extends your stay by 1 year in a university for engineering.they know you are dependent on them for time tableswhats that like save 500 spend 20k?

author: trilerian
author_rank: Regular Contributor
timestamp: October 09, 2024, 10:23:24 pm
content: It's been a minute since I checked into this post. Don't exactly have a lot of free time on my hands now, lol. But since I have posted this I did get my exam back. I was 2 stupid mistakes away from an A-, so not as bad as I originally thought. And now we are off into the world of partial derivatives, which seem much easier than the last topic.Someone mentioned professor Leonard. Well, that was a great suggestion. He is even better than the Organic Chemistry Tutor, the only thing is you are in for a full lecture. Someone else mentioned Matlab. I do have an educational license to Matlab, as I use it is my two engineering courses, but I haven't explored its usefulness for studying math.I think someone said find a book cause learning takes time. I am absolutely positive I could learn calc III from a book, but not in the time frame for the class.But for now, I go to class then go learn it online.Professor Leonard - Great full lectures, wish this guy was my instructor.The Organic Chemistry TutorKhan AcademyChatGPT - Surprisingly useful!I don't want people to get the wrong idea. I really like the course material. I enjoy math, always have, and this course is my favorite course this semester. I want to learn the material, and my TA gave an anecdote about one of his EE friends saying calc III is the most useful to his line of work. I guess, I just haven't been to school in a long time, and it is a whole lot more work than I remember.

author: KE5FX
author_rank: Super Contributor
timestamp: October 09, 2024, 10:51:36 pm
content: You'll catch a lot of grief from various quarters if you even mention ChatGPT, but it's nothing less than a superpower if you know how to use it. It's like having your TA's number 24/7.Tip: sign up for Google Gemini access as well as GPT4 o1-preview, and play them off against each other. This is turning out to be a pretty useful strategy.You will have to learn to recognize hallucination and prevarication in all sorts of brand-new forms, but anyone who plans to remain alive over the next 10 years is going to have to do that anyway.

author: IanB
author_rank: Super Contributor
timestamp: October 09, 2024, 10:52:58 pm
content: As someone who has not been through the American education system, it is hard to know what lies behind these mysterious labels of "Calculus I", "Calculus II", "Calculus III", etc.Although, as someone who really likes mathematics, I can tell you that learning how to manipulate symbols, and rearrange things, and follow rules by rote, in a manner that is often taught, never worked for me. It was just too painful and hard to remember.What I have found most helpful is when I am able to understand underlying concepts, and appreciate what is going on. To understand why the various rules actually work. Along these lines, I think the progression from "I" to "II" to "III" to "IV" is meant to gradually build on what has gone before in small steps, to help understanding grow.I don't know how long ago you did Calc I and Calc II, but if there is a gap it might be adding to your problems? Maybe it could be worth going back over that earlier material and refreshing your understanding of it, and see how it naturally progresses into Calc III (which it should)?Sometimes you can go back to earlier material that you might have learned a bit by rote, and with fresh eyes you might find you start to understand the "why" of it a little better.Not sure if any of this will help, but just some random thoughts.

author: trilerian
author_rank: Regular Contributor
timestamp: October 09, 2024, 11:25:11 pm
content: Quote from: IanB on October 09, 2024, 10:52:58 pmThe basics, calc III is calc I and II (differentiation and integration) in 3d space. And yes, the amount of time since I have taken calc I and II is an issue as I have to relearn some of the concepts again. For example, I remember how to do basic derivatives and integrals. But things like the chain rule and u substitution I had to relearn. Trying to remember all the trig identities again, etcetera. With integrals learning integration by parts again and then just re learning all the weird rules for ln(x) or e^x. And then the graphing of 3d functions, yeah. The other day in class Taylor series were mentioned again. I'm pretty sure I forgot what those are just like you forget how much pain you were in from a broken bone. And yes, I did pick up a calc I, calc II, and calc III text books, and I have looked through calc I and II to help out.

author: trilerian
author_rank: Regular Contributor
timestamp: October 09, 2024, 11:36:35 pm
content: Quote from: KE5FX on October 09, 2024, 10:51:36 pmI'll give that a try. I have been quite impressed with ChatGPT so far, although it isn't always correct. It has returned incorrect results for the determinants of matrices a few times, and it misses things in partial derivates as well, but I am not just copying the answers down. I go through the steps and if I don't understand a step I just ask for it to explain that step differently, then I work out the solutions for myself. I don't think AI is going to go away, so may as well learn to use it. It is going to be a tool, just like any other that needs to be mastered to be successful in the future.

author: IanB
author_rank: Super Contributor
timestamp: October 10, 2024, 12:15:51 am
content: Quote from: trilerian on October 09, 2024, 11:25:11 pmAh, I see. The question, "How do you differentiate a vector function?" is a very deep question, that is a bit of a jump from differentiating scalar functions.QuotePicking out a few things:The chain rule is one of those things that it really helps to understand why it works, rather than just remembering the rule. Whenever I use the chain rule, I am always thinking, "Why am I doing this thing that I'm doing?" If you know why it works, you can forget the rule itself, because you can immediately get the rule back when you need it. The same with integration by parts. Such as this recent video by Michael Penn, where he showed "Integration by Parts" without doing Integration by Parts! I always keep that picture in my head, because it adds so much clarity to the method:Trig identities, nobody remembers all of those. Normally they should come in a formula booklet. I remember the basic ones, but all the others I look them up when needed.Taylor series. Can I recommend some videos from 3Blue1Brown, like this one? He has a whole playlist, "The Essence of Calculus", that is worth watching. Even if you know the material, there is probably something new you will get out of it.

author: IanB
author_rank: Super Contributor
timestamp: October 10, 2024, 12:24:55 am
content: Quote from: trilerian on October 09, 2024, 11:36:35 pmA word to the wise. Never, under any circumstances, trust any numerical or quantitative results from ChatGPT or similar LLM tools. They do not have any real understanding of what they are doing, and they cannot calculate things. They simulate understanding by giving very complex responses that make it seem like they understand what you are asking, but it is all a pretense. There is no actual brain behind the machine.A major area of AI research is to make the leap from simulated cognitive ability to real cognitive ability.

author: KE5FX
author_rank: Super Contributor
timestamp: October 10, 2024, 01:33:45 am
content: Quote from: IanB on October 10, 2024, 12:24:55 amThey can write programs that calculate things.That's actually niftier than just calculating things.QuoteYou're evidently far enough behind the curve that you may not recognize it when it happens.

author: IanB
author_rank: Super Contributor
timestamp: October 10, 2024, 02:39:07 am
content: Quote from: KE5FX on October 10, 2024, 01:33:45 amThat's funny. Have you seen the example where ChatGPT said this?QuoteExcept if you actually ran the program, it would output Y instead. (Which was not X)ChatGPT was not clever enough to actually run the program that it wrote. Or to discover as a result that it was wrong. The hubris is immense.QuoteYou live in your world, and I will live in mine. General AI is still a pipedream, in spite of claims that might suggest otherwise. Even the latest generation of LLM models are still "dumb" in the sense of actual intelligence. Rather than being intelligent, they are just executing ever more sophisticated computational algorithms.

author: trilerian
author_rank: Regular Contributor
timestamp: October 22, 2024, 02:12:43 am
content: Exam 2 is on Wednesday. See if I do any better... Bad news is my professor took the exam already and said it was extremely difficult. She said she asked the exam coordinator to make it easier and they said no. Great...

author: trilerian
author_rank: Regular Contributor
timestamp: December 23, 2024, 05:03:42 pm
content: Figured since I started this thread I would put in the last update with how my class ended up. Through the semester I managed to pull my grade right up to the borderline of an A. However the final kicked my butt and I finished 4 points away from an A. The final was cumulative and it was extremely difficult, the average for all calc III classes was a 61%. I managed a B on it, but not high enough to get my A in the class. So frustrating. I put so much time into that class. The good news I guess is that I did learn some stuff for the later classes.

author: coppercone2
author_rank: Super Contributor
timestamp: December 23, 2024, 06:40:49 pm
content: let us know in 10 years when it helped you professionally lol

author: trilerian
author_rank: Regular Contributor
timestamp: December 23, 2024, 07:00:30 pm
content: Quote from: coppercone2 on December 23, 2024, 06:40:49 pmNot sure if this is meant as sarcasm...But regardless, I'm not sure it will ever help me professionally. Going back to school is to help me better understand my hobby. Professionally, I work in IT, I'm not sure I see that changing. I may leverage the degree I get to help me in my current field, but the scope is purely for me.

author: IanB
author_rank: Super Contributor
timestamp: December 23, 2024, 10:20:26 pm
content: Quote from: coppercone2 on December 23, 2024, 06:40:49 pmI'm not sure why you would say that? I use far more advanced and complex mathematics in my professional life than I ever learned at university. It depends on the career path, obviously, but learning foundational mathematics is not something to be dismissive about. You need the foundation as a start to build upon.

author: coppice
author_rank: Super Contributor
timestamp: December 23, 2024, 10:27:20 pm
content: Quote from: SteveThackery on October 07, 2024, 11:33:48 pmI have no idea what it means. The US seems to have split a range of calculus related topics into nationally standardised chunks with associated numbers. If you haven't studied in the US the terms are meaningless. Perhaps there a list of topics, and an idea of how deeply they treat them, in each chunk available on the web somewhere.

author: tggzzz
author_rank: Super Contributor
timestamp: December 23, 2024, 11:04:39 pm
content: Quote from: IanB on October 10, 2024, 12:24:55 amAgreed.LLMs produce sentences (and paragraphs) made up of words that are statistically likely to occur in a given context.Humans who do that are called "bullshit artists". They fool other people who do not understand the subject.

author: tggzzz
author_rank: Super Contributor
timestamp: December 23, 2024, 11:07:25 pm
content: Quote from: trilerian on October 22, 2024, 02:12:43 amAt university my second year maths exam's rubric was "full marks can be obtained for answers toaboutsix questions".

author: trilerian
author_rank: Regular Contributor
timestamp: December 23, 2024, 11:32:49 pm
content: Quote from: coppice on December 23, 2024, 10:27:20 pmHaving just finished my course, I can give you a decent idea of what was covered. Started out with vectors, doing dot products and cross products, so we could learn about planes and normal vectors... From there we got into partial derivatives and got introduced to gradients, and them we moved into double and triple integrals. Once we had that under our belt we started dealing with vector calculus, which seems really relevant to an EE. We used this theorem called the Fundamental Theorem of Line Integrals, basically it boils down to the difference between two points in a conservative vector field is the difference between f(b) - f(a). Almost like measuring the potential difference between two points in an electric field. Of course we didn't get into theory there, just the math, I kind of put two and two together... We finished with Divergence Theorem, Stokes' Theorem, and Green's Theorem.Next semester is nothing to do with being an EE, and I am moving to 2 classes instead of 3. I'll probably be able to do more online learning this way, but 3 in person classes along with a fulltime job and a side business was stretching me quite thin. Especially since I was relearning calc I & II while taking calc III. I think the semester after that I will be taking Physics II and finally starting on EE courses with a Circuits class.I am happy I am going back to school though, I struggled with the decision for a while, but it has been a good experience.

author: tggzzz
author_rank: Super Contributor
timestamp: December 24, 2024, 12:09:12 am
content: Quote from: trilerian on December 23, 2024, 11:32:49 pmI suspect the course will make little difference to your employability, not least because non-technical recruiters can't see past age, experience, personality - and not taking a chance that might backfire on them. Blasted HR droids belong in the Golgafrinchan Ark Fleet Ship B .But if you have enjoyed it, who cares. You've had fun and by learning something new you've demonstrated you are still alive!

author: Analog Kid
author_rank: Super Contributor
timestamp: December 24, 2024, 12:13:30 am
content: Quote from: BILLPOD on October 08, 2024, 07:29:30 pmNot positive but I'd say the guy was referring to cheating on exams.Pure unhelpful snark there.Sure, pass the exam, but have no understanding of the subject matter. Great.I guess that's what some kids today are doing.

author: coppercone2
author_rank: Super Contributor
timestamp: December 24, 2024, 12:59:17 am
content: you will never have a better appreciation of small optics after you see the calculus III that went into making the gradient in the refraction index of miniaturized binoculars

author: MathWizard
author_rank: Super Contributor
timestamp: December 24, 2024, 04:50:07 am
content: I love Calculus, I really need to make time for what ever all Calculus comes after vector C and basic DE's classes. I'm not getting any younger, the clock is ticking.There's lots of full or nearly full course lectures on youtube. But actually these days with all the ads, it's drives me crazy. But there's definitely some good prof's and high quality recordings, and tons of good short video's too on any given topic.I want to start going through some of the video's where people solve 100's of integral equations. I know most of the common ones, but I wonder how many more and what all other techniques there are past under-grad level ??

author: coppice
author_rank: Super Contributor
timestamp: December 24, 2024, 04:19:58 pm
content: Quote from: trilerian on December 23, 2024, 11:32:49 pmInteresting thoughts. Far more EEs are working with dot and cross products day after day than work with vector calculus.