MATH 7132
FUNCTIONAL ANALYSIS
Syllabus

Instructor:

Jan Mandel

Office:

CU Denver Building 620

Phone:

Office 556-4475, home 494-8837

Electronic mail:

jmandel@copper, cudnvr::jmandel

Office hours:

Monday 2:00--4:00, Wednesday 4:00-5:15, otherwise by appointment. Most of the time, I will be available also right after the class.

Text:

E. Kreyszig: Introductory Functional Analysis with Applications, John Wiley & Sons, 1989.

Course format:

Rigorous, theorem--proof. All abstract concepts will be illustrated on concrete applications.

Topics covered:

Fundamental properties of Banach and Hilbert spaces. Duality and weak convergence (Chapters 2, 3, 4). Applications to differential and integral equations and quadrature formulas (Selected topics from Chapters 5 and 6). Spectral theory of bounded operators, Banach algebras (Chapter 7). Compact operators and Fredholm alternative (Chapter 8).

Homeworks:

Students should work out all exercises and problems from the relevant parts of the book as well as all exercises given in the class. If you turn the exercises in, I will be happy to look at them but they will not count toward the grade. (This policy will change if too few are turned in.)

Exams:

There will be two exams. The midterm will be in class, given on March 25. It will consist of easier problems and definitions. Use of books or notes will not be allowed. The final will be take-home, given May 1 and due May 8. It will consist of more difficult problems. Note that solution of some problems may require the use of (a part of) the proof of some theorem covered in the class.

Attendance and make-up exams:

The course will follow closely the book (except in Chapters 1 and 2), with some extra illustrations and applications. Attendance is recommended but not required. A replacement exam for the midterm may be available in justified cases. Note: If you have a cold, I'd much prefer if you stay home.

• About this document ...