Robert E. O'Malley, Jr – författare

Ordinary differential equations - the building blocks of mathematical modelling - are also key elements of disciplines as diverse as engineering and economics. While mastery of these equations is essential, adhering to any one method of solving them is not: this book stresses alternative examples and analyses by means of which the student can build an understanding of a number of approaches to finding solutions and understanding their behaviour. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application. An important resource for the advanced undergradute, this book would be equally useful for the beginning graduate student investigating further approaches to these essential equations.

Ordinary differential equations - the building blocks of mathematical modelling - are also key elements of disciplines as diverse as engineering and economics. While mastery of these equations is essential, adhering to any one method of solving them is not: this book stresses alternative examples and analyses by means of which the student can build an understanding of a number of approaches to finding solutions and understanding their behaviour. This book offers not only an applied perspective for the student learning to solve differential equations, but also the challenge to apply these analytical tools in the context of singular perturbations, which arises in many areas of application. An important resource for the advanced undergradute, this book would be equally useful for the beginning graduate student investigating further approaches to these essential equations.

Brings together many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and comprehensive fashion. To bridge a gap between analysts of these phenomena, the editors conducted a workshop in April 2002 at University College Cork in Ireland to provide a forum for experts in both fields to share their interests and knowledge. For this book, the editors have compiled research from those practitioners in areas such as reacting systems, semiconductor lasers, shock phenomena in economic modeling, and fluid mechanics, all with an emphasis on hysteresis and singular perturbations.The book begins with a basic introduction to hysteresis and singular perturbation theory, including simple examples from both physics and mathematics. Later chapters address:Applications of hysteresis to economics. Various aspects of the asymptotic theory of singularly perturbed systems. Typical problems of the asymptotic theory of contrast structures.The geometrical approach to an investigation of models with singular perturbations and hysteresis.The editors expect this text not only to be a useful and accessible introduction to techniques and the research literature but also to generate new ideas for researchers and to attract new researchers into this vibrant and dynamic field.

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.