Introduction to perturbation methods
著者
書誌事項
Introduction to perturbation methods
（Texts in applied mathematics, 20）
Springer-Verlag, c1995
- : us
- : gw
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注記
Includes bibliographical reference(p.[313]-329) and index
内容説明・目次
- 巻冊次
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: us ISBN 9780387942032
内容説明
This introductory graduate text is based on a graduate course the author has taught repeatedly over the last ten years to students in applied mathematics, engineering sciences, and physics. Each chapter begins with an introductory development involving ordinary differential equations, and goes on to cover such traditional topics as boundary layers and multiple scales. However, it also contains material arising from current research interest, including homogenisation, slender body theory, symbolic computing, and discrete equations. Many of the excellent exercises are derived from problems of up-to-date research and are drawn from a wide range of application areas.
目次
Series Preface.- Preface.- Chapter 1: Introduction to Asymptotic Approximations.- Chapter 2: Matched Asymptotic Expansions.- Chapter 3: Multiple Scales.- Chapter 4: The WKB and Related Methods.- Chapter 5: The Method of Homogenization- Chapter 6: Introduction to Bifurcation and Stability.- Appendix A1: Solution and Properties of Transition Layer Equations.- Appendix A2: Asymptotic Approximations of Integrals.- Appendix A3: Numerical Solution of Nonlinear Boundary- Value Problems.- References.- Index.
- 巻冊次
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: gw ISBN 9783540942030
内容説明
This text is intended as an introductory graduate text, dealing with many of the perturbation methods currently used by applied mathematicians, scientists and engineers. The author based his book on a graduate course he has taught several times, and the only prerequisite for the course is a background in differential equations. Each chapter begins with an introductory development of the topic and this usually means examples involving ordinary differential equations. The book covers traditional topics, such as boundary layers and multiple-scales; however, it also contains material arising from current research interest. The latter includes homogenization, slender body theory, symbolic computing and discrete equations.
目次
Series Preface.- Preface.- Chapter 1: Introduction to Asymptotic Approximations.- Chapter 2: Matched Asymptotic Expansions.- Chapter 3: Multiple Scales.- Chapter 4: The WKB and Related Methods.- Chapter 5: The Method of Homogenization- Chapter 6: Introduction to Bifurcation and Stability.- Appendix A1: Solution and Properties of Transition Layer Equations.- Appendix A2: Asymptotic Approximations of Integrals.- Appendix A3: Numerical Solution of Nonlinear Boundary- Value Problems.- References.- Index.
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