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Duistermaat J.J., Kolk J.A.C. — Multidimensional Real Analysis II: Integration
Duistermaat J.J., Kolk J.A.C. — Multidimensional Real Analysis II: Integration

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Название: Multidimensional Real Analysis II: Integration

Авторы: Duistermaat J.J., Kolk J.A.C.

Аннотация:

Part two of comprehensive text on multidimensional real analysis. Numerous exercises with partial solutions.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 375

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$C^1$ mapping      51
$\wp$ function, Weierstrass'      185
(Geometric) tangent vector      322
Abel — Ruftini Theorem      102
Abel's integral equation      670
Abel's partial summation formula      189
Abelian group      169
Acceleration      159
action      238
Action, group      162
Action, induced      163
Addition      2
Addition, formula for lemniscatic sine      288
Adjoint linear operator      39 398
Adjoint mapping      168 380
Affine function      216
Affine transformation, bijective      479
Airy function      256
Airy's differential equation      256
Algebraic topology      307 483
Ampere — Maxwell law      748
Amplitude      469
Amplitude function      656
Analog formula      395
Analogs of Delambre — Gauss      396
angle      148 219 301 498
Angle of spherical triangle      334
Angle-preserving      336
Angular momentum operator      230 272
Anti-adjoint operator      41
Anticommutative      169 577
Antiderivation      580
Antiderivative      539 547
Antisymmetric matrix      41
Antisymmetric multilinear mapping      568
Approximation, best affine      44
Arc length      498
Arc-length function      501
Archimedes' law      718
Archimedes' theorem      604
Area, Euclidean      502
Argument function      88
Arzela's Dominated Convergence Theorem      472
Associated Legendre function      177
Associativity      2
Astroid      324 729
Asymptotic expansion      197
Asymptotic expansion, Stirling's      197
Automorphism      28
Autonomous vector Held      163
Axis of rotation      219 301
Ball, closed      8
Ball, open      6
Basic linear mapping      477
Basis, orthonormal      3
Basis, standard      3
Bernoulli function      190
Bernoulli number      186 607
Bernoulli polynomial      187
Bernoulli's summation formula      188 194
Bessel function      634
Bessel's equation      634
Best affine approximation      44
beta function      620
Beta function, generalized      688
Bifurcation set      289
Bijective affine transformation      479
Binet — Cauchy's, formula      677
Binomial coefficient, generalized      181
Binomial series      181
Binormal      159
Biot — Savart law      751
Biregular      160
Bitangent      327
Black body radiation      623
Boost      390 756 758
Boundary      9
Boundary condition, at infinity      721 750
Boundary condition, Dirichlet      535
Boundary condition, Neumann      726
Boundary in subset      11
Boundary, $C^k$, of open set      515
Boundary, lying at one side of      515
Bounded convergence      471
Bounded sequence      21
Brouwer's fixed-point theorem      583 764
Brouwer's theorem      20
Bundle, tangent      322
Bundle, unit tangent      323
Cagnoli's formula      395
Canonical      58
Canonical transformation      772
Cantor's theorem      211
Cardioid      286 299 501
Cartan decomposition      247 385
Cartan decomposition, (infinitesimal)      539
Casimir operator      231 265 370
Catalan's constant      613
Catenary      295
Catenoid      295
Cauchy distribution      660
Cauchy sequence      22
Cauchy — Riemann equation      556 738
Cauchy — Schwarz inequality      4 642
Cauchy — Schwarz inequality, generalized      245
Cauchy's integral formula      734 737
Cauchy's integral formula, generalized      739
Cauchy's integral theorem      557
Cauchy's Minimum Theorem      206
Caustic      351 761
Cayley — Klein parameter      376 380 391
Cayley's surface      309
Centrifugal      604
Centripetal      604
Chain rule      51
Change of coordinates, (regular) $C^k$      88
Change of Variables Theorem      444
Characteristic function      34 428
Characteristic polynomial      39 239 527
Characteristic, Euler      776
Charge (density)      747
Charge density      491 696
Chart      111
Christoffel symbol      408
Circle, osculating      361
Circles, Villarceau's      327
Circulation      538 553
Cissoid, Diodes'      325
Clausen function      614
Clifford algebra      383
Clifford multiplication      379
Closed ball      8
Closed ball in subset      10
Closed differential form      544 574
Closed mapping      20
Closed set      8
Closure      8
Closure in subset      11
Cluster point      8
Cluster point in subset      10
Codimension of submanifold      112
Coefficient of matrix      38
Coefficient, Fourier      190
Cofactor matrix      233
Cohomology, de Rham      590
Commutativity      2
Commutator      169 217 231 407
Commutator relation      231 367
Compactness      25 30
Compactness, sequential      25
Complement      8
Complementary matrix      41
Completeness      22 204
Complex analysis      737
Complex line integral      555
Complex structure      555
Complex-analytic      735
Complex-differentiable      105 556 738
Component function      2
Component of vector      2
Composition of mappings      17
Computer graphics      385
Conchoid, Nicomedes'      325
Cone      447
Cone, unrolling of      684
Confluent hypergeometric differential equation      641
Confluent hypergeometric function      639
conformal      336
Conjugate axis      330
Connected component      35
Connectedness      33
Connection      408
Conservation of charge, law of      748
Conservation of energy      290
Conservation of energy, law of      749
Conservative      566
Constant, Catalan's      613
Continuity      13
Continuity equation      747
Continuity theorem      77
Continuity. Holder      213
Continuous mapping      13
Continuously differentiable      51
Contractible      589
Contraction      23
Contraction factor      23
Contraction Lemma      23
Contraction with vector      570
Contraction with vector field      585
Contraction, FitzGerald — Lorentz      758
Convergence      6
Convergence, uniform      82
Convex      57
Convolution      468 663
Convolution equation      672
Coordinate function      19
Coordinate of vector      2
Coordinate, generalized      770
Coordinates, change of, (regular) C      88
Coordinates, confocal      267
Coordinates, cylindrical      260
Coordinates, polar      88
Coordinates, simplex      691
Coordinates, spherical      261
Coordinatization      111
Cosine rule      331
Cotangent bundle      399
Cotangent space      399
Coulomb gauge condition      750
Coulomb's law      750
Covariance matrix      617 655
Covariant      754
Covariant derivative      407
Covariant differentiation      407
Covering group      383 386 389
Covering, open      30
Cramer's rule      41
Critical point      60
Critical point of diffeomorphism      92
Critical point of function      128
Critical point, nondegenerate      75
Critical value      60
Cross product      147
Cross product operator      363
Curl, of vector field      540 541
Curl-free      546
Current (density)      747
Curvature form      363 410
Curvature of curve      159
Curvature, Gaussian      157
Curvature, mean      775
Curvature, normal      162
Curvature, principal      157
Curve      110
Curve, differentiable (space)      134
Curve, space-filling      211
Cusp, ordinary      144
Cycloid      141 293 499
Cylindrical coordinates      260
d'Alembert's formula      277
d'Alembertian      755 756
Darboux's equation      707 708
De l'Hopital's rule      311
De Rham cohomology      590
Decomposition, (infinitesimal) Cartan      539
Decomposition, Cartan      247 385
Decomposition, Helmholtz — Weyl      751
Decomposition, Hodge      753
Decomposition, Iwasawa      356
Decomposition, polar      247
Decomposition, Stokes      539
Degree of mapping      591 594
DEL      59 528
Delambre-Gauss, analogs of      396
DeMorgan's laws      9
Dense in subset      203
Density, continuous d-dimensional      489
Density, Euclidean      495
Density, Gel'fand — Leray      700
Density, positive      491
Derivation      404 585
Derivation at point      402
Derivation, inner      169
Derivative      43
Derivative, directional      47
Derivative, exterior      544 574
Derivative, partial      47
Derived mapping      43
Descartes' folium      142 554
Diagonal      722
Diameter      355
Diffeomorphism, $C^k$      88
Diffeomorphism, orthogonal      271
Diffeomorphism, volume-preserving C      445
Differentiability      43
Differentiable mapping      43
Differentiable, continuously      51
Differentiable, partially      47
Differential      400
Differential at point      399
Differential equation, Airy's      256
Differential equation, Bessel's      634
Differential equation, confluent hypergeometric      641
Differential equation, Darboux's      707 708
Differential equation, for rotation      165
Differential equation, Hamilton's      717 771
Differential equation, Helmholtz'      636
Differential equation, hypergeometric      638
Differential equation, Legendre's      177
Differential equation, Newton's      290
Differential equation, ordinary      55 163 177 269
Differential equation, partial      470 534
Differential equation, Poisson's      721
Differential equation, Whittaker's      641
Differential form      400 544 571
Differential form, closed      544 574
Differential form, exact      544 574
Differential operator, linear partial      241
Differential operator, partial      164
Differentiation theorem      78 84 473
1 2 3 4 5
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