# Explorations of Mathematical Models in Biology with MATLAB.

Publisher: Hoboken : John Wiley & Sons, Incorporated, 2014Copyright date: ©2015Edition: 1st edDescription: 1 online resource (307 pages)Content type:- text

- computer

- online resource

- 9781118552155

- 570.1/51

- QH323.5 -- .S464 2015eb

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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.

Explore and analyze the solutions of mathematical models from diverse disciplines As biology increasingly depends on data, algorithms, and models, it has become necessary to use a computing language, such as the user-friendly MapleTM, to focus more on building and analyzing models as opposed to configuring tedious calculations. Explorations of Mathematical Models in Biology with Maple provides an introduction to model creation using Maple, followed by the translation, analysis, interpretation, and observation of the models. With an integrated and interdisciplinary approach that embeds mathematical modeling into biological applications, the book illustrates numerous applications of mathematical techniques within biology, ecology, and environmental sciences. Featuring a quantitative, computational, and mathematical approach, the book includes: Examples of real-world applications, such as population dynamics, genetics, drug administration, interacting species, and the spread of contagious diseases, to showcase the relevancy and wide applicability of abstract mathematical techniques Discussion of various mathematical concepts, such as Markov chains, matrix algebra, eigenvalues, eigenvectors, first-order linear difference equations, and nonlinear first-order difference equations Coverage of difference equations to model a wide range of real-life discrete time situations in diverse areas as well as discussions on matrices to model linear problems Solutions to selected exercises and additional Maple codes Explorations of Mathematical Models in Biology with Maple is an ideal textbook for undergraduate courses in mathematical models in biology, theoretical ecology, bioeconomics, forensic science, applied mathematics, and environmental science. The book is also an excellent reference for biologists, ecologists, mathematicians, biomathematicians, and

environmental and resource economists.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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