Principles of Applied Mathematics provides a comprehensive look at how classical methods are used in many fields and contexts. Updated to reflect developments of the last twenty years, it shows how two areas of classical applied mathematics?spectral theory of operators and asymptotic analysis?are useful for solving a wide range of applied science problems. Topics such as asymptotic expansions, inverse scattering theory, and perturbation methods are combined in a unified way with classical theory of linear operators. Several new topics, including wavelength analysis, multigrid methods, and homogenization theory, are blended into this mix to amplify this theme.This book is ideal as a survey course for graduate students in applied mathematics and theoretically oriented engineering and science students. This most recent edition, for the first time, now includes extensive corrections collated and collected by the author.
Table of Contents
Preface to First Edition, Preface to Second Edition, 1 Finite Dimensional Vector Spaces, 2 Function Spaces, 3 Integral Equations, 4 Differential Operators, 5 Calculus of Variations, 6 Complex Variable Theory, 7 Transform and Spectral Theory, 8 Partial Differential Equations, 9 Inverse Scattering Transform, 10 Asymptotic Expansions, 11 Regular Perturbation Theory, 12 Singular Perturbation Theory, Bibliography, Selected Hints and Solutions, Index
JAMES P. KEENER is a Professor of Mathematics at the University of Utah. He received his Ph.D. from the California Institute of Technology in Applied Mathematics in 1972. In addition to teaching and research in applied math¬ematics, Professor Keener served as Editor-in-Chief of the SIAM Journal on Applied Mathematics, and continues to serve as editor for several leading research journals. He is the recipient of numerous research grants. His research interests are in mathematical biology with an emphasis on physiology. His most recent book, co-authored with James Sheyd, is Mathematical Physiology.