Cover

Title Page

Copyright

Contents

Additional Contents onWebsite

Preface

1 Modeling Change

Introduction

1.1 Modeling Change with Difference Equations

1.2 Approximating Change with Difference Equations

1.3 Solutions to Dynamical Systems

1.4 Systems of Difference Equations

2 The Modeling Process,Proportionality,and Geometric Similarity

Introduction

2.1 Mathematical Models

2.2 Modeling Using Proportionality

2.3 Modeling Using Geometric Similarity

2.4 Automobile Gasoline Mileage

2.5 Body Weight and Height,Strength and Agility

3 Model Fitting

Introduction

3.1 Fitting Models to Data Graphically

3.2 Analytic Methods of Model Fitting

3.3 Applying the Least-Squares Criterion

3.4 Choosing a Best Model

4 Experimental Modeling

Introduction

4.1 Harvesting in the Chesapeake Bay and Other One-Term Models

4.2 High-Order Polynomial Models

4.3 Smoothing:Low-Order Polynomial Models

4.4 Cubic Spline Models

5 Simulation Modeling

Introduction

5.1 Simulating Deterministic Behavior:Area Under a Curve

5.2 Generating Random Numbers

5.3 Simulating Probabilistic Behavior

5.4 Inventory Model:Gasoline and Consumer Demand

5.5 Queuing Models

6 Discrete Probabilistic Modeling

Introduction

6.1 Probabilistic Modeling with Discrete Systems

6.2 Modeling Component and System Reliability

6.3 Linear Regression

7 Optimization of Discrete Models

Introduction

7.1 An Overview of Optimization Modeling

7.2 Linear Programming I:Geometric Solutions

7.3 Linear Programming II:Algebraic Solutions

7.4 Linear Programming III:The Simplex Method

7.5 Linear Programming IV:Sensitivity Analysis

7.6 Numerical Search Methods

8 Modeling Using Graph Theory

Introduction

8.1 Graphs as Models

8.2 Describing Graphs

8.3 Graph Models

8.4 Using Graph Models to Solve Problems

8.5 Connections to Mathematical Programming

9 Modeling with Decision Theory

Introduction

9.1 Probability and Expected Value

9.2 Decision Trees

9.3 Sequential Decisions and Conditional Probabilities

9.4 Decisions Using Alternative Criteria

10 Game Theory

Introduction

10.1 Game Theory:Total Conflict

10.2 Total Conflict as a Linear Program Model:Pure and Mixed Strategies

10.3 Decision Theory Revisited:Games against Nature

10.4 Alternative Methods for Determining Pure Strategy Solutions

10.5 Alternative Shortcut Solution Methods for the 2×2 Total Conflict Game

10.6 Partial Conflict Games:The Classical Two-Person Game

10.7 Illustrative Modeling Examples

11 Modeling with a Differential Equation

Introduction

11.1 Population Growth

11.2 Prescribing Drug Dosage

11.3 Braking Distance Revisited

11.4 Graphical Solutions of Autonomous Differential Equations

11.5 Numerical Approximation Methods

11.6 Separation of Variables

11.7 Linear Equations

12 Modeling with Systems of Differential Equations

Introduction

12.1 Graphical Solutions of Autonomous Systems of First-Order Differential Equations

12.2 A Competitive Hunter Model

12.3 A Predator--Prey Model

12.4 Two Military Examples

12.5 Euler's Method for Systems of Differential Equations

13 Optimization of Continuous Models

Introduction

13.1 An Inventory Problem:Minimizing the Cost of Delivery and Storage

13.2 Methods to Optimize Function of Several Variables

13.3 Constrained Continuous Optimization

13.4 Managing Renewable Resources:The Fishing Industry

APPENDIX Problems from the Mathematics Contest in Modeling,1985-2012

Answers to Selected Problems

Index