【MeL】Mathematical Modelling ―A Graduate Textbook―
Moghadas, SM 著
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目次
Dedication Preface Chapter 1 Basic Concepts and Quick Review 1.1 Modelling Types 1.2 Quick Review 1.2.1 First–order differential equations 1.2.2 Second order differential equations 1.2.3 Linear algebra 1.2.4 Scaling Exercises Chapter 2 Compartmental Modelling 2.1 Cascades of Compartments 2.2 Parameter Units . Exercises Chapter 3 Analysis Tools 3.1 Stability Analysis 3.2 Phase–Plane Behaviour 3.3 Direction Field 3.4 Routh–Hurwitz Criterion Exercises Chapter 4 Bifurcation 4.1 Transcritical Bifurcation 4.2 Saddle–Node Bifurcation 4.3 Pitchfork Bifurcation 4.4 Hopf Bifurcation 4.5 Solution Types Exercises Chapter 5 Discretization and Fixed Point Analysis 5.1 Discretization 5.1.1 Method of Euler 5.1.2 Non–standard methods 5.2 Fixed Point Analysis Exercises Chapter 6 Probability and Random Variables 6.1 Basic Concepts 6.2 Conditional Probabilities 6.3 Random Variables 6.3.1 Cumulative distribution function 6.3.2 Discrete random variables 6.3.3 Continuous random variables 6.3.4 Waiting time Exercises Chapter 7 Stochastic Modelling 7.1 Stochastic Processes 7.2 Probability Generating Function 7.3 Markov Chain 7.4 Random Walks Exercises Chapter 8 Computer Simulations 8.1 Deterministic Structure 8.2 Stochastic Structure 8.3 Monte–Carlo Methods Exercises Chapter 9 Examples of Mathematical Modelling 9.1 Traffic Model 9.2 Michaelis–Menten Kinetics 9.3 The Brusselator system 9.4 Generalized Richards Model 9.5 The Spruce Budworm Model 9.6 The FitzHugh–Nagumo Model 9.7 The Decay Model 9.8 The Gambler’s Ruin Exercises Bibliography Index
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