Good Multivariable Calculus reference text

[chipsandwich]

What is a good, solid reference text for multivariable calculus? Ideally something you'd get by following on from Spivak's Calculus into 2/3d/Vectors etc. I've already done the course, but it's sort of slipping my mind these days - I've mostly been doing chemistry subjects, and they're not really as big on mvc as they are on diffyQs. I ask because I'm probably going to be getting into further QM and electromagnetics soon, and I hate seeing all of this math just fly by. I've also been reading into a bit of introductory analysis and I'm starting to hate how I never paid too much attention to apparently innocous, but essential, proofs.

Our university's reference text was Thomas' Calculus 11th ed. (i.e. not really "Thomas'" Calculus at all) just for comparison. Pretty much the exact same contents as Stewart's if you're not familiar.

 

[fresh_42]

Our university's reference text was Thomas' Calculus 11th ed. (i.e. not really "Thomas'" Calculus at all) just for comparison. Pretty much the exact same contents as Stewart's if you're not familiar.

Whatever this means ...

If you don't like Thomas, which I think is ok, then why not consider a book on differential geometry? I'm guessing a bit based on what you ruled out, not what you were interested in. Any standard book on multivariate calculus should match your needs, but you basically ruled them out.

For a good first read on differential geometry I recommend Thorpe:
https://www.amazon.com/dp/0387903577/?tag=pfamazon01-20

An alternative - useful for QM - would be a book about functional analysis:
E. Zeidler: Nonlinear Functional Analysis and its Applications (Vol. I, IIA, IIB, III, IV)
see links under 'Sources' at the end of
https://www.physicsforums.com/insights/tell-operations-operators-functionals-representations-apart/