MATH 481: Introduction to Differential Geometry
suitable for scientists and engineers
Spring 2006

10.30 - 11.50 a.m., Tu Th
343 Altgeld Hall

Instructor:
Stephanie Alexander, Professor
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street (MC-382)
Urbana, Illinois 61801-2975

Office: 322 Illini Hall
Phone: (217) 244-7339
FAX:  (217) 333-9576
e-mail: sba@math.uiuc.edu

The basic tools of differential geometry will be introduced at the undergraduate level, by focusing on examples. This is a good first course for those interested in, or curious about, modern differential geometry, and in applying differential geometric methods to other areas. Graduate students may take for 4 hours of credit, by completing additional problem sets.

1. Manifolds: configuration spaces, differentiable manifolds, tangent spaces, tangent bundles, orientability.
2. Calculus on manifolds: Vector fields, flows, tensor fields.
3. Differential forms and exterior calculus.
4. Integration theory: Generalized Stokes theorem, de Rham cohomology.
5. Riemannian geometry: Riemannian metrics, geodesics.

Prerequisite: Multivariable calculus.

Text: The Geometry of Physics, An Introduction, T. Frankel, Cambridge U.P. 1997 (paperback).

Tensor Analysis on Manifolds, R. Bishop and S. Goldberg, Dover (paperback)(optional).

Last updated 10/20/05