Advanced Calculus Book for Computer Science Student

Question

I study Computer Science, but our mathematic coures are a little bit to basic.

I'm looking for a "advanced Calculus" book for self-study that has a lot of exercises. The book should focus on explaining and not just containing a bunch of formulas.

what I already have learnt:

• Matrices
• Matrix transformation (e.g. Scale, Rotation, Translation and so on)
• Vector calculation in $\mathfrak{R}^2$ / $\mathfrak{R}^3$ (Cross Product, Dot Product, Projection and so on)
• Homogeneous coordinates
• plane / sphere / line equation
• derivation with one variable
• integration
• number series
• limit
• Complex Numbers / Quaternion (only rotation)
• basic in discrete Mathematics

what I especially want to learn:

• vector analysis
• multivariable integration/derivation
• Integral equation

Answer 1

I am rather interested in acquiring this book

http://math.univ-lyon1.fr/~okra/2011-MathIV/Zorich1.pdf

and the 2nd volume

http://math.univ-lyon1.fr/~okra/2011-MathIV/Zorich2.pdf

These two books are quite thorough, and rigorous, and go all the way from the (modern) foundations of calculus in $\mathbb{R}$, to discussing differential forms and their integration over suitable manifolds (a significant generalization of even multivariable calculus).

Edit: Links appear to be dead now...

Answer 2

This book is online, and may be of use to you. It was apparently used at Harvard, and the material may be up to your standards of sophistication. http://www.math.harvard.edu/~shlomo/docs/Advanced_Calculus.pdf