1. MODELING WITH DISCRETE DYNAMICAL SYSTEMS.
Modeling Change with Difference Equations. Approximating Change with Difference Equations. Solutions to Dynamical Systems. Systems of Difference Equations.
2. THE MODELING PROCESS, PROPORTIONALITY AND GEOMETRIC SIMILARITY.
Mathematical Models. Modeling Using Proportionality. Modeling Using Geometric Similarity. Automobile Gasoline Mileage. Body Weight and Height, Strength and Agility.
3. MODEL FITTING.
Fitting Models to Data Graphically. Analytic Methods of Model Fitting. Applying the Least-Squares Criterion. Choosing a Best Model.
4. EXPERIMENTAL MODELING.
Harvesting in the Chesapeake Bay and Other One-Term Models. High-Order Polynomial Models. Smoothing: Low-Order Polynomial Models. Cubic Spline Models.
5. SIMULATION MODELING.
Simulation Deterministic Behavior: Area under a Curver. Generating Random Numbers. Simulating Probabilistic Behavior. Inventory Model: Gasoline and Consumer Demand. Queuing Models.
6. DISCRETE PROBABILITY MODELING.
Probabilistic Modeling With Discrete Systems. Modeling Component and System Reliability. Linear Regression.
7. DISCRETE OPTIMIZATION MODELING LINEAR PROGRAMMING AND NUMERICAL SEARCH METHODS.
An Overview of Discrete Optimization Modeling. Linear Programming I: Geometric Solutions. Linear Programming II: Algebraic Solutions. Linear Programming III: The Simplex Method. Linear Programming IV: Sensitivity Analysis. Numerical Search Methods.
8. DIMENSIONAL ANALYSIS AND SIMILITUDE.
Dimensions as Products. The Process of Dimensional Analysis. A Damped Pendulum. Examples Illustrating Dimensional Analysis. Similitude.
9. GRAPHS OF FUNCTIONS AS MODELS.
An Arms Race. Modeling an Arms Race in Stages. Managing Nonrenewable Resources: The Energy Crisis. Effects of Taxation on the Energy Crisis. A Gasoline Shortage and Taxation.
10. MODELING WITH SYSTEMS OF DIFFERENTIAL EQUATION.
Population Growth. Prescribing Drug Dosage. Braking Distance Revisited. Graphical Solutions of Autonomous Differential Equations. Numerical Approximation Methods.
11. MODELING WITH SYSTEMS OF DIFFERENTIAL EQUATIONS.
Graphical Solutions of Autonomous Systems of First-Order Differential Equations. A Competitive Hunter Model. A Predator-Prey Model. Two Military Examples. Euler's Method for Systems of Differential Equations.
12. CONTINUOUS OPTIMIZATION MODELING.
An Inventory Problem: Minimizing the cost of Delivery and Storage. A Manufacturing Problem: Maximizing Profit in Producing Competing Products. Constrained Continuous Optimization. Managing Renewable Resources: The Fishing Industry.
Appendix A: Problems from the Mathematics Contest in Modeling .1985-1996 (also available on accompanying CD).
Appendix B: An Algorithm for an Elevator Simulation Model.
Appendix C: The Revised Simplex Method.