Models For Life: An Introduction To Discrete Mathematical Modeling With Excel(R)

This book presents an applications-driven approach as well as a rich, hands-on mathematical experience for students. In addition, the book features a step-by-step introduction to the creation and analysis of mathematical models using Microsoft Office Excel. Part I introduces the reader to discrete dynamical systems, which are mathematical models that relate a quantity at one point in time to a previous point. The reader is taken step-by-step through the process, language, and notation required to construct such models along with how to implement them in Excel. Part II introduces students to more complex, multi-compartment models. Examples include age-structured population models, interacting species models, and infectious disease models. New mathematical and graphical techniques are presented including stable population distributions, phase diagrams and nullclines. Students also learn some new Excel techniques in constructing phase diagrams and dealing with multiple dependent variables. Part III focuses on applications of our modeling techniques to models of health related topics. Predicting body weight, body composition, and blood alcohol concentration are some of the applications that will engage students with their relevance and currency. Part IV discusses tochastic models, i.e. those that incorporate some randomness are an important class of models. In this part, students modify some existing models to include random effects. For example, a random chance of natural disasters is presented, and students are introduced to the first stochastic disease model, the Reed-Frost model. Topical coverage includes: Density Independent Population Models; Analytic Tools for Discrete Dynamical Systems; Density Dependent Population Models; The Discrete Logistic Model; Personal Finance; Population Interaction Models; The Spread of Infectious Diseases; Body Weight; Pharmacokinetics of Alcohol and Other Drugs; and Incorporating Random Effects - Stochastic Models.

Jeffrey T. Barton, PhD, is Professor of Mathematics in the Mathematics Department at Birmingham-Southern College. A member of the American Mathematical Society and Mathematical Association of America, his mathematical interests include approximation theory, analytic number theory, mathematical biology, mathematical modeling, and the history of mathematics.