INTRODUCTION TO DIFFERENTIAL GEOMETRY
(suitable for scientists and engineers)

  Spring 2007  MATH 481
MWF, 2pm    Altgeld Hall, rm 143

WWW:     http://www.math.uiuc.edu/~kapovich/481-07/481-07.html


Instructor:  Ilya Kapovich
Telephone: 265-0633
e-mail: kapovich@math.uiuc.edu. (Preferred method of reaching me!)
Office location: Altgeld Hall, room 365
Office hours:   Tue, Thur 9:30am-11am (and at other times by appointment)
Text:     Required:  The Geometry of Physics, An Introduction, T. Frankel, Cambridge U.P. 1997 (paperback)

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


Prerequisites:   Multivariable calculus

Brief course description.

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. Note that the course description differs somewhat form the one given in the course catalogue (that is somewhat out of date). The present course has been developed by Professor Stephanie Alexander over the period of several last years.

  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.

Some course materials:

Grading system:



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