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 presentation balances a variety of opposing modeling methodologies Including theoretical models versus empirical models, analytical models versus simulation, deterministic models versus stochastic models, and discrete models versus continuous models. Most of the examples are drawn from real-worlddataor from models that have been used In various applied fields. The use of computers in both simulation and In mathematical analysis is an integral part of the presentation.
The authors emphasize the teaching of the modeling process as opposed to merely presenting models. They begin their book with the simple discrete exponential growth model, and successively refine it to Include variable growth rates, multiple variables, growth rates fitted to data, and the effects of random factors. The last part of the book moves into continuous-time models. Issues of model validity and purpose are emphasized throughout.
Students taking a course based on this book should have some mathematical maturity but will need little advanced knowledge. The book presents more advanced topics on an as-needed basis and serves to show how the different topics of undergraduate mathematics can be used together to solve problems. This perspective is valuable as either a road map for beginning students or as a capstone for more advanced students. The course presents elements of discrete dynamical systems, basic probability theory differential equations, matrix algebra, stochastic processes, curve fitting, statistical testing, and regression analysis. Computer analysis Is extensively used In conjunction with these topics.
You can also use this book if you are seeking applications to supplement a course in linear algebra, differential equations, difference equations, probability theory or statistics.