Авторизация
Поиск по указателям
Zorich V. — Mathematical Analysis
Обсудите книгу на научном форуме Нашли опечатку?
Название: Mathematical AnalysisАвтор: Zorich V. Аннотация: This softcover edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, integral transforms, and distributions. Especially notable in this course is the clearly expressed orientation toward the natural sciences and its informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems and fresh applications to areas seldom touched on in real analysis books.
The second volume expounds classical analysis as it is today, as a part of unified mathematics, and its interactions with modern mathematical courses such as algebra, differential geometry, differential equations, complex and functional analysis. The book provides a firm foundation for advanced work in any of these directions.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2004Количество страниц: 681Добавлена в каталог: 19.02.2014Операции: Положить на полку |
Скопировать ссылку для форума | Скопировать ID
Предметный указатель
Space, Hilbert 47 Space, locally compact 18 Space, locally connected 20 Space, metric 1 Space, metric, separable 15 Space, normed affine 62 Space, normed vector 42 Space, normed vector, complete 43 Space, path connected 20 34 Space, pre-Hilbert 47 Space, Schwartz 591 592 Space, Sobolev — Schwartz 464 Space, tangent 61 Space, tangent to 337 Space, tangent to a manifold 337 338 Space, topological 9 10 Space, topological, 14 Space, topological, 14 Space, topological, in the strong sense 14 Spectral characteristic 562 Spectrum, bounded 585 Spectrum, discrete 560 Spectrum, frequency 593 Sphere, Alexander horned 162 Spherical functions 524 Stabilizer of a point 335 Stationary phase method 633 635 Stationary phase method, multidimensional 640 Stationary phase method, one-dimensional 638 Stationary phase principle 634 Steklov's inequality 556 Steklov, V. 520 556 Stirling's formula 448 622 Stirling's series 636 Stirling, J. 448 622 636 Stokes' formula 237 345—347 358 Stokes' formula in 245—247 Stokes' formula, general 248—251 345 Stokes, G. 237 249 345—347 358 Stone, M. 400 Structure, smooth 326 Sturm — Liouville problem 523 Sturm, Ch. 523 Submanifold 335 Subset, everywhere dense in 400 Subspace of a metric space 7 Subspace of a topological space 13 Sum, Darboux, lower 114 Sum, Darboux, upper 114 Sum, Riemann 108 Summation method, Abel 384—385 394 Summation method, Cesaro 394 Support of a differential form 344 Support of a function 136 451 Surface integral of first kind 231 Surface integral of second kind 232 Surface of dimension k 178 Surface of measure (area) zero 190 Surface with boundary 178 Surface without boundary 178 Surface, elementary 162 Surface, k-dimenaional 161 Surface, k-dimenaional, smooth 173 Surface, nonorientable 174 Surface, one-sided 176 Surface, orientable 175 Surface, oriented 175 Surface, piecewise smooth 183 Surface, piecewise smooth, orientable 184 Surface, two-sided 176 Surface, zero-dimensional 183 Symmetric operator 519 System function 449 460 System of sets, locally finite 336 System of sets, refinement of another system 336 System of vectors, complete 511—516 System of vectors, condition for completeness 512 System of vectors, linearly independent 500 System of vectors, orthogonal 499—506 System of vectors, orthonormal 500 System of vectors, orthonormalized 500 System, exponential 502 System, Haar 525 System, Rademacher 525 System, trigonometric 501 System, trigonometric, completeness 545 System, trigonometric, in complex notation 502 Tangent mapping 339 349 Tangent paths 347 Tangent space, to 337 Tangent space, to a manifold 337 338 Tangent vector to a manifold 338 339 349 Tauber, A. 395 Taylor, B. 94 415 517 Tempered distribution 591 Tensor product 313 Test function 463 Test, Abel — Dirichlet 376 Test, Weierstrass' 374—376 Test, Weierstrass', for integrals 425 Theorem on asymptotics of a Laplace integral 621 Theorem on existence of solutions of differential equations 36—37 Theorem on interchange of limiting passages 382 Theorem on the principal term of asymptotics of an integral 621 Theorem on uniform continuity 32 Theorem, Abel's 379 Theorem, Arzela — Ascoli 397—399 Theorem, Brouwer, fixed-point 242 Theorem, Brouwer, invariance of domain 321 Theorem, Carnot's 225 Theorem, Cauchy's multidimensional mean-value 287 Theorem, curl 283 Theorem, Darboux' 115 Theorem, de Rham's 359 Theorem, Dini's 386 430 Theorem, divergence 283 Theorem, Earnshaw's 286 Theorem, Fejer's 538 557 Theorem, finite-increment 73—79 Theorem, Fubini's 127—129 580 Theorem, Gauss' 285 496 Theorem, gradient 283 Theorem, Green's 237—242 Theorem, Hardy's 395 Theorem, Helmholtz' 302 Theorem, implicit function 96—106 Theorem, Inverse Function 105 Theorem, Kotel'nikov's 585 Theorem, Lagrange's 309 Theorem, Lebesgue's, dominated convergence 395 Theorem, Lebesgue's, monotone convergence 396 Theorem, mean-value, for harmonic functions 287 Theorem, mean-value, for the integral 125 Theorem, Plancherel's 590 Theorem, Poincare's 353 356 Theorem, Pythagorean 505 Theorem, Pythagorean, for measures of arbitrary dimension 193 Theorem, sampling 585 Theorem, Sard's 236 Theorem, Stone's 400—403 Theorem, Stone's, for complex algebras 405 Theorem, Tauberian 395 Theorem, Translation 587 Theorem, Weierstrass', on approximation by polynomials 400 472 494 Theorem, Weierstrass', on approximation by trigonometric polynomials 484 540 Theorem, Whitney's 169 334 Theorem, Whittaker — Shannon 585 Thomson, W. (Lord Kelvin) 224 237 250 Timbre 518 Tone, fundamental 518 Topological group 72 336 Topological space 9 10 Topological space in the strong sense 14 Topological space, base of 10 Topological space, weight of 11 Topological spaces, product of 13 Topology on a set 9 Topology, base of 10 Topology, induced on a subspace 13 Topology, stronger 14 Torsion of a curve 73 Torus 167 Total boundedness 397 Transform, Fourier, asymptotic properties 573—576 Transform, Fourier, cosine 564 Transform, Fourier, frequency shift 587 Transform, Fourier, in 589 Transform, Fourier, multidimensional 577 Transform, Fourier, of a convolution 569 Transform, Fourier, of generalized functions 592 Transform, Fourier, rate of decrease and smoothness 573 Transform, Fourier, sine 564 Transform, Fourier, time shift 587 Transform, integral 568 Transform, Laplace 612 Transformation, Abel's 376 Transformation, bilinear 49 Transformation, bounded 53 Transformation, continuous, multilinear 56 Transformation, Galilean 595 Transformation, linear 49 Transformation, Lorentz 595 Transformation, multilinear 49 52 56 Transformation, trilinear 49 Transient pulse function 449 Translation operator 449 Translation theorem 587 Translation-invariant operator 449 Triangle inequality 1 Triangular pulse 588 Trigonometric polynomial 526 Trigonometric series 526—560 Trigonometric system 501 Trigonometric system, completeness 545 Trigonometric system, in complex notation 502 Trihedral, companion 73 Triorthorgonal coordinates 268 Uncertainty principle 590 Uniform boundedness 371 397 Uniform boundedness of a family of functions 376 Uniform convergence 397 Uniform convergence, Cauchy criterion 369—370 Uniformly convergent series, Cauchy criterion 378 Unit step 466 Value (Cauchy principal) of an improper integral 155 Vector field on a manifold 348 Vector field on a manifold, smooth 348 Vector field, central 213 Vector potential 295 296 Vector potential of a magnetic field 296 Vector space, tangent to a manifold 337 338 Vector, Angular velocity 70 Vector, tangent to a manifold 338 339 349 Vectors, orthogonal 499 519 Volume element 227 Volume of a ball in 192 444 Volume of a set (Jordan) 119 245 Volume of an interval 107 Wallis' formula 434 448 636 Wallis, J. 434 448 636 Watson's lemma 631 635 Watson, J. 631 635 Wave equation 307—310 581 Wave equation, homogeneous 309 Wave equation, inhomogeneous 309 Weak convergence 463 Weierstrass M-test 374 Weierstrass, K. 374 393 400 425 431 472 484 494 540 Weight of a topological space 11 Whitney, H. 149 169 334 Whittaker, J. 585 Wirtinger's inequality 556 Wirtinger, W. 556 Work of a field 211 Zeta function 447
Реклама
![$C([a, b])$](/math_tex/832be4b4c8ecf2229fb05503c9ec089382.gif)
|
|
О проекте