Preface 11
Chapter 1 Introduction 13
1.1 Mathematical Modelling 13
1.2 Population Models 14
1.3 A Framework for Modelling 20
1.4 Differential Equations: Basic Concepts and Ideas 21
Chapter 2 Growth and Decay-The Differential Equation $\frac{\mathrm{d}y}{\mathrm{d}x}=ky$ 24
2.1 Introduction 24
2.2 Drug Absorption 25
2.3 Carbon Dating 29
2.4 Water Heating and Cooling 33
2.5 Alcohol Absorption: Accident Risk 38
2.6 Artificial Kidney Machine 40
Exercises 45
Chapter 3 Variables Separable Differential Equations 49
3.1 Introduction 49
3.2 Reaction to Stimulus 50
3.3 Rocket Flight 53
3.4 Torricelli's Law for Water Flow 59
3.5 Inhibited Growth Models 63
3.6 The Spread of Technological Innovations 65
Exercises 69
Chapter 4 Linear First Order DitTerential Equations 72
4.1 Introduction 72
4.2 Sales Response to Advertising 73
4.3 Art Forgeries 79
4.4 Electric Circuits 84
4.5 Exploited Fish Populations 86
4.6 Neoclassical Economic Growth 90
4.7 Pollution of the Great Lakes 93
4.8 Exercises 96
Chapter 5 Linear Second Order Differential Equation 98
5.1 Introduction 98
5.2 Mechanical Oscillations 101
5.3 Consumer Buying Behaviour 108
5.4 Electrical Networks 110
5.5 Testing for Diabetes 113
Exercises 116
Chapter 6 Non-Linear Second Order Differential Equations 120
6.1 Introduction 120
6.2 Planetary Motions 121
6.3 Pursuit Curves 126
6.4 Chemical Kinetics 130
Exercises 133
Chapter 7 Systems of Differential Equations 135
7.1 Introduction 135
7.2 Interacting Species 141
7.3 Competing Species: The Struggle for Existence 146
7.4 Epidemics 150
7.5 Spring-Mass System 154
7.6 The Dynamics of Arms Races 159
Exercises 164
References 169
Index 171