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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
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.
Part I: Optimization Models
Chapter 1. One Variable Optimization
1.1 The five-step Method
1.2 Sensitivity Analysis
1.3 Sensitivity and Robustness
Chapter 2. Multivariable Optimization
2.1 Unconstrained Optimization
2.2 Lagrange Multipliers
2.3 Sensitivity Analysis and Shadow Prices
Chapter 3. Computational Methods for Optimization
3.1 One Variable Optimization
3.2 Multivariable Optimization
3.3 Linear Programming
3.4 Discrete Optimization
Part II: Dynamic Models
Chapter 4. Introduction to Dynamic Models
4.1 Steady State Analysis
4.2 Dynamical Systems
4.3 Discrete Time Dynamical Systems
Chapter 5. Analysis of Dynamic Models
5.1 Eigenvalue Methods
5.2 Eigenvalue Methods for Discrete Systems
5.3 Phase Portraits
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
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
Chapter 8. Stochastic Models
8.1 Markov Chains
8.2 Markov Processes
8.3 Linear Regression
8.4 Time Series
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
- No. of pages:
- © Academic Press 2013
- 28th January 2013
- Academic Press
- Hardcover 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
"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
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