A Course in Mathematical Modeling is intended as a text for a modeling course accessible to students who have mastered a one-year course in calculus. Mooney and Swift’s approach to modeling is presented, balancing theoretical versus empirical models, analytic models versus simulation, deterministic versus stochastic models, and discrete versus continuous models. Most examples are drawn from real-world data or from models that have been used in various applied fields.
Table of Contents
To the Teacher
Discrete Dynamical Systems
Stages, States, and Classes
About the Authors
Douglas Mooney’s interest in how the physical world works led him to study physics as an undergraduate, and his interest in the mathematics behind physics led him to obtain his MA and Ph.D. degrees in mathematics from the University of Kansas. A 1993 NSF-sponsored workshop in modeling biological resource issues at the University of Montana ignited Mooney’s interest in applications and sparked an interest in biological modeling. It also led him to team up with colleague Randall Swift to develop the modeling course at Western Kentucky University that is the basis of this textbook. Douglas Mooney has also published a number of refereed papers on extensions and ordered extensions of topological spaces. He currently works at The Center for Healthcare Industry Performance Studies in Columbus, Ohio.
Randall Swift earned his Ph.D from the University of California, Riverside, and is currently associate professor of mathematics at Western Kentucky University in Bowling Green, Kentucky. He has published many refereed papers on harmonizable and other nonstationary processes, applied mathematics, and modeling. In 1997 he received the Western Kentucky University Ogden College of Science, Technology, and Health award for outstanding faculty research. One of his goals as a teacher has been to develop relevant applications of technology for use in the mathematics courses he teaches. This textbook is a result of that continuing effort.
Anyone who writes a new mathematical modeling book like this should be praised for providing us with fresh real-life data sets and ideas for student projects. This book illustrates statistical concepts, for example, with data about The X-files television show. It also introduces many new examples from population biology and ecology. In addition, the book contains familiar examples (e.g. drug levels in the body) as well as new problems inspired by others' such as Davis, Porta, and Uhl's (Calculus&Mathematica, Addison-Wesley, 1994) attention-grabbing problem on blood alcohol levels. Continued...