MATH 241B: Functional Analysis
Winter quarter, 2007

Instructor: Bo Li
(Office: AP&M 5723. Phone: (858) 534-6932. Email:

Class time and place: 12:00 - 12:50, MWF, AP&M 7218

Course Description

This is the second part of a year-long graduate course on an introduction to functional analysis.


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. Barros-Neto, An Introduction to the Theory of Distributions, Reprint ed., Krieger, 1981.
  • W. Rudin, Functional Analysis, 2nd ed., McGraw-Hill, 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.


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.