Instructor: Victor Guillemin
Office: Room 2-270
Email: vwg [at] math . mit .edu
Lectures: M W F, 11am, 2-143
Office Hours: M W F, 2pm - 3pm
Multilinear algebra: tensors and exterior forms. Differential forms on R^n: 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 R^n. 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.
Prerequisites: 18.101; 18.700 or 18.701