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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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Primes, Euclid theorem 480 Primes, Selberg theorem 486 Principal axes 322 Principal part 229 Principe du recollement des morceaux 81 probability 499 probability density 95 probability distribution 92 Probability measure 92 Probability space 93 Probability, concept of 89—93 Probability, conditional 108 110 111 Probability, convergence in 115 Probability, discrete 96 Probability, events and 90 Probability, limit theorems in 119 Probability, objective 89 Probability, subjective 89 Probability, theory of vi 90 Product rule 29 Projection mapping 239 243 Projection mapping, stereographic 194 230 262 Projective plane 259 Projective plane, properties of 259—262 Projective sets 471 Property, descriptive 447 Property, metric 447 Property, strong maximum (minimum) 318 Property, topological 447 Quadratic form 321 326 Quadrature 284 Quadrature of circle 491 Quadrature, elementary problem of 277 quantum mechanics 416 Quarternion 511 Quasilinear 302 321 326 Quaternion function, right-regular 274 Radius, of convergence 216 Rado theorem 275 Rado — Behnke — Stein — Cartan theorem 257 Radon measure 74 82 83 84 Radon measure, derivative of 86 Random variable 93 Random variable, distribution of 94 Random variable, independent 117 121 Random variable, multidimensional 95 Random variable, Poisson-distributed 108 Random variable, probability distribution of 112 Random variable, uniqueness theorem for 104 Range (of a function) 200 Range of influence 309 311 322 Real-analytic functions 215 Reciprocal 190 Reciprocal, left, of matrix 406 Reciprocal, right, of matrix 406 Recursion, process of 353 Recursive law 351 Recursive sequence 351—353 Reflection 194 Regular solution 282 Relation, transitive 12 Relaxation 302 Remak 328 Removable-singularity theorem 274 Residue 224 Residue class ring 512 Residue, calculus of 348 Resolvent kernel 440 Restriction, of a function 448 Revolution number 429 432 Riccati differential equation 290 Riemann conjecture 486 487 Riemann extension, of functional 68 Riemann filter basis 61 Riemann integrable 56 58 59 60 64 Riemann integrable, improperly 59n Riemann integral v 13 53 61 62 133 527 Riemann integral, content associated with 62—64 Riemann integral, definite 59 64 Riemann integral, indefinite 59n Riemann integral, rules for 84 Riemann integral, sum-definition of 60—61 Riemann lemma 226 247 Riemann mapping theorem 317 Riemann sphere 230 263 271 Riemann sphere, Cartesian product of 273 Riemann sum, limiting value of 61 Riemann surface 200 238—241 263 271 513 Riemann surface and points at infinity 257 Riemann surface in the large 246 Riemann surface in the small 246 Riemann surface of algebraic functions 248 Riemann surface of compact meromorphic function 247 Riemann surface of hyperbolic type 250 Riemann surface of parabolic type 250 Riemann surface, abstract 245 Riemann surface, compact 246 Riemann surface, concrete 245 Riemann surface, defined by function element 242 Riemann surface, meromorphic separability of 248 Riemann surface, oriented 246 Riemann surface, simply connected 246 249 Riemann surface, theory of functions on 243 Riemann surface, type of 250 Riemann surface, univalent (schlicht) 239 Riemann zeta-function 481 485 Riemann — Mellin inversion formula 405 Riemann — Stieltjes integral 101 Riemann, G.F.B. 501 507 Riemannian geometry 170 Riemannian manifolds 125 126 Riemannian manifolds, differential forms on 184—186 Riemannian manifolds, theory of 124 Riemannian metric 185 Riesz space 56 Riesz, F. 65 Right reciprocal, of matrix 406 Ring 511 Ring, graded 159 Ring, topological 4 Rotation 135 Rotation group, two-parameter 269 Rotation, surface of 422 Rotation-dilation, of Euclidean plane 189 Roth theorem 492 scalar functions 26 Scalar product 178 192 Schauder 339 Schauder fixed point theorem 432 435 437 Schlicht 239 Schmidt, E. 442 515 Schroedinger differential equation 417 Schur, I. 300 301 Schwartz distribution 53 74 78 84 516 Schwartz distribution, independent 82 Schwartz, L. 53 78 79 82 86 87 Schwarz inequality 342 395 408 Schwarz reflection principle 314 Schwarz theorem 427 Schwarz, H.A. 426 Schwarz, H.A., alternation method of 426 Sebastiao e Silva, J. 82 87 Second category 447 Selberg 489 Selberg theorem 486 Semicontinuity (upper and lower) 464 Semigroup 321 346 347 Seminorm 69 Seminorm in the wider sense 69n Seminorm, defined by abstract measures 68 Sense-preserving (and sense-reversing) conformal mapping 211 Separability 472 Separated functions 297 Separated variables 285 Separation axiom 472 Separation of variables 346 SEQUENCE 2—7 Sequence of points, limit of 197 Sequence, convergence of 196 Sequence, Fibonacci 352 353 Sequence, majorizing 8 Sequence, minorizing 8 Sequence, monotone decreasing 7 Sequence, monotone increasing 7 Sequence, Moore — Smith 12—13 Set function 63 94 Set, 470 Set, 456 Set, 456 Set, analytic 448 458n 465 466 468 469 Set, Borel 458 Set, closed 198 261 450 Set, compact 198 Set, complementary 198 Set, coverable 199 Set, dense 451 Set, dense-in-themselves 449 450 Set, everywhere-dense 451 Set, field of 63 76 Set, hull of 450 Set, larger 446 Set, lim-closed 459 Set, module of 452 Set, nowhere-dense 451 Set, open 261 450 456 Set, ordered 521 Set, perfect 450 451 Set, plane triadic 477 Set, projective 448 Set, richer 446 Set, sequentially compact 432 Set, ternary Cantor 447 450 Set, theory of 508 Set, uncountable analytic 451 Set, well-ordered 470 Set, zero 100n Sheaf theory 520 Sidlovskii 493 Sieve of Eratosthenes 483 Sigma-additivity 76 77 Sigma-algebra 92 Sigma-field 76 77 92n Sigma-finite measure 77 Sigma-module 452 Sigma-operations 466 468 Simple path 219 Simply connected curve 131 Sine function 41 Singular solution 282 Singularity function 315 319 Sir Newton, Isaac 507 Skew field 511 Skew-symmetric tensor 148 Skewes number 488 Smooth segment 131 Solution operator 316 346 Solutions, a priori estimates for 329 Solutions, fundamental 315 316 318 356 Solutions, fundamental system of 288 Solutions, general 380 381 Solutions, linearly independent fundamental 514 Solutions, periodic 302 Solutions, singular 282 Solutions, special 380 Solutions, stable 298 Solutions, trivial 295 Space 507 Space, adjoint 397 Space, complex-projective 273 Space, locally compact 521—522 Space, metric 11—12 423 513 Space, semicompact 265 Space, sequentially compact 265 Space, topological 1 3 230 513 Space, uniform 16—21 Spectral lines 417 Spectrum 415 Spectrum of operator 413 Spherical waves 313 square-integrable 399 Stability 298 Stability, Ljapunov criterion for 301 Stable solution 298 standing waves 417 Star operator 159 Star-shaped domain 161 Starlike 334 State 313 Steinitz 510 Stem function 284 Step function 54—56 99 Step function, integration of 56 Step integral 57 Stereographic projection 194 230 262 Stieltjes integral 64—66 105 Stieltjes integral, generalization of 65 Stieltjes integral, integration function of 65 Stieltjes sum 65 Stirling formula 368—371 501 Stochastic process 89 Stokes' theorem 153 171—175 176 181 Stokes' theorem, special 135 Stoltz, O. 203 Stone isomorphism theorem 92 Stone, M.H. 68n 92 String, infinitely long 308 String, infinitely long, vibrations of 307 309 Strong maximum (minimum) property 318 Structure 507 Structure, algebraic 521 Structure, complex-analytic 245 Structure, hierarchy of 521 Structure, monomorphic 508 Structure, theory of vi Structure, topological 521 Structure, uniform v 2 17 18 71n 513 Subsets, composition of 17 Sum, of two functions 54n Summation method, for difference equations 355 Support, of function 68 Supremum (least upper bound) 55n Surface integral 131 137 179 Surface of rotation 422 Surface, nonorientable 262 Surface, piecewise smooth 130 Surface-element 210 245n Surface-element, vector 135 Surface-segment, oriented 134 137 Suslin 465 470 475 Synchronization 302 Tangent vector 22 43 128 Tangent vector, outwardly directed 132 Taylor formula 36 Taylor formula, remainder term in 22 Taylor series 22 37 38 215 Tensor product 525 Tensor, contravariant 148 Tensor, covariant 148 Tensor, skew-symmetric 148 149 Termwise differentiation 35
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