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Driver R.D. — Ordinary and delay differential equations
Driver R.D. — Ordinary and delay differential equations

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Название: Ordinary and delay differential equations

Автор: Driver R.D.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 512

Добавлена в каталог: 22.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $\frac{1}{2}$      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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