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Explorations of Mathematical Models in Biology with MATLAB®

Mazen Shahin
Publisher: 
Wiley
Publication Date: 
2014
Number of Pages: 
283
Format: 
Hardcover
Price: 
115.00
ISBN: 
9781118032121
Category: 
Textbook
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PREFACE ix

ACKNOWLEDGMENTS xiii

1 OVERVIEW OF DISCRETE DYNAMICAL MODELING AND MATLAB 1

1.1 Introduction to Modeling and Difference Equations / 1

1.2 The Modeling Process / 8

1.3 Getting Started with MATLAB / 13

2 MODELING WITH FIRST-ORDER DIFFERENCE EQUATIONS 28

2.1 Modeling with First-Order Linear Homogenous Difference Equations with Constant Coefficients / 28

2.2 Modeling with Nonhomogenous First-Order Linear Difference Equations / 42

2.3 Modeling with Nonlinear Difference Equations: Logistic Growth Models / 58

2.4 Logistic Equations and Chaos / 74

3 MODELING WITH MATRICES 85

3.1 Systems of Linear Equations Having Unique Solutions / 85

3.2 The Gauss-Jordan Elimination Method with Models / 99

3.3 Introduction to Matrices / 119

3.4 Determinants and Systems of Linear Equations / 147

3.5 Eigenvalues and Eigenvectors / 160

3.6 Eigenvalues and Stability of Linear Models / 185

4 MODELING WITH SYSTEMS OF LINEAR DIFFERENCE EQUATIONS 195

4.1 Modeling with Markov Chains / 195

4.2 Age-Structured Population Models / 219

4.3 Modeling with Second-Order Linear Difference Equations / 231

5 MODELING WITH NONLINEAR SYSTEMS OF DIFFERENCE EQUATIONS 249

5.1 Modeling of Interacting Species / 249

5.2 The SIR Model of Infectious Disease / 264

5.3 Modeling with Second-Order Nonlinear Difference Equations / 270

REFERENCES 277

INDEX 279

 

Dummy View - NOT TO BE DELETED