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Mathematical Modeling: Branching Beyond Calculus

Crista Arangala, Nicolas S. Luke, and Karen A. Yokley
Chapman & Hall/CRC
Publication Date: 
Number of Pages: 
Textbooks in Mathematics
[Reviewed by
Megan Sawyer
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Designed as both a supplemental resource and a stand-alone modeling text, Mathematical Modeling: Branching Beyond Calculus satisfyingly fills both roles.  Each chapter indicates the desired background a reader should have—ranging from first-semester calculus to differential equations and above—and exercises within the chapters are aimed at an appropriate difficulty level for that background.  In addition to examples and exercises, each chapter contains some projects that can be completed without technology and clearly indicates other projects that require the use of software. 
The modeling applications presented throughout the text go farther than the typical “use Newton’s equation for a dead body” story (although, this standard gem is included as a project).  There are several storylines that carry through both projects and chapters—the projects containing Pepsilon and Calcu-cola are particularly prevalent—which allows students to see the connections between the various modeling strategies under the guise of the same story arc.  Each project is supported by material in its chapter and/or clearly referenced previous material; this is a refreshing touch, especially if the text is used as a supplemental resource or simply for project ideas. 
It is evident that the authors of Mathematical Modeling had a clear audience in mind; the reach of the text is clear enough for mid-level undergraduates but also provides opportunities for springboards into course and undergraduate research projects.  The organization is clear, especially with a brief synopsis of the requisite knowledge for each chapter, and provides the opportunity for exploration of breadth and depth of mathematical modeling.


Megan Sawyer is an associate professor of mathematics at Southern New Hampshire University in Manchester, NH.

Chapter 1: Modeling with Calculus; Exploring Extrema; Modeling with The Fundamental Theorem of Calculus; Probability Distributions; Introduction to Stochastic Processes Applications of Sequences and Series; Fibonacci and Lucas Sequences; Taylor Approximations Fourier Series and Signal Processing. Chapter 2: Modeling with Linear Algebra; Modeling with Graphs; Stochastic Models - Markov Chains; Leslie Matrices and other Matrix Models; Linear Programming; Game Theory. Chapter 3: Modeling with Programming; Simulations; Automata Models; Branching Theory. Chapter 4: Modeling with Ordinary Differential Equations; Introduction of Modeling with Differential Equations and Difference Equations; Basic Growth Models; Finding and Analyzing Equilibrium; Multiple Population Models, Coupled Systems; Epidemic Models; Models in a Variety of Fields.