Instructor: David Walnut

Office: Science and Technology I, room 261

Phone: 703 993 1478 (voice); 703 993 1491 (fax)

email: dwalnut@gmu.edu

Course web page: Access through http://math.gmu.edu/coursehomepages.htm

Office hours: TR 1:30--2:30 and by appointment.

Text: E. M. Stein and R. Shakarchi, Fourier Analysis:  An Introduction, Princeton University Press (2003), ISBN 0-691-11384-X.

Prerequisites: Advanced calculus (MATH 315 or equivalent).

Topics: The course will cover some or all of the following topics.

• Solutions to the 1-D wave equation

• Convergence of Fourier series for periodic functions, or functions on the circle (pointwise, uniform, L^2).

• The Fourier transform on R (definition and properties, inversion formula, convolution, decay vs smoothness, Parseval and Plancherel formula)

• Fourier duality in other settings (T, Z, R, Poisson summation formula, the FFT, signals and systems)

• General Orthonormal and related systems (wavelets, frames, Riesz bases, finite frames)

• Applications

• Shannon Sampling and related topics (irregular sampling, Kadec 1/4-theorem, some complex variable techniques)

• The Radon transform (definition, inversion)
  

Grading: There will be regular homework assignments given throughout the semester. Homework counts for approximately 70 % of your final grade.  The remaining 30 % of your grade will be based on a take-home midterm and an in-class final exam.  Precise dates and coverage for these exams will be announced.