University of Illinois at Urbana-Champaign

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.


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