INTRODUCTION TO DIFFERENTIAL GEOMETRY
(suitable for scientists and engineers)
Spring 2011 MATH 481, Section C13
MWF, 10am Altgeld
Hall, rm 145
The final exam has been graded and the results
have been posted via ScoreReports. The high score was 48/48, the low
score was 31.5/48, the median score was 44/48, the mean score was
42.6/48, with the standard deviation of 10.2%.
I have also assigned the final course grades. If you are interested in your course grade, please
ask me by e-mail and I will e-mail you your course grade.
On Monday, May 9, I will hold office hours from 10am to 11:30am. You
can come take a look at your final exam then and discuss your
course grade as well.
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
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
e-mail: email@example.com. (Preferred
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)
Jiajie Xiao, firstname.lastname@example.org
Required: The Geometry of Physics, An Introduction,
Cambridge U.P. 1997 (paperback)
Recommended: Tensor Analysis on Manifolds, R.
Bishop and S. Goldberg,
Multivariable calculus -required; some course in linear
algebra - recommended
REPORTS -Math Department gradebook
where you can look up your h/work and exam grades. (You will be
for your NetId and password).
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
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course catalogue (that is somewhat out of date).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.
- Manifolds: configuration spaces, differentiable manifolds,
tangent bundles, orientability.
- Calculus on manifolds: Vector fields, flows, tensor fields.
- Differential forms and exterior calculus.
- Integration theory: Generalized Stokes theorem, de Rham
- Riemannian geometry: Riemannian metrics, geodesics.
Some course materials:
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
1, Due Friday, January 28
- Assignment 2,
Due Friday, February 4
3, Due Monday, February 14
(deadline extended since the assignment was posted pretty late)
- Assignment 4,
Due Friday, February 18
- Assignment 5,
Due Friday, February 25
- Assignment 6,
Due Friday, March 4
- Assignment 7,
Due Friday, March 11
8, Due Friday, March 18
9, due Friday, April 1
10, due Friday, April 8
- No homework is due on Friday,
11, due Friday, April 22
12, due Friday, April 29
Extra Credit problems, due Monday, May 2.
13, for information purposes only (will not be collected and graded)
- Weekly worksheet assignments [1/5 of the
grade], two one-hour tests [1/5 of the grade for each test], final exam
[2/5 of the grade]. A small number of extra credit problems may be
assigned upon request.
- The first mideterm is scheduled for Mo, Feb 28; the
second midterm is tentatively scheduled for Mo, April 11
- Final Exam: 8:00-1:00 am, Friday, May 6