18.952 Theory of Differential Forms


Class Info

Multilinear algebra: tensors and exterior forms. Differential forms on Rn: exterior differentiation, the pull-back operation and the Poincaré lemma. Applications to physics: Maxwell's equations from the differential form perspective. Integration of forms on open sets of Rn. The change of variables formula revisited. The degree of a differentiable mapping. Differential forms on manifolds and De Rham theory. Integration of forms on manifolds and Stokes' theorem. The push-forward operation for forms. Thom forms and intersection theory. Applications to differential topology.

This class has 18.101, 18.700, and 18.701 as prerequisites.

18.952 will not be offered this semester. It will be instructed by V. W. Guillemin.

Lecture occurs 11:00 AM to 12:00 PM on Mondays, Wednesdays and Fridays in 2-151.

This class counts for a total of 12 credits.

In the Spring 2016 Subject Evaluations, 18.952 was rated 6.3 out of 7.0. You can find more information at the Course Website site or on the 18.952 Stellar site.

MIT 18.952 Theory of Differential Forms Related Textbooks
MIT 18.952 Theory of Differential Forms On The Web
Course Website
Tags
forms differential guillemin topology manifolds stokes munkres de rham

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