An Introduction to Mathematical Biology

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9780130352163: An Introduction to Mathematical Biology

For advanced undergraduate and beginning graduate courses on Modeling offered in departments of Mathematics.

 

This text introduces a variety of mathematical models for biological systems, and presents the mathematical theory and techniques useful in analyzing those models. Material is organized according to the mathematical theory rather than the biological application. Undergraduate courses in calculus, linear algebra, and differential equations are assumed.

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Book Description Pearson, 2006. Book Condition: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Preface xi 1 LINEAR DIFFERENCE EQUATIONS, THEORY, AND EXAMPLES 1 1.1 Introduction 1 1.2 Basic Definitions and Notation 2 1.3 First-Order Equations 6 1.4 Second-Order and Higher-Order Equations 8 1.5 First-Order Linear Systems 14 1.6 An Example: Leslies Age-Structured Model 18 1.7 Properties of the Leslie Matrix 20 1.8 Exercises for Chapter 1 28 1.9 References for Chapter 1 33 1.10 Appendix for Chapter 1 34 1.10.1 Maple Program:Turtle Model 34 1.10.2 MATLAB? Program:Turtle Model 34 2 NONLINEAR DIFFERENCE EQUATIONS, THEORY, AND EXAMPLES 36 2.1 Introduction 36 2.2 Basic Definitions and Notation 37 2.3 Local Stability in First-Order Equations 40 2.4 Cobwebbing Method for First-Order Equations 45 2.5 Global Stability in First-Order Equations 46 2.6 The Approximate Logistic Equation 52 2.7 Bifurcation Theory 55 2.7.1 Types of Bifurcations 56 2.7.2 Liapunov Exponents 60 2.8 Stability in First-Order Systems 62 2.9 Jury Conditions 67 2.10 An Example: Epidemic Model 69 2.11 Delay Difference Equations 73 2.12 Exercises for Chapter 2 76 2.13 References for Chapter 2 82 2.14 Appendix for Chapter 2 84 2.14.1 Proof of Theorem 2.1 84 2.14.2 A Definition of Chaos 86 2.14.3 Jury Conditions (Schur-Cohn Criteria) 86 2.14.4 Liapunov Exponents for Systems of Difference Equations 87 2.14.5 MATLAB Program: SIR Epidemic Model 88 3 BIOLOGICAL APPLICATIONS OF DIFFERENCE EQUATIONS 89 3.1 Introduction 89 3.2 Population Models 90 3.3 Nicholson-Bailey Model 92 3.4 Other Host-Parasitoid Models 96 3.5 Host-Parasite Model 98 3.6 Predator-Prey Model 99 3.7 Population Genetics Models 103 3.8 Nonlinear Structured Models 110 3.8.1 Density-Dependent Leslie Matrix Models 110 3.8.2 Structured Model for Flour Beetle Populations 116 3.8.3 Structured Model for the Northern Spotted Owl 118 3.8.4 Two-Sex Model 121 3.9 Measles Model with Vaccination 123 3.10 Exercises for Chapter 3 127 3.11 References for Chapter 3 134 3.12 Appendix for Chapter 3 138 3.12.1 Maple Program: Nicholson-Bailey Model 138 3.12.2 Whooping Crane Data 138 3.12.3 Waterfowl Data 139 4 LINEAR DIFFERENTIAL EQUATIONS: THEORY AND EXAMPLES 141 4.1 Introduction 141 4.2 Basic Definitions and Notation 142 4.3 First-Order Linear Differential Equations 144 4.4 Higher-Order Linear Differential Equations 145 4.4.1 Constant Coefficients 146 4.5 Routh-Hurwitz Criteria 150 4.6 Converting Higher-Order Equations to First-OrderSystems 152 4.7 First-Order Linear Systems 154 4.7.1 Constant Coefficients 155 4.8 Phase-Plane Analysis 157 4.9 Gershgorins Theorem 162 4.10 An Example: Pharmacokinetics Model 163 4.11 Discrete and Continuous Time Delays 165 4.12 Exercises for Chapter 4 169 4.13 References for Chapter 4 172 4.14 Appendix for Chapte. Bookseller Inventory # ABE_book_new_0130352160

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