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Behnke H., Bachmann F., Fladt K. — Fundamentals of mathematics. Volume III. Analysis
Behnke H., Bachmann F., Fladt K. — Fundamentals of mathematics. Volume III. Analysis



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Название: Fundamentals of mathematics. Volume III. Analysis

Авторы: 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: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 557

Добавлена в каталог: 01.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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, $F_{\sigma \delta}$      470
Set, $F_{\sigma}$      456
Set, $G_{\sigma}$      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
1 2 3 4 5 6
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