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

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