Best book for theoretical multivariable calculus self-study

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Discussion Overview

The discussion centers around recommendations for books suitable for self-study in theoretical multivariable calculus, particularly those that emphasize rigorous proofs and clear explanations. The context is a request for resources that align with an undergraduate math course format.

Discussion Character

  • Exploratory, Debate/contested

Main Points Raised

  • One participant seeks a book that is rigorous and approachable for self-study, emphasizing the need for clear explanations and examples.
  • Another participant suggests Michael Spivak's "Calculus on Manifolds" as a good but not the best option, noting its rigor.
  • A different participant expresses skepticism about Spivak's suitability for self-study due to its conciseness and recommends three alternative texts: Fleming's "Functions of Several Variables," Munkres' "Analysis on Manifolds," and Edwards' "Advanced Calculus of Several Variables."
  • One participant questions why Hubbard's work has not been mentioned in the recommendations.

Areas of Agreement / Disagreement

There is no consensus on the best book, with multiple competing views on the suitability of Spivak's text and alternative recommendations being offered.

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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