Explorations of mathematical models in biology with Maple / Mazen Shahin.

Format:

Book

Author/Creator:

Shahin, Mazen, 1947- author.

Language:

English

Subjects (All):

Maple (Computer file).

Biology--Mathematical models.

Biology.

Biology--Data processing.

Genre:

Electronic books.

Physical Description:

1 online resource (307 pages)

Place of Publication:

Hoboken, New Jersey : Wiley, 2015.

System Details:

text file

Summary:

As biology increasingly depends on data, algorithms, and models, it has become necessary to use a computing language, such as the user-friendly Maple™, 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. Book jacket.

Contents:

1 Overview of Discrete Dynamical Modeling and Maple™ 1

1.1 Introduction to Modeling and Difference Equations 1

1.2 The Modeling Process 8

1.3 Getting Started with Maple 12

2 Modeling with First-Order Difference Equations 37

2.1 Modeling with First-Order Linear Homogeneous Difference Equations with Constant Coefficients 37

2.2 Modeling with Nonhomogeneous First-Order Linear Difference Equations 53

2.3 Modeling with Nonlinear Difference Equations: Logistic Growth Models 72

2.4 Logistic Equations and Chaos 89

3 Modeling with Matrices 100

3.1 Systems of Linear Equations Having Unique Solutions 100

3.2 The Gauss-Jordan Elimination Method with Models 114

3.3 Introduction to Matrices 136

3.4 Determinants and Systems of Linear Equations 164

3.5 Eigenvalues and Eigenvectors 176

3.6 Eigenvalues and Stability of Linear Models 199

4 Modeling with Systems of Linear Difference Equations 209

4.1 Modeling with Markov Chains 209

4.2 Age-Structured Population Models 230

4.3 Modeling with Second-Order Linear Difference Equations 240

5 Modeling with Nonlinear Systems of Difference Equations 258

5.1 Modeling of Interacting Species 258

5.2 The SIR Model of Infectious Diseases 272

5.3 Modeling with Second-Order Nonlinear Difference Equations 280.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Local Notes:

Electronic reproduction. Palo Alto, Calif. : ebrary, 2014. Available via World Wide Web. Access may be limited to ebrary affiliated libraries.

Other Format:

Print version: Shahin, Mazen, 1947- Explorations of mathematical models in biology with Maple.

ISBN:

9781118552155

OCLC:

893680275

Access Restriction:

Restricted for use by site license.