Enhanced descriptions from Syndetics:

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 highlighting only the most 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 showing just how interesting the subject can be.

Table of contents provided by Syndetics

• 1 Introduction
• 2 A Brief Review of Calculus
• 3 Ordinary Differential Equations
• 4 Computer Solution Methods
• 5 Elementary Oscillations
• 6 Planetary Motion
• 7 Waves and diffusion
• 8 The Best of all Possible Worlds?
• 9 Fluid Flow
• 10 Instability and Catastrophe
• 11 Nonlinear Oscillations and Chaos
• 12 The Not-so-simple Pendulum
• Further reading
• Appendix A Elementary programming in QBASIC
• Appendix B Ten programs for exploring dynamics
• Solutions to the exercises
• Index

Reviews provided by Syndetics

CHOICE Review

Acheson presents an introduction to the calculus-based development of dynamics (continuous dynamical systems). The text is a beautiful historical review of physical mathematics from Newton and Leibniz to Lorenz in the late 20th century. It begins with a brief review of projectile and planetary motion and related topics in calculus and differential equations, including numerical (computer) solutions and the theory of oscillations. Later chapters discuss more advanced topics: the three-body problem, wave and diffusion equations, action and Hamilton's principle, calculus of variations, Lagrange's equations, fluid flow, theory of linear stability, bifurcation and catastrophic change, nonlinear oscillations, and the Lorenz equations. Since a very broad range of topics is offered, the principal shortcoming of the work is that it is rather brief in spots. For example, the Mathieu equation is discussed in roughly one page, and a reader not previously familiar with the equation and the concept of instability is not likely to understand the derivation or implications of its stability diagram. The discussion of bifurcation theory is also too brief for the novice. Still, taken as a whole, this is an excellent overview of a broad body of material in a historically accurate setting. Chapter exercises; appendixes with solutions to exercises and an elementary introduction to programming in QBASIC. Undergraduates through professionals. J. D. Fehribach Worcester Polytechnic Institute

Author notes provided by Syndetics

Dr D.J. Acheson Jesus College Oxford OX1 3DW Tel: 01865 279700 Fax: 01865 279687 Email: david.acheson@jesus.ox.ac.uk