What Books Are Best for Calculus II-A and II-B?

[ythamsten]

Good evening guys, next period I'm going to take Calculus II at the University, but turns out that in my university they split it in Calculus II-A and II-B.
The topics covered in each are basically those:
Calculus II-A: Definite Integral, Techniques of integration, Improper integrals, first order differential equations, second order differential equations, linear differential equations of order n.
Calculus II-B: Single variable vector functions, multivariable real functions (scalars and vector), continuity, partial derivatives and differentiability, taylor's formula, maxima and minima.
Last period I took Calculus one, which covered all that basic single variable Calculus, but didn't developed integration that much, only an introduction to the techniques and worked with undefinite integrals. Back then I used a book from a brazilian author which probably you PF guys are not much familiarized with (Guidorizzi). But I started using Spivak quite early on, since I was interested in a different approach. Although it was kind of harsh at the beginning, I got used to the language and really liked it. But I rented it from my university library at the time, and I'm not finding it anywhere here in Rio to buy.
So what books would you recommend for me to take those Calculus II-A and II-B, with this theorem-proof style and as well with some interesting/challenging exercises?
Also, I will take Physics II: Electricity & Magnetism, do you guys have any tips on books for it too? I used Randall's one for Physics I, like it, worth sticking with it?
Sorry for asking that much and for the long text. Thanks in advance!

 

[verty]

Have a look at these notes by William Chen, the First Year Calculus ones and the Multivariable and Vector Analysis ones. They won't be as good as a book but they may be in the style you are looking for, theorem-proof with exercises.

I think all you want is to get a head start on what you will learn in class.

For E&M, Griffiths (though I think any northern hemisphere book is going to be expensive or hard to get).