Lectures: 12:30pm-1:45pm on Tue., Thr., in CSIC 4122. Except: March 9, 11; April 6, 8; May 6, in MATH 0401

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).

Additional References:

• Charles L. Epstein, "Introduction to the Mathematics of Medical Imaging", SIAM 2008.
• 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.

Projects: Students may choose between two types of projects: a theory review of a topic connected to applied harmonic analysis; or a Matlab implementation of an application. In either case there will a 30-minute oral presentation with the instructor.

Exams: The midterm will be scheduled during a regular class (1h15min long). Currently, the mid-term is scheduled for March 25 (Thursday), 2010, 12:30pm-1:45pm. You are allowed with one-sided cheat sheet. The final exam will be 2-hour long, and currently it is scheduled for Tuesday, May 18, 2009, 1:30pm-3:30pm. For the final exam you are allowed with a two-sided cheat sheet.
Review Sessions: March 23 (Monday) 1:00-2:00pm and 5:00-6:00pm in CSIC 4122.
May 17 (Monday) 1:00-3:00pm in CSIC 4122.

Grading:

• 20%: homeworks
• 20%: project
• 20%: midterm
• 40%: final exam