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Calculus List of GOOD multivariable calculus book

  1. Jul 12, 2017 #1
    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.
  2. jcsd
  3. Jul 12, 2017 #2
    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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