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Rektorys K. — Survey of Applicable Mathematics.Volume 2.
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Название: Survey of Applicable Mathematics.Volume 2.Автор: Rektorys K. Аннотация: This major two-volume handbook is an extensively revised, updated second edition of the highly praised Survey of Applicable Mathematics, first published in English in 1969.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2ndГод издания: 1994Количество страниц: 978Добавлена в каталог: 30.08.2014Операции: Положить на полку |
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Theorem(s) on Laplace and Fourier transforms II 575 ff Theorem(s) on maximum for harmonic functions II 177 Theorem(s) on maximum for heat equation II 200 Theorem(s) on minimum of functional of energy II 354 II Theorem(s) on removable singularity II 181 II Theorem(s), "edge of the wedge" (functions of several complex variables) II 286 Theorem(s), "Kugelsatz" (functions of several complex variables) II 286 Theorem(s), Abel I 647 II Theorem(s), Arzela — Ascoli I 639 II Theorem(s), Banach, on continuous extension, of functional II 349 Theorem(s), Banach, on continuous extension, of operator II 349 Theorem(s), Banach, on contraction mapping II 345 Theorem(s), Banach, on fixed point II 345 Theorem(s), Banach, on inverse operator II 349 Theorem(s), Bayes II 693 Theorem(s), Bernoulli II 731 Theorem(s), binomial I 19 I Theorem(s), Bolzano — Weierstrass I 340 Theorem(s), Budan — Fourier II 651 Theorem(s), Cauchy I 349 Theorem(s), Cauchy (complex variable) II 252 II II Theorem(s), Cauchy — Kovalewski II 151 Theorem(s), central limit II 733 Theorem(s), Chebyshev II 669 Theorem(s), comparison II 47 II Theorem(s), cosine I 79 I Theorem(s), Courant II 86 Theorem(s), De Moivre I 11 Theorem(s), Descartes II 650 Theorem(s), embedding II 343 II Theorem(s), Euler I 329 I Theorem(s), expansion II 90 Theorem(s), Floquet II 49 Theorem(s), Fredholm II 225 Theorem(s), Frobenius I 33 Theorem(s), fundamental of algebra I 21 Theorem(s), Gauss I 240 I I I Theorem(s), Gauss — Markov II 770 Theorem(s), Glivenko II 745 Theorem(s), Green I 240 I I Theorem(s), Hahn — Banach II 340 Theorem(s), Harnack (first and second) II 180 Theorem(s), Hilbert — Schmidt II 233 Theorem(s), Hurwitz II 114 Theorem(s), identity (functions of complex variable) II 275 II Theorem(s), immersion II 343 II Theorem(s), implicit functions I 423 I Theorem(s), integral, Cauchy II 252 II Theorem(s), Jackson II 672 Theorem(s), Khintchine II 732 Theorem(s), Kneser II 48 Theorem(s), Kolmogorov II 732 Theorem(s), Kovalewski II 151 Theorem(s), large numbers II 731 ff Theorem(s), Lax — Milgram II 200 Theorem(s), Levy — Lindeberg II 733 Theorem(s), Liapunov II 733 Theorem(s), Liouville II 181 II Theorem(s), Markov II 732 Theorem(s), mean value I 387 I Theorem(s), mean value (for harmonic functions) II 180 II Theorem(s), Moivre — Laplace II 733 Theorem(s), residue II 270 Theorem(s), Riemann (on conformal mapping) II 293 Theorem(s), Riemann — Lebesgue I 688 Theorem(s), Riemann — Schwarz reflection principle II 301 Theorem(s), Riezs — Fischer II 352 Theorem(s), Rolle I 387 Theorem(s), Schwarz — Christoffel II 302 Theorem(s), sine I 79 I Theorem(s), Spaethe II 48 Theorem(s), Stokes I 614 I Theorem(s), Sturm II 47 II Theorem(s), tangent I 79 Theorem(s), Taylor I 396 I Theorem(s), Valle — Poussin II 669 Theorem(s), Weierstrass, approximation by polynomials I 370 II II Theorem(s), Weierstrass, complex variable II 261 Tillot inequality II 649 Time, series II 797 Time, service and waiting II 806 Time, to failure (lifetime) II 786 Time, to failure (lifetime), mean II 786 Toeplitz matrix II 611 Topologic group I 713 Torsal lines I 321 Torus I 111 I II II Total differential I 409 Total discretization enor II 483 Total sum of squares II 770 II Total system of events II 689 Trace of function from Sobolev space II 341 Trace of matrix I 53 Tractrix I 147 Traffic intensity II 807 Trajectory, trajectories of stochastic process II 797 Trajectory, trajectories, orthogonal and isogonal to solutions of differential equations II 30 Transcendent curve I 203 Transcendental branch point II 274 Transcendental functions I 304 I Transcendental real numbers I 5 Transfer of boundary conditions II 520 Transfer, function of filter II 821 Transformation(s) of differential expressions into polar, cylindrical and spherical coordinates I 434 ff Transformation(s) of random variables II 727 ff Transformation(s), affine I 189 Transformation(s), congruent, of cartesian coordinates in plane I 180 Transformation(s), mapping I 40 I Transformation(s), matrix of coordinate systems I 243 Transformation(s), projective, in plane I 190 transforms see "Integral transforms" Transient oscillations I 102 Transition, intensity II 801 Transition, matrix II 804 Transition, probability II 799 II Translation, cartesian coordinate system I 198 Transversality conditions (in variational calculus) II 397 Transverse vibration of rod, differential equation II 142 Trapezoidal rule for definite integrals I 557 Trasportation problem II 828 Trial function II 82 Triangle(s), area of I 169 Triangle(s), centroid of I 200 Triangle(s), formulae for geometric elements of I 95 ff Triangle(s), general (scalene) I 78 Triangle(s), general (scalene), formulae for determining I 79 ff Triangle(s), general (scalene), fundamental and further relations I 79 ff Triangle(s), general (scalene), solution I 80 ff Triangle(s), geometrical formulae I 95 ff Triangle(s), inequality I 8 I I Triangle(s), inequality, in metric and normed space II 331 Triangle(s), spherical I 82 Triangular elements see "Finite elements" Triangular nets (finite difference method) II 550 Triangulation II 430 Trigonometric equations I 77 Trigonometric Fourier series I 678 ff Trigonometric functions, addition formulae I 74 Trigonometric functions, behaviour of I 71 Trigonometric functions, definitions of I 70 Trigonometric functions, difference of I 76 Trigonometric functions, expansion into series I 655 Trigonometric functions, half-angle formulae I 74 Trigonometric functions, higher powers of I 76 Trigonometric functions, inverse I 86 ff Trigonometric functions, multiple-angle formulae I 74 Trigonometric functions, of same angle, relations among I 71 ff Trigonometric functions, powers of I 76 Trigonometric functions, product of I 76 Trigonometric functions, relations between I 71 Trigonometric functions, signs in individual quadrants I 72 Trigonometric functions, sum of I 76 Trigonometric functions, values for some special angles I 73 Trigonometric interpolation II 683 Trigonometry, plane I 78 ff Trigonometry, spherical I 82 ff Trilinear hexagonal three-dimensional element II 442 Triple, integrals I 589 ff Triple, integrals, improper I 594 ff Triple, integrals, method of substitution for I 592 Triple, scalar product of three vectors I 230 Trochoid I 127 Truncation error II 483 Tube, domain II 280 Tube, volume and moment of inertia I 108 Twisted curve I 263 Two or more variables, functions of I 402 ff Two or more variables, functions of, extremes I 438 ff Two or more variables, functions of, introduction of new variables, transformations I 432 ff Two or more variables, functions of, survey of important formulae I 446 Two-sided estimates in eigenvalue problems II 87 Ultrahyperbolic equation II 173 Umbilic, umbilical point I 330 Undamped oscillations, forced, curves of I 157 Undamped oscillations, free, curves of I 156 Undamped vibrations, differential equations II 131 II Undetermined coefficients, Lagrange method I 442 Uniform convergence, sequences with variable terms I 637 II Uniform convergence, series with variable terms I 642 II Uniformly bounded sequences I 638 Uniformly convergent integral I 536 Union of sets I 45 Uniqueness theorem (functions of several complex variables) II 285 Unisolvency (finite element method) II 430 Unit tangent vector of curve I 232 I Unitary space II 333 Univalent (simple) function II 248 Unsubstantially singular point of curve or surface I 261 I Upper integral of Darboux sums I 512 Valle — Poussin theorem II 669 Vandermonde matrix II 611 Variables, functions of two or more I 402 ff Variables, separation of, for solving differential equations II 14 II Variance II 699 Variance of linear transformation of random variables II 728 Variance, sample II 736 Variation of functional II 379 Variation of functional in Du Bois-Reymond form II 380 Variation of functional in Lagrange form II 380 Variation of parameters (constants) II 18 II II II Variational calculus see "Calculus of variations" Variational condition II 411 Variational methods II 409 ff Variational methods in conformal mapping II 305 Vector(s) in algebra I 24 Vector(s) in three-dimensional space I 225 Vector(s) of acceleration, components of I 276 Vector(s) on surface I 252 Vector(s), absolute value I 227 Vector(s), algebra I 24 I Vector(s), analysis I 231 ff Vector(s), circulation along closed curve I 238 Vector(s), collinear (parallel) and coplanar I 227 Vector(s), column and row II 704 Vector(s), complex I 24 Vector(s), components (coordinates) of I 24 I Vector(s), conformably colinear (parallel) I 227 Vector(s), contravariant and covariant I 242 I I Vector(s), cross product I 229 Vector(s), curvilinear and surface integrals I 238 ff Vector(s), derivative I 231 Vector(s), direction angles, direction cosines I 228 Vector(s), dot product of I 228 Vector(s), equation of straight line I 205 Vector(s), field I 231 Vector(s), field, divergence and curl I 234 I Vector(s), field, irrotational I 235 Vector(s), field, potential I 235 Vector(s), field, solenoidal (sourceless) I 234 Vector(s), flux of I 240 Vector(s), function I 231 I Vector(s), inner product I 228 Vector(s), laws I 24 I Vector(s), length or magnitude I 168 I Vector(s), linearly dependent and independent I 24 Vector(s), magnitude, norm, modulus I 227 Vector(s), mixed product I 230 Vector(s), n-component (n-coordinate) I 24 Vector(s), non-coplanar in space I 243 Vector(s), notation for Stokes, Gauss and Green theorems I 230 I Vector(s), outer product I 220 Vector(s), principal normal (unit) I 232 Vector(s), product I 220 Vector(s), rank of system of I 25 Vector(s), real I 24 Vector(s), scalar product of I 228 Vector(s), space, abstract II 330 Vector(s), space, n-dimensional I 24 Vector(s), triple product I 230 Vector(s), zero (null) I 24 I Vibrating string equation II 106 II Vibrations (harmonic, damped, undamped) II 131 II II Virtual cone I 216 Virtual quadric I 218 Virtual sphere I 200 Void set I 45 Volterra integral equations II 240 Volumes, formulae I 104 ff Wallis product I 343 I Wave equation II 101 Weak (Gateaux) differential II 367 II Weak convergence II 350 Weak solution, of boundary value problems II 200 II II Weak solution, of evolution problems II 219 II Weak solution, of parabolic problems II 464 Weak stability II 502 Weber function I 700 Weierstrass M-test I 642 II Weierstrass theorem I 370 II II II Weight I 555 Weight, function I 672 Weingarten fundamental equations for surfaces I 333 Well-posed difference scheme II 564 Well-posed problems II 155 II II II White noise II 798 II II Wilkinson method II 644 Wronskian determinant II 51 Yule — Walker equations II 813 Z-transformation II 739 Zero of polynomial I 21 Zero, divisors I 48 Zero, function in space I 664 II Zero, vector I 25 I Zeta function I 643
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