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
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
Further Reading
Index
