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EDITORIAL INFORMATION

Many of the problems faced today by physicists, engineers, and applied mathematicians involve difficulties, such as nonlinear governing equations, variable coefficients, and nonlinear boundary conditions at complex known or unknown boundaries, which preclude their solutions exactly. To solve these problems we are forced to resort to a form of approximation, a numerical solution, or a combination of both. Foremost among the approximation techniques is the systematic method of perturbations (asymptotic expansions) in terms of a small or large parameter or coordinate. This book is concerned only with these perturbation techniques. The purpose of this book is to present in a unified way an account of some of these techniques, pointing out their similarities, differences, and advantages, as well as their limitations. The different techniques are described using examples which start with model simple ordinary equations that can be solved exactly and progress toward complex partial differential equations.

(Extracted from Preface).

GENERAL TABLE OF CONTENTS

-Preface.

-Contents.

-1. Introduction.

-2. Straightforward Expansions and Sources of Nonuniformity.

-3. The Method of Strained Coordinates.

-4. The Methods of Matched and Composite Asymptotic Expansions.

-5. Variation of Parameters and Methods of Averaging.

-6. The Method of Multiple Scales.

-7. Asymptotic Solutions of Linear Equations.

-References and Author Index.

-Subject Index.