I'm studying Engineering and I'm in my second year, studying Multivariable Calculus, but my University is kind of hard teaching me fresh calculus with topology and analysis, and is kind of hard, so I would like to find a good book, a recent one if possible with Multivariable calculus seen from the perspective of a fresh student but with enough advancement to approach the subject with analysis and topology. Any suggestion?
PS: The problem I find with multivariable analysis is that I don't understand the "importance" or "where am I going with this?" with all those theorems and proofs....is like...is a constant bombarding of theorems and proofs, but without telling me where am I going, or how I use them, or show me a broader perspective of the theory so I can look at it simpler...
Have you checked out Kolk's, if not, this might help you.