UK Nonlinear News, February 1998

From Calculus to Chaos : An Introduction to Dynamics

By David Acheson

Oxford University Press 1997

Reviewed by Professor John Brindley

This is a thoroughly excellent little book and a most valuable addition to the literature on dynamics. Its approach is quite unique, bringing together a vast range of real physical phenomena and elucidating the essential dynamics by means of well chosen toy models in the form of differential equations. All the necessary analytical techniques are slipped in with minimum of fuss, and numerical methods are employed throughout in such a way that the reader is encouraged to use the computer as an experimental tool for exploring behaviour. This is as it should be, and to ease the way, Acheson has provided a hatful of simple programmes within the capabilities of the most humble beginner. Specifically, chapters concerned with calculus, ordinary differential equations and simple particle motion (oscillations, orbits) are followed by brief mention of spatially extended systems and pointers to some of the excitements of fluid mechanics (so well introduced by the same author in his earlier book on Elementary Fluid Dynamics). Final chapters introduce a number of more advanced topics including stability concepts, nonlinear oscillators and some elements of catastrophe theory and chaos theory; many of these features are exemplified by complexities of the motion of a not so simple pendulum.

A feature of the book is its use of graphs, diagrams and visual aids of all sorts, including the odd historic or (in at least one case) unlikely picture. It is also distinguished by the care with which solutions to exercises are presented and analysed - no less than 30 pages are devoted to this vital but usually neglected function.

In his introduction the author hopes for a wide readership and trusts that readers will enjoy discovering the excitements of dynamics. I think he has done much to ensure that they will, and the book deserves a place on the shelves of all serious students, teachers and researchers.

A news item relating to this book was carried in UK Nonlinear News 10. --- UK Nonlinear News.

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