Best book for theoretical multivariable calculus self-study

In summary, the person is looking for a book on multivariable calculus for self-study with a focus on rigorous proofs, theorems, and clear explanations. Recommendations are given for books such as Michael Spivak's Calculus on Manifolds, Fleming's Functions of Several Variables, Munkres' Analysis on Manifolds, and Edwards' Advanced Calculus of Several Variables. However, no one mentioned Hubbard's book.
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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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  • #2
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?
 

Related to Best book for theoretical multivariable calculus self-study

1. What is the best book for self-studying theoretical multivariable calculus?

The best book for self-studying theoretical multivariable calculus will depend on personal learning style and level of mathematical background. However, some popular options include "Vector Calculus" by Jerrold E. Marsden and Anthony J. Tromba and "Calculus: Early Transcendentals" by James Stewart.

2. What topics should be covered in a book for self-studying theoretical multivariable calculus?

A good book for self-studying theoretical multivariable calculus should cover topics such as vector functions, partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss.

3. Are there any online resources that can supplement a book for self-studying theoretical multivariable calculus?

Yes, there are many online resources that can supplement a book for self-studying theoretical multivariable calculus. Some popular options include Khan Academy, MIT OpenCourseWare, and Paul's Online Math Notes.

4. How much time should I dedicate to self-studying theoretical multivariable calculus?

The amount of time needed to self-study theoretical multivariable calculus will vary depending on individual learning pace and prior knowledge. However, it is recommended to dedicate at least 4-6 hours per week for consistent progress.

5. Can someone with no background in calculus self-study theoretical multivariable calculus?

It is not recommended for someone with no background in calculus to jump straight into self-studying theoretical multivariable calculus. It is important to have a strong foundation in single-variable calculus before tackling more advanced topics. However, with dedication and the right resources, it is possible to self-study theoretical multivariable calculus without prior knowledge.

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