Explorations of Mathematical Models in Biology with Maple 1st Edition Shahin Mazen 9781118552179

Explorations of Mathematical Models in Biology with Maple 1st Edition Shahin Mazen – Ebook PDF Instant Download/Delivery ISBN(s): 9781118552179

Product details:

• ISBN 13:  9781118552179
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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

Table contents:

1 Overview of Discrete Dynamical Modeling and Maple™

1.1 Introduction to Modeling and Difference Equations

1.2 The Modeling Process

1.3 Getting Started with Maple

2 Modeling with First-Order Difference Equations

2.1 Modeling with First-Order Linear Homogeneous Difference Equations with Constant Coefficients

2.2 Modeling with Nonhomogeneous First-Order Linear Difference Equations

2.3 Modeling with Nonlinear Difference Equations: Logistic Growth Models

2.4 Logistic Equations and Chaos

3 Modeling with Matrices

3.1 Systems of Linear Equations Having Unique Solutions

3.2 The Gauss–Jordan Elimination Method with Models

3.3 Introduction to Matrices

3.4 Determinants and Systems of Linear Equations

3.5 Eigenvalues and Eigenvectors

3.6 Eigenvalues and Stability of Linear Models

4 Modeling with Systems of Linear Difference Equations

4.1 Modeling with Markov Chains

4.2 Age-Structured Population Models

4.3 Modeling with Second-Order Linear Difference Equations

5 Modeling with Nonlinear Systems of Difference Equations

5.1 Modeling of Interacting Species

5.2 The SIR Model of Infectious Diseases

5.3 Modeling with Second-Order Nonlinear Difference Equations

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