This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe matics, Ginn-Blaisdell, 1968. We present the material at a level which 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. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B.
Erscheinungsdatum: 01.12.2010

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J. Kevorkian, J. D. Cole, J.D. Cole

IIASA International Institute for Applied Systems Analysis

Springer New York : Imprint : Springer

Springer Science & Business Media

Springer London, Limited

Applied mathematical sciences (Springer-Verlag New York Inc.), A revised and updated version of J.D. Cole's Perturbation methods in applied mathematics, 1968, New York, NY, 2010

Applied mathematical sciences, 1., st ed. 1981. corr. 2nd printing. Softcover version of original hardcover edition 1981, New York, NY, 2010

Applied mathematical sciences (Springer-Verlag New York Inc.), 34, New York, NY, 1981

Applied mathematical sciences, Nachdr, New York, NY, 2010

United States, United States of America

Springer Nature, New York, NY, 2013

Austria, Austria

Dec 01, 2010

lg1123732

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Source title: Perturbation Methods in Applied Mathematics (Applied Mathematical Sciences)

This book is a revised and updated version, including a substantial portion of new material, of J.D. Cole's text Perturbation Methods in Applied MatheƯ matics, Ginn-Blaisdell, 1968. We present the material at a level which 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. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differƯ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B

Front Matter....Pages i-x
Introduction....Pages 1-16
Limit Process Expansions Applied to Ordinary Differential Equations....Pages 17-104
Multiple-Variable Expansion Procedures....Pages 105-329
Applications to Partial Differential Equations....Pages 330-480
Examples from Fluid Mechanics....Pages 481-545
Back Matter....Pages 546-559

2013-08-01