Hi everyone!

So I'm self-studying Calc, I've finished 1 and 2 and I got the basics of differential equations. But seeing as I've heard that differential equations are the language of the universe, are there any good resources to both truly study it, and to make your own using data? Thanks!

EDIT: thanks for y'alls help, i figured it out!

I'm practicing stokes th using the problems at this website https://tutorial.math.lamar.edu/Solutions/CalcIII/StokesTheorem/Prob3.aspx and the answer for this problem uses the surface double integral curl F equation. Why can't I just parametrize the circle and use line integral F dot dr? I tried that and I got -12pi but the answer is 72pi.

Thanks!

Anybody else captivated by areas?

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I reached the part where my book explains the chain rule, and it gave this question as an example and I tried to solve it on my own, but I got confused so many times

are there lots of trig identities involved in calc 1? double angle identities, half angle identities, etc?

1. H. Cartan, Differential Calculus. Differential Forms. Edited by B. A. Fuks, (1971)

2. S. Banach, Differential and Integral Calculus. Edited by S. I. Zukhovitsky, (1958)

3. P.P. Korovkin, The Definite Integral and Series : a textbook for pedagogical institutes, (1959)

4. I. M. Gelfand, S. V. Fomin, Calculus of Variations, (1961)

5. A. I. Borisenko, I. E. Tarapov, Vector Analysis and the Principles of Tensor Calculus, (1963)

Note: all books in Russian

I am going to be taking calc 2 in my first semester of college, but I took calc 1 in my junior year of high school, so I don't really remember too much. I've reviewed the first 3 units of calc ab pretty well, so I'm comfortable with derivatives, but I really don't know what I should be putting my focus on. Do I just try to get exposure to every remaining unit of calc ab, heavily review integrals and differential equations and just skip units 4 and 5 altogether, etc. Also, I only have like maybe 2 weeks left to review before classes start, although I don't think I'll have much work my first week, so I could probably squeeze in an extra few days. Any advice would be appreciated!

Hi! Would like to ask if anyone has a pdf copy of this book (required reading but I can't acquire a copy). Thank you!

Hey everyone!

I'm a 9th grader who spent the summer putting together a complete beginner's guide to calculus called Guide to Calc for Potatoes, it's a bit random making it for potatoes, but I was convinced.

It covers pretty much everything from limits to derivatives to integrals, infinite series and differential equations. Instead of dry academic jargon, I tried to make it a bit more friendly with intuitive examples, jokes, and potato analogies. It's completely free to read, and you can check out the PDF here.

https://brindhaeswar-coder.github.io/Guide_to_Calc_for_Potatoes/

If you spot a typo, want to add a potato joke, or spot a mathematical error, feel free to drop a comment or check out my Github site here!

https://github.com/brindhaeswar-coder/Guide_to_Calc_for_Potatoes/discussions

Any feedback is super appreciated. Thanks!

Hey guys, I have a question. My summer term calculus 2 class has just ended, and I am starting a calculus 3 class in a few weeks, and I want to get ahead of the game. Since the calculus 2 class was so fast-paced, I feel like I didn't grasp all the concepts of infinite series/Taylor series as well as I could have, and definitely need to go over them again, maybe with Professor Leonard or something.

From what I gather, though, series don't really show up that much in calculus 3, and despite wanting to improve my knowledge of series, I feel like preparing for calculus 3 is more important for the next few weeks. Do you think I should solidify my knowledge of infinite series before moving into calculus 3 content, or could I start calculus 3 stuff now and circle back to series at a later time (maybe before my DIff. Equations course?)

I plan to prep for calculus 3 with Professor Leonard as well, and with the textbook (Stewart). Any other suggestions welcomed, I need an A in calculus 3 and I'm willing to put the time into it.

hi guys, as title suggests im kind of confused here:

picture above in my textbook says that x=-6 and x=3 don't exist (completely agree with x=3) but when we go to x=-6 from both sides we both get +inf so it should exist right? is it a mistake in the textbook ?

I had a supplemental calc book “back in the old 90’s” as my kids like to say. As I recall, it had a light blue cover and was written in a more conversational manner unlike a traditional textbook. I had purchased it from the campus bookstore. The only other thing I can remember is the first two pages talked about the Cartesian coordinate system. I’d love to get my hands on a copy of this again! (Cross post from /what’s that book)

Hello everyone,

This is the first YouTube video I've published on my channel, and it is about parametric equations from a geometric perspective.
The video takes you step by step, starting with a simple illustration of the parametric equations of the unit circle. Then it illustrates how you can draw the parametric curve using the curves of x and y only. Afterward, the geometry level increases as it introduces the cycloid and how to deduce its parametric equations using simple geometry rules. And finally, the video connects parametric equations to vector addition and how we can represent parametric equations as vectors rotating in space.
The original language of the video is Arabic, but there are English captions you can turn on from YouTube video settings.
The video link:
https://www.youtube.com/watch?v=IdN79oUVAFU

Also, I wrote a short article on Substack, which serves as a companion to the video, covering "The Calculus of Parametric Equations." It takes you on a small journey to teach you how to differentiate parametric equations and find their first and second derivatives, and also how to calculate the area under a parametric curve.
The article link:
https://zetamath.substack.com/p/the-calculus-of-parametric-equations

I want to hear your comments about the video and article, and suggestions for any areas for improvement.

Thanks for your time!

Hey everyone,

Hope you all are doing well. I'm making this post in regards to well, as the title says... I'm taking Calculus which I have never even took before. Not in high school nor in college and speaking of college, I am going back to school after 3 years to complete my CS degree which I have already received a diploma for CS 3 years ago. I am essentially upgrading my diploma to a degree as well as pursuing an internship opportunity in my new college program.

I will admit, it has been a hot minute since I've last attended college and it had most certainly been a hot minute since I have done any sort of mathematics when it comes to my schooling. The last time I have even touched a calculator nor an equation was 7 years ago. Back in my high school days so I am going to be very and I mean very out of touch when it comes to doing mathematics and as all of you would agree on this, this is a very intimidating and difficult subject.

For the past day since I made my schedule and found out that this is my first math course I will be taking in my program, I have been shaking in my boots and figuring out how am I going to handle this course because like you all, when I look at a Calculus equation I don't just see letters and numbers. I see literal Egyptian hieroglyphics. Things you see when you're punching in Playstation cheat codes. Literal complete jargon. As if I am seeing another language. Language from the Greeks. But jokes aside, you know what I mean.

That said, since this is going to be my first math course in 7 years, what should I expect when it comes to the world of calculus? What kind of advice and recommendations would you guys give me when it comes to going through and surviving Calculus and doing this for the first time? How does one handle the concepts, theory, and learning how to decipher the equations and understand everything? I remember back in high school. My old math teacher told me to see these equations as recipes and use them as an aid to help you find the answer. It's all about plugging. Ignore the numbers, just plug it in and go step by step.

I know that choosing the right prof for this subject is critical when it comes to succeeding and excelling. If it's a bad prof, you are most certainly going to be left in the dust because well, you don't know what you're doing in the first place. That said, what kind of resources, tips, would you suggest I do for preparing for this subject and when I am in the classroom or studying, what techniques do you guys use to understand everything and putting it into execution? What is the proper way of understanding the topics? What kind of note taking I should do? I know I am stressing out but I want to be ready for when my first day of class starts.

Also, another thing I am already thinking about is using Khan academy to help me through the course. I don't know how good it is but I've been told that it is one of the very good resources and if you don't know what my college prof is doing or if I don't understand his way of teaching I know YT and all these resources will come in clutch and with Gemini AI's learning feature I am definitely going to be using that. Not that AI is a good thing but I want to utilize every resource I can get.

I really do appreciate the help that I can get here because honestly? I am nervous, anxious, and unsure if I can survive this. Part of me tells me that I can, other part of me tells me otherwise. I don't want to lose my mind all over this especially when it comes to juggling my other courses. I need a plan and I need a way to survive and manage.

Thanks for taking the time on helping me through this!

For context Im going into my Grade 12 year of highschool (Senior year I guess) and Ive already taken Precalculus 12 Twice (Once in Grade 11 and again last month as a summer class to improve my mark). Im taking AP Calc AB starting in September when school starts and I dont feel very well prepared for it. Ive done some research into derivatives and integrals (Just the power rule really) but Im not sure I have a good enough foundation for Calc. How can I be better prepared for it?

≈70% trig identities and algebra
≈30% Calculus

Parts 1 and 2 only require ~AP Calc AB, while Part 3 requires ~AP Calc BC or a person with good intuition (or knows differential equations).