Overview

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. 

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9781441999573

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Reviews

From the reviews: 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) 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 Popovic, Mathematical Reviews, Issue 2012 g) 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)

From the reviews: 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)

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