文档介绍：Contents
Preface Page xi
Part I Modelling techniques
1 The basics of modelling 3
Introduction 3
What do we mean by a model? 4
Principles of modelling: physical laws and constitutive relations 6
Conservation laws 11
General remarks 12
Exercises 12
2 Units, dimensions and dimensional analysis 15
Introduction 15
Units and dimensions 16
Electric fields and electrostatics 18
Sources and further reading 20
Exercises 20
3 Nondimensionalisation 28
Nondimensionalisation and dimensional parameters 28
The Navier–Stokes equations and Reynolds numbers 36
Buckingham’s Pi-theorem 40
Sources and further reading 42
Exercises 42
4 Case studies: hair modelling and cable laying 50
The Euler–Bernoulli model for a beam 50
Hair modelling 52
Undersea cable laying 53
Modelling and analysis 54
Sources and further reading 58
Exercises 58
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5 Case study: the thermistor (1) 63
Heat and current flow in thermistors 63
Nondimensionalisation 66
A thermistor in a circuit 67
Sources and further reading 69
Exercises 69
6 Case study: electrostatic painting 72
Electrostatic painting 72
Field equations 73
Boundary conditions 75
Nondimensionalisation 76
Sources and further reading 77
Exercises 77
Part II Analytical techniques
7 Partial differential equations 81
First-order quasilinear partial differential equations: theory 81
Example: Poisson processes 85
Shocks 87
Fully nonlinear equations: Charpitt’s method 90
Second-order linear equations in two variables 94
Further reading 97
Exercises 97
8 Case study: traffic modelling 104
Simple models for traffic flow 104
Traffic jams and other discontinuous solutions 107
More sophisticated models 110
Sources and further reading 111
Exercises 111
9 The delta function and other distributions 114
Introduction 114
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