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This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians.
The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus.
Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
List of contents
Preface.- Ludwig Prandtl's Boundary Layer Theory.- Asymptotic Approximations.- The Method of Matches Asymptotic Expansions and Its Generalizations.- Wendepunkts and Canards (Turning Points and Delayed Bifurcations).- Two-timing, Geometric, and Multi-scale Methods.- A Simple Multi-scale Procedure for Both Oscillatory and Boundary Layer Problems.- References.- Index.
About the author
Robert O'Malley is a Professor Emeritus at the University of Washington. Dr. O'Malley has studied Electrical Engineering and Mathematics at the University of New Hampshire where he received his baccalaureate and masters degrees. He received his doctorate in Mathematics from Stanford University in 1966. Dr. O'Malley serves on a number of boards, including advisory committees for the National Institute of Standards and Technology, the Electric Power Research Institute, and Argonne National Laboratory.
Summary
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians.
The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus.
Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.
Additional text
“This book covers a wide range of topics in the history of singularly perturbed differential equations. … This is a lucid book written in a deceptively easy style. The book will be useful both for specialists in the theory of asymptotical methods and for experts in various fields of applications. Moreover, it may equip students and young scientists with the essential tools needed for understanding the literature and doing research in the field of asymptotical analysis and its applications.” (Vladimir Sobolev, zbMATH 1336.34002, 2016)
Report
"This book covers a wide range of topics in the history of singularly perturbed differential equations. ... This is a lucid book written in a deceptively easy style. The book will be useful both for specialists in the theory of asymptotical methods and for experts in various fields of applications. Moreover, it may equip students and young scientists with the essential tools needed for understanding the literature and doing research in the field of asymptotical analysis and its applications." (Vladimir Sobolev, zbMATH 1336.34002, 2016)
