Concepts of Mathematical ModelingCourier Corporation, 1 ene 2004 - 440 páginas 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. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each section is preceded by an abstract and statement of prerequisites, and answers or hints are provided for selected exercises. 1984 edition. |
Índice
THE SCOPE OF MATHEMATICAL MODELING | 1 |
STEPS INBUILDINGA MATHEMATICAL MODEL | 13 |
APPROXIMATEAND LIMITED MODELSGRAVITY ROCKETS AND RAINDROPS | 23 |
MACRO AND MICRO POPULATION MODELS I EXPONENTIAL GROWTH | 39 |
MACRO AND MICRO POPULATION MODELS II THE LESLIE MATRIX | 43 |
MACRO AND MICRO POPULATION MODELS III FAMILYPLANNING MODELS | 53 |
DESCRIPTIVE AND PRESCRIPTIVE MODELS INVENTORY POLICY | 60 |
THE RELATION OF MODELS TO DATA | 69 |
ACCURACYMULTIPLE LINEARREGRESSION | 180 |
PRECISIONMALTHUS AND THE DISMAL THEOREM | 198 |
GENERALITY AND FRUITFULNESSFROM ASTROLOGY TO TECHNOLOGY WITH KEPLER AND NEWTON | 211 |
ROBUSTNESSTHE UPS AND DOWNS OF ANCIENT ASTRONOMY | 222 |
OPTIMIZATION | 236 |
LINEARPROGRAMMINGFORMULATION AND GRAPHICAL SOLUTION | 246 |
AN OUTLINE OF THE SIMPLEX METHOD | 266 |
INTEGER PROGRAMM1NGTHE KNAPSACK AND TRAVELING SALESMAN PROBLEMS | 274 |
ADJUSTING DATA I THE EASY WAYTHE MEAN AND THE MAXIMUM LIKELIHOOD | 81 |
ADJUSTING DATA II THE HARD WAYMISCELLANEOUS METHODS AND EXAMPLES | 100 |
TEST1NG MODELSWEIGHTEDVOTING GAMES | 121 |
PUTTING THE FACTS IN ORDERMENDELEEV AND THE PERIODIC TABLE | 132 |
EVALUATION OF MATHEMATICAL MODELS | 139 |
DESCRIPTIVE REALISMSIMPLE LINEAR REGRESSION | 150 |
DESCRIPTIVE REALISMCORRELAT1ON IS NOT CAUSATION | 170 |
THE TRANSPORTAT1ON PROBLEM | 282 |
COMBINATORIAL OPTIMIZATIONTHE CHINESE POSTMAN PROBLEM | 298 |
CHOOSING THE MATHEMATICS FOR THE MODEL | 310 |
DISCRETE VERSUS CONTINUOUS MODELS | 324 |
DETERMINISTIC VERSUS STOCHASTICMODELS FORECASTING EPIDEMICS | 376 |
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