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I want to get used to differential forms. Thus I would like to solve a bunch of problems, especially on integration of differential forms.

So I need a collection of problems with answers/solutions, starting from really elementary ones. No theorem proving, just straightforward calculations.

Yrogirg
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    This is a textbook, not a problem book, but perhaps try the exercises in Hubbard & Hubbard, Vector Calculus, Linear Algebra, and Differential Forms. – Neal Jul 01 '12 at 16:45
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    I would recommend the book of Do Carmo "Differential Forms and Applications". Personally I first learn differential form from this book, and I did all the exercises which I benefit a lot. – Paul Jul 01 '12 at 18:35
  • +1 Hubbard and Hubbard is not only one of the best beginners' introduction to differential forms there is, but one of the best textbooks ON ANY SUBJECT PERIOD. If you're serious about learning and doing research in mathematics, you NEED to have a copy if only for reference. Seriously. – Mathemagician1234 May 07 '21 at 03:11

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You may like Chapter 10 "Differential Forms, Integral Formulae, De-Rham Cohomology" of Mishchenko, Solovyev, Fomenko "Problems in Differential Geometry and Topology" (English translation, Mir Publishers, 1985). I have not seen a newer version of it that may be even better: A.T. Fomenko, A.S. Mischenko, Y.P. Solovyev: Selected problems in differential geometry and topology. Cambridge Scientific Publishers, Cambridge, 2006

Update 1. There is also a very interesting collection of problems by Prof. W.-H. Steeb. See Ch.4 Differential Forms and Applications in "Problems and Solutions in Differential Geometry"

Update 2. A comprehensive set of problems on differential geometry can be found in Analysis and Algebra on Differentiable Manifolds: A Workbook for Students, by P. M. Gadea, J. Munoz Masqué, see Ch.2 "Tensor Fields and Differential Forms".

Yuri Vyatkin
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