List of GOOD multivariable calculus book

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SUMMARY

The discussion highlights several highly recommended books on multivariable calculus, specifically mentioning "Vector Calculus, Linear Algebra, and Differential Forms" by Hubbard and Hubbard, and "Vector Calculus" by Colley. The conversation suggests that while Edwards and Marsden's works are considered dry, Hubbard's book is preferred for its clarity and depth. Additionally, "Functions of Several Variables" by Fleming is noted for its inclusion of measure theory and Lebesgue integration, making it suitable for students pursuing advanced topics such as mathematical probability and algebraic topology. The need for a practical guide on applying Stokes' Theorem is also emphasized.

PREREQUISITES
  • Understanding of basic calculus concepts
  • Familiarity with linear algebra
  • Knowledge of differential forms
  • Basic exposure to measure theory and Lebesgue integration
NEXT STEPS
  • Research "measure theory" and its applications in advanced calculus
  • Explore "Lebesgue integration" and its significance in analysis
  • Investigate "Stokes' Theorem" and its practical applications in proofs
  • Look into "algebraic topology" as a follow-up discipline
USEFUL FOR

Students and educators in mathematics, particularly those focusing on multivariable calculus, advanced calculus, and related fields such as mathematical physics and computational geometry.

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Books on multivariable calculus that I often see get good recommendations are,

Vector Calculus, Linear Algebra, and Differential Forms by Hubbard and Hubbard
Vector Calculus by Colley

What are other good books with some material on differential forms like Hubbard and Colley?

Books by Edwards, Marsden , etc are just too dry, Hubbard is a better version of Marsden while Colley is fine and includes a short chapter on forms. Are there any books comparable to Hubbard? Hubbard's book is just too long.
 
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Fleming's Functions of Several Variables is good. It technically has the same prerequisites as something like Hubbard & Hubbard or Spivak's Calculus on Manifolds.

However, Fleming has a slightly different overall focus. It covers the same material, but also introduces measure theory and Lebesgue integration. This makes it a good book to recommend as part of a sequence of books on a path to various graduate level disciplines. I'd say that Fleming would be a particularly good recommendation for those who intend to eventually study mathematical probability, algebraic topology, mathematical physics, the mathematical side of computational geometry and graphics, or analysis. I'm surely missing some other disciplines Fleming is good in preparation for.

Also, it's pretty decent pedagogically. It's like a combination of some of the good qualities from Munkres and Spivak. Like most of these books, though, I find it to be light on practical applications and exercises for the generalized Stokes' Theorem. If someone made a book like Fleming with two extra chapters on how and when to apply Stokes' Theorem to proofs or calculations, that would be great.
 
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