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| Enns R.H., Mc Guire G.C. — Nonlinear physics with mathematica for scientists and engineers |
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| Предметный указатель |
Mathematica Command, Method->Gear 263
Mathematica Command, Method->RungeKutta 18 56 61 256 371
Mathematica Command, Module 123 394
Mathematica Command, N 43 49 187 379 408 467 469 487 527 531
Mathematica Command, NDSolve 18 24 49 56 61 68 79 112 116 118 144 160 215 256 270 271 273 275 288 320 325 326 347 371 387 414 527 539 546 551 568 590 608 628
Mathematica Command, Nest 120 359 361
Mathematica Command, NestList 359 361 368 374 379 381
Mathematica Command, NIntegrate 11
Mathematica Command, Normal 11 104 193 226 531
Mathematica Command, NSolve 32 49 161 219 261 399
Mathematica Command, ParametricPlot 18 49 56 112 116 144 215 270 271 273 275 288 628
Mathematica Command, ParametricPlot3D 24 56 61 68 79 116 160 347 628
Mathematica Command, Part 519 531 575 628
Mathematica Command, Partition 359 361 371 379
Mathematica Command, Pi 8 11 20 184 215 442 460 462 469 496 523 527 575
Mathematica Command, Play 20 531
Mathematica Command, PlayRange->All 20
Mathematica Command, Plot 15 18 20 49 56 79 101 128 143 168 176 182 184 187 200 209 215 219 242 248 256 273 275 300 326 329 359 361 371 374 379 416 420 438 460 472 519 528 531 536 539 546 551 559 568 578 590 607 608
Mathematica Command, Plot3D 344 394 414 418 420 628
Mathematica Command, PlotJoined->True 182 184 236 320 356 359 361 379 386 459 462 467 469 472 482 485 531 635
Mathematica Command, PlotLabel 49 61 79 112 116 118 215 219 248 270 271 273 312 320 325 326 359 374 379 381 485 527 531 539 551 568 590 607 608 635
Mathematica Command, PlotPoints 18 20 24 56 61 68 79 101 116 128 140 144 148 160 187 215 254 256 270 271 273 288 300 326 344 347 371 394 414 416 418 420 438 442 527 546 551 559 568 590
Mathematica Command, PlotRange 15 18 56 68 79 85 101 116 118 120 140 143 144 168 182 184 187 215 219 248 256 261 273 275 298 300 325 329 344 347 356 361 371 374 379 402 416 438 442 459 460 462 467 469 472 482 485 519 528 531 536 539 551 653
Mathematica Command, PlotRange->All 254 320 359 368 381 414 420 635
Mathematica Command, PlotStyle 15 18 49 56 85 101 104 118 120 121 144 168 176 182 184 187 200 209 219 228 233 242 248 254 256 261 267 270 271 275 288 298 300 320 325 326 329 368 371 374 379 381 386 399 402 408 416 420 438 442 459 460 462 467 472 482 485 519 527 528 531 539 546 551 559 568 590 607 635
Mathematica Command, PlotVectorField 140 144 148 270 271 288
Mathematica Command, PlotVectorField3D 160
Mathematica Command, Plus 374
Mathematica Command, Point 61 68 79 118 128 140 143 144 148 399
Mathematica Command, PointSize 15 61 68 79 85 118 120 121 128 140 143 144 148 242 248 325 329 344 399 402 528 536 551 607
Mathematica Command, PointStyle 519
Mathematica Command, PolarPlot 267 270
Mathematica Command, Polygon 347
Mathematica Command, Precision 242
Mathematica Command, PrecisionGoal 61
Mathematica Command, Print 523
Mathematica Command, Random 85 329
Mathematica Command, Re 128
Mathematica Command, Rectangle 325
Mathematica Command, ReleaseHold 215 527 578
Mathematica Command, ReplacePart 93 320
Mathematica Command, RGBColor 49 61 79 85 116 118 128 140 143 182 184 187 200 209 219 228 233 242 248 261 270 271 288 325 329 344 356 399 408 528 531 539 551 607
Mathematica Command, RotateLeft 487
Mathematica Command, RotateRight 487
Mathematica Command, ScaleFactor 140 160 270 271 288
Mathematica Command, ScaleFunction 140 144 160 270 271 288
Mathematica Command, ScatterPlot 402
Mathematica Command, ScatterPlot3D 228 236 261 387
Mathematica Command, Sech 20 438 472
Mathematica Command, semi-colon 8
Mathematica Command, Series 11 104 182 187 193 226 531
Mathematica Command, SetCoordinates 628
Mathematica Command, SetPrecision 12 14 242
Mathematica Command, Show 15 49 140 144 148 182 184 187 200 209 215 219 242 248 270 271 288 300 325 329 347 359 361 379 408 414 416 420 459 467 469 482 487 519 528 531 536 551 607
Mathematica Command, Sign 371
Mathematica Command, Simplify 13 41 70 96 143 168 187 203 267 418 426 430 438 441 442 492 496
Mathematica Command, Sin 12 18 20 41 49 104 187 193 209 215 267 379 381 408 418 426 459 462 467 469 485 487 527 531 575 578
Mathematica Command, Sinh 442 496
Mathematica Command, Solve 12 14 24 43 128 143 144 203 209 226 267 300 344 347 438 442 460 496 628
Mathematica Command, Sqrt 8 24 49 70 104 143 182 184 267 438 442 472 485 496 575 590 628
Mathematica Command, StyleForm 61 160 184 200 209 325 374 379 607 608
Mathematica Command, Sum 20 197 200 203 209 460 628
Mathematica Command, Switch 462 467 469
Mathematica Command, Table 49 85 93 118 121 128 144 184 197 200 203 209 228 233 242 248 261 270 271 273 275 320 326 329 356 359 361 368 371 379 381 386 387 399 402 408 416 420 459 462 467 469 472 482 485 487 507 531 578 628 653
Mathematica Command, TableForm 197 200 203 209 507
Mathematica Command, Take 635
Mathematica Command, Tan 8
Mathematica Command, Tanh 10 438
Mathematica Command, Text 56 61 68 118 128 143 184 200 275 298 300 361 399 416 528
Mathematica Command, TextStyle 15 18 24 49 56 61 79 85 101 116 121 143 144 168 182 184 187 219 228 233 242 248 254 256 261 267 270 271 298 312 325 326 329 344 347 359 361 368 371 374 379 381 386 394 399 402 408 414 416 418 420 438 442 459 460 462 467 472 482 485 519 527 531 539 546 551 559 568 590 607 608 635 653
Mathematica Command, Thickness 176 184 200 273 472 482 485 559
Mathematica Command, Ticks 15 24 56 61 68 79 101 116 120 121 182 184 200 215 219 228 233 242 248 254 256 275 298 300 326 344 347 356 359 371 374 379 381 394 399 402 414 416 418 420 438 442 459 467 469 482 485 531 551 559 568 590 608 635
Mathematica Command, TimeUsed[] 228 233
Mathematica Command, Transpose 15 320 329 386 459 462 467 469 472 482 485 528 536 551 607
Mathematica Command, TrigExpand 12 430
Mathematica Command, TrigReduce 12 102 203 209 531
Mathematica Command, Union 368
Mathematica Command, UnitStep 551 628
Mathematica Command, VectorHeads 160
Mathematica Command, ViewPoint 56 61 68 79 160 228 344 347 402 414 418 420
Mathematica Command, Which 85 248 329
Mathematica Command, While 123 394
Mathematica Command, With 374
Mathematica Example, 01-1: Diff. and Integ. 7
Mathematica Example, 01-2: Taylor Expansion 11
Mathematica Example, 01-3: Mathematica Algebra 12
Mathematica Example, 01-4: Plotting 15
Mathematica Example, 01-5: Numerical ODE Sol. 17
Mathematica Example, 01-6: Animation and Sound 20
Mathematica Example, 01-7: Classical Mechanics 23
Mathematica Example, 02-1: Parametric Excitation 41
Mathematica Example, 02-2: Phase Plane Traj. 56
Mathematica Example, 02-3: Tunnel Diode 70
Mathematica Example, 03-1: Barnsley’s Fern 85
Mathematica Example, 03-2: 1 Out of 8 Rule 93
Mathematica Example, 03-3: sine-Gordon equation 104
Mathematica Example, 03-4: Logistic Map 120
Mathematica Example, 03-5: Predator-prey Map 121
Mathematica Example, 04-1: Damped SHO 130
Mathematica Example, 04-2: Roots 135
Mathematica Example, 04-3: Tangent Field 140
Mathematica Example, 04-4: Competing Armies 144
Mathematica Example, 04-5: Stability Analysis 161
Mathematica Example, 05-1: Nonlinear drag 168
Mathematica Example, 05-2: Solving for V 171
Mathematica Example, 05-3: Riccati Example 178
Mathematica Example, 05-4: Hard Spring Sol 187
Mathematica Example, 05-5: Series Solution 193
Mathematica Example, 05-6: Perturbation Eqs. 197
Mathematica Example, 05-7: Hard Spring Pert. 203
Mathematica Example, 06-1: Alternate Approx. 226
Mathematica Example, 06-2: Euler Algorithm 228
Mathematica Example, 06-3: Modified Euler Code 233
Mathematica Example, 06-4: RK4 Algorithm 242
Mathematica Example, 06-5: Stiff Equation 254
Mathematica Example, 06-6: RKF-Stiff equation 256
Mathematica Example, 07-1: Stable Limit Cycle 267
Mathematica Example, 07-2: Relaxation Osc 275
Mathematica Example, 08-1: Nonlinear Response 298
Mathematica Example, 08-2: A versus  300
Mathematica Example, 08-3: Basins of Attraction 312
Mathematica Example, 08-4: Fractal Dimension 329
Mathematica Example, 08-5: Henon — Heiles Potential 344
Mathematica Example, 08-6: HH Poincare Sections 347
Mathematica Example, 09-1: Logistic Map 2 356
Mathematica Example, 09-2: Geometric Picture 361
Mathematica Example, 09-3: Douady’s Rabbit 394
Mathematica Example, 09-4: Fixed Points 399
Mathematica Example, 09-5: Chaos Control 402
Mathematica Example, 09-6: Saturn’s Rings 408
Mathematica Example, 10-1: Burgers’ Eq. 414
Mathematica Example, 10-2: Nonlinear Term 416
Mathematica Example, 10-3: Laplace Transform 418
Mathematica Example, 10-4: Fourier Transform 420
Mathematica Example, 10-5: SG Transformation 426
Mathematica Example, 10-6: KdV Solitary Wave 438
Mathematica Example, 10-7: 2-Soliton Solution 441
Mathematica Example, 10-8: sine-Gordon soliton 442
Mathematica Example, 11-1: Representation of  453
Mathematica Example, 11-2: Variable Separation 460
Mathematica Example, 11-3: Explicit Method 462
Mathematica Example, 12-1: Lax Formulation 492
Mathematica Example, 12-2: Z-S/AKNS Eqs. 507
Mathematica File, 01: Simple Pendulum 43
Mathematica File, 02: Air Drag on a Sphere 48
Mathematica File, 03: Golf Ball Drag/Lift 49
Mathematica File, 04: Rabbits — Foxes Eq. 56
Mathematica File, 05: Fox Rabies Model 61
Mathematica File, 06: Arms Race 68
Mathematica File, 07: Oregonator Model 79
| Mathematica File, 08: Two Soliton Solution 101
Mathematica File, 09: Duffing’s Eq. 112
Mathematica File, 10: Lorenz System 116
Mathematica File, 11: Poincare Section 118
Mathematica File, 12: Mandelbrot Set 123
Mathematica File, 13: Undamped Pendulum 128
Mathematica File, 14: Phase Plane Analysis 143
Mathematica File, 15: Higher Ord. Sing. Pt. 148
Mathematica File, 16: Three-D Vector Field 160
Mathematica File, 17: Laser Beam Compet. 176
Mathematica File, 18: Period of Simp. Pend. 182
Mathematica File, 19: Anharmonic Period 184
Mathematica File, 20: Elliptic Integrals 184
Mathematica File, 21: Jacobian Elliptic Func 187
Mathematica File, 22: Poisson Method 200
Mathematica File, 23: Lindstedt Method 209
Mathematica File, 24: Krylov — Bogoliubov 215
Mathematica File, 25: Ritz Method 219
Mathematica File, 26: Adaptive Step Sizing 248
Mathematica File, 27: Semi-Implicit Scheme 261
Mathematica File, 28: Semistable Limit Cycle 270
Mathematica File, 29: Multiple Limit Cycles 271
Mathematica File, 30: Relaxation Oscillations 273
Mathematica File, 31: Brusselator Limit Cycle 288
Mathematica File, 32: Power Spectrum 320
Mathematica File, 33: Poincare Section 325
Mathematica File, 34: Sensitivity-Initial Cond. 326
Mathematica File, 35: Geo. Rep. Log. Map 359
Mathematica File, 36: Bifurcation Diagram 368
Mathematica File, 37: Lorenz Map 371
Mathematica File, 38: Lyapunov Exponent 374
Mathematica File, 39: Circle Map 379
Mathematica File, 40: Devil’s Staircase 381
Mathematica File, 41: Noise vs Chaos 386
Mathematica File, 42: Reconst. Lor. Attr. 387
Mathematica File, 43: Mandelbrot Set 394
Mathematica File, 44: Explicit Method 459
Mathematica File, 45: Explicit Scheme — Fisher 467
Mathematica File, 46: Klein — Gordon Eq. 469
Mathematica File, 47: KdV Sol. Wave Coll. 472
Mathematica File, 48: Colliding Laser Beams 482
Mathematica File, 49: Kink — Antikink Collision 485
Mathematica File, 50: Reaction-Diffusion Eqs. 487
Mathematica File, 51: QM Tunneling 496
Mathematica File: Experiments, X01: Magnetic Force Law 519
Mathematica File: Experiments, X02: Magnetic Tower 523
Mathematica File: Experiments, X03A: Spin Toy Pendulum 527
Mathematica File: Experiments, X03B: Spin Toy Best Fit 528
Mathematica File: Experiments, X04: Eardrum 531
Mathematica File: Experiments, X05: Nonlinear Damping 536
Mathematica File: Experiments, X06: Anharmonic Potential 539
Mathematica File: Experiments, X07: Iron Core Inductor 546
Mathematica File: Experiments, X08A: LRC Best Fit 551
Mathematica File: Experiments, X08B: Nonlin. LRC Circuit 551
Mathematica File: Experiments, X08C: LRC Piecewise 551
Mathematica File: Experiments, X10: Tunnel Diode OscilL 559
Mathematica File: Experiments, X11: Forced Duffing Eq. 568
Mathematica File: Experiments, X13: Compound Pendulum 575
Mathematica File: Experiments, X14: Damped Pendulum 578
Mathematica File: Experiments, X16: VdP Oscillator 590
Mathematica File: Experiments, X20A: Hard Spring Fit 607
Mathematica File: Experiments, X20B: Hard Spring 608
Mathematica File: Experiments, X26: 5-Well Potential 628
Mathematica File: Experiments, X27: Power Spectrum 635
Mathematica File: Experiments, X33: Mapping 653
Mathematica files, how to use 28
Mathematica files, symbol for 28
Mathematica Help 26
Mathematica Help, Help Browser 26
Mathematica random number generator 384
Mathematica system 6
Mathematica, capital letters 8
Mathematica, case sensitivity 8
Mathematica, cell 8
Mathematica, curly brackets 8
Mathematica, double square brackets 8
Mathematica, lists 8
Mathematica, multiplication 8
Mathematica, operations 7
Mathematica, square brackets 8
Mathematica, Standard Form 8
Mathematica, tags 8
Mathematica, TraditionalForm 8
Matrix, inverse 476
Matrix, Jacobian 397
Matrix, multiplication 458
Matrix, representation 458
Matrix, tridiagonal 458 469
May, Robert 60 119 356
Mayer-Kress, Gottfried 67
McAvity, David 123
McCall, S. 107
McLaughlin, D. W. 500
Measles outbreaks 387
Mechanics, nonlinear 39
Melting 52
Mesh point 451 468
Method of characteristics 483
Method of least squares 217
Metropolis, N. 372
MICRO-CAP program 616
Miura, Robert 491
Mixer circuit 529
Model, arms race 66
Model, arms race, Rapoport’s 150 263
Model, baleen whale 247
Model, beating heart 80
Model, big fish-little fish 54 59
Model, biochemical switch 238
Model, Brusselator 285
Model, competing armies 144
Model, competition, quasi-species 62
Model, disk dynamo 163
Model, eardrum 46
Model, epidemic 61
Model, fish harvesting 246
Model, Fitzhugh — Nagumo 253
Model, fox rabies 59 60
Model, game of life 90
Model, genetic control 156
Model, human population growth 176
Model, logistic 119
Model, Lorenz 90 291
Model, nonlinear spring 147
Model, Oregonator 79
Model, owl 165
Model, predator prey, 3 species 164
Model, Prigogine — Lefever 286
Model, quasi-species 252
Model, rabbits and sheep 59
Model, rabbits-foxes 54
Model, Rossler 116
Model, saturable Volterra 58
Model, SIR 61 165
Model, spruce budworm infestation 237
Model, squid-herring 153
Model, tenure 153
Modified Euler method 232 241
Modulation frequency 586
Modulator 529
monopole 518
Montroll, Elliot 57
Multi-soliton solution 501
Murray, A. B. 92
Murray, J. D. 59
Muskat, M. 424
Mutation coefficients 252
Neff, R. B. 54
Negative damping 570
Negative feedback 580
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