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A first course in mathematical modeling. (English)
Monterey, California: Brooks/Cole Publishing Company, a division of Wadsworth, Inc., Belmont, Calif. XVII, 382 p. (Gö: 89A 14436) (1985).
Contents: Part one: Creative model construction and the modeling process. 1. Graphs of Functions as Models: A Nuclear Arms Race, Managing Nonrenewable Resources: The Energy Crisis, Effects of Taxation on the Energy Crisis, An Oil Embargo. 2. The Modeling Process: Mathematical Models, Some Illustrative Examples: Vehicular Stopping Distance, Automobile Gasoline Mileage, The Assembly Line, Morning Rush Hour. 3. Modeling Using Proportionality: Proportionality and Geometric Similarity, A Bass Fishing Derby, Vehicular Stopping Distance, Automobile Gasoline Mileage, Elapsed Time of a Tape Recorder, Body Weight Versus Height. Part two: Model fitting and models requiring optimization. 4. Model Fitting: Fitting Models to Data Graphically, Analytic Methods of Model Fitting, Applying the Least-Squares Criterion, Choosing a Best Model: Some Examples: Vehicular Stopping Distance, The Elapsed Time of a Tape Recorder. 5. Models Requiring Optimization: Classifying Optimization Problems, Formulation of Optimization Models, An Inventory Problem: Minimizing the Cost of Delivery and Storage, The Assembly Line, Managing Renewable Resources: The Fishing Industry. Part three: Empirical model construction. 6. Experimental Modeling: The Pace of Life and Other One-Term Models, Interpolation using Higher-Order Polynomials, Smoothing Using Polynomials, Cubic Spline Interpolation. 7. Dimensional Analysis and Similitude: Dimensions as Products, The Process of Dimensional Analysis, A Damped Pendulum, Examples Illustrating Dimensional Analysis: Explosion Analysis, How Long Should You Roast a Turkey?, Similitude. 8. Simulation Modeling: Modeling Deterministic Behavior: Area Under a Curve, Developing Submodels for Probabilistic Processes, A Harbor System, Morning Rush Hour. 9. Modeling Using the Derivative: Population Growth, Prescribing Drug Dosage, Scenarios Revisisted: Braking Distance, Elapsed Time of a Tape Recorder, Numerical Approximation Methods. 10. Interactive Dynamic Systems: Graphing Solutions to First-Order Differential Equations, A competitive Hunter Model, A predator-Prey Model, Two Military Examples: The Nuclear Arms Race Revisited, Lanchester Combat Models.