INTRODUCTION TO DIFFERENTIAL GEOMETRY
(suitable for scientists and engineers)

Spring 2011  MATH 481, Section C13

MWF, 10am    Altgeld Hall, rm 145

WWW:     http://www.math.uiuc.edu/~kapovich/481-10/481-10.html

The second midterm has been graded and the results have been posted via Score Reports. Here are the solutions to Midterm 2. Although formal letter grades are not assigned for the midterms, you may approximately interpret the results as follows: A: 24-28; B: 19-23.75; C: 14-18.75. The median score was 24.5/28, the mean score was 24.1/28, with the standard deviation of 14.6%.

The first midterm has been graded and the results have been posted via Score Reports. Solutions are posted below. I do not assign formal letter grades for midterms. However, you may approximately interpret the scores as follows: A: 26-29; B: 22-25.75; C: 17-21.75. For what it's worth, here is some statistical data: the median score was 25/29, the mean score was 25.25/29, with the standard deviation of 8.3%

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 (preliminary, subject to change):
Tue, Thur 10am-11:30am (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 -required; some course in linear algebra - recommended

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. Note that the course description differs somewhat form the one given in the course catalogue (that is somewhat out of date).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. We will largely follow class notes and handouts, rather than the textbook.

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:

NOTE: The correct due date for each h/work is the one shown in this web page, NOT the one shown in the pdf file of a particular h/wk (the reason is that I am reusing h/wks from previous years when the semester calendar was different).

Homeworks:
1. Assignment 1, Due Friday, January 28
2. Assignment 2, Due Friday, February 4
3. Assignment 3, Due Monday, February 14 (deadline extended since the assignment was posted pretty late)
4. Assignment 4, Due Friday, February 18
5. Assignment 5, Due Friday, February 25
6. Assignment 6, Due Friday, March 4
7. Assignment 7, Due Friday, March 11
8. Assignment 8, Due Friday, March 18
9. Assignment 9, due Friday, April 1
10. Assignment 10, due Friday, April 8
11. No homework is due on Friday, April 15
12. Assignment 11, due Friday, April 22
13. Assignment 12, due Friday, April 29
14. Optional Extra Credit problems, due Monday, May 2.
15. Assignment 13, for information purposes only (will not be collected and graded)