Applied Harmonic Analysis

Math 658-200 -- Summer II 2002

Instructor: Dr. Francis J. Narcowich

Office: 302 Milner Hall

E-mail: fnarc@math.tamu.edu

Phone: 845-7369

URL: /~francis.narcowich/

Office Hours: MTWRF 1:35-2:30 and by appointment.

Catalogue Description: Applied Harmonic Analysis. (3-0). Credit 3. Fourier series and Fourier Transform; discrete (fast) Fourier transform; discrete cosine transform; local cosine transform; Radon transform; filters; harmonic analysis on the sphere; radial, periodic, and spherical basis functions; applications. Prerequisite: MATH 657.

Time & Place

M-F 12-1:35, MILN 216.

Required Text

J. J. Benedetto, Harmonic Analysis and Applications, CRC Press, Boca Raton, FL, 1997.

Tests

Midterm, Friday, July 26.

Tentative Schedule

Week	Monday	Tuesday	Wednesday	Thursday	Friday
7/8		1.1,1.3	1.3,1.2	1.4,1.5	1.7,1.8.1
7/15	Filters, 1.10	1.10, 2.1	2.2, 2.3	2.4, 2.5, 2.6.5, 2.7.8	2.7.9-10, 3.1
7/22	3.1, Gibbs' phenomenon	3.3-3.4	3.4, review	3.4, 3.5, review	Midterm
7/29	Filters	DFT, Matlab	FFT, sampling theorem	FT on Rn, RBFs	Interpolation, RBFs
8/5	RKHS, error estimates	Radon transform, S2	Spherical harmonics	Geodesy, SBFs	Presentations
8/12	Presentations

Grading. Your grade will be based on homework, a midterm test, and a presentation of a special topic. The homework will count for 20% of your grade, the midterm for 45%, and the presentation will count for the remaining 35%. Your letter grade will be assigned this way: 90-100%, A; 80-89%, B; 70-79%, C; 60-69%, D; 59% or less, F.

Make-up Policy: I will give make-ups (or satisfactory equivalents) only in cases authorized under TAMU Regulations. In borderline cases, I will decide whether or not the excuse is authorized. Also, if you miss a test, contact me as soon as possible.

Copying Course Materials: ``All printed hand-outs and web-materials are protected by US Copyright Laws. No multiple copies can be made without written permission by the instructor.''