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| Driver R.D. — Ordinary and delay differential equations |
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| Предметный указатель |
Abel's formula 109 150
Applications of delay differential equations 226
Applications of delay differential equations, references 239
Asymptotic stability 363
Asymptotic stability, uniform 364
Automobile shock absorbers 91
Autonomous systems 329 349 400
Backwards solution of a delay differential equation 248
Barbasin — Krasovskii Thm. 371
Basic initial problem 255
Bendixson 400 431 448
Bernoulli's equation 38
Bessel's eq. of order  138
Bolzano — Weierstrass Thm. 460
Boundary value problems 78
Bounded delays 285
Capacitance 119 177 178
Cauchy criterion 461
Center 423
Characteristic equation 92 163 320
Closed interval 449 452
Closed set 451
Complex exponentials 67
Complex functions 63
Continuation of solutions 275 304
Continuity Condition (C) 290
Continuous dependence on initial conditions 74 193 264 297 350
Control system with delay 234
Convergence estimate 202
Critical damping 91
Critical point 407
Critical point, isolated 425
Damped oscillations 90 168
Damping coefficient 90
Decoupling method 152
Diagonalizing matrices 151
Differential inequality 33 73
Differential inequality with delay 389
Differential operators 85
Eigenvalues 147
Eigenvectors 147
Eigenvectors, generalized 156
electrical circuits 16 18 40 77 119 177 178
Electron two-body problem 237
Energy 280
Error estimate 202 220 273
Errors, growth of 74 193 265 266 297
Euler's equation 108 127 129 135
Existence of solutions 212 270 299
Exponential decay 244 325 363 373 377 386
Exponential of a matrix 197
First integral 432 437
First order o.d.e. 7 27
Fixed point of a mapping 274
Focus 421
Frequency, natural 119
Friction 52 119 173
Functional diff. eq. 225 288
Functions 452
Functions of a matrix 197
Fundamental matrix 187
Generalized eigenvectors 156
Global behavior of solutions 431
Global existence 281
Gravitation 58 62
Gronwall's lemma 72
Growth of solutions 168 195 267 324 336
Heine — Borel theorem 460
Homogeneous linear equations 85 140 247 314
Inductance 17 119 178
Inequalities delay differential 389
Inequalities, Gronwall's 72
Inequalities, Halanay's 390
Inequalities, Reid's 72
Infimum 35
Infinitesimal upper bound 354
Initial conditions 3 7 41 53
Initial function 227
Integral equations 212
Integral inequality 72 75
Integrating factor 9 208
Interchanging order of integration 464 465
Lienard, A. 441
Limit cycle 441
linear combination 99 162
Linear delay differential equations 246 313
Linear delay differential equations with constant coefficients 319
Linear delay differential equations, stability 384
Linear delay differential equations, variation of parameters 331
Linear dependence 101 142
Linear independence 101 142
Linear operations 43
Linear operators 86 99 246
Linear ordinary diff. eqs. systems 49 75 139 414
| Linear ordinary diff. eqs., first order scalar 7
Linear ordinary diff. eqs., higher order scalar 57 84 222
Linear ordinary diff. eqs., variation of parameters 125 180
Linear vector space 42
Lipschitz conditions for functionals 292
Lipschitz conditions for scalar functions 36
Lipschitz conditions for vector functions 46 258
Lipschitz conditions, local 259 261 293 300
Lotka — Volterra equations 232 435
Lyapunov functions and functionals 353
Lyapunov's direct method 352
Matrix exponentials 197
Matrix sequences 198
Matrix series 199
Matrix-valued function 140
Matrix-valued function, continuous 141 192
Matrix-valued function, differentiable 141 192
Matrix-valued function, integrable 141
Mean value theorem 454
Mean Value Theorem, function of n variables 457
Method of steps 228
Minorsky's equation 399
Mixing of liquids 13 18 226 240
Nodes, improper 416 418
Nodes, proper 417
Noncontinuable solutions 275 304
Nonunique solutions 24 37 39 80 82 241 248 250 267
Norm of a function 291
Norm of a matrix 190
Norm of a vector 45
Norm, weighted 283
Open interval 449 451
Open set 451
Order of a diff. eq. 6
oscillations 119 168 235 243 244
Overdamping 90
Peano 72
Pendulum 278 362 381 383 428 430 431
Periodic solutions 408
Perron 379 400
Phase plane 405
Phase portrait 405
Phase space 405
Picard iteration 212
Planetary motion 58
Poincare 400 405 431 448
Polar coordinates 420 427
Population growth 229
Positive definite functional 354
Prey-predator models 232 435
Prime number theorem 237
Quasi-bounded functionals 305
Quasi-linear differential eqs., delay 384
Quasi-linear differential eqs., ordinary 374 424
Radio tuning 119
Radioactive decay 2 17
Reid's Lemma 72
Resistance 119
Resonance 119
Saddle point 419
Separation of variables 19
Spiral point 421
Spring-mass systems 51 68 173 346 369
Stability 340
Stability, asymptotic 363
Stability, uniform 344
Stability, uniform asymptotic 364
Stable matrix 169
Steady state solution 120 317 319
Successive approximations 212 271
Superposition theorems 99 141 314
Supremum 37
Taylor's theorem 454
Trajectories 403
Transient part of a solution 120 317 319
Transition matrix 184
Two-body problem of electrodynamics 237
Uncoupled equations 152
Underdamping 90
Undetermined coefficients 117 148 165
Uniform convergence 462
Uniqueness, delay diff. eqs. 230 241 255 296
Uniqueness, ord. diff. eqs. 26 267
Uniqueness, systems of o.d.e.'s 44 193
Unit step function 331 388
Unstable solution 342
van der Pol equation 284 441
Variation of constants see "Variation of parameters"
Variation of parameters 125 180 331
Vector space 42
vector-valued functions 41
Volterra 232 435
Weighted norm 283 312
wronskian 102 145
Zeros of a polynomial 169
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