In this book the author presents the theory and techniques underlying perturbation methods in a manner that will make the book widely appealing to readers in a broad range of disciplines. Methods of algebraic equations, asymptotic expansions, integrals, PDEs, strained coordinates, and multiple scales are illustrated by copious use of examples drawn from many areas of mathematics and physics. The philosophy adopted is that there is no single or best method for such problems, but that one may exploit the small parameter given some experience and understanding of similar perturbation problems. The author does not look to perturbation methods to give quantitative answers but rather uses them to give a physical understanding of the subtle balances in a complex problem.
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"...a suitable text book for a one semester graduate course in perturbation methods. It may also be used for self study by physicists who need to know more about perturbation methods for their work....a good starting point for those who wish to enlarge their knowledge of perturbation methods." Edward G. Harris, American Journal of Physics
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Most Helpful Customer Reviews
6 of 6 people found the following review helpful:
2.0 out of 5 stars
Starting Perturbations,
By G. Rogers (Los Angeles) - See all my reviews
This review is from: Perturbation Methods (Cambridge Texts in Applied Mathematics) (Paperback)
This is a nice place to start when learning basic perturbation methods. There are numerous examples and the material is clearly presented. However, there are weak points. One is brevity, as pointed out by the first reviewer. The coverage of the subject of perturbation methods is minimal and some of the topics that are covered are done so with little depth. Another drawback is the emphasis, when discussing applications, on fluids and to a lesser extent mechanics. This makes it somewhat old fashioned. The greatest drawback is the exercises. It is impossible to learn mathematics, and perturbation methods in particular, without doing lots of problems. This text, unfortunately, falls far short in the number and range of problems it provides the reader.
7 of 9 people found the following review helpful:
4.0 out of 5 stars
Great Intro to Perturbation Methods,
By A Customer
This review is from: Perturbation Methods (Cambridge Texts in Applied Mathematics) (Paperback)
This is a wonderful first introduction to perturbation methods. Extremley readable, my only criticism of this text is its brevity. In some places, it lacks detail and doesn't go very deeply into several areas. However, it is the type of book that one can easily pick up, read and learn something usefull. The author's do lot's of examples and once this text is mastered, the student is certaintly ready to read Kevorkian and Cole's classic text on the subject.
3.0 out of 5 stars
Decent Book,
By
This review is from: Perturbation Methods (Cambridge Texts in Applied Mathematics) (Paperback)
This was a decent book. It is especially good for graduate level students. I purchased the book to teach myself perturbation methods for my research project. I used the book in conjunction with Perturbation Methods in Fluid Mechanics. Together I was able to get a complete understanding. Overall this a decent book with a few examples.
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Inside This Book
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First Sentence:
Many of the techniques of perturbation analysis can be introduced in the simple setting of algebraic equations. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Many of the techniques of perturbation analysis can be introduced in the simple setting of algebraic equations. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Van Dyke New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
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100
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- Perturbation Methods (Wiley Classics Library) by Ali Hasan Nayfeh in Back Matter
- Linear Elastic Waves (Cambridge Texts in Applied Mathematics) by John G. Harris on 4 pages
- Mathematical Modeling: Case Studies from Industry by Ellis Cumberbatch on page 20, page 21, and page 65
- Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations (Cambridge Texts in Applied Mathematics) by Paul Glendinning in Front Matter, and Back Matter
- Handbook of Exact Solutions for Ordinary Differential Equations by Valentin F. Zaitsev in Back Matter (1), and Back Matter (2)
- A Modern Introduction to the Mathematical Theory of Water Waves (Cambridge Texts in Applied Mathematics) by R. S. Johnson in Front Matter, and Back Matter
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