I am currently taking a course on multivariable calculus and our professor is following the book by Do Carmo: Differential forms and applications. I feel the text is too rigorous, which I really appreciate and it appeals to me as well, but it is making things quite difficult for me to understand.Definitions and theorems are becoming increasingly complex. Could anyone suggest a book I could use together with Do Carmo's book so that I am able to understand the text better. My goal is to master the material presented in Do Carmo's book.As of now we have completed the first three chapters from the text which are- Differential forms, Line integrals and Differentiable manifolds. Thanks.

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    $\begingroup$ "Formes différentielles" by Cartan. There's an english translation if you don't know French. $\endgroup$ – user40276 Oct 11 '15 at 23:54
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    $\begingroup$ amazon.com/Differential-Forms-Dover-Books-Mathematics/dp/… . But, of course, you can find a pdf copy online in that Russian site that I don't know if I can write the name here. $\endgroup$ – user40276 Oct 11 '15 at 23:59
  • $\begingroup$ Bachman's A Geometric Approach to Differential Forms may be nice, and has a draft available on the arXiv. $\endgroup$ – pjs36 Oct 12 '15 at 0:08

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