| Preface |
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| Chapter 1 The Scope of Mathematical Modeling |
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1 | (68) |
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1 Models, Mathematical and Otherwise |
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1 | (12) |
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2 Steps in Building a Mathematical Model |
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13 | (10) |
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3 Approximate and Limited Models-Gravity, Rockets, and Raindrops |
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23 | (16) |
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4 Macro and Micro Population Models I-Exponential Growth |
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39 | (4) |
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5 Macro and Micro Population Models II-The Leslie Matrix |
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43 | (10) |
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6 Macro and Micro Population Models III-Family-Planning Models |
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53 | (7) |
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7 Descriptive and Prescriptive Models-Inventory Policy |
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60 | (9) |
| Chapter 2 The Relation of Models to Data |
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69 | (70) |
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1 Sources of Error-Underground Exploration of the Earth |
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69 | (12) |
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2 Adjusting Data I (The Easy Way)-The Mean and the Maximum Likelihood |
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81 | (19) |
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3 Adjusting Data 11 (The Hard Way)-Miscellaneous Methods and Examples |
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100 | (21) |
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4 Testing Models-Weighted-Voting Games |
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121 | (11) |
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5 Putting the Facts in Order-Mendeleev and the Periodic Table |
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132 | (7) |
| Chapter 3 Evaluation of Mathematical Models |
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139 | (97) |
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1 A Bird's-Eye View of Evaluation-College Enrollment |
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139 | (11) |
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2 Descriptive Realism-Simple Linear Regression |
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150 | (20) |
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3 Descriptive Realism-Correlation Is Not Causation |
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170 | (10) |
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4 Accuracy-Multiple Linear Regression |
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180 | (18) |
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5 Precision-Malthus and the Dismal Theorem |
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198 | (13) |
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6 Generality and Fruitfulness-From Astrology to Technology with Kepler and Newton |
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211 | (11) |
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7 Robustness-The Ups and Downs of Ancient Astronomy |
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222 | (14) |
| Chapter 4 Optimization |
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236 | (74) |
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236 | (10) |
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2 Linear Programming-Formulation and Graphical Solution |
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246 | (20) |
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3 An Outline of the Simplex Method |
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266 | (8) |
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4 Integer Programming-The Knapsack and Traveling Salesman Problems |
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274 | (8) |
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5 The Transportation Problem |
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282 | (16) |
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6 Combinatorial Optimization-The Chinese Postman Problem |
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298 | (12) |
| Chapter 5 Choosing the Mathematics for the Model |
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310 | (103) |
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1 Simulation versus Analytic Solution-Queueing Up in the Doctor's Waiting Room |
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310 | (14) |
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2 Discrete versus Continuous Models |
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324 | (52) |
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2A Introduction to Difference Equations |
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325 | (6) |
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2B Exponential Population Growth-Difference and Differential Equations |
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331 | (8) |
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2C Logistic Population Growth-Difference and Differential Equations |
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339 | (6) |
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2D Equilibrium, Stable and Unstable |
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345 | (9) |
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2E Stability of Linear Difference Equations-Commodity Prices and Cobweb Analysis |
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354 | (9) |
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2F Stability of Some Nonlinear Difference Equations-Logistic Population Growth |
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363 | (13) |
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3 Deterministic versus Stochastic Models-Forecasting Epidemics |
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376 | (37) |
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3A An Outline of Probability |
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377 | (15) |
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3B A Day in the Life of an Epidemic-Stochastic and Deterministic Views |
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392 | (8) |
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3C The Lifetime of a Deterministic Epidemic |
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400 | (5) |
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3D The Lifetime of a Simple Stochastic Epidemic |
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405 | (8) |
| Appendix |
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413 | (4) |
| Answers to Selected Exercises |
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417 | (16) |
| Index |
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433 | |
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