Perturbations

by Murdock, James A.

• ISBN13: 9780898714432
• ISBN10: 0898714435
• Format: Paperback
• Copyright: 1999-09-01
• Publisher: Society for Industrial & Applied

Summary

Perturbations: Theory and Methods gives a thorough introduction to both regular and singular perturbation methods for algebraic and differential equations. Unlike most introductory books on the subject, this one distinguishes between formal and rigorous asymptotic validity, which are commonly confused in books that treat perturbation theory as a bag of heuristic tricks with no foundation. The meaning of 'uniformity' is carefully explained in a variety of contexts. All standard methods, such as rescaling, multiple scales, averaging, matching, and the WKB method are covered, and the asymptotic validity (in the rigorous sense) of each method is carefully proved.

Table of Contents

Preface to the classics edition; Preface

Introduction to Perturbation Theory

Root finding

Regular perturbations

Direct error estimation

Oscillatory Phenomena

Periodic solutions and Lindstedt series

Multiple Scales

Averaging

Transition Layers

Initial layers

Boundary layers

Methods of the WKB type

Taylor's theorem

The implicit function theorem

Second order differential equations

Systems of differential equations

Fourier series

Lipschitz constants and vector norms

Logical quantifiers and uniformity

Symbol index

Index

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