Mathematical modeling

• Main Author: Meerschaert, Mark M.
• Format: eBook Book
• Language: English
• Published: Amsterdam Elsevier 2013; Elsevier Science & Technology; Academic Press
• Edition: 4
• Subjects: Mathematical models
• ISBN: 9780123869128; 0123869129
• DOI: 10.1016/C2010-0-66940-9

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 ma...

Table of Contents:

• Front Cover -- Mathematical Modeling -- Copyright -- Contents -- 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 -- Further Reading -- Chapter 2: Multivariable Optimization -- 2.1 Unconstrained Optimization -- 2.2 Lagrange Multipliers -- 2.3 Sensitivity Analysis and Shadow Prices -- 2.4 Exercises -- Further Reading -- 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 -- Further Reading -- 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 -- 4.4 Exercises -- Further Reading -- Chapter 5: Analysis of Dynamic Models -- 5.1 Eigenvalue Methods -- 5.2 Eigenvalue Methods for Discrete Systems -- 5.3 Phase Portraits -- 5.4 Exercises -- Further Reading -- 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 -- Further Reading -- 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 -- Further Reading -- Chapter 8: Stochastic Models -- 8.1 Markov Chains -- 8.2 Markov Processes -- 8.3 Linear Regression -- 8.4 Time Series -- 8.5 Exercises -- Further Reading -- 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 -- Further Reading -- Afterword -- Index