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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