Best online resource to help with Calculus III?

[trilerian]

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. 

[Smokey]

...
 I'm in over my head.  I want to quit every day. 
...

welcome to an engineering degree program   Great 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.   

[5U4GB]

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 as text or an 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.

[coppercone2]

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.

[10101]

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/featured
http://www.ilectureonline.com/lectures/subject/MATH/22

Good luck 

[EPAIII]

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.

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.

[rstofer]

<removed link to Khan Academy>

It costs money but Calc Workshop is VERY good

https://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.html


Symbolab for solving:

https://www.symbolab.com/solver

Desmos for graphing (now integrated with symbolab)

https://www.desmos.com/

[SteveThackery]

My question: do any EEs here actually use Calc III to do their work?

[HuronKing]

My question: do any EEs here actually use Calc III to do their work?

I 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 OP

First 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. 

[BILLPOD]

Has it been determined how the small binoculars will help

[Bicurico]

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.

[jonpaul]

FIND AND READ A BOOK


Online and videos WILL NOT teach you.

Learning takes time and effort there is no shortcut

j

[DimitriP]

but my instructor has an accent that I have difficulty with.

You 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" !

[coppercone2]

but my instructor has an accent that I have difficulty with.

You 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" !

that 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 tables

whats that like save 500 spend 20k?

[trilerian]

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 Tutor
Khan Academy
ChatGPT - 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. 

[KE5FX]

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.

[IanB]

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.

[trilerian]

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.

The 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.

[trilerian]

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.

I'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. 

[IanB]

The basics, calc III is calc I and II (differentiation and integration) in 3d space.

Ah, 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.

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.

Picking 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.

[IanB]

I'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

A 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.

[KE5FX]

A 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 can write programs that calculate things.

That's actually niftier than just calculating 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.

You're evidently far enough behind the curve that you may not recognize it when it happens.

[IanB]

A 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 can write programs that calculate things.

That's actually niftier than just calculating things.

That's funny. Have you seen the example where ChatGPT said this?

Here's a program that will calculate what you want. When you run this program it will output X

Except 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.

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.

You're evidently far enough behind the curve that you may not recognize it when it happens.

You 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.

[trilerian]

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...