I'm a looking for a good book to self-study differential forms. Particularly, I'm looking for a book that is as similar as possible to Bert Mendelson's "Introduction to topology" (i.e. a book that procede by following a: "Definition, theorem, proof" style). In addition, the book that I'm looking for should be as much self consistent as possibile. I'm a first year graduate student in nuclear engineering. My prerequisites are a good understanding of (multivariate and vector) calculus, linear algebra, and a little of functional analysis, Lebesgue integration theory, PDE. I know nothing about differential geometry, but to my (very) poor understanding differential forms and concept like manifolds and so on are linked to each other.


Differential forms are things that live on manifolds. So, to learn about differential forms, you should really also learn about manifolds. To this end, the best recommendation I can give is Loring Tu's An Introduction to Manifolds. Tu develops the basic theory of manifolds and differential forms and closes with a exposition of de Rham cohomology, which allows one to extract topological information about a manifold from the behavior of the differential forms on it.

  • $\begingroup$ Bott and Tu's book is also quite good. $\endgroup$ – Cheerful Parsnip Aug 19 '15 at 11:28
  • $\begingroup$ @GrumpyParsnip Though it is great, I hesitate to recommend that book to someone without a firm grounding in basic manifold theory. Tu says in the introduction to the book I recommend that he intended it as a prelude to Bott and Tu, to fill in the necessary background. $\endgroup$ – Potato Aug 19 '15 at 12:45
  • 2
    $\begingroup$ I agree completely. $\endgroup$ – Cheerful Parsnip Aug 19 '15 at 12:47

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