Studying Leisure Math Textbook: Moving from AP Calc BC to Multivariable/Vector Calc

[theJorge551]

Hello all, just a question I've been tossing about lately. I've been recently given the chance to get any math textbook I'd like (outside of school), because I'm a tad bored with my current math classes. Right now, I'm taking the first year of IB Math HL (the junior course), and it is pathetically simple...so I'm simultaneously taking it with AP Calculus BC. The latter is certainly more involved and I enjoy it much more, but I really enjoy advancing my knowledge independently as well (I was doing differentiation and integration on my own last year, while I was in an Algebra II / Trigonometry class.) So, does anyone have a suggestion for what textbook I should purchase for independent progression? As in, which course/area is a student likely to move on to after the topics covered in AP Calculus BC? I'd like to move forward into multivariable/vector calculus (I can take statistics when I get into college.)

Any comments much appreciated!

- Jorge

 

[Fragment]

It is hard to recommend anything without knowing your proficiency level in calculus. However, whatever textbook you might end up choosing, in my opinion, should be supplemented with its Schaum's outline equivalent. Also, you might want to use Khan Academy videos concurrently to your independent study. Best of luck to you.

 

[theJorge551]

I've done nearly all types of differentiation (product, quotient, & chain rule; implicit differentiation, trigonometric differentiation, logarithmic differentiation, etc.), as well as some basic integration (integration by parts; u-substitution; areas under curves; volumes of revolution), limits, and not a great deal more than that. My Calculus BC course this year will cover much more (e.g., infinite series, more complex integration, l'Hopital's rule, improper integration), but I tend to jump the gun with new topics...hence, I'll likely have done the next few weeks of curriculum by the time I learn something, but I'm also fine with physics texts that employ the use of calculus. The calculus-based physics book I'm reading from now is pretty basic, and I'm interested in something more advanced. And, thanks for your advice! I will definitely check out those resources.

 

[General_Sax]

Stewart's is good.

 

[theJorge551]

This is partially a mere thread bump, but I've also considered a new question to pose (this seems to be the thread to post it in.)

I've been very interested in pure mathematics lately, and would like to study various fields of mathematics alongside AP Calculus that don't necessarily require it. Perhaps introductory topology? Analytic geometry? What do all of you, educated in these areas, think I would likely be best suited to get a head-start on, and with what texts? I think it would be very helpful for me to have some practice with formal proofs and more pure math (an example would be the epsilon-delta conjecture to prove limits, rather than just taking it from an intuitive sense.) Comments?

I've got my hands on an older Stewart book from my calculus teacher, and it's quite involved. I'm enjoying it, but would like to extend myself a bit more in other fields simultaneously.

 

[jgens]

Try Calculus by Michael Spivak. If you work through the problems, there's no way that you can avoid learning elementary proof techinique.

https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20