Multivariable calculus book recommendations

Question

I would like some recommendations on multivariable calculus books.

I already have Susan Jane Colley's "Vector Calculus" and I am planning to get Marsden's book as well(mainly because I can get it for free).

I am not completely satisfied with Colley's book for a few reasons, the main one being the lack of rigour in certain points ( previously I worked through most of Spivak's book and that was quite a transition as far as rigour is concerned).

Any further recommendations?

Answer 1

I recommend Hubbard&Hubbard since it has some sophistication that might be appreciated after becoming acquainted with Spivak, but also does not adopt the same ultra-rigorous style.

Answer 2

Analysis on manifolds by James Munkres is probably better than Spivak. Should be rigorous enough.

Answer 3

Vector Calculus by Liebeck and Baxandall would be my recommendation. I purchased it in the same situation as you -- frustration about the lack of rigor in Colley's book.

To build up to a deeper level of manifold theory, albeit in $\mathbf{R}^n$, I would use Munkres' Analysis on Manifolds.

When you are ready, an excellent graduate-level text on abstract manifold theory is Lee's Introduction to Smooth Manifolds.