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Mathematical Modeling, Third Edition 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.
- Increased support for instructors, including MATLAB material
- New sections on time series analysis and diffusion models
- Additional problems with international focus such as whale and dolphin populations, plus updated optimization problems
Advanced undergraduate or beginning graduate students in mathematics and closely related fields. Formal prerequisites consist of the usual freshman-sophomore sequence in mathematics, including one-variable calculus, multivariable calculus, linear algebra, and differential equations. Prior exposure to computing and probability and statistics is useful, but is not required.
I. OPTIMIZATION MODELS
- One-Variable Optimization
- Multivariable Optimization
- Computational Methods for Optimization
II. DYNAMIC MODELS
- Introduction to Dynamic Models
- Analysis of Dynamic Models
- Simulation of Dynamic Models
III. PROBABILITY MODELS
- Introduction to Probability Models
- Stochastic Models
- Simulation of Probability Models
- No. of pages:
- © Academic Press 2007
- 18th June 2007
- Academic Press
- Paperback ISBN:
- eBook ISBN:
Mark M. Meerschaert is Chairperson of the Department of Statistics and Probability at Michigan State University and Adjunct Professor in the Department of Physics at the University of Nevada, having previously worked in government and industry roles on a wide variety of modeling projects. Holding a doctorate in Mathematics from the University of Michigan, Professor Meerschaert’s expertise spans the areas of probability, statistics, statistical physics, mathematical modeling, operations research, partial differential equations, and hydrology. In addition to his current appointments, he has taught at the University of Michigan, Albion College, and the University of Otago, 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, see http://www.stt.msu.edu/~mcubed
University Distinguished Professor, Michigan State University, East Lansing, MI, USA
"I think this is the best book in its genre. I haven't been tempted to use another. The mathematics in it is interesting, useful, and still within reach of typical undergraduates." --John E. Doner, Department of Mathematics, University of California-Santa Barbara