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Polyanin A., Manzhirov A.V. — Handbook of Mathematics for Engineers and Scientists
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Название: Handbook of Mathematics for Engineers and ScientistsАвторы: Polyanin A., Manzhirov A.V. Аннотация: The Handbook of Mathematics for Engineers and Scientists covers the main fields of mathematics and focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. To accommodate different mathematical backgrounds, the preeminent authors outline the material in a simplified, schematic manner, avoiding special terminology wherever possible.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2006Количество страниц: 600Добавлена в каталог: 30.06.2008Операции: Положить на полку |
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Transposition 178 Transversality condition 577 1001 Transverse vibration of elastic rods 1294 trapezoid 54 Trapezoid, altitude 54 Trapezoid, base 54 Trapezoid, isosceles 54 Trapezoid, leg 54 Trapezoid, median 54 Trapezoidal rule 315 808 810 824 Trapezoidal rule, computation of integrals 315 Traveling-wave equation 1439 Traveling-wave solution 554 667 775 790 796 Traveling-wave solution, generalized 697 Trefoil 373 Trials independent 1037 triangle 43 Triangle incircle 46 47 Triangle inequality 14 44 73 193 314 Triangle rule 113 176 Triangle, altitude 46 Triangle, area 48 Triangle, center of gravity 45 Triangle, circumcircle 46 Triangle, equilateral 43 51 Triangle, excircle 47 Triangle, isosceles 43 50 Triangle, median 45 Triangle, obtuse 43 Triangle, orthocenter 46 Triangle, plane 43 Triangle, right 43 50 Triangle, right-angled 43 Triangle, scalene 43 Triangle, spherical 71 72 Triangles, Euler 71 Triangles, plane 43 Triangular decomposition 180 Triangular pyramid 63 Triangular representation 201 Triaxial ellipsoid 144 Tricomi equation 1403 Trigonometric circle 24 Trigonometric form of complex number 400 Trigonometric functions 24 Trigonometric functions integration formulas 30 Trigonometric functions of half argument 29 Trigonometric functions of multiple arguments 29 Trigonometric functions, differentiation formulas 29 Trigonometric functions, expansion in power series 30 Trigonometric series 1122—1128 Trigonometric substitutions 280 Trihedral angle 60 Trihedral angle, edge 60 Trihedral angle, face 60 Trihedral angle, vertex 60 Trihedral, moving 382 Trihedral, natural 382 Trihedral, right-handed 121 Triple cross product of vectors 122 Triple integral 324 Triple integral, change of variables 326 Triple integral, estimation theorem 325 Triple integral, geometric applications 327 Triple integral, mean value theorem 325 Triple integral, physical applications 327 Triple integral, properties 324 Triple point 371 Trivial representation of group 230 Trivial solution 197 Truncated cylinder 66 Truncated expansion 749 Truncated prism 62 Tube, cylindrical 67 Two-body problem 1260 Two-dimensional Helmholtz equation 599 Two-dimensional Klein — Gordon equation 618 Two-dimensional Poisson equation 599 Two-dimensional random variable initial moment 1060 Two-dimensional random variable, moment 1060 Two-dimensional random vector, distribution function 1057 Two-dimensional wave equation 618 Two-person game 1024 Two-sheeted hyperboloid, imaginary semiaxis 144 Two-sided Laplace transform 449 Two-term asymptotic expansions 478 Types of linear PDEs 585 Types of matrices 167 Ultrahyperbolic equation 590 Ultraspherical polynomials 987 Umbilical point 393 Unbalanced transportation 1020 Unbiased estimator 1089 Unbounded set 263 Uncomputable integrals 276 Uncorrelated random variables 1061 Underdetermined system of linear algebraic equations 197 Undetermined coefficients method 17 277 Uniform convergence of functions 249 Uniform convergence, Weierstrass criterion 349 Uniform distribution 1051 Uniformly convergent functional series 349 Uniformly convergent series 349 Unimodal distribution 1045 Union of events 1031 Uniqueness and existence theorems for first-order ODEs 454 Uniqueness theorem 171 413 Unit normal vector 389 Unit sphere 220 Unit vector 113 Unit, imaginary 399 Unitarity condition 206 Unitary group 229 Unitary matrix 171 Unitary operator 206 Unitary space 195 Unitary space, isomorphic 196 Unitary space, normed 195 Unitary space, orthogonal elements 195 Unitary transformation 183 Unitary transformation of matrices 183 Universal invariant 731 Unknown quantities 199 201 Unstable focus 536 537 Unstable solution 546 Unstable spiral point 537 Upper bound 235 Upper half-plane 79 Upper limit of sequence 240 Upper price of game 1025 Upper triangular matrix 168 Urysohn equation with degenerate kernel 863 864 Urysohn integral equation 856 Value of segment 77 Value, Cauchy principal, for singular integral 311 Value, characteristic 829 834 Value, characteristic of operator 209 Value, game 1025 Van der Pol — Krylov — Bogolyubov scheme (method) 503 Vandermonde determinant 179 Vandermonde matrix 179 Variable density 327 Variable incomplete separation 597 Variable parameter 87 Variable, artificial 1016 Variable, basic 1015 Variable, nonbasic 1015 Variable, phase 546 1010 Variable, random 1039 Variable, symmetric random 1041 Variables independent 236 variables, dependent 236 Variables, random independent 1060 1067 Variance 1044 Variance of empirical distribution 1088 Variance of random variable 1044 Variance, multifactor analysis 1108 Variance, population 1087 Variance, residual 1066 1108 Variance, sample 1088 Variate value, frequency 1083 Variation of argument 992 Variation of functional 992 Variation, coefficient 1045 Variation, second of functional 993 Variation, total of function 247 Vector 113 167 187 Vector field, flux 333 Vector field, potential 331 Vector opposite to vector 113 Vector space 187 Vector stochastic process 1072 Vector, associated 213 Vector, curvature 383 Vector, Darboux 386 Vector, geodesic curvature 392 Vector, issuing from point A with endpoint B 189 Vector, length 113 Vector, normal 124 Vector, normal curvature 392 Vector, normal unit 389 Vector, position 115 Vector, tangential curvature 392 Vector, two-dimensional random 1057 Vector, unit 113 Vector, zero 113 Vectors in space 113 Vectors, collinear 113 Vectors, coordinate 388 Vectors, coplanar 113 Vectors, cross product 121 Vectors, difference 113 188 Vectors, linear combination 188 Vectors, parallel 113 Vectors, scalar product 120 Vectors, scalar triple product 123 Vectors, sum 113 Vectors, triple cross product 122 Velocity, characteristic 790 Versatile trigonometric substitution 282 Vertex 43 Vertex of ellipse 99 Vertex of hyperbola 102 Vertex of parabola 105 Vertex of polygon 51 Vertex of polyhedral angle 60 Vertex of polyhedron 61 Vertex of second-order curve 109 Vertex of trihedral angle 60 Vertical asymptote 242 Vertices of spherical triangle 71 Vibration equation with axial symmetry 1282 Vibration of string 1276 Viete theorem 158 159 163 Viscosity solution 564 Volterra integral equation with quadratic nonlinearity 856 Volterra integral equation, first kind 801 807 Volterra integral equation, nonlinear 856 Volterra integral equation, second kind 807 810 858 von Mises transformation 667 Von Neumann minimax theorem 1026 Wald test 1097 Watson formula 292 Wave equation, linear 585 1278 Wave equation, linear, three-dimensional 618 Wave equation, linear, two-dimensional 618 Wave equation, nonlinear 723 1312—1317 Wave, breaking 559 Wave, centered rarefaction 558 Wave, rarefaction 559 785 1255 Wave, Riemann 782 783 Wave, shock 561 790—793 1255 Wave, “overturn” 559 Weak convergence 1069 Weak law of large numbers 1069 Weak local maximum 993 1001 1002 1006 Weak maximum of functional 991 Weak neighborhood 991 Weak singularity 801 Weak singularity of second kind 829 Weak solution 563 Weber parabolic cylinder function 967 Weber transform 449 wedge 63 65 Weierstrass condition 998 Weierstrass criterion of uniform convergence 349 Weierstrass example 997 Weierstrass function 998 1000 Weierstrass function, elliptic 976 Weierstrass transform 449 Weierstrass — Erdmann conditions 997 999 Weierstrass — Erdmann conditions in multidimensional case 999 Weight of variate value 1083 Weingarten formulas 396 Whitham rule of “equal areas” 562 Whittaker equation 960 Whittaker functions 960 Wiener process 1086 Wiener — Hopf equation, first kind 825 1401 Wiener — Hopf equation, second kind 829 1406 Willier formula 74 wronskian 473 482 518 Wronskian determinant see “Wronskian” Wronskian of degenerate hypergeometric functions 958 Wronskian of Legendre functions 967 Wronskian, for system of ODEs 539 Y-transform 448 449 Zero asymptotic 364 Zero matrix 167 Zero of function 413 Zero operator 204 Zero simple 413 Zero vector 113 Zero-order neighborhood 991 Zeros of Bessel functions 951 Zhukovskii function 404 424 Zone, spherical 69 “Games with nature” 1024 “Hoof” 67
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