|
|
Авторизация |
|
|
Поиск по указателям |
|
|
|
|
|
|
|
|
|
|
Blanchard P., Devaney R.L. — Differential Equations |
|
|
Предметный указатель |
-substitution 26 724
Air resistance 4
Alligood, Kathleen 347
Analytic methods 13 62
Analytic methods, systems 164 187
Angular frequency 299
Annihilation parameter 671
Apollo 13 666
Asymptotic stability 86
Attractor, Lorenz 710
Attractor, strange 710
Australia 15
Autonomous equations 24 40 76 96
Autonomous systems 181
Baby bottle 379
Beating 411
Bernoulli equation 729
Beth 16
Bifurcation 96—107
Bifurcation diagram 100
Bifurcation, creating equilibrium points 98 101
Bifurcation, definition 97
Bifurcation, discrete dynamical systems 692
Bifurcation, linear systems 348 375
Bifurcation, period-doubling 694
Bifurcation, pitchfork 693
Bifurcation, tangent 692
Bifurcation, value 100 103
Biography, Alligood, Kathleen 347
Biography, Curry, James H. 202
Biography, Kopell, Nancy 85
Biography, Lorenz, Edward N. 215
Biography, McKenna, Joseph 440
Biography, Smale, Stephen 63
Biography, Xia, Zhihong 495
Bob see Boat
Boston 95
Braun 152 433
Bridges, Millennium 417
Bridges, Tacoma Narrows 433 448
Carbon dating 17
Carrying capacity 9—10
CD stores model 235
Cell phones 142
Center 299 301
Changing variables 455 724
Changing variables, -substitution 724
Chaos 218 532 543 700 701
Chaos, sensitive dependence on initial conditions 703 706
Characteristic polynomial 265
Characteristic polynomial, three-dimensional matrix 358 361
Checking solutions 21 188
Chemical reactions 169 483
Chopping function 704
Circuit theory see RC and RLC circuits
COBWEB 683
Coefficient matrix 238
Coefficient matrix, three-dimensional 354
Coefficient o:F damping 193
Competing species system 179 225 453 472
complex numbers 291 744
Compound interest 28 36 125
Computers 628 642 653
Conservation of energy 492
Conserved quantity 486 488
Constant-coefficient equations 325
Convolution 605 625
Cool picture 163
Cooling model 35 141
Cooperative species system 225 483
Critical loci 347
Critically damped harmonic oscillator 331
Curry, James H. 202
Cycles 674 679 683—690
Cycles, classification 689
Damping 193
Damping, adjustable see MR fluids
Decoupled systems 189
Delayed logistic equation 718
Delta function see Dirac delta function
Dempster, J. P. 18 152
Dense subset 705
dependent variables 3—4 20
Dependent variables, systems 173
Determinant 242 342
Determinant, three-dimensional matrix 357
Determinant, Wronskian 258
Dick see Glen
Difference equation see Discrete dynamical system
Dirac delta function 597
Direction field 173
Discontinuous forcing 572
Discrete dynamical system 634 670
Discrete dynamical system, bifurcation 692—696
Discrete dynamical system, bifurcation, logistic difference equation 696
Discrete dynamical system, bifurcation, period-doubling 694
Discrete dynamical system, bifurcation, pitchfork 693
Discrete dynamical system, bifurcation, tangent 692
Discrete dynamical system, cycles 674 679 683—690
Discrete dynamical system, cycles, attracting 689
Discrete dynamical system, cycles, classification 689
Discrete dynamical system, cycles, neutral 689
Discrete dynamical system, cycles, repelling 689
Discrete dynamical system, eventually fixed points 673
Discrete dynamical system, eventually periodic points 674
Discrete dynamical system, fixed points 673 683—690
Discrete dynamical system, fixed points, attracting 685
Discrete dynamical system, fixed points, classification 686
Discrete dynamical system, fixed points, finding 677
Discrete dynamical system, fixed points, neutral 685 689
Discrete dynamical system, fixed points, repelling 685
Discrete dynamical system, graphical iteration 683
Discrete dynamical system, histograms 676
Discrete dynamical system, Newton’s method 717
Discrete dynamical system, orbits 673
Discrete dynamical system, period-doubling route to chaos 698
Discrete dynamical system, periodic orbits 674
Discrete dynamical system, renormalization 699
Discrete dynamical system, seed 673
Discrete dynamical system, time series 676
Discrete dynamical system, web diagram 683
Discrete logistic equation see Logistic difference equation
Dissipative systems 502—518
Dottie number 678
Duffing equation, periodically forced 532
Dynamical system, discrete time 670
D’Ancona, U. 13
Eigenvalue 263 264
Eigenvalue, complex 290
Eigenvalue, real distinct 268
Eigenvalue, repeated 309 310
Eigenvalue, three-dimensional matrix 357
Eigenvalue, zero 319
Eigenvector 263 266
Eigenvector, three-dimensional matrix 357
Electric circuit theory see RC and RLC circuits
Energy 489 492
Energy, dissipation 505
Equilibrium points 5 70 78
Equilibrium points, bifurcation 102—104 348
Equilibrium points, center 299 301
Equilibrium points, classification 86 284 462
Equilibrium points, creation 101
Equilibrium points, Hamiltonian systems 496—497
Equilibrium points, linear systems 240—242
Equilibrium points, linearization 87 729
Equilibrium points, node 86
Equilibrium points, saddle 274 362 463
Equilibrium points, sink 86 279 362 463
Equilibrium points, source 86 283 362 463
| Equilibrium points, spiral saddle 360
Equilibrium points, spiral sink 299 463
Equilibrium points, spiral source 299 463
Equilibrium points, stable 86 285
Equilibrium points, systems 156 177
Equilibrium points, unstable 285
Equilibrium solutions 5 10 70
Equilibrium solutions, systems 152 177
Eric see Initial value
Euler’s formula 293 746
Euler’s method 53—60 641
Euler’s method, errors 62 72 628
Euler’s method, errors, first step 630
Euler’s method, errors, second step 633
Euler’s method, errors, total 635
Euler’s method, formula 56
Euler’s method, improved 641—647
Euler’s method, order 637
Euler’s method, step size 54 629
Euler’s method, systems 198—204
Eventually fixed points 673
Eventually periodic points 674
Existence and Uniqueness Theorem, applications 70—73
Existence and Uniqueness Theorem, first-order equations 68
Existence and Uniqueness Theorem, systems 205
Existence theorem 66
Explicit solutions 13 23
Exponential growth 562 670;
Extendability of solutions 66 82
Extended Linearity Principle 116 384
External forcing 383
Extinction 104
Extra firm mattress 168
Finite arithmetic 660—663
First-order differential equation 5 20
First-order differential equation, autonomous 24
First-order differential equation, Bernoulli equation 729
First-order differential equation, bifurcation 96
First-order differential equation, changing variables 724
First-order differential equation, Euler’s method 53
First-order differential equation, existence 68
First-order differential equation, linear 112
First-order differential equation, one-parameter family 97
First-order differential equation, power series 736
First-order differential equation, Riccati equation 731
First-order differential equation, separable 20
First-order differential equation, slope fields 36
First-order differential equation, uniqueness 68
First-order numerical method 637
Fixed points 673 683—690
Fixed points, attracting 685
Fixed points, classification 686
Fixed points, finding 677
Fixed points, neutral 685 689
Fixed points, Poincar return map 536
Fixed points, repelling 685
Floating cube 441
Food chain model 525
Forced equation 383
Forced harmonic oscillator 382
Forced harmonic oscillator, beating 411
Forced harmonic oscillator, discontinuous forcing 586
Forced harmonic oscillator, glass harmonica 430
Forced harmonic oscillator, impulse forcing 595 598
Forced harmonic oscillator, phase angle 421
Forced harmonic oscillator, phase plane 401
Forced harmonic oscillator, resonance 415
Forced harmonic oscillator, sinusoidal forcing 397 413 421 589
Forced harmonic oscillator, undamped 409
Forced response 387
Fourier transform 560
Frequency, angular 299
Frequency, natural 299
Frequency, WEEI 299
General solution 7 23
General solution, systems 190
Gib 187 212
Gift 296 325
Glass armonica see glass harmonica
Glass harmonica 430
Glen see Dick
Glider 556
Gradient systems 513
Gradient systems, definition 516
Gradient systems, lobster motion 513
Gradient systems, Lyapunov functions 513
Graphical iteration 683
Gravitational force 489
Growth-rate coefficient 4
Guess-and-test method 118 194 388
Guess-and-test method, ultimate guess 736
Half-life 17
Hamilton, William R. 488
Hamiltonian function 488
Hamiltonian function, construction 493
Hamiltonian systems 484—497
Hamiltonian systems, conserved quantity 486
Hamiltonian systems, definition 488
Hamiltonian systems, energy 489
Hamiltonian systems, equilibrium points 496
Hamiltonian systems, Hamiltonian function 488
Hamiltonian systems, ideal pendulum 490
Hamiltonian systems, phase portraits 488
Hamiltonian systems, undamped harmonic oscillator 488
Hammer strike 421 595
harmonic oscillator 159 160 193 234 250 269 315 377 379
Harmonic oscillator, as Hamiltonian system 488
Harmonic oscillator, classification 330
Harmonic oscillator, clock 340
Harmonic oscillator, coefficient of damping 193
Harmonic oscillator, critically damped 331 334—335
Harmonic oscillator, damped 507
Harmonic oscillator, forced see Forced harmonic oscillator
Harmonic oscillator, hard spring 552
Harmonic oscillator, modified damping 227
Harmonic oscillator, natural frequency 207 330
Harmonic oscillator, overdamped 331 333—334
Harmonic oscillator, resonance 415
Harmonic oscillator, sinusoidal forcing 397 421
Harmonic oscillator, soft spring 552
Harmonic oscillator, spring constant 160
Harmonic oscillator, trace-determinant plane 346
Harmonic oscillator, undamped 301 330
Harmonic oscillator, underdamped 331—332
Harry 187 212
Harvesting 146
Heaviside function 573
Heaviside function, derivative of 602
Heaviside, Oliver 573
Hedgpath, J.W. 15
Hermite equation 739
Hermite polynomials 739
Hey, Jude 420
Histograms 676
Homogeneous equations 114 325 383 734
Hooke’s law of springs 160
Ideal pendulum 490
Identity matrix 264
Implicit solutions 28
Improved Euler’s method 641—647
Improved Euler’s method,cost 646
Improved Euler’s method,definition 644
Improved Euler’s method,errors 644
Improved Euler’s method,order 646
Impulse forcing 595
Independent variable 3 4 20
INDEX 827
Initial condition 5 22 154
Initial condition, discrete dynamical system see seed
Initial point 155
|
|
|
Реклама |
|
|
|