Mathematical Modeling

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.

The new edition of Mathematical Modeling, the survey text of choice for mathematical modeling courses, adds ample instructor support and online delivery for solutions manuals and software ancillaries. From genetic engineering to hurricane prediction, mathematical models guide much of the decision making in our society. If the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor. With mathematical modeling growing rapidly in so many scientific and technical disciplines, Mathematical Modeling, Fourth Edition provides a rigorous treatment of the subject. The book explores a range of approaches including optimization models, dynamic models and probability models. Offers increased support for instructors, including MATLAB material as well as other on-line resources Features new sections on time series analysis and diffusion models Provides additional problems with international focus such as whale and dolphin populations, plus updated optimization problems

The new edition of Mathematical Modeling, the survey text of choice for mathematical modeling courses, adds ample instructor support and online delivery for solutions manuals and software ancillaries. From genetic engineering to hurricane prediction, mathematical models guide much of the decision making in our society. If the assumptions and methods underlying the modeling are flawed, the outcome can be disastrously poor. With mathematical modeling growing rapidly in so many scientific and technical disciplines, Mathematical Modeling, Fourth Edition provides a rigorous treatment of the subject. The book explores a range of approaches including optimization models, dynamic models and probability models. Offers increased support for instructors, including MATLAB material as well as other on-line resources Features new sections on time series analysis and diffusion models Provides additional problems with international focus such as whale and dolphin populations, plus updated optimization problems

1;Front Cover;12;Mathematical Modeling;43;Copyright;54;Contents;65;Preface;86;Part I: Optimization Models;146.1;Chapter 1: One Variable Optimization;166.1.1;1.1 The five-step Method;166.1.2;1.2 Sensitivity Analysis;226.1.3;1.3 Sensitivity and Robustness;276.1.4;1.4 Exercises;296.1.5;Further Reading;326.2;Chapter 2: Multivariable Optimization;346.2.1;2.1 Unconstrained Optimization;346.2.2;2.2 Lagrange Multipliers;446.2.3;2.3 Sensitivity Analysis and Shadow Prices;546.2.4;2.4 Exercises;636.2.5;Further Reading;686.3;Chapter 3: Computational Methods For Optimization;706.3.1;3.1 One Variable Optimization;706.3.2;3.2 Multivariable Optimization;796.3.3;3.3 Linear Programming;876.3.4;3.4 Discrete Optimization;1046.3.5;3.5 Exercises;1156.3.6;Further Reading;1247;Part II: Dynamic Models;1267.1;Chapter 4: Introduction to Dynamic Models;1287.1.1;4.1 Steady State Analysis;1287.1.2;4.2 Dynamical Systems;1337.1.3;4.3 Discrete Time Dynamical Systems;1397.1.4;4.4 Exercises;1457.1.5;Further Reading;1507.2;Chapter 5: Analysis of Dynamic Models;1527.2.1;5.1 Eigenvalue Methods;1527.2.2;5.2 Eigenvalue Methods for Discrete Systems;1577.2.3;5.3 Phase Portraits;1637.2.4;5.4 Exercises;1777.2.5;Further Reading;1827.3;Chapter 6: Simulation of Dynamic Models;1847.3.1;6.1 Introduction to Simulation;1847.3.2;6.2 Continuous-Time Models;1917.3.3;6.3 The Euler Method;1997.3.4;6.4 Chaos and Fractals;2047.3.5;6.5 Exercises;2197.3.6;Further Reading;2328;Part III: Probability Models;2348.1;Chapter 7: Introduction to Probability Models;2368.1.1;7.1 Discrete Probability Models;2368.1.2;7.2 Continuous Probability Models;2418.1.3;7.3 Introduction to Statistics;2448.1.4;7.4 Diffusion;2498.1.5;7.5 Exercises;2548.1.6;Further Reading;2638.2;Chapter 8: Stochastic Models;2648.2.1;8.1 Markov Chains;2648.2.2;8.2 Markov Processes;2748.2.3;8.3 Linear Regression;2848.2.4;8.4 Time Series;2938.2.5;8.5 Exercises;3038.2.6;Further Reading;3128.3;Chapter 9: Simulation of Probability Models;3148.3.1;9.1 Monte Carlo Simulation;3148.3.2;9.2 The Markov Property;3218.3.3;9.3 Analytic Simulation;3308.3.4;9.4 Particle Tracking;3368.3.5;9.5 Fractional Diffusion;3488.3.6;9.6 Exercises;3608.3.7;Further Reading;3709;Afterword;37210;Index;376