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18.952 Theory of Differential Forms

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Prereq: 18.101 and (18.700 or 18.701)
Units: 3-0-9

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.
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