**Math 442 (Functional Analysis) Spring 2004**

**
**### Course Description

This course is a continuation of Math 441. In the first part of the
course, we will cover the fundamental aspects of the theory of
functional analysis (Banach spaces, Open Mapping and Closed Graph
Theorems, Principle of Uniform Boundedness, weak topologies and
Alaoglu's theorem, linear operators), following Chapters III--VI of
Conway's book. In the second (shorter) half of the course, we will
treat abstract measure theory and integration of functions valued in
Banach spaces. We will draw on several sources for this latter
material, including the texts by Rudin and Diestel--Uhl. Time
permitting, we will conclude the course with a brief introduction to
distributions and Sobolev spaces, with applications to PDE's.

**Instructor:** Prof. Jeremy Tyson

**Office Location:** 227B Illini Hall (go through the door
for 227 Illini Hall---my office is one of the two offices located
inside 227 IH)

**Office Phone:** 244-4132

**Email:**
`tyson@math.uiuc.edu`

**Office Hours:** TueThu 11:00-12:00, Wed 1:00-2:00 or by appointment

**Lecture Times:** TueThu 9:00-10:20

**Lecture Location:** 341 Altgeld Hall

**Course Text:**
*A Course in Functional Analysis* by J. B. Conway, *Graduate
Texts in Mathematics*, #96, Springer-Verlag, 1990.

**Other recommended texts:**
*Functional Analysis* by W. Rudin, *International Series in
Pure and Applied Mathematics*, McGraw-Hill, 1991.
*Vector Measures* by J. Diestel and J. J. Uhl,
*Mathematical Surveys*, #15, AMS, 1977.
*Real Analysis* by H. L. Royden, MacMillan Publishing
Company, 1988.
*Measure Theory* by P. R. Halmos, van Nostrand, 1950.

Syllabus

Lecture Log

**Homework Assignments:**

Homework #1
--- Notes for Homework #1

Homework #2
--- Notes for Homework #2

Homework #3
--- Notes for Homework #3

Homework #4
--- Notes for Homework #4

Homework #5
--- Notes for Homework #5

Homework #6

Homework #7