Explorations of Mathematical Models in Biology With Maple

Informationen zum Autor MAZEN SHAHIN, PhD, is Professor in the Department of Mathematical Sciences at Delaware State University. He has extensive background and experience in designing interdisciplinary instructional materials that integrate mathematics and other disciplines, such as biology, ecology, and finance. Dr. Shahin's research interests include boundary value problems, dynamical systems, impulsive differential equations, and mathematics education. Dr. Shahin is the author of Explorations of Mathematical Models in Biology with MATLAB(R), also published by Wiley. Klappentext Explore and analyze the solutions of mathematical models from diverse disciplinesAs 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 codesExplorations 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. Zusammenfassung Explore and analyze the solutions of mathematical models from diverse disciplinesAs 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...

List of contents

Preface viiAcknowledgments xi1 Overview of Discrete Dynamical Modeling and Maple(TM) 11.1 Introduction to Modeling and Difference Equations 11.2 The Modeling Process 81.3 Getting Started with Maple 122 Modeling with First-Order Difference Equations 372.1 Modeling with First-Order Linear Homogeneous Difference Equations with Constant Coefficients 372.2 Modeling with Nonhomogeneous First-Order Linear Difference Equations 532.3 Modeling with Nonlinear Difference Equations: Logistic Growth Models 722.4 Logistic Equations and Chaos 893 Modeling with Matrices 1003.1 Systems of Linear Equations Having Unique Solutions 1003.2 The Gauss-Jordan Elimination Method with Models 1143.3 Introduction to Matrices 1363.4 Determinants and Systems of Linear Equations 1643.5 Eigenvalues and Eigenvectors 1763.6 Eigenvalues and Stability of Linear Models 1994 Modeling with Systems of Linear Difference Equations 2094.1 Modeling with Markov Chains 2094.2 Age-Structured Population Models 2304.3 Modeling with Second-Order Linear Difference Equations 2405 Modeling with Nonlinear Systems of Difference Equations 2585.1 Modeling of Interacting Species 2585.2 The SIR Model of Infectious Diseases 2725.3 Modeling with Second-Order Nonlinear Difference Equations 280Bibliography 286Index 288

Product details

• Authors: M Shahin, Mazen Shahin, Shahin Mazen
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 23.12.2014
• EAN: 9781118032114
• ISBN: 978-1-118-03211-4
• No. of pages: 304
• Subjects: Natural sciences, medicine, IT, technology > Mathematics; Biologie, Mathematik, Life Sciences, Biowissenschaften, Mathematische Modellierung, Mathematics, Computational biology, Methods & Statistics in Ecology, Ökologie / Methoden, Statistik, Mathematical Modeling, Modell (Math.), Mathematik in der Biologie