Math 322. Calculus on Manifolds

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Vectors and covectors. Alternating multilinear functions. Differential r-forms. The exterior algebra of forms. The pull back of a differential form by a transformation. The exterior derivative. Vector fields and local groups with one parameter. The volume n-form and orientation. Manifolds. Measure, orientation and the integration of forms on manifolds. Generalised Stoke’s theorem. Closed and exact forms. Poincaré’s lemma.
Prerequisite: Math 222 or consent of the instructor.
Core for Math.

Instructors: Andrei Ratiu
Assistants:

Analysis Lecture Notes (Ali Nesin): dvi pdf ps
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