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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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"Smallest complete measure" 77 110n (mu*-)almost everywhere 70 (mu*-)integrable function 71 (mu*-)zero function 70 (mu-)measurable, function of 74 (mu-)summable function 71 A priori estimate 339 a-points, of function 225 A-set see "Analytic set" Abelian group 521 526 Absolute value 190 Accumulation, point of 196 Adjoint differential form 157 167 Adjoint operator 403 Adjoint space 397 Algebra 524 Algebra, boolean 91 92 Algebra, fundamental theorem of 195—196 Algebra, homological 519—520 Algebra, normed 516 Almost all 479 Almost continuous 460 Almost equal 479 Almost everywhere 70 Almost linear equation 321 323 Alternating differential form 185 Alternating differential form, differential operations for 159—165 Alternating differential form, theory of vi 143 Alternative theorem 296 413 Analysis v 1 Analysis and number theory 500—501 Analysis, axiomatic method in 512—518 Analysis, complex vi Analysis, functional 391 Analysis, harmonic 518 Analytic function, defined by function element 242 Analytic number theory 480 Analytic operation 468 Analytic set 448 458 465 468 469 Analytic set, linear 466 Angle-preserving transformation 194 Approximately equal 479 Approximation, best 496 Approximation, Diophantine 495 497 ARC 125 Arc, smooth 127 Arc-length 128 Artin, E. 510 Arzela theorem 410 435 437 Asymptotically equal 479 Atlas 231 Atlas of holomorphically related charts 245 Atomic theory 415 Automorphism group 510 511 Axiomatic method, in geometry 507—508 B-set see "Borel set" Baire classes 460 Baire classes of functions 448 Baire classes, first 460 462 463 Baire condition 464 Baire function 464 473 Baire function, non- 474 Baire space 464 Baire system, of functions 459 460 Baire theorem 448 460 462 Banach fixed point theorem 423 Banach space 338 340 393 399 432 435 437 516 Banach space, adjoint 400 Banach space, conjugate 400 Banach space, dual 400 Banach space, theory of vi Banach theorem 446 447 Banach, S. 516 Band spectra 418 Bayes theorem 109 Beltrami differential equation 325 Bernoulli distribution 96 Bernoulli law, of large numbers 116 Bernoulli numbers 360 362 Bernoulli polynomials 360 362n Bernoulli, Daniel 23 Bernoulli, Jacob 89 360 Bernoulli, Johann 23 Bertrand — Cebysev theorem, for primes 483 Bessel differential equation 313 Bessel inequality 398 Bicompactification 257 Bieberbach closure 274 Bieberbach, L. 274 321 Bilateral 132 Bilinear form, bounded 402 Binomial distribution 96 Bohr — Landau theorem 486 487 Boltzmann, L. 89 Bolzano theorem 447 Boolean algebra 91 92 Borel measurable function 93 101 111 474n Borel set 93 110 448 458 464 465 469 Borel set, projection of 470 Borel system 458 Borel — Cantelli theorem 119 Borel, F.E.E. 499 500 Bound, least upper and greatest lower 55n Boundary condition 308 Boundary point 125 Boundary value problem 294 314 336 Boundary value problem for elliptic differential equations 337 Boundary value problem, first 295 Boundary value problem, second 295n Boundary value problem, third 295n Bounded 402 Bounded convergence 104 Bounded variation, function of 65 Bourbaki, N. v vi 67 78n 506 521 522 525 527 Branching case for integral equations 440n 442 Briggs 494 Brouwer fixed point theorem 303 432 433 CA-set 471 472 473 Cahen 501 Calculus, of alternating differentials 154 Calculus, of differential forms 125 Calculus, of residues 348 Calculus, of variations 349 422 Calculus, theorems of infinitesimal 136 Cantor intersection theorem 451n Cantor set 447 450 Cantor theory, of sets 513 Cantor, Georg 508 513 Caratheodory, C. 194 cardinal number 524 Carlson 487 Carmichael conjecture 503 Cartan, Elie 124 Cartan, Henri v Cartesian coordinates 430 Cartesian space 26 42 45 Cartesian space, n-dimensional 49 Casus irreducibilis 191 Category 447 Category, first 451 Category, second 451 Catenary 422 Cauchy condition 2 396 Cauchy criterion, generalization of 12 Cauchy filter 18 19 Cauchy integral representation 238 Cauchy integral theorem 207 217 220 223 224 236 237 Cauchy integral, and power series 222—223 Cauchy principal value 347n 407 Cauchy remainder formula 37 216 Cauchy sequence 396 424 425 Cauchy theorem, fundamental 2 10—11 16 18 19 Cauchy — Kovalevski theorem 336 Cauchy — Riemann differential equations 204 205 Cauchy, A.L. 89 Cayley, A. 509 Cebysev 89 497 Cebysev approximation theorem 497 Cebysev function 489 Cebysev inequality 102—103 Cebysev theorem 484 Chain conductor 353 Chain rule 29 203 205 Chain rule, generation of 44 Characteristic curve 303 333 Characteristic equation 287 380 Characteristic function 54n 107 Characteristic function, continuity of 105 Characteristic function, definition of 103 Characteristic initial value problem 335 Characteristic manifold 309 311—321 322 337 344 Chart 231 Chart, holomorphically related 232 Chordal distance 263 Chowla 494 Circle, quadrature of 491 Closed curve 130 Closed form 161 Closed hull 64n Closed plane 233 Closed plane, theory of functions on 229—238 Closure, of complex plane 194 Closure, torus-like 267 Codifferentiation 164 Coefficients, undetermined 280 Cohen independence theorem 475 Cohomology 520 Combinatorial topology 519 Compact support 68 Compactification 257 261 262 269 Compactification, axioms for 265 Compactification, concept of 253 Compactification, neighborhoods and 264 Compactness 233 comparison function 294 Comparison theorem 298 Compatibility conditions 522 Complement 91 Complementary set 198 Complete (content) 76 Complete differential 202 Complete set function 63 Completeness 11 19 Completeness, property of 2 Complex analysis vi Complex manifold 272 Complex number 188 Complex number, fundamental laws for 189 Complex number, Gauss representation of 192 Complex number, relation to elementary geometry 191—195 composition 514 Composition of subsets 17 Composition, outer 524 Cone 322 Configuration 508 Conformal mapping 210 325 Congruence 189 Congruence class 189 conjugate 190 Conjugate, harmonic 211 Connectedness 26 Conoid 322 Consistency 5 55 Consistency, amount of 97 Constructibility, questions of 474 Content 76 Content axiom 63 Content, n-dimensional elementary-geometric 57 Content, Peano — Jordan 62 Continuation, analytic 481 Continuation, holomorphic 217 Continuation, meromorphic 241 Continued fractions 499 Continuity 23—28 454 Continuity of addition 6 Continuity of characteristic function 105 Continuity of inverse 7 Continuity of measure 92 Continuity of multiplication 7 Continuity, concept of v Continuity, definition of 396 Continuity, points of 462 Continuity, uniform 410 Continuous function 26 Continuous function, power series as 34 Continuous mapping 24 455 Continuous spectrum 413 Continuum Hypothesis 448 475 476 Convergence v 3 10 12 427 Convergence in probability 115 Convergence, bounded 104 Convergence, concept of 1 479 Convergence, coordinate-wise 25 Convergence, maximal 438 Convergence, normwise 71n Convergence, radius of 216 Convergence, strong 396 Convergence, theorem of Peano 278 Convergence, uniform 20—21 27 Convergence, weak 105 Convergent sequence 1 424 Convergent sequence of functions 33 Convex 32 Convolution 108 404n Convolution theorem 404 Coordinates, introduction of 143 Coordinates, Laplace operator in 177 Coordinates, local 185 Coordinates, momentum 416 Coordinates, negative order of 131 Coordinates, polar 177 Coordinates, position 416 Coordinates, positive order of 131 Coordinates, transformation of 165—171 Cosine function 41 Countable base 264 Countable topology 264 Covering domain 200 CPCA-set 471 Cudakov theorem 484 485 Curl 135 Curvature 280 Curve 42 Curve, characteristic 303 333 Curve, closed 130 Curve, definition of 22 Curve, parabolic 325 Curve, piecewise smooth 130 131 Curve, simple 130 Curve, simply connected 131 Curvilinear integral 127 128 205 235 Cylinder waves 313 D'Alembert inertia 410 Damping factor 302 Darboux integral 62 Darboux integral, lower 60 Darboux integral, upper 60 Darboux theorem 277 Davenport 491
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