Explorations of Mathematical Models in Biology with Maple.
Shahin, Mazen.
Explorations of Mathematical Models in Biology with Maple. - 1st ed. - 1 online resource (307 pages) - New York Academy of Sciences Series . - New York Academy of Sciences Series .
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 -- 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 -- 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 -- 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 Newton´s 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 -- 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 -- 3.2.7 Model 3: Balancing Chemical Equations -- 3.3 Introduction to Matrices -- 3.3.1 Some Matrix Notation -- 3.3.2 Some Matrix Notation in Maple -- 3.3.3 Matrix Equality -- 3.3.4 Scalar Multiplication -- 3.3.5 Matrix Addition -- 3.3.6 Matrix Scalar Multiplication, Addition, and Subtraction in Maple -- 3.3.7 Matrix Multiplication -- 3.3.8 Matrix Multiplication with Maple -- 3.3.9 Special Matrices -- 3.3.10 Special Matrices in Maple -- 3.3.11 Systems of Linear Equations -- 3.3.12 Matrix Powers -- 3.3.13 Matrix Powers in Maple -- 3.3.14 Matrix Transpose -- 3.3.15 Matrix Transpose in Maple -- 3.3.16 Model 1: A Population Movement Model-Part I -- 3.3.17 Inverse of a Square Matrix -- 3.3.18 Finding a Matrix Inverse -- 3.3.19 Inverse of a Square Matrix in Maple -- 3.3.20 Solving a Linear System Using Matrix Inverse. 3.4 Determinants and Systems of Linear Equations -- 3.4.1 Definition -- 3.4.2 Minors and Cofactors in Maple -- 3.4.3 Determinants in Maple -- 3.4.4 The Adjoint of a Matrix in Maple -- 3.4.5 Determinants and Systems of Linear Equations -- 3.5 Eigenvalues and Eigenvectors -- 3.5.1 Exploration 1 -- 3.5.2 Eigenvalues and Eigenvectors -- 3.5.3 Complex Numbers -- 3.5.4 Arithmetic of Complex Numbers -- 3.5.5 Complex Eigenvalues and Complex Eigenvectors -- 3.6 Eigenvalues and Stability of Linear Models -- 3.6.1 Investigation 1 -- 3.6.2 Repeated Eigenvalues -- 3.6.3 Complex Eigenvalues -- Chapter 4 Modeling with Systems of Linear Difference Equations -- 4.1 Modeling with Markov Chains -- 4.1.1 A Population Movement Model -- 4.1.2 Matrix Representation of Markov Chains -- 4.1.3 Regular Markov Chains -- 4.1.4 Genetics Modeling -- 4.2 Age-Structured Population Models -- 4.2.1 Exploration 1 -- 4.2.2 Exploration 2 -- 4.2.3 Exploration 3 -- 4.3 Modeling with Second-Order Linear Difference Equations -- 4.3.1 Introduction to Second-Order Difference Equations -- 4.3.2 Model 1: Seals Population Dynamics -- 4.3.3 Model 2: Seals Population Dynamics Revisited -- 4.3.4 Model 3: A Plant Population Dynamics -- Chapter 5 Modeling with Nonlinear Systems of Difference Equations -- 5.1 Modeling of Interacting Species -- 5.1.1 A Predator-Prey Model -- 5.1.2 Predator-Prey Interaction with Refuges for the Prey -- 5.1.3 Predator-Prey Interaction with Logistic Growth for the Prey -- 5.1.4 A Competition Model -- 5.1.5 Mutualism Models -- 5.2 The SIR Model of Infectious Diseases -- 5.2.1 Exploration 1 -- 5.2.2 How Are the Transmission Coefficient and Recovery Rate Determined? -- 5.2.3 SIS Model of Infectious Disease -- 5.3 Modeling with Second-Order Nonlinear Difference Equations -- 5.3.1 Model 1: A Nonlinear Delayed Logistic Models -- 5.3.2 Model 2: A Nonlinear Delayed Population. 5.3.3 Model 3: Delayed Nonlinear Competing Species -- Bibliography -- Index -- End User License Agreement.
9781118552155
Maple (Computer file).
Biology-Data processing.
Biology-Mathematical models.
Electronic books.
QH323.5 .S464 2015
570.1/51
Explorations of Mathematical Models in Biology with Maple. - 1st ed. - 1 online resource (307 pages) - New York Academy of Sciences Series . - New York Academy of Sciences Series .
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 -- 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 -- 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 -- 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 Newton´s 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 -- 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 -- 3.2.7 Model 3: Balancing Chemical Equations -- 3.3 Introduction to Matrices -- 3.3.1 Some Matrix Notation -- 3.3.2 Some Matrix Notation in Maple -- 3.3.3 Matrix Equality -- 3.3.4 Scalar Multiplication -- 3.3.5 Matrix Addition -- 3.3.6 Matrix Scalar Multiplication, Addition, and Subtraction in Maple -- 3.3.7 Matrix Multiplication -- 3.3.8 Matrix Multiplication with Maple -- 3.3.9 Special Matrices -- 3.3.10 Special Matrices in Maple -- 3.3.11 Systems of Linear Equations -- 3.3.12 Matrix Powers -- 3.3.13 Matrix Powers in Maple -- 3.3.14 Matrix Transpose -- 3.3.15 Matrix Transpose in Maple -- 3.3.16 Model 1: A Population Movement Model-Part I -- 3.3.17 Inverse of a Square Matrix -- 3.3.18 Finding a Matrix Inverse -- 3.3.19 Inverse of a Square Matrix in Maple -- 3.3.20 Solving a Linear System Using Matrix Inverse. 3.4 Determinants and Systems of Linear Equations -- 3.4.1 Definition -- 3.4.2 Minors and Cofactors in Maple -- 3.4.3 Determinants in Maple -- 3.4.4 The Adjoint of a Matrix in Maple -- 3.4.5 Determinants and Systems of Linear Equations -- 3.5 Eigenvalues and Eigenvectors -- 3.5.1 Exploration 1 -- 3.5.2 Eigenvalues and Eigenvectors -- 3.5.3 Complex Numbers -- 3.5.4 Arithmetic of Complex Numbers -- 3.5.5 Complex Eigenvalues and Complex Eigenvectors -- 3.6 Eigenvalues and Stability of Linear Models -- 3.6.1 Investigation 1 -- 3.6.2 Repeated Eigenvalues -- 3.6.3 Complex Eigenvalues -- Chapter 4 Modeling with Systems of Linear Difference Equations -- 4.1 Modeling with Markov Chains -- 4.1.1 A Population Movement Model -- 4.1.2 Matrix Representation of Markov Chains -- 4.1.3 Regular Markov Chains -- 4.1.4 Genetics Modeling -- 4.2 Age-Structured Population Models -- 4.2.1 Exploration 1 -- 4.2.2 Exploration 2 -- 4.2.3 Exploration 3 -- 4.3 Modeling with Second-Order Linear Difference Equations -- 4.3.1 Introduction to Second-Order Difference Equations -- 4.3.2 Model 1: Seals Population Dynamics -- 4.3.3 Model 2: Seals Population Dynamics Revisited -- 4.3.4 Model 3: A Plant Population Dynamics -- Chapter 5 Modeling with Nonlinear Systems of Difference Equations -- 5.1 Modeling of Interacting Species -- 5.1.1 A Predator-Prey Model -- 5.1.2 Predator-Prey Interaction with Refuges for the Prey -- 5.1.3 Predator-Prey Interaction with Logistic Growth for the Prey -- 5.1.4 A Competition Model -- 5.1.5 Mutualism Models -- 5.2 The SIR Model of Infectious Diseases -- 5.2.1 Exploration 1 -- 5.2.2 How Are the Transmission Coefficient and Recovery Rate Determined? -- 5.2.3 SIS Model of Infectious Disease -- 5.3 Modeling with Second-Order Nonlinear Difference Equations -- 5.3.1 Model 1: A Nonlinear Delayed Logistic Models -- 5.3.2 Model 2: A Nonlinear Delayed Population. 5.3.3 Model 3: Delayed Nonlinear Competing Species -- Bibliography -- Index -- End User License Agreement.
9781118552155
Maple (Computer file).
Biology-Data processing.
Biology-Mathematical models.
Electronic books.
QH323.5 .S464 2015
570.1/51