Mathematical Modeling, Third Edition

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9780123708571: Mathematical Modeling, Third Edition

Mathematical Modeling 3e is a general introduction to an increasingly crucial topic for today's mathematicians. Unlike textbooks focused on one kind of mathematical model, this book covers the broad spectrum of modeling problems, from optimization to dynamical systems to stochastic processes. Mathematical modeling is the link between mathematics and the rest of the world. Meerschaert shows how to refine a question, phrasing it in precise mathematical terms. Then he encourages students to reverse the process, translating the mathematical solution back into a comprehensible, useful answer to the original question. This textbook mirrors the process professionals must follow in solving complex problems.

Each chapter in this book is followed by a set of challenging exercises. These exercises require significant effort on the part of the student, as well as a certain amount of creativity. Meerschaert did not invent the problems in this book--they are real problems, not designed to illustrate the use of any particular mathematical technique. Meerschaert's emphasis on principles and general techniques offers students the mathematical background they need to model problems in a wide range of disciplines.

This new edition will be accompanied by expanded and enhanced on-line support for instructors. MATLAB material will be added to complement existing support for Maple, Mathematica, and other software packages, and the solutions manual will be provided both in hard copy and on the web.

* Increased support for instructors, including MATLAB material as well as other on-line resources
* New sections on time series analysis and diffusion models
* Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems

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From the Back Cover:

The Second Edition of this popular text offers a unique approach to mathematical modeling. Meerschaert offers an inviting introduction and applies a problem-solving methodology in the three major areas of optimization, dynamical systems, and stochastic processes.
This edition takes a practical approach toward the solution of a variety of real problems including docking two vehicles in space, the growth rate of an infectious disease, and wildlife management. Rigorous mathematical techniques required for a reasonable solution are introduced as necessary.
Key Features Include:
* A large collection of real-world problems
* An integration of computer outputs from the latest versions of Mathematica, Maple, Lindo, Minitab
* A systematic five-step modeling method
* Applies calculus, differential equations, linear algebra, and probability
New To This Edition:
* Material on discrete modeling, including integer programming
* Extended treatment on chaos and fractals
* Additional material on linear programming, including the use of spreadsheet tools
* More applications in probability and statistics
Reviewer Comments:
"The author is very clear and careful in his presentation. The exercises are excellent. The examples are one of the strongest features. Honestly, I have not considered using any other text for my course."
--Blaise Morton, University of Minnesota
"It is the best modeling book for this audience that I have found. I find that Meerschaert's idea of an undergraduate course in modeling is very close to how I think such a course should run."
--W. George Cochran, Louisiana State University

About the Author:

Mark M. Meerschaert is Chairperson of the Department of Statistics and Probability at Michigan State University and an Adjunct Professor in the Department of Physics at the University of Nevada. Professor Meerschaert has professional experience in the areas of probability, statistics, statistical physics, mathematical modeling, operations research, partial differential equations, ground water and surface water hydrology. He started his professional career in 1979 as a systems analyst at Vector Research, Inc. of Ann Arbor and Washington D.C., where he worked on a wide variety of modeling projects for government and industry. Meerschaert earned his doctorate in Mathematics from the University of Michigan in 1984. He has taught at the University of Michigan, Albion College, Michigan State University, the University of Nevada in Reno, and the University of Otago in Dunedin, New Zealand. His current research interests include limit theorems and parameter estimation for infinite variance probability models, heavy tail models in finance, modeling river flows with heavy tails and periodic covariance structure, anomalous diffusion, continuous time random walks, fractional derivatives and fractional partial differential equations, and ground water flow and transport. For more details, see his personal web page http://www.stt.msu.edu/~mcubed

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