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Publisher:

Wiley

Publication Date:

2014

Number of Pages:

283

Format:

Hardcover

Price:

115.00

ISBN:

9781118032121

Category:

Textbook

[Reviewed by , on ]

Peter T. Olszewski

12/29/2014

Applied mathematics has increasingly come to the forefront in research, conferences, in teaching, and with our students. Mathematical biology in particular is a growing field of interest among many mathematicians, so the timing of *Explorations of Mathematical Models in Biology with MATLAB®* couldn’t have been better. With the use of MATLAB® throughout the book, the reader is introduced to a wide variety of biological data and models, which are then translated into mathematical models and analyzed. The main goal of Shahin’s book is to help students create models for problems in biology, ecology, and the environmental sciences. With the increasing interest in mathematics and biology and publications such as *Math & Bio 2010: Linking Undergraduate Disciplines, *there will be an increasing need to know how to model such data and to be able to get our students ready for related professions.

The approach Shahin takes throughout the book is to look at the applications using difference equations and matrices in MATLAB®. This is a very elementary approach but it works well. Each example is very clear and easy to follow. When reading through the examples, one can tell that Shahin used lots of time and care writing up each solution. When analyzing the models, Shahin’s preference is to rely on graphical and numerical , rather than theoretical, techniques.

Using MATLAB® was a good decision, as many of the calculations are long. For example, in “Exploration 4.1: A Population Movement Model,” once the MATLAB® functions are written to iterate the general form for the two-state Markov Chain, the example goes on to ask about what will happen after 100 years. This is where MATLAB® really comes in handy along, especially the resulting graphs.

The only negative about MATLAB®, which of course affects any computer program, is to learn how to setup the various programs. Shahin has very clear examples, however, which provide a solid basis for the introductory steps of using MATLAB®. For example, on pages 242–247, “Model 4.3: Plant Population Dynamics” is a great example of how a biology can be modeled using a second-order linear difference equation and how MATLAB® is used to help in the calculations of the eigenvalues and eigenvectors.

Reordering of some of the chapters and sections might have improved the book, as would having some group discovery projects. The chapter on “Modeling with Matrices” might fit better before the introductory chapter on difference equations. Also, sections 3.4–3.6 could be split off from chapter 3 and made into a new chapter before chapter 4. Group projects could ask students to obtain data and analyze it; these might also go into a supplemental guide for instructors to use in the classroom with students.

Another area of concern with the book is getting students access to MATLAB®. There is a 30-day trial version and a student edition costs $99.00, which could be high in price for some students. The publishers might want to look into a way to offer a combined package of MATLAB® with the book.

Overall, the book is a great resource to use across many diverse fields. I see the book being used in a mathematical biology class, as an independent study, or in an honors course. There are many modern day problems presented in the book, such as the SIR Model of Infectious Diseases, which our students need and want to see.

Students have always wanted to know the answer to the question, “How will I use this in the real-world?” As important as this question was years ago, it is even more important today, as technology has consumed us and we seem to be always running to catch up. Students want to know applications more than ever before. This book is a great example of how we, as instructors, can provide our students with more applications to be better prepared for the future.

Peter Olszewski is a Mathematics Lecturer at Penn State Erie, The Behrend College, an editor for Larson Texts, Inc. in Erie, PA, and is the 362nd Pennsylvania Alpha Beta Chapter Advisor of Pi Mu Epsilon. He has written several book reviews for the MAA and his research fields are mathematics education, Cayley Color Graphs, Markov Chains, and mathematical textbooks, along with online homework various software. He can be reached at pto2@psu.edu. Outside of teaching and textbook editing, he enjoys playing golf, playing guitar, reading, gardening, traveling, and painting landscapes.

PREFACE ix

ACKNOWLEDGMENTS xiii

**1 OVERVIEW OF DISCRETE DYNAMICAL MODELING AND MATLAB 1**

1.1 Introduction to Modeling and Difference Equations / 1

1.2 The Modeling Process / 8

1.3 Getting Started with MATLAB / 13

**2 MODELING WITH FIRST-ORDER DIFFERENCE EQUATIONS 28**

2.1 Modeling with First-Order Linear Homogenous Difference Equations with Constant Coefficients / 28

2.2 Modeling with Nonhomogenous First-Order Linear Difference Equations / 42

2.3 Modeling with Nonlinear Difference Equations: Logistic Growth Models / 58

2.4 Logistic Equations and Chaos / 74

**3 MODELING WITH MATRICES 85**

3.1 Systems of Linear Equations Having Unique Solutions / 85

3.2 The Gauss-Jordan Elimination Method with Models / 99

3.3 Introduction to Matrices / 119

3.4 Determinants and Systems of Linear Equations / 147

3.5 Eigenvalues and Eigenvectors / 160

3.6 Eigenvalues and Stability of Linear Models / 185

**4 MODELING WITH SYSTEMS OF LINEAR DIFFERENCE EQUATIONS 195**

4.1 Modeling with Markov Chains / 195

4.2 Age-Structured Population Models / 219

4.3 Modeling with Second-Order Linear Difference Equations / 231

**5 MODELING WITH NONLINEAR SYSTEMS OF DIFFERENCE EQUATIONS 249**

5.1 Modeling of Interacting Species / 249

5.2 The SIR Model of Infectious Disease / 264

5.3 Modeling with Second-Order Nonlinear Difference Equations / 270

REFERENCES 277

INDEX 279

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