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Mathematical modeling

Mathematical modeling

  • ISBN: 9780123708571
  • Editorial: Academic Press, Inc.
  • Lugar de la edición: London. Reino Unido
  • Edición número: 3rd ed.
  • Encuadernación: Cartoné
  • Medidas: 24 cm
  • Nº Pág.: 325
  • Idiomas: Inglés

Papel: Cartoné
86,30 € 81,98 €
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Resumen

"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.This title provides increased support for instructors, including MATLAB material as well as other on-line resources. It includes new sections on time series analysis and diffusion models. It covers additional problems with international focus such as whale and dolphin populations, plus updated optimization problems.

Preface vii
I. OPTIMIZATION MODELS
1 (110)
One Variable Optimization
3 (16)
The Five-Step Method
3 (6)
Sensitivity Analysis
9 (4)
Sensitivity and Robustness
13 (2)
Exercises
15 (4)
Multivariable Optimization
19 (36)
Unconstrained Optimization
19 (10)
Lagrange Multipliers
29 (10)
Sensitivity Analysis and Shadow Prices
39 (9)
Exercises
48 (7)
Computational Methods for Optimization
55 (56)
One Variable Optimization
55 (9)
Multivariable Optimization
64 (8)
Linear Programming
72 (17)
Discrete Optimization
89 (11)
Exercises
100 (11)
II. DYNAMIC MODELS
111 (108)
Introduction to Dynamic Models
113 (24)
Steady State Analysis
113 (5)
Dynamical Systems
118 (6)
Discrete Time Dynamical Systems
124 (6)
Exercises
130 (7)
Analysis of Dynamic Models
137 (32)
Eigenvalue Methods
137 (5)
Eigenvalue Methods for Discrete Systems
142 (5)
Phase Portraits
147 (15)
Exercises
162 (7)
Simulation of Dynamic Models
169 (50)
Introduction to Simulation
169 (7)
Continuous-Time Models
176 (3)
The Euler Method
179 (12)
Chaos and Fractals
191 (13)
Exercises
204 (15)
III. PROBABILITY MODELS
219 (110)
Introduction to Probability Models
221 (28)
Discrete Probability Models
221 (5)
Continuous Probability Models
226 (3)
Introduction to Statistics
229 (5)
Diffusion
234 (5)
Exercises
239 (10)
Stochastic Models
249 (50)
Markov Chains
249 (10)
Markov Processes
259 (10)
Linear Regression
269 (9)
Time Series
278 (10)
Exercises
288 (11)
Simulation of Probability Models
299 (30)
Monte Carlo Simulation
299 (6)
The Markov Property
305 (10)
Analytic Simulation
315 (6)
Exercises
321 (8)
Afterword 329 (4)
Index 333

Resumen

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