18 952 - Theory of Differential Forms

Institution:

Massachusetts Institute of Technology

Subject:

Description:

Multilinear algebra: tensors and exterior forms. Differential forms on Rn: exterior differentiation, the pull-back operation and the Poincare 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.

Credits:

3.00

Credit Hours:

Prerequisites:

Prereq: 18.101; 18.700 or 18.701

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

web.mit.edu/student/

Phone Number:

(617) 253-1000

Regional Accreditation:

New England Association of Schools and Colleges

Calendar System:

Four-one-four plan

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