Best book for theoretical multivariable calculus self-study

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SUMMARY

The discussion centers on recommendations for self-study books in multivariable calculus, emphasizing rigorous proofs and clear explanations. Key suggestions include "Functions of Several Variables" by Fleming, "Analysis on Manifolds" by Munkres, and "Advanced Calculus of Several Variables" by Edwards. Michael Spivak's "Calculus on Manifolds" is noted for its rigor but deemed less suitable for self-study due to its conciseness. The participants agree on the importance of accessible yet thorough resources for mastering the subject.

PREREQUISITES
  • Understanding of single-variable calculus concepts
  • Familiarity with proof-based mathematics
  • Basic knowledge of mathematical analysis
  • Ability to interpret mathematical theorems and definitions
NEXT STEPS
  • Research "Functions of Several Variables" by Fleming for comprehensive multivariable calculus concepts
  • Explore "Analysis on Manifolds" by Munkres for a rigorous approach to manifold theory
  • Study "Advanced Calculus of Several Variables" by Edwards for advanced techniques in multivariable calculus
  • Investigate additional resources or books by Hubbard for further insights into multivariable calculus
USEFUL FOR

Students and self-learners in mathematics, particularly those pursuing rigorous understanding in multivariable calculus, as well as educators seeking effective teaching materials.

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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