The text aims
Trade Review
Undergraduate textbooks on calculus, differential equations, and linear algebra usually contain a few exercises per chapter that use their subject to model a phenomenon from outside mathematics—typically from physics, biology, chemistry, engineering, or economics. In a typical class, these applications do not amount to more than ten percent of class time. In this book, the authors collect modeling examples from those three areas and make them the central focus of their book. For most of the book, no new theory is covered; instead, the authors provide brief refreshers on some of the necessary theoretical concepts from calculus, differential equations, and linear algebra. The intended audience is second- or third-year students who have already taken those classes. A few exercises accompany each section, with solutions included at the end of the book. The fifth and last chapter does contain material that will be new to most mid-career undergraduates, such as Monte-Carlo simulations and the Prisoners' Dilemma. This book seems ideally suited to an undergraduate class on modeling—a class that few institutions likely offer—and may serve some as a means of independent study.
--M. Bona, University of Florida
Table of Contents
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.
