Introduction to Perturbation Methods (Texts in Applied Mathematics Book 20) 2nd Edition by Mark H. Holmes (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book introduce ideas behind perturbation methods in a very natural form. There is a lot of good examples from which you can learn important techniques and theory. Chapter about homogenization techniques is very well written and useful. If you study engineering of any kind, physics or applied math you need this book.

⭐Useful as a companion text but hard to read on its own. But this is typical of books in this springer series of texts in applied mathematics

⭐Well written and organized clearly. Definitely a good starting point for an applied mathematics course. Sometimes the examples skip important steps.

⭐Mark Holmes: Introduction to Perturbation Methods, Second Edition, Springer, New York, NY, 2013Reviewed by D. Subbaram Naidu, Idaho State UniversityThe book is composed of 6 chapters with the topics of Introduction to Asymptotic Approximations, Matched Asymptotic Expansions, Multiple Scales, The WKB and Related Methods, The Method of Homogenization, and Introduction to Bifurcation and Stability and appendices on Taylor Series, Solution and Properties of Transition Layer Equations, Asymptotic Approximations of Integrals, Second-Order Difference Equations, and Delay Equations.This reviewer, with background in singular perturbations and time scales in automatic control theory and applications, enjoyed reading this book that has a refreshing flavor to perturbation methods. Some of the interesting and useful features of this book are the coverage of both ordinary and partial differential equations related to applications to nonlinear wave and diffusion problems and others, generous sprinkling of a number of examples and both section-wise and chapter-wise exercises throughout the book paving the best way of “learning mathematics”, solutions to some of the exercises available from the author’s home page and the MATLAB® files, that were used to generate the figures, also available from author’s web page.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.

⭐Exercises are almost impossible to solve, even for the professor who assign this book as textbook.

⭐presented with high quality

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