Textbook for Vector Calculus Can anyone recommend a textbook for studying vector calculus (vector analysis) only, that focuses on the theoretical mathematics behind vector calculus?
Currently, I am using vector analysis by Snider. I have also taken a look at vector calculus by Marsden. Both of these books skip a large amount of the theory behind what we are doing and why it matters.
 A: Rigorous yet accessible text by J. H. Hubbard and B. B. Hubbard. Vector calculus, linear algebra, and differential forms: a unified approach with Maple 10 VP. Pearson Education, Limited, Mar. 2006.
A: I'm not sure what level you're looking for (your question could be more precisely worded), but I recently liked the look of


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*Vector Analysis and Cartesian Tensors, by Bourne and Kendall.


If you're not interested in the "Cartesian Tensors" part of the title then don't worry, that's left until the end; just focus on the first six chapters.
A: A really excellent book about that argument is:


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*Vector Analysis by Homer E. Newell, Jr - Dover Publications.

A: Colley's Vector Calculus is very good for a more-formal-than-normal treatment of multivariable calculus. The focus is on things like partial derivatives, div, grad, curl, and multiple integrals. It could be used as a first exposure to these topics, and proofs are supplied. 
For texts on a subject better described as multivariable analysis, I highly recommend Munkres's Analysis on Manifolds and/or Spivak's Calculus on Manifolds. These focus on topological and analytical aspects (unlike Colley) and are intended to extend the ideas of multivariable analysis to manifolds.
