CS 660 - Fourier Analysis

Prerequisites, MATH 211, MATH 450. This course introduces students to the theory and applications of Fourier analysis. Theoretical topics include Fourier series and their convergence, generalized Fourier series based on orthogonal sets of functions, L^2 spaces, convolutions, the Schwartz class, continuous and discrete Fourier transforms, the Laplace transform. Applications include trigonometric interpolations, mean square approximations, boundary value problems for ordinary and partial differential equations, eigenfunction expansions, Heisenberg’s inequality, random walks, sampling theorems for band-limited signals, frequency analysis of time series, signal and image transformations. Students will develop their analytical and computational skills through a range of theoretical exercises and numerical projects, which are closely related to the above theoretical topics and applications. Although Mathematica will be used for numerical demonstrations in class, students can use any programming languages (Java, C, Python, R, MATLAB, etc.) for the numerical projects. Letter grade. (Offered as needed.) 3 credits