Spring 2011. MATH5341. Section 001.

### Functional Analysis II

Instructor: Luan Thach Hoang
Office: MA 234. Phone: (806) 742-2580 Ext 232. Fax: (806) 742-1112
Homepage: http://www.math.ttu.edu/~lhoang/
Office hours: MWF 3:00 pm - 4:00 pm

Classroom and Time: MA 011, MWF 2:00 pm - 2:50 pm.

Course website: http://www.math.ttu.edu/~lhoang/2011Spr-M5341/

Text: A course in Functional Analysis, 2nd edition by John B. Conway, published by Springer.

Course Description: Linear operators on a Banach space and spectral theory, normal operators on Hilbert space, unbounded operators, Fredholm theory, and applications.

Course Outline: Selected topics among the following:

• Chapter V: Weak topologies
• Chapter VI: Linear Operators on a Banach Space
• Chapter VII: Banach Algebras and Spectral Theory for Operators on a Banach Space
• Chapter IX: Normal Operators on Hilbert Space
• Chapter X: Unbounded Operators
• Chapter XI: Fredholm Theory
• Additional Topics: Distribution Theory, Fourier Analysis, Theory of Semi-groups.

Expected Learning Outcomes: Bounded operators on Banach and Hilbert spaces and their spectral theories, Fredhom theory, unbounded operators, and applications.

Methods of Assessment of Learning Outcomes: Assessment of the learning outcomes will be achieved through homework assignments, two midterm exams, and a final exam.

Grading policy: Homework will be assigned weekly and will count for 30% of the grade. There will be two midterm exams in class, each will count for 20% of the grade. The final exam will count for 30% of the grade. All in-class exams are closed-book. No make-up exams are given unless legitimate documents for excuses are presented to the instructor at least a week in advance. Grading Scale: A: 90%-100%, B: 80%-89%, C: 70%-79%, D: 60%-69%, F: below 60%.

Attendance Policy: Students are expected to attend every class and are responsible for all information given in class.

Examination Schedule:

• Midterm 1: Friday, February 18.

• Midterm 2: Friday, April 8.

• FINAL EXAM: Monday, May 9, 4:30 p.m. - 7:00 p.m., Room MA 011.

Critical Dates:

• Jan. 12: Classes begin.
• Jan. 17: Martin Luther King Jr. Day. Holiday.
• Jan. 28: Last day to drop a course and receive a refund.
• Mar. 12 - 20: Spring Break.
• Apr. 25: No classes.
• Apr. 27 - May 3: No exams.
• May 3: Last day of classes.

Academic Misconduct: Academic dishonesty is intolerable and will be punished to the full extent allowed by the University policy.

Civility in the Classroom: Students are expected to assist in maintaining a classroom environment that is conducive to learning.

Students with Disabilities: Any student who because of a disability may require special arrangements in order to meet course requirements should contact the instructor as soon as possible. "I would appreciate hearing from anyone who has a disability that may require special accommodations. I am sure we can work out whatever arrangements are necessary. Please see me during my office hours."

NOTE: When needed, the instructor will communicate with the students using their TTU email addresses. At the beginning of the semester, the instructor will send out a message to confirm the students' email addresses.