Singular Perturbation Theory

The key feature of this volume is its rigorous development of the method of matched asymptotic expansions, the primary tool for analyzing singular perturbation problems. Yet it also covers the basic theory and applications of symbolic programming.

This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and is followed by four chapters of applications to ordinary differential equation problems of increasing complexity. Exercises are included as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems.

Rigorourous development and rigorous application of the method of matched asymptotic expansions

Contains a number of previously unpublished results

Contains several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems

Includes supplementary material: sn.pub/extras

Contenu
Uniform Expansion.- First Order Differential Equations.- Second Order Differential Equations.- Logarithm Problems.- Oscillation Problems.- References.