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| Blanchard P., Devaney R.L. — Differential Equations |
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| Предметный указатель |
Initial-value problem 6 22—23
Initial-value problem, system 162
Integral equation 642
Integral transform 560
Integrating factor 128
Inverse Laplace transform 566
Iteration 670 673
Iteration, graphical 683
Iteration, notation 679
Jacobian matrix 460
Kopell, Nancy 85
Laplace transform 560
Laplace transform, convolution 605 625
Laplace transform, definition 561
Laplace transform, Dirac delta function 597
Laplace transform, discontinuous functions 572
Laplace transform, exponential functions 562
Laplace transform, first-order equations 565
Laplace transform, Heaviside function 573
Laplace transform, inverse 566
Laplace transform, linearity 564
Laplace transform, periodic functions 580
Laplace transform, poles 614 624
Laplace transform, product rule 603
Laplace transform, qualitative theory 612
Laplace transform, ramp function 579
Laplace transform, rules 620
Laplace transform, sawtooth function 581
Laplace transform, second-order equations 581
Laplace transform, square wave 581
Laplace transform, table 620
Laplace transform, trigonometric functions 582
Lazer, A. C. 433
Learning model 15 144
Legendre equation 743
Legendre polynomials 743
Levy, Matthys 208 433
Linear approximation see Linearization
Linear combinations 243
Linear equations, first-order 112
Linear equations, integrating factor 128
Linear equations, Linearity Principle 114 243
Linear equations, Linearity Principle, Extended 116 384
Linear equations, nonhomogeneous 114 383
Linear equations, second-order 325
Linear independence 249
Linear independence, in three dimensions 355
Linear systems, angular frequency 299
Linear systems, bifurcation 348 375
Linear systems, center 299
Linear systems, characteristic polynomial 265
Linear systems, classification 284
Linear systems, classification, three-dimensional 361
Linear systems, coefficient matrix 238
Linear systems, complex eigenvalues 290
Linear systems, constant coefficients 237
Linear systems, critical loci 347
Linear systems, determinant 242
Linear systems, dimension 240
Linear systems, eigenvalues 263
Linear systems, eigenvectors 263
Linear systems, equilibrium points 240—242
Linear systems, general solution 250 268 292 313
Linear systems, harmonic oscillator see Harmonic oscillator
Linear systems, Linearity Principle 243
Linear systems, Linearity Principle, Extended 384
Linear systems, linearly independent solutions 250
Linear systems, matrix notation 237
Linear systems, natural frequency 299 330
Linear systems, natural period 299
Linear systems, Principle of Superposition see Linearity Principle
Linear systems, real distinct eigenvalues 268
Linear systems, repeated eigenvalues 309 318
Linear systems, saddle 274 362
Linear systems, sink 279 362
Linear systems, source 283 362
Linear systems, spiral sink 299
Linear systems, spiral source 299
Linear systems, straight-line solutions 267
Linear systems, three dimensions 354—365
Linear systems, trace-determinant plane 342
Linear systems, Wronskian 258
Linear systems, zero eigenvalue 319
Linearity Principle 114 243
Linearity Principle, Extended 116 384
Linearity Principle, three-dimensional systems 355
Linearization 87 453 458 727
Linearization, failure 464—465
Linearly independent solutions 250
Logistic difference equation 671
Logistic difference equation, annihilation parameter 671
Logistic difference equation, bifurcation 696
Logistic difference equation, chaotic example 702
Logistic difference equation, delayed logistic 718
Logistic difference equation, fixed points 687
Logistic difference equation, without chaos 701
Logistic equation 9—11 148 727
Logistic equation, harvesting 104
Logistic equation, modified version 89
Logistic equation, predator-prey system 157
Logistic equation, qualitative analysis 10
Long-term behavior 10 13
Lorenz equations 214 368 528 709—714
Lorenz equations, attractor 710
Lorenz equations, Poincare return map 712
Lorenz equations, template 711
Lorenz, Edward N. 214 215
Lori see Gib and Harry
Lost in space 666
Lucky guess method 329
Lyapunov function 507
Lyapunov function, damped harmonic oscillator 507
Lyapunov function, nonlinear pendulum 505
Lyapunov, Aleksandr 507
Magic fingers 340
Magnetorheological fluid see MR fluid
Maple 112
Mass-spring see Harmonic oscillator
Mathematics 112
Matrices, characteristic polynomial 265
Matrices, degenerate 242
Matrices, determinant 342
Matrices, diagonal 358
Matrices, eigenvalue 263
Matrices, eigenvector 263
Matrices, identity 264
Matrices, Jacobian 460
Matrices, singular 242
Matrices, symmetric 273
Matrices, trace 342
Matrices, upper triangular 273
Matrix notation 237
McKenna, Joseph 433 440
Memorization model 144
Metaphor of the parking lot 175
Metaphor of the rope 77
Millennium Bridge 417
Miracle 729 732
Missing solutions 27
Mixing problems 31—32 43 131
Modeling 2—13
Models, baby bottle 379
Models, bridges, Millennium 417
Models, bridges, Tacoma Narrows 433 448
Models, carbon dating 17
Models, CD stores 235
Models, cell phones 142
Models, chemical reactions 169 483
Models, cholesterol 34
Models, circuit see RC and RLC circuits
| Models, clock 340
Models, competing species 179 225 453 472
Models, compound interest 28 36 125
Models, cooperative species 225 483
Models, delayed logistic 718
Models, electric circuits see RC and RLC circuits
Models, exponential growth 670
Models, extinction 104
Models, extra firm mattress 168
Models, food chain 525
Models, forced harmonic oscillator 382
Models, glass harmonica 430
Models, glider 556
Models, hammer strike 421 595
Models, harmonic oscillator see Harmonic oscillator
Models, harvesting 104 146
Models, housing market 254
Models, ideal pendulum 490
Models, learning 15 144
Models, lobster motion 513
Models, logistic population model see Logistic equation and Logistic difference equation
Models, measuring mass in space 377
Models, memorization 144
Models, Millennium Bridge 417
Models, mixing problems 31—32 43 131
Models, modified logistic 89
Models, mold growth 145
Models, MR fluid 231 426
Models, Newton’s law of cooling 35 141
Models, oil production 149
Models, opera singer 382 420 430
Models, pendulum 489 502
Models, population see Population models
Models, predator-prey see Predator-prey system
Models, radioactive decay 16
Models, RC circuit 44 61 568 577
Models, RLC circuit 375 391 447
Models, rubber band 229 448
Models, saving 28
Models, shock absorbers 339
Models, shock absorbers, active 231
Models, state populations 148
Models, suspension bridge 417 433 448
Models, suspension system 339
Models, swaying skyscraper 206—209
Models, Tacoma Narrows Bridge 433 448
Models, trolley cars 95
Models, truck seats 231
Models, tuned-mass damper 509
Models, Volterra — Lotka 482
Models, washing machines 426
Models, weather 214
Moldy bread 145
Mozart, The Marriage of Figaro 487
MR fluid 231 426
Natural frequency 207 299 330
Natural period 299
Natural response 387
Newton’s Law of Cooling 35 141
Newton’s method 717
Newton’s second law of motion 159 382 490
Node, first-order equation 86
Nonhomogeneous equations 114 383
Nonlinear equation 9
Nullcline 472 476—479
Numerical integration 642
Numerical integration, Riemann sums 642
Numerical integration, Simpson’s rule 650
Numerical integration, trapezoid rule 642 650
Numerical methods 13 62
Numerical methods, errors 62 72 628 644 653
Numerical methods, Euler’s method 53—60 198 628
Numerical methods, finite arithmetic 660—663
Numerical methods, improved Euler’s method 644
Numerical methods, in practice 662
Numerical methods, order 637 641 646
Numerical methods, round-off error see Finite arithmetic
Numerical methods, Runge — Kutta 649—658
Numerical methods, Runge — Kutta, Mathematica program 655
Numerical methods, Runge — Kutta, Older 653
Numerical methods, Runge — Kutta, TI calculator program 654
Numerical methods, Runge — Kutta, С program 656
Numerical methods, systems 164 198 657
Oil production 149
Old joke 2
Opera singer 382 420 430
Orbit 673
Order, differential equation, first-order 5 20
Order, differential equation, second-order 161
Order, numerical method 637 641
Order, numerical method, Euler’s method 637
Order, numerical method, Improved Euler’s method 646
Order, numerical method, Runge — Kutta 653
Ordinary differential equation 5
Overdamped harmonic oscillator 331
Oxford 18
P — Delta effect 207
Parameterized family of differentia] equations 96
Parameters 3 4 20
Parameters, bifurcation value 100
Parameters, family of equations 97
Parking lot 175
Particular solution, initial-value problem 7
Particular solution, nonhomogeneous equations 384
Pendulum 489
Pendulum, damped 457 502
Pendulum, higher order approximation of 553
Pendulum, ideal 490
Pendulum, periodically forced 540
Pendulum, periodically forced, Poincar return map 540
Period 155
Period, forcing 397
Period, natural 299
Period-doubling bifurcation 694
Period-doubling route to chaos 698
Periodic solution 154
Phase angle 421
Phase line 77
Phase line, equilibrium points 78 84
Phase line, metaphor of the rope 77
Phase line, sketching solutions 81
Phase plane 156
Phase plane, metaphor of the parking lot 175
Phase portrait 156
Phase shift 401 425
Phase space, three-dimensional 356
Phasor 408
Pitchfork bifurcation 693
Poincar return map 533
Poincar return map, fixed point 536
Poincar return map, Lorenz equations 712
Poincar, Henri 214 534 543
Poles of Laplace transform 614 624
Population models, carrying capacity 9—10
Population models, competing species 179 225 453 472
Population models, cooperative species 225 483
Population models, delayed logistic 718
Population models, exponential growth 4 148 670
Population models, growth-rate coefficient 4
Population models, harvesting 104 146
Population models, logistic equation see Logistic equation and Logistic difference equation
Population models, modified logistic 89
Population models, predator-prey see Predator-prey system
Population models, predator-prey, modified 157
Population models, state populations 148
Population models, three species 525
Population models, U.S. population 7
Population models, Volterra — Lotka 482
Power series methods 736
Predator-prey system 11—13 152—158
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