ebook img

Singular Perturbation Theory Math and Analyt Technique w. appl to Engineering PDF

309 Pages·2004·6.69 MB·English
Save to my drive
Quick download
Download
Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.

Preview Singular Perturbation Theory Math and Analyt Technique w. appl to Engineering

SINGULAR PERTURBATION THEORY MATHEMATICAL AND ANALYTICAL TECHNIQUES WITH APPLICATIONS TO ENGINEERING MATHEMATICAL AND ANALYTICAL TECHNIQUES WITH APPLICATIONS TO ENGINEERING Alan Jeffrey, Consulting Editor Published: Inverse Problems A. G. Ramm Singular Perturbation Theory R. S. Johnson Forthcoming: Methods for Constructing Exact Solutions of Partial Differential Equations with Applications S. V. Meleshko The Fast Solution of Boundary Integral Equations S. Rjasanow and O. Steinbach Stochastic Differential Equations with Applications R. Situ SINGULAR PERTURBATION THEORY MATHEMATICAL AND ANALYTICAL TECHNIQUES WITH APPLICATIONS TO ENGINEERING R. S. JOHNSON Springer eBookISBN: 0-387-23217-6 Print ISBN: 0-387-23200-1 ©2005 Springer Science + Business Media, Inc. Print ©2005 Springer Science + Business Media, Inc. Boston All rights reserved No part of this eBook maybe reproducedor transmitted inanyform or byanymeans,electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Springer's eBookstore at: http://ebooks.springerlink.com and the Springer Global Website Online at: http://www.springeronline.com To Ros, who still, after nearly 40 years, sometimes listens when I extol the wonders of singular perturbation theory, fluid mechanics or water waves —usually on a long trek in the mountains. This page intentionally left blank CONTENTS Foreword xi Preface xiii 1.Mathematicalpreliminaries 1 1.1 Some introductory examples 2 1.2 Notation 10 1.3Asymptotic sequences and asymptotic expansions 13 1.4 Convergent series versus divergent series 16 1.5 Asymptotic expansions with a parameter 20 1.6 Uniformity or breakdown 22 1.7 Intermediate variables and the overlap region 26 1.8 The matching principle 28 1.9Matching with logarithmic terms 32 1.10 Composite expansions 35 Further Reading 40 Exercises 41 viii Contents 2.Introductory applications 47 2.1 Roots of equations 47 2.2 Integration of functions represented by asymptotic expansions 55 2.3Ordinary differential equations: regular problems 59 2.4 Ordinary differential equations: simple singular problems 66 2.5 Scaling of differential equations 75 2.6 Equations which exhibit a boundary-layer behaviour 80 2.7 Where is the boundary layer? 86 2.8 Boundary layers and transition layers 90 Further Reading 103 Exercises 104 3. Further applications 115 3.1 A regular problem 116 3.2 Singular problems I 118 3.3 Singular problems II 128 3.4 Further applications to ordinary differential equations 139 Further Reading 147 Exercises 148 4.The method of multiple scales 157 4.1 Nearly linear oscillations 157 4.2 Nonlinear oscillators 165 4.3 Applications to classical ordinary differential equations 168 4.4 Applications to partial differential equations 176 4.5 A limitation on the use of the method of multiple scales 183 4.6 Boundary-layer problems 184 Further Reading 188 Exercises 188 5.Some worked examples arising from physical problems 197 5.1 Mechanical & electrical systems 198 5.2 Celestial mechanics 219 5.3 Physics of particles and of light 226 5.4 Semi- and superconductors 235 5.5 Fluid mechanics 242 ix 5.6 Extreme thermal processes 255 5.7 Chemical and biochemical reactions 262 Appendix: The Jacobian Elliptic Functions 269 Answers and Hints 271 References 283 Subject Index 287

Description:
The theory of singular perturbations has evolved as a response to the need to find approximate solutions (in an analytical form) to complex problems. Typically, such problems are expressed in terms of differential equations which contain at least one small parameter, and they can arise in many field
See more

The list of books you might like

Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.