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I'm looking for a book at the undergraduate level on multivariable calculus (for a 2nd course of multivariable calculus) that introduces and makes use of tensors to describe higher order derivatives -- and maybe differential forms for integration. Does anyone know of a multivariable book that takes this tact?

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Calculus on Manifolds - Spivak - A beautiful short little book. It carries you all the way to proving Stokes theorem.

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    $\begingroup$ I looked at that book earlier and I can't remember anything on tensors or even higher order derivatives except partial derivatives. I believe it does go over differential forms, but I'd really like a textbook that goes into tensor theory. Does this book go into that topic very far? $\endgroup$ – user244322 May 29 '15 at 7:08
  • $\begingroup$ Must have been a different one of his books then. Take a look at: amazon.com/Calculus-On-Manifolds-Approach-Classical/dp/… and click the look inside option. $\endgroup$ – muaddib May 29 '15 at 7:10
  • $\begingroup$ I'm not sure I would call it a textbook, it's very trimmed down. If you wanted to teach with it, I think you would need to augment with other notes / problems. $\endgroup$ – muaddib May 29 '15 at 7:11
  • $\begingroup$ @user244322 It's in Chapter 4 - I couldn't recall either, and had to dig out my copy. $\endgroup$ – izœc May 29 '15 at 7:58

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