Prereq.:MATH 1552 or MATH 1553, and one of MATH 2057, MATH 2058, MATH 2065, MATH 2070, MATH 2085, MATH 2090. For students majoring in mathematics, physics and engineering. Fourier analysis on the real line, the integers and finite cyclic groups; the fast Fourier transform; generalized functions; attention to modern applications and computational methods.