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Theory of Functions of a Real Variable II, Math 502

Spring 2009

Eric Carlen

Hill Center 632, 732-445-5788, carlen at math.rutgers.edu

OFFICE HOURS:  Thursday, 3:20-4:40

COURSE DESCRIPTION:


This course continues the introduction to real analysis that was begun the previous semster in Math 501. The text for the course is Real Analysis: Modern Techniques and their Applications by G. Folland. The focus of the course will be on material from Chapters 4 through 8 of this text. On certain topics I will post additional class notes, and will sometimes suggest additional reading from the text Analysis by Lieb and Loss. For more information on the course, see the departmental description.

There will be weekly problem assignments. These will be graded, with the lowest grade dropped, and will account for 30 percent of the course grade. A midterm will account for another 30 percent, and a final exam the final 40 percent.

A detailed syllabus will be posted shortly, once I get a feel for the pace at which we can best proceed. In the meantime, the reading for the lectures of Jan 20, 23 and 27 is Section 1-4 and 6-7 in Chapter 4 of the text, together with these notes on topology.

The first homework assignment, due February 3 in class, consists of the exercises at the end of the notes.

The second homework assignment is due Feb 17 in class.

The third homework assignment will be due Tuesday March 2 in class. Notes on the solutions of the exercises that focus on points that were less clearly dealt with in several homework solutions are now available.

Here are some sample review exercises to prepare for the midterm. These are the "leftovers" from preparing the midterm, and some of them are leftover because I decided the solutions were a bit too tricky for an in class exam. Others should be O.K. for that, and still all of them should be good to consider: Try asking yourself which ones might be Hahn-Banach exercises, which ones might be Uniform Boundeedness exercises, which ones might turn on the Projection Lemma, etc. I'll be available Thursday during my office hour to provide soluitions or hints.

Here is the midterm exam that was given in class March 13. I will go over this exam in class on Tuesday, March 24 before moving on to the new lecture topics.

Here are notes on uniform convexity and smoothness. The excercises at the end are due in class, Fiday, April 3.

Here is the FINAL EXAM. Please turn it in to me by noon on Monday, May 11 so that I will have time to carefully grade these. Instructions are included, but as advertised, you are to do 5 out of 6. And of course, unlike homework,all work is to be entirely your own. Do not discuss the problems with anyone else.

A very good follow up course, beside the functional analysis course, is the partial differential equations course. Yanyan Li is teaching it this coming Fall, and I will teach it next Spring. It is a great course in which to see the ideas we have deen developing here "come to life".