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| Duistermaat J.J., Kolk J.A.C. — Multidimensional Real Analysis II: Integration |
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| Предметный указатель |
Second-order partial derivative 61
Section 400 404
Section, normal 162
Segment of great circle 333
Self-adjoint operator 41
Self-adjointness of Laplacian 718
Semicubic parabola 144 309 678
Semigroup property 661
Semimajor axis 330
Semiminor axis 330
Separation Theorem, Jordan — Brouwer 596
Sequence, bounded 21
Sequential compactness 25
Series, binomial 181
Series, Dirichlet's 664
Series, Eisenstein's 658
Series, Euler's 615
Series, hypergeometric 637
Series, MacLaurin's 70
Series, Taylor's 70
Set, closed 8
Set, open 7
Shifted factorial 180
Shuffle 578
Side of spherical triangle 334
Signature, of function at point 73
Signature, of operator 73
Simple zero 101
Simplex coordinates 691
Simplex standard (n - 1)- 690 691
Simply connected 550
Sine rule 331
Singular point of diffeomorphism 92
Singular point of function 128
Singularity of mapping  92
Slerp 385
Sobolev's inequality 645
Solenoidal 566
Solid of revolution, volume of 604
Solid, Viviani's 681
Sonine's formula 670
Source-free 546
Space, linear 2
Space, metric 5
Space, vector 2
Space-filling curve 211 214
Special linear group 303
Special orthogonal group 302
Special orthogonal group in  219
Special relativity, theory of 756
Special unitary group 377
Spectral theorem 72 245 355
Sphere 10
Spherical coordinates 261
Spherical diangle 681
Spherical function 271
Spherical harmonic function 272
Spherical mean 689 706 708
Spherical rule of cosines 334
Spherical rule of sines 334
Spherical triangle 333 681
Spinor 389
Spinor group 383
Spinor representation 383 389
Spiral 107 138 296
Spiral, logarithmic 350
SPLINE 675
Stability, of atom 728
Standard basis 3
Standard deviation 617 645
Standard embedding 114
Standard inner product 2
Standard projection 121
Star-shaped 548
Stationary phase, principle of 656
Stationary point 60
Steiner's hypocycloid 343 346 731
Steiner's Roman surface 307
Step function 435
Stereographic projection 306 336
Stirling's asymptotic expansion 197
Stirling's formula 624
Stochastics 617
Stokes decomposition 539
Stokes' Integral Theorem 560
Stokes' theorem 575
Stratification 304
Stratum 304
Structure, complex 555
Subcovering 30
Subcovering, finite 30
Subimmersion 315
Submanifold 109
Submanifold at point 109
Submanifold, affine algebraic 128
Submanifold, algebraic 128
Submersion 112
Submersion at point 112
Submersion Theorem 121
Sum of mappings 17
Summation convention, Einstein 583
Summation formula of Bernoulli 188 194
Summation formula of Euler — MacLaurin 194
Summation formula of Poisson 650 651
Superposition 469
Support 427
Supremum 21
surface 110
Surface integral 560
Surface of revolution 294
Surface of revolution, area of 603
Surface, Cayley's 309
Surface, Steiner's Roman 307
Sylvester's law of inertia 73
Sylvester's theorem 376
Symbol, total 241
Symmetric matrix 41
Symmetry identity 201
Symplectic form 771
Symplectic group 772
Tangent bundle 322 403
Tangent cluster 684
Tangent mapping 137
Tangent space 134
Tangent space, "intrinsic" description 397
Tangent space, algebraic description 400
Tangent space, geometric 135
Tangent sweep 684
Tangent vector 134
Tangent vector field 163
Tangent vector, geometric 322
Tautological form 770
Taylor polynomial 68
Taylor's formula 68 250
| Taylor's series 70
Test, Dirichlet's 189
tetrahedron 274 692
Theorem, Abel — Ruffini's 102
Theorem, Archimedes' 604
Theorem, Arzela's Dominated Convergence 472
Theorem, Brouwer's 20
Theorem, Brouwer's Fixed-point 583
Theorem, Cantor's 211
Theorem, Cauchy's Integral 557
Theorem, Cauchy's Minimum 206
Theorem, change of variables 444
Theorem, Continuity 77
Theorem, differentiation 78 84 473
Theorem, Dini's 31
Theorem, Divergence, Gauss' 529
Theorem, Euler's 219
Theorem, Fourier's Inversion 468
Theorem, Fubini's 476
Theorem, Fundamental, of Algebra 291 593 735
Theorem, Gauss — Bonnet's 776
Theorem, Global Inverse Function 93
Theorem, Green's Integral 554
Theorem, Hamilton — Cayley's 240
Theorem, Hamilton's 375
Theorem, Heine — Borel's 30
Theorem, Immersion 114
Theorem, implicit function 100
Theorem, Implicit Function, over C 106
Theorem, Integral, Cauchy's 557
Theorem, Integral, Green's 554
Theorem, Isomorphism, for groups 380
Theorem, Jordan — Brouwer's Separation 596
Theorem, Lagrange's 377
Theorem, Liouville's 708 726 772
Theorem, Local Inverse Function 92
Theorem, Local Inverse Function, over C 105
Theorem, mean value 57
Theorem, Mean Value, for harmonic functions 707 723
Theorem, Multinomial 241
Theorem, Newton's Binomial 240
Theorem, Pythagoras' 678
Theorem, rank 314
Theorem, residue 737
Theorem, Rodrigues' 382
Theorem, Rolle's 228
Theorem, Sard's 610
Theorem, Schwarz' 725 746
Theorem, Spectral 72 245 355
Theorem, Stokes' 575
Theorem, Stokes' Integral 560
Theorem, Submersion 121
Theorem, Sylvester's 376
Theorem, Tietze's Extension 608
Theorem, Weierstrass' Approximation 216 667
Theorema egregium 409
Theory of special relativity 756
Thermodynamics 290
Tietze's extension theorem 608
Tope, standard (n + 1)- 274
topology 10
Topology, algebraic 307 483 550 563
Topology, relative 10
Toroid 349
Torsion 159
Torus, n-dimensional 696
Total derivative 43
Total symbol 241
Totally bounded 209
Trace 39 527
Tractrix 357 685
Transformation, canonical 772
Transformation, orthogonal 218
Transition mapping 118
Transport equation 451
Transpose matrix 39
Transversal 172
Transverse axis 330
Transverse intersection 396
Triangle inequality 4
Triangle inequality, reverse 4
Trisection 326
Tubular neighborhood 319
Tubular neighborhood, integration over 698
Umbrella, Whitney's 309
Uncertainty 645
Uncertainty relations, Heisenberg's 645
Uniform continuity 28
Uniform convergence 82
Uniformly continuous mapping 28
Unit hyperboloid 390
Unit sphere 124
Unit tangent bundle 323
Unitary operator 663
UNKNOWN 97
Unrolling of cone 684
Upper Riemann integral 426
Upper sum 425
Urysohn's lemma 608
Value, critical 60
Variance 617
Vector analysis 527
Vector field 268 404 527
Vector field, gradient 59 527
Vector field, harmonic 546
Vector field, Newton 529
Vector field, Poynting 748
Vector potential 547
Vector space 2
Vector-valued function 12
Villarceau's circles 327
Viviani's solid 681
Volume, d-dimensional 492
Volume, of Jordan measurable set 429
Volume, of rectangle 423
Volume-preserving  diffeomorphism 445
Wallis' product 184 627
Wave equation 276 749
Wave equation, inhomogeneous 761
Wave function 644
Wave operator 755 756
Weierstrass'  function 185
Weierstrass' approximation theorem 216 667
Weingarten mapping 157
Whitney's umbrella 309
Whittaker's equation 641
Winding number 595 736
wronskian 233
Young's inequality 353
Zeeman effect 272
Zero, simple 101
Zero-set 108
Zeta function, Riemann's 191 197 612 622
Zonal spherical function 271
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