Flanders, Harley Differential forms. (English) Zbl 0683.53011 Global differential geometry, MAA Stud. Math. 27, 27-72 (1989). [For the entire collection see Zbl 0683.53001.] A discussion is given of the calculus of differential forms and several aspects of differential geometry in which differential forms are a natural tool. For the sake of simplicity the calculus is demonstrated for differential forms on \(E^ n\) at first and generalized to manifolds later on. Then de Rham’s theorem is presented and illustrated by simple examples. As applications we get a proof of the Brouwer fixed point theorem and another proof of the Gauss-Bonnet theorem. The presentation is very motivating. Reviewer: Bernd Wegner Cited in 1 ReviewCited in 1 Document MSC: 53A45 Differential geometric aspects in vector and tensor analysis 58A10 Differential forms in global analysis 53-02 Research exposition (monographs, survey articles) pertaining to differential geometry Keywords:differential forms; de Rham’s theorem; Brouwer fixed point theorem; Gauss-Bonnet theorem Citations:Zbl 0683.53001 PDFBibTeX XML