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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
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
1 2 3 4 5 6
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