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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ONE VARIABLE OPTIMIZATION
12 Sensitivity Analysis
13 Sensitivity and Robustness
22 Lagrange Multipliers
23 Sensitivity Analysis and Shadow Prices
62 ContinuousTime Models
63 The Euler Method
64 Chaos and Fractals
INTRODUCTION TO PROBABILITY MODELS
72 Continuous Probability Models
73 Introduction to Statistics
COMPUTATIONAL METHODS FOR OPTIMIZATION
32 Multivariable Optimization
33 Linear Programming
34 Discrete Optimization
INTRODUCTION TO DYNAMIC MODELS
42 Dynamical Systems
43 Discrete Time Dynamical Systems
ANALYSIS OF DYNAMIC MODELS
52 Eigenvalue Methods for Discrete Systems
53 Phase Portraits
SIMULATION OF DYNAMIC MODELS
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