| Description |
1 online resource (307 p.) |
| Series |
New York Academy of Sciences Ser |
|
New York Academy of Sciences Ser
|
| Contents |
Intro -- Explorations of Mathematical Models in Biology with Maple™ -- Copyright -- Contents -- Preface -- Acknowledgments -- Chapter 1 Overview of Discrete Dynamical Modeling and Maple™ -- 1.1 Introduction to Modeling and Difference Equations -- 1.1.1 Model 1: Population Dynamics-A Discrete Dynamical System -- 1.1.2 Model 2: Population Dynamics-A Continuous Dynamical System -- 1.1.3 Why Modeling with Difference Equations Is Adopted -- 1.1.4 What Is a Mathematical Model? -- 1.1.5 Basic Terminology of Difference Equations -- 1.2 The Modeling Process -- 1.3 Getting Started with Maple |
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1.3.1 Start Maple -- 1.3.2 Conducting Computations -- 1.3.3 Quitting Maple -- 1.3.4 Simple Arithmetic and Definition of Variables -- 1.3.5 Comments in Maple -- 1.3.6 Solving Equations -- 1.3.7 Complex Numbers -- 1.3.8 Functions and Expressions in Maple -- 1.3.9 Lists and Sets -- 1.3.10 For Loops -- 1.3.11 Arrays -- 1.3.12 Graphing Functions and Expressions in Maple -- 1.3.13 Graphing Arrays, Lists, and Sets -- 1.3.14 Some Plot Options -- 1.3.15 Iteration -- 1.3.16 Programs -- Chapter 2 Modeling with First-Order Difference Equations |
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2.1 Modeling with First-Order Linear Homogeneous Difference Equations with Constant Coefficients -- 2.1.1 Model 1: Drugs -- 2.1.2 Analytical Solution -- 2.1.3 Analytical Solution of a First-Order Difference Equation with Maple -- 2.1.4 Model 2: Population Dynamics-First Pass -- 2.1.5 Radioactive Decay -- 2.1.6 Model 3: Radioactive Decay -- 2.1.7 Carbon Dating -- 2.1.8 Model 4: Carbon Dating -- 2.2 Modeling with Nonhomogeneous First-Order Linear Difference Equations -- 2.2.1 Model 1: Drugs Revisited -- 2.2.2 Analytical Solution of a First-Order Linear Difference Equation |
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2.2.3 Constant Solutions and Equilibrium Values -- 2.2.4 Model 2: Population Dynamics-Revisited -- 2.2.5 Model 3: Drugs Revisited -- 2.2.6 Model 4: Forensic Application of Newtonś Law of Cooling -- 2.3 Modeling with Nonlinear Difference Equations: Logistic Growth Models -- 2.3.1 Linear Equations -- 2.3.2 Logistic Equations -- 2.3.3 Model 1: Logistic Population Dynamics -- 2.3.4 Carrying Capacity -- 2.3.5 A Model of Logistic Population Growth with Harvesting -- 2.3.6 Model 2: Population with Fixed Harvest Dynamics -- 2.4 Logistic Equations and Chaos -- Chapter 3 Modeling with Matrices |
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3.1 Systems of Linear Equations Having Unique Solutions -- 3.1.1 Matrices and Systems of Equations -- 3.1.2 Elementary Row Operations -- 3.1.3 Model 1: Mixture Problem -- 3.1.4 Model 2: Nutrition -- 3.1.5 Introduction to Matrices in Maple -- 3.1.6 Solving a System of Linear Equations with Maple -- 3.2 The Gauss-Jordan Elimination Method with Models -- 3.2.1 Gauss-Jordan Method -- 3.2.2 Reduced Echelon Form -- 3.2.3 Reduced Row Echelon Form of a Matrix in Maple -- 3.2.4 Homogeneous Systems of Linear Equations -- 3.2.5 Model 1: Nutrition -- 3.2.6 Model 2: Allocation of Resources |
| Summary |
"This book focuses on mathematical models in biology and utilizes difference equations, matrix algebra, and Markov chains as the main mathematical tools. In addition, Maple, a computer algebra system, as well as cooperative learning initiatives are integrated"-- Provided by publisher |
| Notes |
Description based upon print version of record |
|
3.2.7 Model 3: Balancing Chemical Equations |
| Genre/Form |
Electronic books
|
| Form |
Electronic book
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| ISBN |
9781118552155 |
|
1118552156 |
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