Introduction

The advent of powerful desktop computers has revolutionized scientific analysis and engineering design in fields as disparate as particle physics and telecommunications. "Modern Mathematical Methods for Physicists and Engineers" provides an up-to-date mathematical and computational education for students, researchers, and practicing engineers. It is an ideal textbook and reference for senior undergraduate and graduate students in the physical sciences and electrical and telecommunications engineering.

The book begins with a review of computation and then develops a range of key concepts including sets, groups, fields, and linear algebra. More advanced topics covered include solution of linear equations, inner products and norms, least-squares approximations, the discrete Fourier transform, eigenvalues and eigenvectors, the singular-value decomposition, best approximations in the maximum norm, Hilbert and Banach spaces, and matrix representations of groups. The treatment of special functions is noteworthy for being based on group representation theory, rather than complex variables or differential equations.

The book contains well over 400 homework problems, which make it useful for self-study as well as classroom use.

C. D. Cantrell received his Bachelor's degree from Harvard in 1962 and his Ph.D. from Princeton in 1968. He joined the faculty of Swarthmore College in 1967. In 1973 he left to join the staff at the Los Alamos National Laboratory, where he carried out research on molecular spectroscopy and laser isotope separation through 1979. Since then he has been at the University of Texas at Dallas, where he is Professor of Electrical Engineering and Physics, Director of the Photonic Technology and Engineering Center, and Associate Dean of the Erik Jonsson School of Engineering and Computer Science. Professor Cantrell is a Fellow of the IEEE, the American Physical Society, and the Optical Society of America, and is a recipient of the IEEE Third Millennium Medal.