Lectures: 11.00am-12.15pm on Tue., Thr., in Math 1308.

Prerequisites: MATH 246

Textbook:
Required Textbook: "A First Course in Fourier Analysis" by David W. Kammler, Cambridge University Press 2000 (1st Edition), or 2007 (2nd Edition).

Recommended Textbook: "Introduction to the Mathematics of Medical Imaging", by Charles L. Epstein, SIAM 2008

Additional References:

• Elliott H. Lieb and Michael Loss, "Analysis", AMS 2001.
• John J. Benedetto, "Harmonic Analysis and Applications", CRC Press 1996.

Description: MATH 464 is an introduction to transformed methods used in science and engineering applications. Lectures will cover topics including: Fourier transform, Fourier series, discrete and fast Fourier transform (DFT and FFT), Laplace transform, Poisson Summation, and sampling. Optional Topics: Distributions and operational calculus, PDEs, Wavelet transform, Radon transforms. Applications: Imaging, Speech Processing, PDEs of Mathematical Physics, Communications, Inverse Problems.

Assignments: Homework must be submitted on the date assigned. Homework must be prepared without consulting any other person. You may however consult any written reference. In this case you should cite the reference. Results taken from the reference should be (re)stated to the notation used in the course. Explanation should be given in complete English sentences. Written work must be legible and clear.

Exams: The midterm will be scheduled during a regular class (1h15min long). Currently, the mid-term is scheduled for March 12, 2009, 11am-12.15noon. You are allowed with one-sided cheat sheet. The final exam will be 2-hour long, and currently it is scheduled for Thursday, May 14, 2009, 8.00am-10.00am. For the final exam you are allowed with a two-sided cheat sheet.

Grading:

• 25%: homeworks
• 25%: midterm
• 50%: final exam