From Calculus to Chaos
An Introduction to Dynamics
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Product details:
- Publisher OUP Oxford
- Date of Publication 28 August 1997
- ISBN 9780198500773
- Binding Paperback
- No. of pages280 pages
- Size 233x156x17 mm
- Weight 432 g
- Language English
- Illustrations halftones, numerous line figures, tables 0
Categories
Short description:
What is calculus really for? It helps tell us how - and why - things change with time. This is the purpose of dynamics, which lies at the heart of much of applied mathematics, science and engineering. From calculus to chaos takes a fresh approach to the subject as a whole. This is a highly readable and well-illustrated introduction to dynamics which aims to inspire the interest and enthusiasm of students embarking on a course of mathematical study. The writing is inviting, illuminating, and informative, not heavy or pedantic. Acheson explains why the mathematics which students learn is useful by exploring the most central and interesting ideas of calculus and dynamics from Newton to the present.
MoreLong 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 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.
'The book is aimed at a wide readership, and assumes only some knowledge of elementary calculus. There are exercises (with full solutions) and a simple but powerful computer program.' L'Enseignement Mathematique
Table of Contents:
Introduction
A brief review of calculus
Ordinary differential equations
Computer solution methods
Elementary oscillations
Planetary motion
Waves and diffusion
The best of all possible worlds?
Fluid flow
Instability and catastrophe
Nonlinear oscillations and chaos
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
