Singular Perturbation Theory

This book is a rigorous presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems.   A knowledge of conventional asymptotic analysis is assumed. The first chapter introduces the theory and is followed by four chapters of applications to ordinary differential equation problems of  increasing complexity.  Exercises are included as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems. 

• matched asymptotic expansions
• singular perturbations
• ordinary differential equations

From the reviews:

“The book is composed of five chapters on Uniform Expansion … . There are a number of exercises at the end of each chapter for those readers who want to try to solve problems to understand the theory described in the chapter. Although the book is aimed at senior or graduate students in applied mathematics, it can as well be used by graduate students in engineering (electrical, mechanical, aerospace) and other researchers working in national labs and industry.” (D. Subbaram Naidu, Amazon.com, May, 2013)

“The motivation underlying this book is the rigorous development, and application, of the method of matched asymptotic expansions, one of the principal techniques used in the analysis of singularly perturbed differential equation problems … . Exercises at the end of each section provide problems for further study … . In sum, this slim volume thus contains a treasure trove of interesting examples of singularly perturbed differential equation problems, many of which do not seem to have been published before.” (Nikola Popović, Mathematical Reviews, Issue 2012 g)

“For all of us who are still challenged by matched expansions, Skinner’s short, unique monograph will be valuable.”­­­ (Robert E. O’Malley Jr., SIAM Review, Vol. 53 (4), 2011)

“This book provides a nice presentation of the method of matched asymptotic expansions, the primary tool for attacking singular perturbation problems. … Exercises are included at the end of each chapter as well as several Maple programs for computing the terms of the various asymptotic expansions that arise in solving the problems. … This book intents to be a supplement or follow-up to a first year graduate course in asymptotic and perturbation analysis.” (Vasile Dragan, Zentralblatt MATH, Vol. 1223, 2011)

• , Mathematical Sciences, University of Wisconsin- Milwaukee, Milwaukee, USA

  Lindsay A. Skinner

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