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DifferentialForms - MIT Mathematics

Draft: March 28, 2018 Differential FormsVictor Guillemin & Peter J. HaineDraft: March 28, 2018 Draft: March 28, 2018 ContentsPrefacevIntroductionvOrganizatio nviNotational ConventionsxAcknowledgmentsxiChapter 1. Multilinear Quotient spaces & dual Alternating The space ( ) The wedge The interior The pullback operation on ( ) Orientations29 Chapter 2. Differential Vector fields and Integral Curves for Vector Differential Exterior The interior product The pullback operation on Divergence, curl, and Symplectic geometry & classical mechanics63 Chapter 3. Integration of The Poincar lemma for compactly supported forms on The Poincar lemma for compactly supported forms on open subsets of The degree of a differentiable The change of variables Techniques for computing the degree of a Appendix: Sard s theorem92 Chapter 4.

Draft: March28,2018 Organization vii of dual space and quotient space. Then inSection 1.3 we will turn to the main topics of this chapter, the concept of …

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