Calculus Best book for theoretical multivariable calculus self-study

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For studying multivariable calculus with a focus on rigorous proofs suitable for an undergraduate math course, several books are recommended. Michael Spivak's "Calculus on Manifolds" is noted for its rigor but may not be ideal for self-study due to its concise nature. Alternative suggestions include "Functions of Several Variables" by Fleming, "Analysis on Manifolds" by Munkres, and "Advanced Calculus of Several Variables" by Edwards, all of which are praised for their clarity and structured presentation. The discussion also highlights that Hubbard's work was not mentioned, indicating it may also be a viable option worth considering.
PhysicsPrincess
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Hi,

I'm looking for a good book to study multivariable calculus from that would fit a proof-based undergraduate math course.
The emphasis should be on RIGOROUS proofs, theorems and presentation of concepts.
I really need a book that would be approachable for self-study with clear and easy-to-follow explanations and examples.

Can you recommend the best book? Thank you! :)
 
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I have heard that Michael Spivak's Calculus on Manifolds is a pretty good book, not as good as his single variable calculus book but still pretty good and rigorous.
 
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No one mentioned Hubbard?
 

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