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 be offered this semester (Spring 2018). It is instructed by V. W. Guillemin.

Lecture occurs 11:00 AM to 12:00 PM on Mondays, Wednesdays and Fridays in 2-143.

This class counts for a total of 12 credits.

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