Math 555 WINTER 2006
LINEAR ANALYSIS
Instructor: Jim Burke TA: Tony Jin
E-Mail: burke@math.washington.edu E-Mail: jin@math.washington.edu
Office: C-443 Padelford Office: C-414 Padelford
Office Hours: Wed. \& Fri. 1:30-2:20 Office Hours: Thur. 2:30-4:30pm
Phone: 543-6183

URL for the course website:

Text:

Course Notes: available through the course website

A supplementary book on ODES might also be helpful. For example, the book by Coddington \& Levinson is very good.

Course Content:

Math 555 is the second quarter of a three-quarter sequence covering advanced linear algebra and matrix analysis, ordinary differential equations (existence and uniqueness theory, linear systems, numerical approximations), Fourier analysis, introductions to functional analysis and partial differential equations, distribution theory. The topics covered in the second quarter are (1) more on ODEs, (2) an overview of Lebesgue integration on real n-dimensional space, (3) Hilbert Spaces, (4) Fourier series, (5) Fourier transforms and convolutions, (6) compact operators and the spectral theory of bounded linear operators.

Grading:

Homework: 75% -- Final Exam: 25%

Final Exam:

There is an in class final exam on Thursday, March 16, from 8:30am to 10:20am. The final exam will be closed book and notes and will consist of questions similar to those that are to be found on the preliminary exam for this course content.

Incomplete:

A grade of Incomplete will be given only if a student is doing satisfactory work up until the end of the quarter, and then misses the final exam due to a documented medical or family emergency.

OFFICE HOURS

Office hours will be held immediately following class on Wednesdays and Fridays. You may also make an appointment to see me at another time. In addition, if I am in my office and not otherwise occupied, you can stop by my office to ask questions. I prefer that you not drop by just before class as I am usually preparing the lecture at that time.

Important Dates:

Holidays: January 16, M.L.~King Day: February 20, Presidents Day.

Final Exam: Thursday, March 16, from 8:30am to 10:20am.