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Behnke H., Bachmann F., Fladt K. — Fundamentals of mathematics. Volume III. Analysis
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Название: Fundamentals of mathematics. Volume III. AnalysisАвторы: Behnke H., Bachmann F., Fladt K.Аннотация: Fundamentals of Mathematics represents a new kind of mathematical publication. While excellent technical treatises have been written about specialized fields, they provide little help for the nonspecialist; and other books, some of them semipopular in nature, give an overview of mathematics while omitting some necessary details. Fundamentals of Mathematics strikes a unique balance, presenting an irreproachable treatment of specialized fields and at the same time providing a very clear view of their interrelations, a feature of great value to students, instructors, and those who use mathematics in applied and scientific endeavors. Moreover, as noted in a review of the German edition in Mathematical Reviews , the work is "designed to acquaint [the student] with modern viewpoints and developments. The articles are well illustrated and supplied with references to the literature, both current and ‘classical’".
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1984Количество страниц: 557Добавлена в каталог: 01.12.2013Операции: Положить на полку |
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Dedekind, J.W.R. 508 512 513 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, higher 35—38 Derivative, partial complex 202 Descartes, R. 507 Determinism 313 Diagonal 17 Diametrical point relation 194 Difference equation vi 353 Difference equation for phi-function 358 Difference equation, characteristic equation of 380 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 of first order 287 Differential equation of nth order 281 Differential equation of second order 289 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, 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 in Euclidean plane 176 Differential form in Euclidean three-dimensional space 177 Differential form of first degree 145 Differential form of second order 150 237 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, module of 146 Differential form, normal form of 156 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 Dirac measure, derivative of 86 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 of random variable 95 Distribution function, conditional 111 Distribution function, cumulative 94 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, infinitely divisible, 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 of definition 392 Domain of dependence 309—311 Domain of operators 524 Domain, connected 199 Domain, fundamental 392 Domain, multivalent 242 Domain, non-schlicht 242 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 Mathimatique 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" 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 as mapping 215 Function element 241 Function theory in the large 125 Function theory in the small 125 206 290 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
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