7
$\begingroup$

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.

  • 3
    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.2012-07-01

1 Answers 1

7

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".