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

I am rather interested in acquiring this book


and the 2nd volume


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...

  • 1
    $\begingroup$ The links do not work. $\endgroup$ – Anton Petrunin Dec 7 '16 at 16:32
  • $\begingroup$ Those links used to work, but I guess they no longer do... $\endgroup$ – Justin Benfield Dec 14 '16 at 7:33
  • 1
    $\begingroup$ It was a violation of copyright, no wonder they disappeared. But I recommend those books too. For more information: volume 1 and volume 2. $\endgroup$ – Jean-Claude Arbaut May 28 '18 at 13:09

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

  • $\begingroup$ Thanks for the link. Nice book (and even nicer that it's on one of the authors' sites, so presumably perfectly legal rather than a pirated copy). Might not be exactly what the op's looking for -- sounds to me like he maybe wants a book that would be used in the engineering school rather than the math department. $\endgroup$ – John Forkosh Jul 3 '16 at 22:30

Let me recommend Corral's Vector Calculus. The book is short and good, altho I would not call it "advanced". In addition it is written under free license (GFDL).

I used it to teach Vector Calculus at Penn State and made some minor changes which available here.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.