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Fox W.P., Goirdano F.R., Weir M.D. — First Course in Mathematical Modeling
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Название: First Course in Mathematical ModelingАвторы: Fox W.P., Goirdano F.R., Weir M.D.Аннотация: This text provides an introduction to the entire modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem solving process to enhance a student's problem solving capabilities. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible, beginning with short projects, the book facilitates their progressive development and confidence in mathematics and modeling.
Язык: Рубрика: Технология /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: Third EditionГод издания: 2003Количество страниц: 538Добавлена в каталог: 17.04.2008Операции: Положить на полку |
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Предметный указатель
Mutualism, problem 436 Natural spline 164 Newton's inverse square law 303 Newton's method 291 Nonrenewable resources 355 Nuclear arms race 336 Nuclear arms race, civil defense 345 Nuclear arms race, economic model 444 Nuclear arms race, graphical model 343 Nuclear arms race, MIRV's 347 Nuclear arms race, mobile launching pads 346 Numerical methods 405 Numerical methods, Euler's algorithm 406 Nutritional requirements problem 245 Objective functions 237 One-term model 127 Optimization 236 Optimization, basic model 237 Optimization, formulation of 236 Orbit 413 Oscillation 143 Outliers (in data) 133 Path 413 Pendulum, damped 313 Pendulum, simple 293 298 Period 293 Periodic trajectories 431 Phase plane 413 Piecewise linear function 241 Pinch test 96 Pivot 264 Polynomials 138 Polynomials, advantages for interpolation 142 Polynomials, Lagrangian form 141 Polynomials, oscillation 143 Polynomials, sensitivity of coefficients 144 Polynomials, smoothing 146 Population growth 371 Population models 371 Postage Stamp Problem 171 Power 89 Power curve 115 Power, problem 317 Predator-prey model 427 Predator-prey model, harvesting effects 433 Predator-prey model, trajectories 432 Predict 98 Pressure coefficient 319 334 Pressure drop problem 334 Principle of Competitive Exclusion 422 Probabilistic process 186 Probabilistic process, submodels 186 Producing electronics equipment problem 247 PRODUCT 295 Product, dimensionless 295 Production schedule 251 Production schedule, problem 246 Projectile problem 312 Proportional 65 Proportional, geometric interpretation 66 Proportional, modeling 67 Propulsion force 88 Prototype 330 Purchasing trucks problem 467 Random number 182 Random number, algorithm 185 Range (of data) 101 Ratio rule 267 Real-world systems 52 Real-world systems and modelling process 53 Regression 227 Regression, residual plots 229 Relative error 66 Reliability 223 Reliability, computer components reliability 225 Reliability, parallel systems 224 Reliability, series systems 224 Reliability, space shuttle components reliability 225 Reliability, stereo system components reliability 225 Renewable resources 480 Rental car problem 35 Replacing a car project 65 Residual plots 229 Residuals 121 229 Resisting force 77 Resources, allocation 245 Resources, nonrenewable 355 Resources, renewable 480 Rest point 413 414 Reynolds number 318 332 Reynolds number, laminar flow 334 Reynolds number, turbulent flow 334 Rickover, Admiral Hyman G. 337 Right-hand side 237 Roasting a turkey 324 Robust 63 Round-off error 100 Rousseau, Jean Jacques 379 Satellite problem 391 Scalar multiple 305 scatterplot 128 Schmidt, Robert M. 319 Scientific method 61 Search techniques 279 Second divided difference 150 Sensitivity 63 Sensitivity analysis 273 Sensitivity of coefficients 274 Separation of variables 409 Sequence (DDS) 4 Shape factor 332 Similitude 330 simple pendulum 293 298 Simplex method 263 Simplex method, revised simplex 535 Appendix Simulation 175 Simulation labs 186 Simulation labs, flip of a coin 186 Simulation labs, roll of a fair die 187 Simulation labs, roll of an unfair die 188 Simulation, Monte Carlo 177 Smith, Adam 480 Smoothing 146 Social diffusion problem 381 Social optimum yield 483 Solution, algebraic system 305 Solution, autonomous system 413 Solution, complete set 306 Solution, independent set 306 Solution, scalar multiple 305 Solution, sum 305 Solution, trivial 305 Space shuttle problem 240 Space shuttle water container 476 Species coexistence 422 Speed of sound problem 313 Spheres in a fluid problem 313 SPLINE 159 Spline interpolation 160 Spotted owl population model 41 Stable rest point 414 Stationary point 414 Stochastic program 239 Stock-outs 465 Storage costs 194 Submarine 331 Submodel 57 sum of absolute deviations 102 Sum of absolute deviations, minimization of 110 252 Sum of solutions 305 Sum of squared deviations 110 Sum of squared deviations, least-squares criterion 110 Supply curve 360 Survival of whales problem 428 480 Sustainable yield 484 system 52 Systems of difference equations 35 Tableau 266 Taylor, General Maxwell D. 337 terminal velocity 77 309 Theory of the firm 359 thermal conductivity 325 Total cost 356 Total profit 356 Total revenue 356 Trajectory 413 Trajectory, basic Lanchester combat model 437 Trajectory, competitive hunter 419 Trajectory, nuclear arms race 444 Trajectory, predator-prey 427 Trajectory, properties 413 Transformed least-squares 116 Transforming data 102 Trend (of data) 127 Trivial solution 305 Truncation errors 100 UMAP no. 211, The Human Cough 468 UMAP no. 232, Kinetics of Single Reactant Reactions 394 UMAP no. 234, Radioactive Chains: Parents and Daughters 394 UMAP no. 269, Monte Carlo: The Use of Random Digits to Simulate Experiments 185 UMAP no. 270, Lagrange Multipliers: Applications to Economics 479 UMAP no. 292—293, Listening to the Earth: Controlled Source Seismology 330 UMAP no. 294, Price Discrimination and Consumer Surplus 367 UMAP no. 303, The Diffusion of Innovation in Family Planning 17 381 UMAP no. 304, The Growth of Partisan Support I: Model and Estimation 51 427 UMAP no. 305, The Growth of Partisan Support II: Model Analytics 51 427 UMAP no. 308, The Richardson Arms Race Model 354 449 UMAP no. 311, The Geometry of the Arms Race 354 UMAP no. 321, The Curve Fitting via the Criterion of Least Squares 119 UMAP no. 322, Difference Equations with Applications 34 381 UMAP no. 327, Nuclear Deterrence 354 UMAP no. 332, The Budgetary Process: Incrementalism 427 UMAP no. 333, The Budgetary Process: Competition 427 UMAP no. 340, The Poisson Random Process 205 UMAP no. 341, Five Applications of Max-Min Theory from Calculus 468 UMAP no. 376, Differentiation, Curve Sketching, and Cost Functions 367 UMAP no. 468, Calculus of Variations with Applications in Mechanics 249 UMAP no. 506, The Relationship Between Directional Heading of an Automobile and Steering Wheel Deflection 394 UMAP no. 509, The Cobb-Douglas Production Function 381 UMAP no. 517, Lagrange Multipliers and the Design of Multistage Rockets 479 UMAP no. 518, An Application of Calculus to Economics: Oligopolistic Competition 468 UMAP no. 520, Random Walks: An Introduction to Stochastic Processes 427 UMAP no. 522, Unconstrained Optimization 249 UMAP no. 539, I Will if You Will: A Critical Mass Model 367 UMAP no. 551, The Pace of Life, An Introduction to Model Fitting 138 UMAP no. 553, Graphical Analysis for Some Difference Equations in Biology 51 437 UMAP no. 564, Keeping Dimension Straight 304 UMAP no. 590, Random Numbers 185 UMAP no. 60—62, The Distribution of Resources 354 UMAP no. 610, Whales and Krill: A Mathematical Model 418 UMAP no. 67, Modeling the Nervous System: Reaction Time and the Central Nervous System 391 UMAP no. 69, The Digestive Process of Sheep 411 UMAP no. 737, Geometric Programming 249 418 UMAP no. 74, Tracer Methods in Permeability 390 UMAP no. 75, Feldman's Model 411 UMAP no. 79, Selection in Genetics 390 Unconstrained optimization problem 238 Unimodal function 279 Unstable rest point 413 414 Variable costs 356 Vehicular stopping distance 59 68 Vehicular stopping distance, constructed model 72 Vehicular stopping distance, cubic spline interpolation 168 Vehicular stopping distance, differential equations submodel 391 Vehicular stopping distance, divided difference table 153 Vehicular stopping distance, empirical quadratic table 153 Vehicular stopping distance, least-squares fit 122 Vehicular stopping distance, traffic flow problem 466 Verhulst, Pierre-Francois 374 Verhulst, Pierre-Francois, model of population growth 374 Volterra's principle 435 Volume of a sphere in the first octant 180 Voting in an election problem 44 Wallace, Michael 336 Weber number 318 Weight of a fish 79 Weight-lifting problem 84 159 Whales and krill 428 Wind force on a van 301 Wine making project 64 Work 70 Yeast growth 155 376 Yeast growth, divided difference table 156 Yeast growth, empirical quadratic model 156
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