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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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Function, negative part of 55n Function, nowhere differentiable 446 Function, of a-points 225 Function, perturbation of 296 Function, positive definite 304 Function, positive part of 55n Function, real-analytic 215 Function, real-differentiable 202 Function, reciprocal 231n Function, regular 207 Function, restrictions on 448 Function, scalar 26 Function, separated 297 Function, set 63 94 Function, sine 41 Function, singularity of 315 319 Function, stem 284 Function, step 54—56 99 Function, upper- (lower-) semicontinuous 463 Function, value of 55n Function, variance of 107 Function, variation of 454n 456 Function, wave 416 Functional 57 Functional analysis 391 Functional dependence 51 Functional equation 353 367 Functional matrix 45 Functional matrix, rank of 51 Functional, bounded 396 Functional, continuation of 58 Functional, extension of 58 Functional, linear 56 392 393 397 Functional, positive 58 Functional, Riemann extension of 68 Fundamental solution 315 316 317 356 Fundamental theorem of algebra 195—196 Fundamental theorem of Cauchy 10 Fundamental vibration 411 G-set, universal 476 Galois group 510 Galois theory 518 Galois, E. 510 Gamma-function vi 355 365—379 500—501 Gamma-function, Euler functional equation for 367 Gamma-function, Euler integral representation of 371—374 Gamma-function, Stirling formula for 371 Gauss complex plane 255 Gauss distribution 96 Gauss integral theorem 176 181 334 Gauss plane 226 354 355 Gauss plane, line at infinity in 253 Gauss representation, of complex numbers 192 Gauss theorem 430 Gauss — Kronecker integral 429 431—432 Gauss, K.F. 89 Gel'fond, A.O. 517 Gellerstedt problem 335 General solution 292 Geodesic lines 422 Geometry, absolute 508 Geometry, axiomatic method in 507—508 Geometry, Euclidean 507 Geometry, Riemannian 170 Gleason, A. 517 Global behavior, of distributions 81 Global Properties 453 Global uniformizing parameter 250 Global, meaning of 439 Gnedenko, B.W. 121 Goedel 471 Goedel independence theorem 475 Goldbach conjecture 489 490 Goursat, E.J.B. 207 Graded ring 159 Gradient 129 Grassman algebra 159 Grassman algebra of alternating differential forms 154—159 Grassman algebra, exterior 525 Grassman ring, of differential forms 159 Grassman, H. 124 Green formulas 182 314 316 Green's function 329 410 434 Green's function, existence of 317 Group 313 321 509 519 Group of automorphisms 510 511 Group with operators 511 Group with parameter 526 Group, abelian 521 526 Group, Lie 511 Group, topological 4—5 517 518 Guinea-pig problem 351—352 Hadamard method, of descent 310 Hadamard, J. 313 314 321 Hardy, G.H. 498 Harmonic analysis 518 Harmonic functions 211 318 Hausdorff axioms 264 472 Hausdorff space 2 4 245n 264 266 Hausdorff space, connected 245n Hausdorff space, connected compact 272 Hausdorff space, example of 6 Hausdorff space, locally Euclidean 262 Hausdorff, separation axiom 4 Heat conduction, equation of 307 319 Heaviside function H 80 85 Heilbronn 491 Heine — Borel theorem 141 198 233n 256 433 513 Helly, theorem of 105—106 Helmert — Pearson, distribution of 108 Hensel, L. 501 519 Hermite theorem 494 Hermite, C. 494 Hesse normal form 192 Hierarchy of structures 521 Hilbert axioms 253 259 Hilbert sequence space 395 397 Hilbert space 393 394 399 400 401 405 412 515 516 Hilbert space, complete 397 Hilbert space, theory of vi Hilbert's fifth problem 517 Hilbert's seventh problem 494 Hilbert, D. 491 507 508 515 517 523 Hincin 121 Hincin theorem, of continued fractions 499 Hoelder continuous function 337 Hoelder theorem 354 375—379 Hoheisel 487 Holomorphic differential 234 Holomorphic function 207 Holomorphic function in complex plane 215—226 Holomorphic function, differential of 208 Holomorphic function, local derivative 234 Holomorphic function, sequence of 223 Holomorphic part 229 Holomorphy vi Hopf sigma-process 275 Hull of a set 450 Hurwitz polynomial 300 Hyperbolic see also "Differential equation" Hyperbolic motion 194 Hyperbolic Riemann surface 250 Hypercomplex system 525 Hypertranscendental number 493 Ideal 512 Identity Theorem 223 228 247 Incidence theorem 259 inclusion 428 521 Indefinite integral 87n Indefinite integral of holomorphic function 208 Independence 98—99 Independent Schwartz distribution 82 Indeterminacy, limits of 8—10 Index set 2 Inertia, index of 322 Infimum (greatest lower bound) 55n Infinitely divisible distribution 122 Infinitesimal increment 44 45 Infinity, line at 253 Infinity, neighborhoods of 230 Infinity, plane at 273 Infinity, point at 252 253—259 260 Influence, range of 309 311 322 Ingham 486 Initial conditions 292 Initial data, continuous dependence on 308 Initial point 126 Initial value problem 343 Initial values, propagation of 313 Inner composition 514 Inner-mathematical 509 Integrability condition 284 Integrable form 161 integral 53 Integral curve 278 290 291 Integral equation 292 341 514 Integral equation of second kind 410 Integral equation, algebraic 421 435 Integral equation, nonlinear 437—444 Integral equation, theory of vi Integral representation 220 Integral representation of functional 64 Integral ring 224 Integral, curvilinear 127 178 235 Integral, definite 57 Integral, step 57 Integral, surface 131 137 179 Integral, volume 179 Integrating factor 285 Integration and measure, theory of 77 Integration, elementary theory of 53—66 Integration, Lebesgue theory of 86 Integration, methods of 277—290 Integration, Stieltjes 65 Interior points 125 interval 54 Inverse, continuity of 7 Isolated 198 449 Isomorphism 92 Isoperimetric problem 422 Iteration 428 Jentzsch theorem 435 Jordan arc 201 Jordan content 62 63 66 76 Jordan curve 200 201 Jordan-measurable 62 Kellogg theorem 339 Kepler, J. 254 Kernel 436 Kernel function 349 438 Kernel matrix 401 403 407 Kernel, open 64n kernel, resolvent 440 kinetic energy 416 Kirchhoff law 353 Klein, Felix 507 509 Koenig, H. 86 87 Koksma, J.K. 497 Kolmogorov inequality 114—122 Kolmogorov, A.N. 89 118 121 Krull 511 512 Kurepa 475 485 L-integrable see "Lebesgue integrable" L-integral see "Lebesgue integral" Lagrange remainder formula 37 Lagrange, J.L. 491 Lame theorem 383 Landau symbol 479 482 Landau, E. 484 487 491 Laplace differential equation 211 Laplace operator 164 177 Laplace transform 346 386—389 404 405 Lattices, structure of 522 Lattices, theory of 512 Laurent series 229 236 Law of large numbers, "empirical" 115 Law of Large Numbers, strong 116—119 Law of large numbers, weak 115 Lebesgue convergence theorem 72 Lebesgue extension, of functional 68 Lebesgue integrability, of functions 87 Lebesgue integrable theorem 73 Lebesgue integral v 53 66 68 101 453 Lebesgue integral, definite 73 87n Lebesgue measure 53 66 Lebesgue measure zero 60 Lebesgue theory 53 Lebesgue theory of integration 86 Lebesgue theory of measure and integration 508 Lebesgue theory, classical 78 Lebesgue — Stieltjes integral 68 73 78 Lebesgue, H.L. 72 470 Lebesgue-integrable 83 399 Left reciprocal, of matrix 406 Leibniz 23 507 Leonardo of Pisa see "Fibonacci" Levi, B. 72 Levy, P. 121 Lewy, H. 313 Liber abbaci 351 Lie groups 511 517 Lie ring 511 Lie, Sophus 517 Limes inferior (lower limit) 8 Limes superior (upper limit) 8 Limit number 196 Limit point 11 196 198 Limit, calculation with 5—6 Limit, concept of 2 3 512 Limit, monotone 58 Limit, theorems of 114—122 Limit, uniqueness of 4 Limits of indeterminacy 8—10 Lindeberg — Feller, theorem of 120 Lindeloef conjecture 487 Lindemann — Weierstrass theorem 495 Line at infinity 259 260 Line-element 278 325 Line-element, regular 282 Line-element, singular 282 Linear difference equation 353 354 Linear difference equation, existence theorems for 388 Linear differential equations 286 Linear differential equations of second order 289 Linear form 57 Linear functionals 392 393 Linear functionals and operators 393 Linear functionals, integration of 56 Linear independence, of functions 388 Linear operator 203 392 393 Linear operator, completely continuous 408 Liouville theorem 221 233 492 Liouville, J. 221 296 496 Lipschitz condition 279 281 291 292 425 426 Lipschitz constant 279 Littlewood 498 Ljapunov criterion, for stability 301 Ljapunov Theorem 120 122 Local compactness 453 Local coordinates 185
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