Course Description
This is the second part of a yearlong graduate course on an introduction to
functional analysis.

Topics
We will mainly cover the following standard topics:
 Locally convex spaces;
 Weak topologies; and
 Distributions.
If time permits, we will also cover the basics of the following special topic of applications:
 Weak convergence methods for variational problems of multiple integrals.

Textbook and References
For the standard topics, we will follow closely the textbook

J. B. Conway, A Course in Functional Analysis, 2nd ed., Springer, 1990.
We will also occasionally consult the following references:
 J. BarrosNeto, An Introduction to the Theory of Distributions,
Reprint ed., Krieger, 1981.
 W. Rudin, Functional Analysis, 2nd ed., McGrawHill, 1991.
 H. H. Schaefer and M. P. Wolff, Topological Vector Spaces,, 2nd ed., Springer, 1999.
 K. Yosida, Functional Analysis,, 6th ed., Springer, 2003.
Lecture notes on the special topic of applications will be distributed in the class.

Homework
There will be a few homework assignments.
Lecture Notes
Weak convergence methods for energy minimization
(pdf)
Homework Assignments
 Assignment 1
(pdf)
 due Wednesday, January 24, 2007.
 Assignment 2
(pdf)
 due Wednesday, February 14, 2007.
 Assignment 3
(pdf)
 due Wednesday, March 14. February 7, 2007.
Last updated by Bo Li on January 26, 2007.
