Mathematical Modeling

"Mathematical Modeling, Second Edition", offers a unique approach to mathematical modeling by providing an inviting overview, and applying problem-solving methodology throughout concerning three major areas: optimization, dynamical systems, and stochastic processes. Providing a thorough revision, the author takes a practical approach toward the solution of a variety of real problems such as docking two vehicles in space, growth rate of an infectious disease, and wildlife management. Rigorous mathematical techniques required for reasonable solutions are introduced as necessary. This work provides a large collection of real-world problems. It features an integration of computer outputs from the latest versions of Mathematica, Maple, Lindo, Minitab. It presents a systematic five-step modeling method. It 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; and more applications in probability and statistics.

Table of Contents:
Optimization Models One-Variable Optimization Multivariable Optimization Computational Methods of Optimization Dynamic Modeling Introduction to Dynamic Models Analysis of Dynamic Models Simulation of Dynamic Models Probability Models Introduction to Probability Models Stochastic Models Simulation of Probability Models Afterword Index

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

Review :
"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