Multiple Scale and Singular Perturbation Methods, Kevorkian, Cole
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Description
Multiple Scale and Singular Perturbation Methods
Authors: (view affiliations) J. Kevorkian, J. D. Cole
Part of the book series: Applied Mathematical Sciences (AMS, volume 114)
Front Matter
Pages i-viii
Introduction
Pages 1-35
Limit Process Expansions for Ordinary Differential Equations
Pages 36-117
Limit Process Expansions for Partial Differential Equations
Pages 118-266
The Method of Multiple Scales for Ordinary Differential Equations
Pages 267-409
Near-Identity Averaging Transformations: Transient and Sustained Resonance
Pages 410-521
Multiple-Scale Expansions for Partial Differential Equations
Pages 522-620
Back Matter
Pages 621-633
About this book
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is “close” to a simpler problem that can be solved