Concepts of Mathematical Modeling

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ISBN: 9780486435152 | 0486435156
Cover: Paperback
Copyright: 8/13/2004

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Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Excerises. 1984 edition.

Preface

Chapter 1 The Scope of Mathematical Modeling

(68)

1 Models, Mathematical and Otherwise

(12)

2 Steps in Building a Mathematical Model

(10)

3 Approximate and Limited Models-Gravity, Rockets, and Raindrops

(16)

4 Macro and Micro Population Models I-Exponential Growth

(4)

5 Macro and Micro Population Models II-The Leslie Matrix

(10)

6 Macro and Micro Population Models III-Family-Planning Models

(7)

7 Descriptive and Prescriptive Models-Inventory Policy

(9)

Chapter 2 The Relation of Models to Data

(70)

1 Sources of Error-Underground Exploration of the Earth

(12)

2 Adjusting Data I (The Easy Way)-The Mean and the Maximum Likelihood

(19)

3 Adjusting Data 11 (The Hard Way)-Miscellaneous Methods and Examples

100

(21)

4 Testing Models-Weighted-Voting Games

121

(11)

5 Putting the Facts in Order-Mendeleev and the Periodic Table

132

(7)

Chapter 3 Evaluation of Mathematical Models

139

(97)

1 A Bird's-Eye View of Evaluation-College Enrollment

139

(11)

2 Descriptive Realism-Simple Linear Regression

150

(20)

3 Descriptive Realism-Correlation Is Not Causation

170

(10)

4 Accuracy-Multiple Linear Regression

180

(18)

5 Precision-Malthus and the Dismal Theorem

198

(13)

6 Generality and Fruitfulness-From Astrology to Technology with Kepler and Newton

211

(11)

7 Robustness-The Ups and Downs of Ancient Astronomy

222

(14)

Chapter 4 Optimization

236

(74)

1 Classical Optimization

236

(10)

2 Linear Programming-Formulation and Graphical Solution

246

(20)

3 An Outline of the Simplex Method

266

(8)

4 Integer Programming-The Knapsack and Traveling Salesman Problems

274

(8)

5 The Transportation Problem

282

(16)

6 Combinatorial Optimization-The Chinese Postman Problem

298

(12)

Chapter 5 Choosing the Mathematics for the Model

310

(103)

1 Simulation versus Analytic Solution-Queueing Up in the Doctor's Waiting Room

310

(14)

2 Discrete versus Continuous Models

324

(52)

2A Introduction to Difference Equations

325

(6)

2B Exponential Population Growth-Difference and Differential Equations

331

(8)

2C Logistic Population Growth-Difference and Differential Equations

339

(6)

2D Equilibrium, Stable and Unstable

345

(9)

2E Stability of Linear Difference Equations-Commodity Prices and Cobweb Analysis

354

(9)

2F Stability of Some Nonlinear Difference Equations-Logistic Population Growth

363

(13)

3 Deterministic versus Stochastic Models-Forecasting Epidemics

376

(37)

3A An Outline of Probability

377

(15)

3B A Day in the Life of an Epidemic-Stochastic and Deterministic Views

392

(8)

3C The Lifetime of a Deterministic Epidemic

400

(5)

3D The Lifetime of a Simple Stochastic Epidemic

405

(8)

Appendix

413

(4)

Answers to Selected Exercises

417

(16)

Index

433

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Concepts of Mathematical Modeling

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