Preface Preface to the Second Edition In the second edition of this book, much of the material has been rewritten to clarify the presentation. It also has provided the opportunity for correcting many minor typographical errors or mistakes. Also, the definition of a chaotic attractor has been changed to include the requirement that the chaotic attractor is transitive. This is the usual definition and it eliminates some attractors that should not be called chaotic. Several new applications are included for systems of differential equations in Part 1. I would encourage readers to email me with suggestions and further corrections that are needed. R. Clark Robinson March 2012 Preface to the First Edition This book is intended for an advanced undergraduate course in dynamical sys- tems or nonlinear ordinary differential equations. There are portions that could be beneficially used for introductory master level courses. The goal is a treatment that gives examples and methods of calculation, at the same time introducing the mathematical concepts involved. Depending on the selection of material covered, an instructor could teach a course from this book that is either strictly an intro- duction into the concepts, that covers both the concepts on applications, or that is a more theoretically mathematical introduction to dynamical systems. Further elaboration of the variety of uses is presented in the subsequent discussion of the organization of the book. The assumption is that the student has taken courses on calculus covering both single variable and multivariables, a course on linear algebra, and an introductory xiii

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