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Singular-Perturbation Theory : An Introduction with Applications - Donald R. Smith

Singular-Perturbation Theory

An Introduction with Applications

Hardcover Published: 30th November 2006
ISBN: 9780521300421
Number Of Pages: 520

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This book presents an introduction to singular-perturbation problems, problems which depend on a parameter in such a way that solutions behave nonuniformly as the parameter tends toward some limiting value of interest. The nature of the nonuniformity can vary from case to case, and so the author considers and solves a variety of problems, mostly for ordinary differential equations. He constructs (approximate) solutions for oscillation problems, using the methods of averaging and of multiple scales. For problems of the nonoscillatory type, where solutions exhibit 'fast dynamics' in a thin initial layer, he derives solutions using the O'Malley/Hoppensteadt method and the method of matched expansions. He obtains solutions for boundary-value problems, where solutions exhibit rapid variation in thin layers, using a multivariable method. After a suitable approximate solution is constructed for each problem, the author linearizes the problem about the proposed approximate solution, and, emphasizing the use of the Banach/Picard fixed-point theorem, presents a study of the linearization. This book will be a welcome text and reference to students at the graduate and senior undergraduate levels studying perturbation theory for differential equations, and to pure and applied mathematicians, engineers, and scientists who use differential equations in the modeling of natural phenomena.

Preliminary results
Initial-Value Problems of Oscillatory Type
Precession of the planet Mercury
Krylov/Bogoliubov averaging
The multiscale technique
Error estimates for perturbed-oscillation problems
Initial-Value Problems of Overdamped Type
Linear overdamped initial-value problems
Nonlinear overdamped initial-value problems
Conditionally stable problems
Boundary-Value Problems
Linear scalar problems
Linear first-order systems
Nonlinear problems
Name index
Subject index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521300421
ISBN-10: 0521300428
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 520
Published: 30th November 2006
Country of Publication: GB
Dimensions (cm): 22.86 x 15.24  x 3.33
Weight (kg): 0.93

Earn 982 Qantas Points
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