Reviews elsewhere on the web: Nonlinear News SIAM News (pdf)

# From Calculus to Chaos

The aim of David Acheson's book: From Calculus to Chaos:An Indroduction to Dynamics is to make the mathematics of dynamical systems available to a wider audience than those choose to study it at university.

Acheson has taken on a challenging task, but I felt that he succeeded very well. It's not a book for math-phobics - there are plenty of equations in the book - but it made the subject accessible to anyone with a firm grasp of the later parts of school mathematics. A central theme in the book is the modelling of the equations using simple computer programs, and there are plenty of diagrams of the output, thus helping the reader to get a feel for what the equations are saying.

The book starts by considering differential equations in general, and moves on to those for simple oscillators such as pendulums. This is followed by a look at the motion of the planets. Acheson then describes the equations of waves and diffusion which leads on to a study of fluid flow. Now fluid flow can result in turbulence, and the later part of the book looks at the origins of instability and chaos. The final chapter is 'chaos in reverse' - how to stabilise an upside down pendulum. There are appendices with the QBasic programs used in the book (also available at http://home.jesus.ox.ac.uk/~dacheson/calchaos.html) and an introduction to the QBasic language. (The DOS based QBasic programs look very dated now though).

In summary, if you want a 'taster' of the mathematics of dynamics, or if you are interesting in the computer modelling of differential equations, then you should take a look at this book.

Product Description
What is calculus really for? This book is a highly readable introduction to applications of calculus, from Newton's time to the present day. These often involve questions of dynamics, i.e., of how--and why--things change with time. Problems of this kind lie at the heart of much of applied mathematics, physics, and engineering. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by focusing on the many important and interesting ideas which can get lost amid a snowstorm of detail in conventional texts. The book is aimed at a wide readership, and assumes only some knowledge of elementary calculus. There are exercises (with full solutions) and simple but powerful computer programs which are suitable even for readers with no previous computing experience. David Acheson's book will inspire new students by providing a foretaste of more advanced mathematics and some of its liveliest applications.