Struggling with Calculus? Here's How to Master the Concepts and Applications

[Mu naught]

Sorry if this isn't the right forum. I'm aspiring to be a physics major next year, and I'm in my 2nd semester of physics. I've also taken calculus 2. What I've learned this past year is the following:

1) I'm fairly good at physics and I really enjoy it.
2) I'm horrible at calculus and have no idea how to apply it.

I got an A in calc 1 and calc 2, yet I really have no clue how to even use calculus! Somehow I missed the key ideas along the way, and that's probably my fault although I can't say I had the greatest teacher... So I'm really scared that I'm setting myself up for failure if i don't fix this problem I have. I want to re-teach myself calculus from the ground up over the summer, so what I'm asking from you bright folks is any books you might suggest for doing this.

I do have my calculus textbook, but I'd like a supplement to this that focuses on the concepts and applications of calculus, and not just the formulas and steps for messing with functions, without understanding what it is you're actually doing with those functions. Hopefully that makes sense...

 

[fizz_it]

Two books that I really like

how to ace calculus
how to ace the rest of calculus

both by Abigail Thompson

These books are fun to read and they explain calculus very well

good luck

 

[cappadonza]

hey i had to re-learn calculus too! it has been over almost 10 years since my undergrad degree. what i did was i worked throught some of the exercises provided by mit open course ware http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2006/Readings/detail/course-reader-.htm

I also bought this excellent book by Tom Apostol, https://www.amazon.com/dp/0471000051/?tag=pfamazon01-20 (it quite expensive i got it second-hand)
Another good book to get a deep understanding is spivaks book, https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20

These books arent easy to study but are very rewarding indeed.

 

[sponsoredwalk]

Yeah I have both Apostol & Spivak but they are really challenging.

My honest advice is to steer clear of these books until you can pick up a run of the mill calculus book & eat it for breakfast.

I've been looking and I've come across a few books in calculus that I wish I'd read before as they would of saved me so much hassle.

1: A First Course in Calculus - Serge Lang

This book has nearly everything you'd want. Personally I think it's laid out in such a way as to make everything clear. It doesn't include everything but as far as I know it's only one or two small things.

2: The Calculus Lifesaver - Adrian Banner

This book has a lot of things I'd never seen before & he explained some things brilliantly. I'd say this book would do a lot for you pretty fast.

 

[gauss^2]

I really enjoyed the MIT OCW lectures for their Calculus II class (18.02); prof Denis Auroux gives very cool motivation for the results, so it might be something to check up on to brush up on your skills with vectors, partial derivatives, curl, divergence, integrals over surfaces and volumes, and so on after you're confident in your calc skills in 1D. I haven't looked at their Calc I class (18.01), but that one also has video lectures.

Here's a link to the 18.02 class:
http://ocw.mit.edu/OcwWeb/Mathematics/18-02Fall-2007/VideoLectures/index.htm

I'm not a huge fan of Apostol's calculus volumes. They just seemed way too hard for calc books last time I read them (then again, that was maybe 15 years ago). If you want to do calculus rigorously, you might as well go all out and do real analysis with a book like Baby Rudin, using Apostol's Mathematical Analysis as a supplement for whenever Rudin starts blowing your mind with unmotivated symbol manipulations. But for learning calculus for applications in physics, I would definitely steer clear of everything mentioned so far in this paragraph and instead run through the main ideas of Calculus I (derivatives, integrals, sequences, series, polar coords, parametric equations, conics) pretty quickly and then work closely on that 18.02 video lecture series I mentioned above. Calculus in 3-dimensional space is pretty critical to know well, since it'll build up your geometric intuition, which is a hell of a lot more important than doing everything rigorously IMO.

 

[Mu naught]

Thanks for all the responses so far. I should have expected everyone to suggest a different book! After finals when I have a lot of spare time I'll go through all these suggestions and hopefully I can find a copy of whatever one I decide to go with cheap.

 

[Je m'appelle]

I haven't looked at their Calc I class (18.01), but that one also has video lectures

18.01 (Calculus I) was even better. The lecturer, David Jerison is awesome. If you enjoyed 18.02, you'll be amazed by 18.01.

 

[sponsoredwalk]

I have to totally disagree about 18.01. The lecturer made everything sound way more complicated than it had to be and ignored a lot of useful things. You'd need to have done calculus before to get anything from these lectures (I hadn't and I suffered because of it) but you'll come away having learned nothing you can't pick up in a textbook with better explanation & better proofs.

http://press.princeton.edu/video/banner/

These lectures along with the guys book will teach you way more, more in depth for sure, then you can go straight to 18.02 lectures on the MIT website, but I'd advise either Serge Lang, Stewart calculus or Thomas Calculus for both different point of view and extra questions/ different proofs, (they all contain variations tbh). That said check out the MT lectures yourself and see if you can get past lecture 9 without cringing and realizing there are better and easier explanations elsewhere.

toodles...

 

[Evo]

Anyone receiving a solicitation via PM needs to report it to a mentor.