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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 Modeling
Авторы: 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.
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Рубрика: Технология /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Издание: Third Edition
Год издания: 2003
Количество страниц: 538
Добавлена в каталог: 17.04.2008
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Предметный указатель
Absolute deviations 110
Agility in sports 95
Anchoveta 480
Approximation 99
Area under a curve 177
Area under a curve, Monte Carlo algorithm 178
Arms race 336 444
assumptions 57
Asymptotic stability 414 423
Attrition-rate coefficient 438
Automobile gasoline mileage 88 311
Automobile gasoline mileage, autonomous system 413
Average rate of change 369 371
Average weight density 92
Baleen whale 480
Bass fishing derby 79—83
binary variables 241
Biological optimum, population level 483
Birthrate 371
Blood volume flow-rate problem 313
Body temperature problem 86
Body weight, versus blood flow through the heart 85 86
Body weight, versus height model 91
Body weight, versus pulse rate 85 86
Bornstein, Marc and Helen 134
Borrie, M.S. 393
Brahe, Tycho 67
Braking distance 59 68
Braking distance, differential equations model 391
Brewed coffee project 64
Buckingham, E. 307
Buckingham, theorem 307
Buffer stock 464
Burghes, David 393
Buying or renting a home project 65
Canadian lynx and hare problem 436
Centrifugal force problem 313
Characteristic dimension 76 79
Chebyshev approximation criterion 107
Chebyshev approximation criterion, compared with least-squares criterion 119
Choosing a best model 119
Clamped spline 164
Classification of variables 57
Coefficient of heat conduction 324
Collected data 98
Communicable disease problem 380
Competitive hunter model 419
Competitive hunter model, trajectories 422
Complete set of dimensionless products 306
Complete set of solutions to algebraic system 306
Concave downward 129
Concave upward 128
Constrained optimization problem 237
Constraints 237
Consumption (of gasoline) 88
Cost 55
Crater volume 320 323
Critical point 396
Cubic spline interpolation 159
Cumulative frequency 197
Damped pendulum 313
Dantzig, George 263
Data analysis 98
Deathrate 371
Decision variables 237
Deer population problem 403
Delivery costs 194
Demand curve 361
density 79 91
dependent variables 57
Derivative 369
Derivative, rate of change 370
Derivative, slope of tangent line 370
Design condition 332
Deterministic process 177
Dichotomous 282
Difference equation 4
Difference table 149 150
Differential equation 368
Differential equation, graphing solutions 395
Differential equation, systems of 412
DIMENSION 292
Dimension, table of physical entities 302
Dimensional analysis process 304
Dimensional analysis process, summary 309
Dimensional homogeneity 297
Dimensional homogeneity, Buckingham's theorem 307
Dimensionless product 295
Dimensionless product, Buckingham's theorem 307
Dimensionless product, complete set 306
Dimensionless product, solutions to homogeneous system 306
Direction field 395
Discrete dynamical systems 7
Discrete dynamical systems, approximating change 9
Discrete dynamical systems, iterating solutions 12
Discrete dynamical systems, numerical solutions 12
Discrete dynamical systems, spotted owl population 32
Discrete mathematics 368
Distortion of data points 104
Divided differences 148 151
Drag force 97
Drag force on a sphere problem 313
Drag force on a submarine 331
Drag force, damped pendulum 313
Drug dosage 382
Dynamic programs 239
Dynamical system 5
Economic optimum population level 484
Elimination constant 384
Empirical model 98 126
Equilibrium values 22 396
Equilibrium values, stability 29 398
Error 100
Euler's algorithm 406
Exhaustible resource 355 480
Explosion analysis 319
Explosion analysis, cube-root law 320
Explosion analysis, energy set 323
Explosion analysis, gravity scaling 321
Explosion analysis, one-fourth root law 320
Exponential decay 384
Exponential growth model 373
Extreme points 251
Falling raindrop 77
Falling raindrop, dimensional analysis 309
Falling raindrop, problem 304
Farming problem 248
Feasible region 250
Feasible region, empty 255
Feasible region, unbounded 254 255
Feasible solutions 250
Fibonacci search 290
Fidelity 55
Finite mathematics 368
First divided difference 148
Fishing industry model 480
Fishing regulation 488
fixed costs 356
flexibility 55
Fluid mechanics 318
Fluid mechanics, flow in a channel problem 335
Formulation error 100
Fragile 63
French curve 160
Frequency of demand 196
Froude number 318
Fuel rating (energy) 88
Function 336
Function, concavity 128
Function, decreasing 128
Function, increasing 128
Function, piecewise linear 241
Gause's principle 422
Gaussian elimination 306
Geometrically similar 75
Geometrically similar, fish 79
Geometrically similar, submarines 330
Goal programs 243
Golden ratio 283
Golden section search 283
Gradient method 470
Graphical analysis, limitations of 422
Graphical model fitting 101
Gravity scaling 321
Gross national product 394
Growth of yeast 376
Harbor system simulation 205
Harbor system simulation, algorithm 207
Harvest the Chesapeake Bay Problem 127
Harvest the Chesapeake Bay Problem, Blue crabs problem 131
Harvest the Chesapeake Bay Problem, Blue fish problem 130
Harvesting submodel 480
Hatton, Bob 166
Heat loss 85 86
Heating of a cooled object 14
Helicopter transportation project 64
histogram 196
Homogeneous system 305
Horelick, Brindell 382
Hydrostatic pressure problem 304
Hyperbola 462
Independent solution set 305
Independent variables 57
Infeasible 260
Initial value problem 404
Instantaneous rate of change 369
Integer program 239
Interest compounded continuously 410
Interpolation 98
Interpolation, approximation 99
Interpolation, cubic spline 159
Interpolation, linear 160
Interpolation, smoothing 146
Intersection points 260
Inventory model, deterministic 459
Inventory model, probabilistic 194
Investment in college education project 65
Investment problem 242
Iterated solutions (DDS) 31
Jaye, Michael 317
Kepler, Johannes 67
kinetic energy 70
Koont, Sinan 382
Ladder of Powers 128
Ladder of transformations 130
Lagrange multipliers 474
Lagrangian form 474
Laminar flow 334
Lanchester combat models 437
Lanchester combat models, conventional-guerilla combat 448
Lanchester combat models, parabolic law model problem 448
Lanchester combat models, refinements 441
Lanchester combat models, square law model 439
Lanchester, F.W. 438
Largest absolute deviation 107
Largest absolute deviation, Chebyshev approximation criterion 107
Launching a satellite problem 391
Least-squares criterion 110
Least-squares criterion, applications of 114
Least-squares criterion, compared with Chebyshev criterion 112
Least-squares criterion, power curve 115
Least-squares criterion, quadratic 116
Least-squares criterion, straight line 114
Least-squares criterion, transformed data 102 116
Leja, Stanley 419
Limit cycle 423
Limited growth model 374
linear combination 306
Linear interpolation 160
Linear program 239 251
Linear program, example 251
Linear programming, algebraic 259
Linear programming, geometric 250
Linear programming, revised simplex 535 Appendix
Linear programming, sensitivity analysis 273
Linear programming, simplex 263
Linear spline 160
Linear spline, demand submodel 199
Linear spline, harbor system simulation 212
Logistic curve 375
Logistic growth 374
Long jump problem 65
Long-term behavior 22
Lotka — Volterra model 435
Lottery problem 181
Lottery problem, lumber yield problem 86
Mach number 318
Malthus, Thomas 371
Malthus, Thomas, model of population growth 373
Mansfield, Ralph 301
Marginal cost 357
Marginal cost and taxation 360
Marginal revenue 357
Marginal value 279
Markov chain 217
Mathematical Contest in Modeling (COMAP) Appendix A
Mathematical Contest in Modeling (COMAP), problems 491
Mathematical model 54
Mathematical model, construction 57
Mathematical model, cost 56
Mathematical model, deterministic 177
Mathematical model, fidelity 56
Mathematical model, flexibility 56
Mathematical model, fragile 63
Mathematical model, implementation 58
Mathematical model, interpretation 58
Mathematical model, maintenance 58
Mathematical model, predict versus explain 52
Mathematical model, probabilistic 177
Mathematical model, robust 63
Mathematical model, sensitivity 63
Mathematical model, types 55 56
Mathematical model, verification 58
Mathematical world 52
Maximum profit 356
McNulty, Jim 166
Measurement errors 100
Medical records 65
Mixed integer program 239
Mixing nuts problem 246
MLT system 296
Model fitting 97
Model fitting, analytic methods 107
Model fitting, empirical model fitting 126
Model type 53
Model type, deterministic 177
Model type, probabilistic 177
Modeling process 52
Modeling process as a closed system 54
Modeling process, iterative nature of 62
Modeling process, model construction 57
Modeling process, scientific method 61
Monte Carlo simulation 177
Monte Carlo simulation, area under a curve 177
Monte Carlo simulation, elevator system algorithm 525 Appendix
Monte Carlo simulation, harbor system algorithm 205
Monte Carlo simulation, inventory algorithm 202
Morning rush hour 213
Multiobjective program 242
Mutualism 412
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