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| Behnke H., Bachmann F., Fladt K. — Fundamentals of Mathematics, Volume III: Analysis |
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| Предметный указатель |
Definite integral vi
Definition, domain of 392
Degenerate 96
Delta-function 79
Delta-operations 466 468
DeMoivre equation 191
DeMoivre — Laplace theorem 120
Denjoy process 462
Dense, nowhere and everywhere 447
density 449
Dependence, domain of 309 311
Derivative 29 43
derivative of 86
Derivative, higher 35—38
Derivative, partial complex 202
Descartes, R. 507
Determinism 313
Diagonal 17
Diametrical point relation 194
Difference equation vi 353
Difference equation, characteristic equation of 380
Difference equation, for phi-function 358
Difference equation, general solution of 385
Difference equation, homogeneous 379
Difference equation, linear 379
Difference equation, summation method for 355—364
Difference equation, theory of 354
Difference quotient 22 28 30—31 38
Differentiability v 28—35 78 215 230
Differentiability, total 45
Differentiable function 39
Differentiable manifold 184—186 513
Differential derivative 204
Differential equation, Beltrami 325
Differential equation, Bessel 313
Differential equation, Cauchy — Riemann 204—205
Differential equation, direction field of 278
Differential equation, eigenvalue problem for 341
Differential equation, elliptic 322 323 326 327 337 341
Differential equation, elliptic-parabolic 325
Differential equation, Euler 287 422
Differential equation, exact 284
Differential equation, explicit 277 290—294
Differential equation, homogeneous 286—287
Differential equation, hyperbolic 322 323 326 343
Differential equation, hyperbolic-parabolic 325
Differential equation, hyperbolic-parabolic-elliptic 358
Differential equation, implicit 277 282
Differential equation, Laplace 211
Differential equation, linear 286
Differential equation, nonhomogeneous 286
Differential equation, nonlinear 518
Differential equation, of first order 287
Differential equation, of n-th order 281
Differential equation, of second order 289
Differential equation, order of 277
Differential equation, ordinary 306 424
Differential equation, parabolic 322 323 326 330
Differential equation, partial, of second order 306
Differential equation, perturbed 302
Differential equation, quasilinear 302 321
Differential equation, quasilinear system 326
Differential equation, Riccati 290
Differential equation, Schroedinger 417
Differential equation, singular points of 282
Differential equation, solution of 276 278
Differential equation, ultrahyperbolic 322
Differential equation, uniqueness theorem for 291
Differential form, adjoint 157 167 170
Differential form, alternating 154—159 185
Differential form, complex-valued linear 205
Differential form, conjugate 207
Differential form, exact 206
Differential form, exterior multiplication of 151
Differential form, Grassman ring of 159
Differential form, in Euclidean plane 176
Differential form, in Euclidean three-dimensional space 177
Differential form, module of 146
Differential form, normal form of 156
Differential form, of first degree 145
Differential form, of second order 150 237
Differential of a pole 235
Differential of second kind 237
Differential of zero 235
Differential quotient 22 29 30—31
Differential, basis transformation of 167
Differential, complete 202
Differential, complex 204
Differential, elementary 154
Differential, Frechet 419 421 423 439
Differential, holomorphic 234 245
Differential, independent of parameter 234
Differential, meromorphic 234 237 245 246
Differential, residue of 236 246
Differential, total 129 145 202 204
Diophantine approximation 495
Diophantine equation 495
Dirac delta-function 79
Dirac measure 83
Directed set 12 14
Direction filter 15
Dirichlet approximation theorem 497
Dirichlet discontinuous factor 104
Dirichlet function 214 448 459
Dirichlet series 489
Dirichlet theorem 479
Dirichlet theorem, on prime numbers 488
Dirichlet, P. G. L. 23 497
Discontinuity, points of 463
Discriminant manifold 282
Distance 11
Distance, definition of 338
Distance, Euclidean 192 196
Distance, notion of 71
Distribution function, conditional 111
Distribution function, cumulative 94
Distribution function, of random variable 95
Distribution function, one-dimensional 94
Distribution, binomial 96
Distribution, differentiation of 84
Distribution, Gauss 96
Distribution, global behavior of 81
Distribution, infinitely divisible 122
Distribution, marginal 97
Distribution, multidimensional normal 97
Distribution, normal 96
Distribution, partial derivative of 85
Distribution, Poisson 96 122
Distribution, probability 92
Distribution, Schwartz 53 74 78 82 84 516
Distribution, theory of 80—82
Distribution, uniform 497
Distributive lattice 90
Distributive law 467
Distributive law, dual 90
Divergence 431
Domain 261
Domain, connected 199
Domain, fundamental 392
Domain, multivalent 242
Domain, non-schlicht 242
Domain, of definition 392
Domain, of dependence 309—311
Domain, of operators 524
Domain, perturbation 312
Domain, simply connected 199
Domain, star-shaped 161
Double points 130
Duffing equation 434
Eigenfunction 296 341 410 411 414 417 435
| Eigenvalue 296 348 410 411 412 417 435
Eigenvalue problem 515
Eigenvalue problem, regular 341
Eigenvalue problem, singular 341
Eilenberg 271
Elastic body, vibrations of 307
Electron, motion of 417
Elementary differential 154
Elementary function 67 214
Elementary function, potential theoretic method of 249
Elementary integral 67
Elements de Mathematique 506 521
Elliptic See Differential equation
End point 126
Energy integral method 327 331 332 334
Energy operator 417
Entire function 481
Entourage 18
Epsilon-language 479
Epsilon-neighborhood 6
Equal in the limit 479
Equation (see also differential equation), almost linear 321 323
Equation, branching 443
Equation, characteristic 287 380
Equation, potential 306 314
Equivalence class, of number triples 259
Equivalence class, of parallel lines 259
Eratosthenes, sieve of 483
Erdoes 485 489
Ergodic theorems 119
Erlanger Programm 509 517
Esenin 475
Estermann 491
Estimate, a priori 339
Euclid — Hilbert system of axioms 253
Euclid's theory of primes 480
Euclidean algorithm 383
Euclidean distance 192 196
Euclidean geometry 507
Euclidean geometry, points at infinity in 255
Euclidean motion 194
Euclidean plane 192
Euclidean plane, differential forms in 176
Euclidean plane, function-theoretic closure of 262—263
Euclidean space, four-dimensional 274
Euclidean space, subsets of 24—25
Euclidean three-dimensional space, differential forms in 177
Euler constant 364 365
Euler differential equation 287 422
Euler equation 421 422
Euler function 489 495
Euler functional equation 367
Euler gamma-function 355
Euler identity 479
Euler integral formula 374 388
Euler integral representation, gamma-function 371—374
Euler multiplier 285
Euler summation formula 363 364
Euler — Riemann zeta-function 481
Euler, L. 489 493 494
Events 90
Events, certain 91
Events, possible 91
Exact differential equation 284
Exact differential form 206
Existence condition 308
Existence problem 327 328
Existence, questions of 336—348 474
Expansion theorem 343 414
Expectation 99—103
Expectation, conditional 108 112—113
Exponential function 22 38—42
Extended matrix 51
Extension for measures, theorem of 95
Extension, methods of 73—74
Extension, theorem of 95
Exterior multiplication 155
Exterior multiplication, of differential forms 151
Fechner 89
Feller, W. 121
Fermat numbers 488
Fermat theorem 252
Fibonacci (Leonardo of Pisa) 351
Fibonacci numbers 352 383
Fibonacci sequence 352 353 383
Field 510
Field of sets 63 76
Filter v 2 12—16 525
Filter basis 15
Filter, Cartan 513
Filter, Cauchy 18
Filter, direction 15
Filter, finer 15
Filter, Frechet 14
Filter, image 15
Filter, system of 14
First (second) mean value property 318
Fixed point theorem 430
Fixed point theorem, nonlinear 434—437
Fixed point, of mapping 423
Flow of gases 336
Forced oscillation 302
Foundations of mathematics 509
Fourier coefficients 398 399 401
Fourier integral 518
Fourier integral theorem 347
Fourier series 23 518
Fourier transform 403
Fractions, continued 499
Frankl's problem 334
Frechet differential 419 421 423 439
Frechet filter 14
Fredholm 440n 515
Fredholm theorems 413
Friedrichs, K. O. 313
Fueter, Rudolph 274
Function element 241
Function theory in the large 125
Function theory in the small 125 206 290
Function, as mapping 215
Function, comparison 294
Function, complex-differentiable 204
Function, complex-valued 200
Function, connected with measures 82
Function, continuous 26
Function, definition of 23
Function, differentiable 39
Function, Dirichlet 214 448 459
Function, domain of 200
Function, domain-continuous 201
Function, elementary 67 214
Function, entire 481
Function, exponential 22 38—42
Function, extension of 448
Function, general theory of 251
Function, harmonic 211 318
Function, holomorphic 207 232 240 246 250 257 271
Function, implicit 473
Function, influence 410
Function, inverse 231n
Function, kernel 349
Function, lim-closed set of 459
Function, locally constant 454
Function, many-valued 238
Function, measurable 93
Function, meromorphic 228 232 240 243 246 250
Function, minorant (majorant) 328
Function, monotone 463
Function, negative part of 55n
Function, nowhere differentiable 446
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