A Course in Mathematical Modeling

Douglas Mooney, Randall Swift

430 pages, parution le 27/09/2004

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Résumé

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. The use of computers in both simulation and analysis is an integral part of the presentation.

The authors emphasize teaching modeling as opposed to presenting models, beginning their book with the simple discrete exponential growth model as a building block, and successively refining it. This refinement includes adding variable growth rates and multiple variables, fitting growth rates to data, including random elements, testing goodness of fit, using computer simulations, and moving to a continuous setting.

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 the beginning student or as a capstone for the 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 use this book if you are seeking applications to supplement a course in linear algebra, differential equations, difference equations, probability theory or statistics.

Sommaire

Discrete Dynamical Systems
Discrete Stochasticity
Stages, States, and Classes
Empirical Modeling
Continuous Models
Continuous Stochasticity

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	PAPIER
Éditeur(s)	The Mathematical Association of America (MAA)
Auteur(s)	Douglas Mooney, Randall Swift
Parution	27/09/2004
Nb. de pages	430
Format	17,5 x 25,5
Couverture	Broché
Poids	791g
Intérieur	Noir et Blanc
EAN13	9780883857120
ISBN13	978-0-88385-712-0