Fourier Analysis

Writing primarily for advanced undergraduate or graduate students in mathematics, engineering and physics or for "real life" users of Fourier analysis, Stade (mathematics, U. of Colorado, Boulder) assumes readers have background in calculus in one and several variables. Stade gives weight both to applications in the natural sciences and to the impact Fourier analysis has had on mathematics. He uses a systematic, cause-and-effect approach to his topics, beginning with Fourier coefficients and series, then applying Fourier series to boundary value problems. He then proceeds to the vector space, Sturm-Liouville problems, convolution and the delta function ("a splat and a spike"), Fourier transforms and integrals, local frequency analysis and wavelets. He includes special topics and applications such as the discrete Fourier transform, Fraunhofer diffraction and Fourier optics. Stade includes exercises with each chapter. Annotation c2004 Book News, Inc., Portland, OR (booknews.com)

ERIC STADE, PhD, is Professor of Mathematics at the University of Colorado at Boulder. He received his doctorate in 1988 from Columbia University and has authored a number of refereed journal articles in number theory and physics. He is a member of the American Association of University Professors and the Mathematical Association of America.