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I am seeking to compile a list of textbooks that provide self-contained treatments of Stokes's Theorem in the language of differential forms and manifolds. By "self-contained", I mean the statements and proofs of all theorems from algebra, analysis and topology that are required to formulate and prove the theorem. I know of a few that satisfy this criterion or at least come pretty close and they are:

Calculus on Manifolds (Spivak)

Analysis on Manifolds (Munkres)

Functions of Several Variables (Fleming)

Vector Calculus, Linear Algebra and Differential Forms, A Unified Approach (Hubbard)

Advanced Calculus of Several Variables by Edwards

Multidimensional Real Analysis, Vols 1/2 (Duistermaat & Kolk)

Mathematical Analysis Vols 1/2 (Zorich)

What are others?

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closed as off topic by Nate Eldredge, Grigory M, Jonas Teuwen, Qiaochu Yuan Aug 3 '11 at 22:15

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His name was "Stokes", not "Stoke". The correct possessive is "Stokes's" (though often spelled "Stokes'", which according to the Chicago Manual of Style and to Strunk and White, would be technically incorrect). – Arturo Magidin Aug 3 '11 at 17:40
Thanks. I did a whole bunch of grammatical research for a paper I did on Gauss's Lemma, and now it bugs me no end to see "Stoke's", and bothers about half as much to see "Stokes' " (-: – Arturo Magidin Aug 3 '11 at 17:44
@Arturo: You could write Gauß's, then it would not look so weird ;-). – Jonas Teuwen Aug 3 '11 at 17:47
-1: I don't see how this list is useful, and I don't see how compiling it relates to Math.SE's purpose. – Nate Eldredge Aug 3 '11 at 18:24
Well, although I didn't tag it as such, it is effectively a reference request about a particular mathematical topic. As such, if reference requests have no place on Math.SE, then I suppose you're right. If reference requests are indeed inappropriate as you seem to suggest, then the community probably ought to consider removing the "reference request" tag. In any event, I believe such a list could be useful to any student studying Stokes's theorem since multiple viewpoints on the same subject are usually helpful. – ItsNotObvious Aug 3 '11 at 18:37
up vote 1 down vote accepted

Shigeyuki Morita's Geometry of Differential Forms, is always an excellent source regarding differential forms and also almost self-contained. If you speak german, i recommend Konrad Königsberger's Analysis 2 for a more elementary treatment, which also includes a proof of Stokes's theorem.

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You're not the first person to suggest the Konigsberger text and I would like to be able to read it but, unfortunately do not speak German! – ItsNotObvious Aug 17 '11 at 21:35

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