# Mathematical Modeling

## 4th Edition

Authors:
eBook ISBN: 9780123869968
Hardcover ISBN: 9780123869128
Published Date: 28th January 2013
Page Count: 384
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## Description

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.

## Key Features

• 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

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.

Preface

Part I: Optimization Models

Chapter 1. One Variable Optimization

1.1 The five-step Method

1.2 Sensitivity Analysis

1.3 Sensitivity and Robustness

1.4 Exercises

Chapter 2. Multivariable Optimization

2.1 Unconstrained Optimization

2.2 Lagrange Multipliers

2.3 Sensitivity Analysis and Shadow Prices

2.4 Exercises

Chapter 3. Computational Methods for Optimization

3.1 One Variable Optimization

3.2 Multivariable Optimization

3.3 Linear Programming

3.4 Discrete Optimization

3.5 Exercises

Part II: Dynamic Models

Chapter 4. Introduction to Dynamic Models

4.2 Dynamical Systems

4.3 Discrete Time Dynamical Systems

4.4 Exercises

Chapter 5. Analysis of Dynamic Models

5.1 Eigenvalue Methods

5.2 Eigenvalue Methods for Discrete Systems

5.3 Phase Portraits

5.4 Exercises

Chapter 6. Simulation of Dynamic Models

6.1 Introduction to Simulation

6.2 Continuous-Time Models

6.3 The Euler Method

6.4 Chaos and Fractals

6.5 Exercises

Part III: Probability Models

Chapter 7. Introduction to Probability Models

7.1 Discrete Probability Models

7.2 Continuous Probability Models

7.3 Introduction to Statistics

7.4 Diffusion

7.5 Exercises

Chapter 8. Stochastic Models

8.1 Markov Chains

8.2 Markov Processes

8.3 Linear Regression

8.4 Time Series

8.5 Exercises

Chapter 9. Simulation of Probability Models

9.1 Monte Carlo Simulation

9.2 The Markov Property

9.3 Analytic Simulation

9.4 Particle Tracking

9.5 Fractional Diffusion

9.6 Exercises

Afterword

Index

## Details

No. of pages:
384
Language:
English
Published:
Imprint:
eBook ISBN:
9780123869968
Hardcover ISBN:
9780123869128

### Mark Meerschaert

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

### Affiliations and Expertise

Michigan State University, East Lansing, MI, USA

## Reviews

"This book distinguishes itself from comparable texts by its broad treatment of the field. It offers an extensive survey of mathematical modeling problems and techniques that is organized into three big sections corresponding to optimization, dynamics and probability models."--MAA Reviews, March 19, 2014