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I'm looking to study the analysis of differential and integral calculus for functions of several variables from a rigorous perspective, with a particular emphasis on differential forms.

My background includes:

  • Real analysis of single-variable functions
  • Abstract and linear algebra
  • Complex analysis

I also have some familiarity with multivariable calculus, roughly at the level of Anton's Calculus textbook and I never had a formal vector calculus course.

Any recommendations for books that approach this subject rigorously and incorporate differential forms would be greatly appreciated!

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    $\begingroup$ Calculus on Manifolds by Spivak should be good to start. $\endgroup$ Commented Sep 18 at 15:13
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    $\begingroup$ Of the books listed in my answer to Advanced calculus book recommendations, consider [9] or [10] or [11]. And if I had to pick only one of these (without knowing anything more about you), it'd be [10] -- Harold Mortimer Edwards, Advanced Calculus, Houghton Mifflin Company, 1969, xv + 508 pages. Reprinted (and retitled Advanced Calculus. A Differential Forms Approach) by Birkhäuser in 1994 (xvi + 508 pages). $\endgroup$ Commented Sep 18 at 18:03
  • $\begingroup$ @beginner I was thinking the same. Despite the book being dense, is short and I will be able to complete it fast. $\endgroup$ Commented Sep 19 at 9:26
  • $\begingroup$ @DaveL.Renfro Thanks, I will check these books. $\endgroup$ Commented Sep 19 at 9:27

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