Nonlinear Functional Analysis

Math 689-001

Spring 2007

This is the web page http://math.gmu.edu/~wanner/courses/m689s07/index.html
It will be updated regularly and always contain the latest information on the course.

General Information:

Instructor: Thomas Wanner
Office: Room 226E, ST1
E-mail: wanner@math.gmu.edu
Web Page: http://math.gmu.edu/~wanner/
Phone: (703) 993-1472
Fax: (703) 993-1491
Office hours: MW 3:00-4:00pm, and by appointment

Lectures: W 4:30-7:10pm, Room A248, Robinson Hall
Prerequisites: Math 675 (Linear Analysis); some familiarity with elementary differential equations.
Textbook: There is no required textbook for this course.

Important Links:

Syllabus:

This course covers fundamental techniques in nonlinear functional analysis, as well as selected applications. Topics include the contraction mapping principle, Frechet derivatives and higher derivatives of nonlinear functions between Banach spaces, the implicit function theorem, Lyapunov-Schmidt reduction, Newton polygon method, topological degree theory, and bifurcation theory. A more detailed syllabus can be found here. It will be updated weekly.

Homework Assignments:

Homework problems will be assigned at the end of each class and posted on the homework page. Some of these assignments will be graded and count towards your homework score. While the remaining ones do not have to be handed in, I do advise everyone strongly to study them and write out the solutions properly. I will go through many of the homework problems in the following class and you will not benefit from this if you have not made a serious attempt at solving them.

Grading Policy:

Your final grade in the course will be determined from graded homework assignments, your performance in a midterm exam, and a comprehensive final exam (dates and details to be announced). Weights for these items will be distributed approximately according to the following schedule:

Homework Midterm Exam Final Exam
40% 30% 30%

Thomas Wanner, January 11, 2007.