Singular Perturbation Theory 2011th Edition by Lindsay A. Skinner (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review 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) From the Back Cover 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.

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

⭐Reading this book made me realize that I do enjoy mathematics. Written in easy to understand language. Truly a great read. Thank You Dr. Skinner

⭐Lindsay Skinner, Singular Perturbation Theory, Springer, New York, NY, 2011Reviewed by D. Subbaram Naidu, Idaho State UniversityThe book is composed of five chapters on Uniform Expansion; First Order Differential Equations; Second Order Differential Equations; Logarithm Problems; and Oscillation Problems. The basic theory is given in the first chapter on Uniform Expansions and the applications to differential equations and oscillatory problems are given in the remaining chapters.In spite of the fact that there are a number of books on singular perturbations, according to the author, “what distinguishes this book from others is the rigorous development and rigorous application of the method of matched asymptotic expansions”. Another unique feature of the book is the integration of the material with a well-known software Maples for solving the problems in the book. 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. Finally, this reviewer, with background in singular perturbations and time scales in automatic control theory and applications [1-6], enjoyed reading this book that has a refreshing flavor to asymptotic expansions in the theory of singular perturbations.1) D.S. Naidu, Applications of Singular Perturbation Technique to Problems in Control Systems, Ph.D. Thesis, Indian Institute of Technology (IIT), Kharagpur, 1977.2) D.S. Naidu and A.K. Rao, Singular Perturbation Analysis of Discrete Control Systems, Lecture Notes (Research Monograph) in Mathematics, Vol.~1154, Springer-Verlag, Berlin, West Germany, 1985.3) D.S. Naidu, Singular Perturbation Methodology in Control Systems, IEE Control Engineering Series, Peter Peregrinus Limited, Stevenage Herts, UK, 1988.4) D.S. Naidu, “Singular Perturbations and Time Scales in Control Theory and Applications: Overview”, Special Issue on Singularly Perturbed Dynamic Systems in Control Technology (edited by Z. Gajic) in Dynamics of Continuous, Discrete and Impulsive Systems (DCDIS) Journal, Vol.~9, pp.~233-278, June 2002 (Invited Survey Paper: 46 pages and 467 references).5) D.S. Naidu and A.J. Calise, “Singular perturbations and time scales in guidance and control of aerospace systems: a survey”, AIAA Journal of Guidance, Control and Dynamics, Vol.~24, Nr.~6, pp.~1057-1078, November-December 2001 (Invited Survey Paper: 22 pages and 412 references; Presented by AIAA with a plaque inscribed “Survey Paper Citation” by AIAA).6) D.S. Naidu, “Singular Perturbation Analysis of a Flexible Beam Used in Underwater Exploration”, International Journal of Systems Science, Vol. 42, No. 1, pp.~183-194, January 2011. © Maplesoft, a division of Waterloo Maple Inc.

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