This 400-page book offers an introduction
to a wide variety of topics in continuous and discrete
time dynamical systems. In 20 short chapters, both
theoretical concepts and specific sytems and
applications are treated, in a clear and non-detailed way. Throughout the
book, Maple is used for
the symbolic computations, and simulation and visualisation of the various
dynamical systems.
The level of the book varies quite a bit. Most of the chapters are useful
at senior undergraduate
and graduate level, but later chapters require more introduction and details
than are given. The
author suggests that these chapters be used for projects. For this, the
list of references that
accompanies each chapter is very helpful.
In general, the book focuses on explaining concepts, and providing exercises
and examples that
make the concepts come alive, in the form of Maple programs. The author
never goes into much
detail. Theorems are usually given without proof. The book will be useful
for all kinds of dynamical
systems courses, but for theoretically oriented ones it will not be the
main text.
The various Maple programs in the book are relatively short, written out
in full, and readable. To use
them, no previous experience with Maple is needed, as the language is straightforward.
Its few
syntactical quirks are covered in Chapter 0, a short and practical introduction
to Maple.
The book shows the power of using a computer algebra program to study dynamical
systems, and, by
giving so many worked examples, provides ample opportunity for experiments.
At the same time, the
book gives a broad overview of dynamical systems, covering all standard
examples, and many interesting
and less familiar ones. The book is well written and a pleasure to read,
which is helped by its attention to
historical background.
Reviewed by Gerton Lunter 2002.