Overview
- Lots of examples and exercises
- Class test for over 20 years
- Includes delay equations
- Includes supplementary material: sn.pub/extras
Part of the book series: Texts in Applied Mathematics (TAM, volume 20)
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Table of contents (6 chapters)
Keywords
About this book
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.
One hundred new pages added including new material on transcedentally small terms, Kummer's function, weakly coupled oscillators and wave interactions.
Reviews
From the reviews of the second edition:
“The book is composed of 6 chapters with the topics of Introduction to Asymptotic Approximations, Matched Asymptotic Expansions … Second-Order Difference Equations, and Delay Equations. … enjoyed reading this book that has a refreshing flavor to perturbation methods. … The book can be used for both undergraduate and graduate courses in mathematics and physics and also in aerospace, electrical and mechanical engineering areas. Those working in industry will find this book useful in addressing some of the nonlinear problems in real-world situations.” (D. Subbaram Naidu, Amazon.com, March, 2013)
“This introduction to perturbation methods is a rich, well-written … textbook. … Students and their instructors will benefit greatly from this author’s evident broad understanding of applied mathematics and mechanics and his uncommon pedagogical abilities and scholarship. … Holmes’s text will be tough to beat for the ambitious and talented.” (Robert E. O’Malley, Jr., SIAM Review, Vol. 55 (3), 2013)
“This is the second edition of the well-known book widely used by researchers in applied mathematics and physics, engineers, graduate and postgraduate students. Its distinctive feature is that it includes a variety of substantive physically motivated examples on various kinds functional equations and also exercises both in and at the end of every chapter.” (Boris V. Loginov, zbMATH, Vol. 1270, 2013)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Introduction to Perturbation Methods
Authors: Mark H. Holmes
Series Title: Texts in Applied Mathematics
DOI: https://doi.org/10.1007/978-1-4614-5477-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-1-4614-5476-2Published: 05 December 2012
Softcover ISBN: 978-1-4899-9613-8Published: 28 January 2015
eBook ISBN: 978-1-4614-5477-9Published: 05 December 2012
Series ISSN: 0939-2475
Series E-ISSN: 2196-9949
Edition Number: 2
Number of Pages: XVIII, 438
Topics: Partial Differential Equations, Ordinary Differential Equations, Analysis