# Mathematical Modeling

Elsevier, 2007 - Mathematics - 335 pages
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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### Contents

 ONE VARIABLE OPTIMIZATION 3 12 Sensitivity Analysis 9 13 Sensitivity and Robustness 13 14 Exercises 15 MULTIVARIABLE OPTIMIZATION 19 22 Lagrange Multipliers 29 23 Sensitivity Analysis and Shadow Prices 39 24 Exercises 48
 62 ContinuousTime Models 176 63 The Euler Method 179 64 Chaos and Fractals 191 65 Exercises 204 PROBABILITY MODELS 219 INTRODUCTION TO PROBABILITY MODELS 221 72 Continuous Probability Models 226 73 Introduction to Statistics 229

 COMPUTATIONAL METHODS FOR OPTIMIZATION 55 32 Multivariable Optimization 64 33 Linear Programming 72 34 Discrete Optimization 89 35 Exercises 100 DYNAMIC MODELS 111 INTRODUCTION TO DYNAMIC MODELS 113 42 Dynamical Systems 118 43 Discrete Time Dynamical Systems 124 44 Exercises 130 ANALYSIS OF DYNAMIC MODELS 137 52 Eigenvalue Methods for Discrete Systems 142 53 Phase Portraits 147 54 Exercises 162 SIMULATION OF DYNAMIC MODELS 169
 74 Diffusion 234 75 Exercises 239 STOCHASTIC MODELS 249 82 Markov Processes 259 83 Linear Regression 269 84 Time Series 278 85 Exercises 288 SIMULATION OF PROBABILITY MODELS 299 92 The Markov Property 305 93 Analytic Simulation 315 94 Exercises 321 Afterword 329 Index 333 Copyright