I'm currently going over Multivariable Real Analysis using the book by Jerry Shurman "Calculus and Analysis on Euclidean Space" and I came across "Advanced Calculus: A geometric View" by James Callahan. Would James's book be great to use alongside a real analysis level textbook or would I be better off searching for other books? I'm asking since I want to boost my understanding of the subject by utilizing other books. I'm just trying to see what works well with learning this subject.

BTW my current knowledge is: General Topology, Single Variable Real Analysis, Abstract Algebra up to ring theory, Linear Algebra.

  • $\begingroup$ I like Callahan's book. The book by Hubbard and Hubbard may be a little bit cluttered in terms of notation, but contains proofs of all its theorems in the text or in appendices. I never took a multivariate analysis course in undergrad, but I pieced together my knowledge from these books, and Rudin, and turned out pretty okay! $\endgroup$ – Alfred Yerger Jul 16 '17 at 3:14
  • $\begingroup$ Spivak's Calculus on Manifolds or Zorich's Mathematical Analysis I and II. The latter is overwhelmingly comprehensive, imo. $\endgroup$ – Nap D. Lover Jul 16 '17 at 12:32

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