| |
| |
| Preface | |
| |
| |
| |
| The Scope of Mathematical Modeling | |
| |
| |
| |
| Models, Mathematical and Otherwise | |
| |
| |
| |
| Steps in Building a Mathematical Model | |
| |
| |
| |
| Approximate and Limited Models--Gravity, Rockets, and Raindrops | |
| |
| |
| |
| Macro and Micro Population Models I--Exponential Growth | |
| |
| |
| |
| Macro and Micro Population Models II--The Leslie Matrix | |
| |
| |
| |
| Macro and Micro Population Models III--Family-Planning Models | |
| |
| |
| |
| Descriptive and Prescriptive Models--Inventory Policy | |
| |
| |
| |
| The Relation of Models to Data | |
| |
| |
| |
| Sources of Error--Underground Exploration of the Earth | |
| |
| |
| |
| Adjusting Data I (The Easy Way)--The Mean and the Maximum Likelihood | |
| |
| |
| |
| Adjusting Data II (The Hard Way)--Miscellaneous Methods and Examples | |
| |
| |
| |
| Testing Models--Weighted-Voting Games | |
| |
| |
| |
| Putting the Facts in Order--Mendeleev and the Periodic Table | |
| |
| |
| |
| Evaluation of Mathematical Models | |
| |
| |
| |
| A Bird's-Eye View of Evaluation--College Enrollment | |
| |
| |
| |
| Descriptive Realism--Simple Linear Regression | |
| |
| |
| |
| Descriptive Realism--Correlation Is Not Causation | |
| |
| |
| |
| Accuracy--Multiple Linear Regression | |
| |
| |
| |
| Precision--Malthus and the Dismal Theorem | |
| |
| |
| |
| Generality and Fruitfulness--From Astrology to Technology with Kepler and Newton | |
| |
| |
| |
| Robustness--The Ups and Downs of Ancient Astronomy | |
| |
| |
| |
| Optimization | |
| |
| |
| |
| Classical Optimization | |
| |
| |
| |
| Linear Programming--Formulation and Graphical Solution | |
| |
| |
| |
| An Outline of the Simplex Method | |
| |
| |
| |
| Integer Programming--The Knapsack and Traveling Salesman Problems | |
| |
| |
| |
| The Transportation Problem | |
| |
| |
| |
| Combinatorial Optimization--The Chinese Postman Problem | |
| |
| |
| |
| Choosing the Mathematics for the Model | |
| |
| |
| |
| Simulation versus Analytic Solution--Queueing Up in the Doctor's Waiting Room | |
| |
| |
| |
| Discrete versus Continuous Models | |
| |
| |
| |
| Introduction to Difference Equations | |
| |
| |
| |
| Exponential Population Growth--Difference and Differential Equations | |
| |
| |
| |
| Logistic Population Growth--Difference and Differential Equations | |
| |
| |
| |
| Equilibrium, Stable and Unstable | |
| |
| |
| |
| Stability of Linear Difference Equations--Commodity Prices and Cobweb Analysis | |
| |
| |
| |
| Stability of Some Nonlinear Difference Equations--Logistic Population Growth | |
| |
| |
| |
| Deterministic versus Stochastic Models--Forecasting Epidemics | |
| |
| |
| |
| An Outline of Probability | |
| |
| |
| |
| A Day in the Life of an Epidemic--Stochastic and Deterministic Views | |
| |
| |
| |
| The Lifetime of a Deterministic Epidemic | |
| |
| |
| |
| The Lifetime of a Simple Stochastic Epidemic | |
| |
| |
| Appendix | |
| |
| |
| Answers to Selected Exercises | |
| |
| |
| Index | |