Math 481. Vector and Tensor Analysis (formerly Math 381)
Syllabus for Instructors

Text: T. Frankel, The Geometry of Physics, Cambridge University Press, 1999.

Basic tools of differential geometry will be introduced at the undergraduate level, using many examples. A good first course for those interested in, or curious about, modern differential geometry, or in applying differential geometric methods to other areas.

1. Manifolds. Differentiable manifolds, tangent spaces, tangent bundles.
2. Calculus on manifolds. Vector fields and f lows.
3. Differential forms and exterior calculus.
4. Integration theory. Generalized Stokes theorem.
5. Riemannian geometry. Riemannian metrics, geodesics, and curvature.

Prerequisites: Math. 280 or equivalent, or consent of instructor.

Courses webpage
Department of Mathematics

Last modified November 12, 2002