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.
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23 of 23 people found the following review helpful:
4.0 out of 5 stars
Best available introduction to perturbation methods,
By
This review is from: Introduction to Perturbation Methods (Hardcover)
I have read several books on perturbation methods, and this book absolutely the best. Perturbation methods are used in problems where the equations (algebraic, ODEs, or PDEs) involve a small parameter, or that evolve on multiple time scales that differ by orders of magnitude. The basic idea is to build an approximate solution to the equation based on a series expansion involving the small parameter. Usually two or more series expansions are built and then combined to yield a solution to the equation that incorporates dynamics on both the slow and fast time scales (for example).The first two chapters introduce the basic concepts of asymptotic expansions. Several informative, though relatively simple, examples are developed in detail to illustrate the techniques. The third chapter introduces techniques for solving problems involving multiple scales. Chapters four and five discuss the WKB method and homogenization techniques. The final chapter shows how perturbation methods can be used in conjunction with techniques from dynamical systems analysis, especially stability analysis and bifurcation theory. The contents of the book are extremely well-chosen and pertinent. Many of the problems and techniques are based on realistic physical systems, and represent the types of problems an applied mathematician is likely to encounter in practice. The book's prose is clear and informative. Only occasionally did I feel that the author had explained something poorly or left out an important piece of information. There are of course a couple of problems with the book. First, most of the exercises are significantly more difficult than the examples, and no hints or solutions are given. This can be a draw-back if you are using the book for self-study. There are a number of typos and errors in the text, though the author's website has a list of errata. Finally, solving perturbation problems in practice often involves subtle tricks, and unfortunately, this book does not discuss or give examples of many of those tricks. Overall, this is definitely the best introductory book on perturbation methods. You should definitely consider this book if you work in applied math or with differential equations.
7 of 8 people found the following review helpful:
5.0 out of 5 stars
nice introduction,
By G. Rogers (Los Angeles) - See all my reviews
This review is from: Introduction to Perturbation Methods (Hardcover)
I found this book explains the ideas very well and also provides examples that help to understand the methods. I also liked all the exercies at the end of each chapter. This is one book that anyone who studies applied mathematics should have on their bookshelf.
0 of 1 people found the following review helpful:
1.0 out of 5 stars
Bad luck???,
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This review is from: Introduction to Perturbation Methods (Hardcover)
I bought it for my textbook at school.
It may not be revised any more, the price is not that cheap. The printing quality is like 10-year-old version, moreover, the hardcover is detached from the pages for just 7 days. I just keep the book in my shelf. It's really terrible.
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Inside This Book
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First Sentence:
In this book, we are interested in using what are known as asymptotic expansions to find approximate solutions of differential equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
composite expansion, next order problem, simple turning point, homogenized problem, homogenized equation, using multiple scales, outer expansion, outer solution, regular expansion, smooth positive function, result from part, appropriate expansion, eikonal equation, connection formulas, traveling wave solutions, possible steady states, homogenization procedure, inner expansion, asymptotic approximation, slow scale, singular perturbation problems, bifurcation value, pitchfork bifurcation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Periodic Substructure, Van Dyke, Multidimensional Problem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this book, we are interested in using what are known as asymptotic expansions to find approximate solutions of differential equations. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
composite expansion, next order problem, simple turning point, homogenized problem, homogenized equation, using multiple scales, outer expansion, outer solution, regular expansion, smooth positive function, result from part, appropriate expansion, eikonal equation, connection formulas, traveling wave solutions, possible steady states, homogenization procedure, inner expansion, asymptotic approximation, slow scale, singular perturbation problems, bifurcation value, pitchfork bifurcation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Periodic Substructure, Van Dyke, Multidimensional Problem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 70
books:
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62
books
cite this book:
See all 62 books citing this book
- Confluent Hypergeometric Functions by L. J. Slater in Back Matter (1), and Back Matter (2)
- Perturbation Methods in Applied Mathematics (Applied Mathematical Sciences) by J. Kevorkian in Back Matter (1), and Back Matter (2)
- Dynamics and Bifurcations (Texts in Applied Mathematics, Vol. 3) by Jack K. Hale in Front Matter, and Back Matter
- Reaction-Diffusion Equations & Applications by N. F. Britton in Back Matter
- Differential Equations and Dynamical Systems by J.K. Hale in Front Matter
See all 70 books this book cites
- Linear Elastic Waves (Cambridge Texts in Applied Mathematics) by John G. Harris on page 36, page 76, and page 119
- Perturbation Methods for Differential Equations by Bhimsen Shivamoggi in Back Matter (1), and Back Matter (2)
- Principles Of Applied Mathematics (Advanced Book Program) by James P. Keener on page 551, and Back Matter
- Applied Mathematics by J. David Logan on page 102
- Waves and Compressible Flow (Texts in Applied Mathematics) by Hilary Ockendon in Front Matter
See all 62 books citing this book
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