Introduction to Mathematical Biology

ISBN-10: 0130352160
ISBN-13: 9780130352163
Edition: 2007
List price: $117.80
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Description: KEY BENEFIT: This reference 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  More...

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Book details

List price: $117.80
Copyright year: 2007
Publisher: Prentice Hall PTR
Publication date: 7/19/2006
Binding: Paperback
Pages: 368
Size: 8.50" wide x 10.50" long x 1.00" tall
Weight: 1.892
Language: English

KEY BENEFIT: This reference 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.Contains applications of mathematical theory to biological examples in each chapter. Focuses on deterministic mathematical models with an emphasis on predicting the qualitative solution behavior over time. Discusses classical mathematical models from population , including the Leslie matrix model, the Nicholson-Bailey model, and the Lotka-Volterra predator-prey model. Also discusses more recent models, such as a model for the Human Immunodeficiency Virus - HIV and a model for flour beetles.KEYMARKET: Readersnbsp;seeking a solid background in the mathematics behind modeling in biology and exposure to a wide variety of mathematical models in biology.

Preface
Linear Difference Equations, Theory, And Examples
Introduction
Basic Definitions and Notation
First-Order Equations
Second-Order and Higher-Order Equations
First-Order Linear Systems
An Example: Leslies Age-Structured Model
Properties of the Leslie Matrix
Exercises for Chapter 1
References for Chapter 1
Appendix for Chapter 1
Maple Program:Turtle Model
MATLAB? Program:Turtle Model
Nonlinear Difference Equations, Theory, And Examples
Introduction
Basic Definitions and Notation
Local Stability in First-Order Equations
Cobwebbing Method for First-Order Equations
Global Stability in First-Order Equations
The Approximate Logistic Equation
Bifurcation Theory
Types of Bifurcations
Liapunov Exponents
Stability in First-Order Systems
Jury Conditions
An Example: Epidemic Model
Delay Difference Equations
Exercises for Chapter 2
References for Chapter 2
Appendix for Chapter 2
Proof of Theorem 2.1
A Definition of Chaos
Jury Conditions (Schur-Cohn Criteria)
Liapunov Exponents for Systems of Difference Equations
MATLAB Program: SIR Epidemic Model
Biological Applications Of Difference Equations
Introduction
Population Models
Nicholson-Bailey Model
Other Host-Parasitoid Models
Host-Parasite Model
Predator-Prey Model
Population Genetics Models
Nonlinear Structured Models
Density-Dependent Leslie Matrix Models
Structured Model for Flour Beetle Populations
Structured Model for the Northern Spotted Owl
Two-Sex Model
Measles Model with Vaccination
Exercises for Chapter 3
References for Chapter 3
Appendix for Chapter 3
Maple Program: Nicholson-Bailey Model
Whooping Crane Data
Waterfowl Data
Linear Differential Equations: Theory And Examples
Introduction 141
Basic Definitions and Notation 142
First-Order Linear Differential Equations 144
Higher-Order Linear Differential Equations 145
Constant Coefficients 146
Routh-Hurwitz Criteria 150
Converting Higher-Order Equations to First-OrderSystems 152
First-Order Linear Systems 154
Constant Coefficients 155
Phase-Plane Analysis 157
Gershgorins Theorem 162
An Example: Pharmacokinetics Model
Discrete and Continuous Time Delays
Exercises for Chapter 4
References for Chapter 4
Appendix for Chapte

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