Modelling with Differential Equations

✍ Scribed by D. N. Burghes, M.S. Borrie

• Publisher: Ellis Horwood Ltd , Publisher
• Year: 1981
• Tongue: English
• Leaves: 178
• Series: Mathematics and its Applications
• Category: Library

✦ Synopsis

Motivated by the authors' combined ability and
experience, this book is about the concepts of
mathematical modelling with the use of differential
equations, as a powerful technique of mathematical
analysis. It is both enjoyable to read, and informative.
The reader's mind is continually exercised by
enlightenment, or recollection, or enquiry; either
something new is to be learned, or something
known is to be re-examined.
It is with mathematical clarity that the authors
explain the theory of ordinary differential equations
and introduce their manifold applications.
They show a skilful and imaginative succession of applications introducing such instances as accident risk or fish population; forgery detection in old masters or kidney life-support machines; and many others. They show the influence of these mathematical probes into problems occurring in biology, economics, geography, medicine, planning, psychology, or sociology.

Readership: Introductory courses for University undergraduates from a wide range of disciplines, and bright scholars in Sixth Forms.

✦ Table of Contents

Cover

About the Book

S Title

ELLIS HORWOOD SERIES IN MATHEMATICS AND ITS APPLICATIONS

MODELLING WITH DIFFERENTIAL EQUATIONS

COPYRIGHT
©D. N. Burghes and M. S. Borrie/Ellis Horwood Ltd. 1981
ISBN 0-85312-286-5
ISBN 0-470-27101-9
ISBN 0-85312-296-2
ISBN 0-470-27360-7
LCCN 80-41936

List of Illustrations

Contents

Preface

Chapter 1 Introduction
1.1 MATHEMATICAL MODELLING
1.2 POPULATION MODELS
1.3 A FRAMEWORK FOR MODELLING
1.4 DIFFERENTIAL EQUATIONS: BASIC CONCEPTS AND IDEAS

Chapter 2 Growth and Decay: The Differential Equation `dy/dx=ky'
2.1 INTRODUCTION
2.2 DRUG ABSORPTION
2.3 CARBON DATING
2.4 WATER HEATING AND COOLING
2.5 ALCOHOL ABSORPTION: ACCIDENT RISK
2.6 A MATHEMATICAL MODEL FOR AN ARTIFICIAL KIDNEY MACHINE
EXERCISES

Chapter 3 Variables Separable Differential Equations
3.1 INTRODUCTION
3.2 REACTION TO STIMULUS
3.3 ROCKET FLIGHT
3.4 TORRICELLI'S LAW FOR WATER FLOW
3.5 INHIBITED GROWTH MODELS
3.6 THE SPREAD OF TECHNOLOGICAL INNOVATIONS
EXERCISES

Chapter 4 Linear First Order Differential Equations
4.1 INTRODUCTION
4.2 SALES RESPONSE TO ADVERTISING
4.3 ART FORGERIES
4.4 ELECTRIC CIRCUITS
4.5 EXPLOITED FISH POPULATIONS
4.6 NEOCLASSICAL ECONOMIC GROWTH
4.7 POLLUTION OF THE GREAT LAKES
EXERCISES

Chapter 5 Linear Second Order Differential Equations
5.1 INTRODUCTION
5.2 MECHANICAL OSCILLATIONS
5.3 CONSUMER BUYING BEHAVIOUR
5.4 ELECTRICAL NETWORKS
5.5 TESTING FOR DIABETES
EXERCISES

Chapter 6 Non-Linear Second Order Differential Equations
6.1 INTRODUCTION
6.2 PLANETARY MOTION
6.3 PURSUIT CURVES
6.4 CHEMICAL KINETICS
EXERCISES

Chapter 7 Systems of Differential Equations
7.1 INTRODUCTION
7.2 INTERACTING SPECIES
7.3 COMPETING SPECIES: THE STRUGGLE FOR EXISTENCE
7.4 EPIDEMICS
7.5 SPRING MASS SYSTEM
7.6 THE DYNAMICS OF ARMS RACES
EXERCISES

References

Index

About the Authors

Back Cover

✦ Subjects

Математика;Дифференциальные уравнения;