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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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Polynomial, Bernoulli 891 988 Polynomial, characteristic of linear operator 211 Polynomial, characteristic of matrix 185 Polynomial, Chebyshev of first kind 983 Polynomial, Chebyshev of second kind 984 Polynomial, derivative 157 Polynomial, Euler 989 Polynomial, expansion in powers of linear binomial 156 Polynomial, Gegenbauer 987 Polynomial, Hermite, xxxi 957 958 985 Polynomial, Jacobi 986 Polynomial, Laguerre 982 957 Polynomial, Laguerre generalized 983 Polynomial, Legendre, xxxi 962 1217 Polynomial, minimal 186 Polynomial, number of real roots 165 Polynomial, remainder theorem 156 Polynomial, ultraspherical 987 Polynomials, difference 155 Polynomials, division 155 Polynomials, equal 155 Polynomials, multiplication 155 Polynomials, nonorthogonal 988 Polynomials, orthogonal 982 Polynomials, product 155 Polynomials, sum 155 Pontryagin function 1011 Pontryagin maximum principle 1011 Population 1081 Population, expectation 1087 Population, variance 1087 Position vector of point 115 Positive definite kernel 837 Positive definite quadratic form 216 Positive definite quadratic functional 993 Positive Hermitian operator 207 Positive index of inertia of quadratic form 218 Positive integer power of complex number 399 Positive integer power of matrix 172 Positive normal direction 389 Positive operator 207 Positive sense 367 Positive sense of boundary 402 Positive sense of normal 369 Positive sense of tangent 369 Positive sequence 238 Positive symmetric operator 207 Post — Widder formula 441 Potential 331 760 1021 Potential of gravitational field 328 Potential of vector field 331 Potential-type integrals 291 Power function 19 Power function, graphs 19 Power function, properties 19 Power Laplace integral 294 Power Laplace integral, multiple 328 Power series 350 1120 Power series interval of convergence 351 Power series, Abel theorem 350 Power series, addition 354 Power series, convergence radius 350 Power series, division 354 Power series, Maclaurin 350 Power series, multiplication 354 Power series, properties 350 Power series, solution of nonlinear functional equations 922 Power series, subtraction 354 Power series, summation formulas 357 Power series, Taylor 350 Power, test 1096 Powers 8 Powers of hyperbolic functions 37 Powers of linear operators 205 Powers of matrices 172 Powers of trigonometric functions 28 Price, upper of game 1025 Primal linear programming problem 1017 Prime number 3 Primitive function 273 Principal axis 109 151 152 Principal axis of hyperbola 101 Principal axis of second-order curve 109 Principal diameter of ellipse 100 Principal diameter of hyperbola 104 Principal diameter of parabola 106 Principal directions of second-order curve 109 Principal normal 381 Principal normal sections 393 Principal part of Laurent series 412 Principal plane 151 Principal value, Cauchy of singular integral 311 Principle of linear superposition, for PDEs 594 Principle, boundary correspondence 420 Principle, Duhamel first 646 Principle, Duhamel second 648 Principle, maximin 1025 Principle, maximum modulus 403 Principle, minimax 1025 Principle, Rayleigh — Ritz 484 513 Principle, Riemann localization 358 Principle, Schwarz analytic continuation 426 Principle, superposition, for homogeneous system of linear ODEs 528 539 Principle, superposition, for linear functional equations 880 883 Principle, superposition, for linear PDEs 594 Principle, superposition, for nonhomogeneous linear ODE 519 Principle, superposition, for nonhomogeneous system of linear ODEs 541 prism 61 Prism, base face 61 Prism, joining face 61 Prism, right 62 Prism, truncated 62 Privalov boundary value problem 432 Probabilistic models 1031 probability 1032—1034 Probability density function 1040 Probability element 1040 1059 1065 Probability function, joint 1059 1064 Probability function, marginal 1059 Probability integral 939 1265 Probability multiplication theorem 1035 Probability of event 1032 Probability space 1032 Probability space, discrete 1033 Probability theory 1031 Probability, classical definition 1033 Probability, conditional 1035 Probability, convergence 1068 Probability, geometric 1034 Probability, multiplication theorem 1035 Probability, transition 1075 Probability-generating function of random variable 1047 Problem initial value 580 785 Problem inverse scattering 760 Problem of propagation of signal 566 Problem with higher derivatives 1006 Problem, Banach 1038 Problem, Bolza 1001 Problem, boundary value, first 480 593 627 Problem, boundary value, for difference equations 879 Problem, boundary value, for elliptic equations 631 Problem, boundary value, for hyperbolic equations 623 Problem, boundary value, for ODEs 480 Problem, boundary value, for parabolic equations 645 Problem, boundary value, Hilbert — Privalov 432 Problem, boundary value, mixed 480 593 627 Problem, boundary value, nonhomogeneous 620 624 Problem, boundary value, second 480 593 627 Problem, boundary value, third 480 593 627 Problem, Cauchy, for difference equations 889 Problem, Cauchy, for first-order ODEs 454 Problem, Cauchy, for first-order PDEs 556 576 Problem, Cauchy, for Hamilton — Jacobi equation 577 Problem, Cauchy, for hyperbolic equations 617 Problem, Cauchy, for parabolic equations 615 Problem, Cauchy, for PDEs 591 592 785 1308 Problem, Cauchy, for second-order ODEs 488 Problem, Cauchy, for system of PDEs 785 Problem, Cauchy, generalized, for PDEs 627 Problem, Dido 1003 Problem, diet 1012 Problem, direct scattering 760 Problem, Dirichlet 427 Problem, Dirichlet, for elliptic equations 593 1330 Problem, Dirichlet, generalized 428 Problem, dual linear programming 1017 Problem, eigenvalue 604 Problem, first boundary value 593 Problem, general mathematical programming 1012 Problem, Goursat 592 629 Problem, isoperimetric 1002 Problem, Lagrange 1008 Problem, linear programming 1012 Problem, Neumann 429 Problem, Neumann, for elliptic equations 593 1328 Problem, nonlinear programming 1027 Problem, primal linear programming 1017 Problem, Privalov boundary value 432 Problem, product mix 1012 Problem, programming linear 1012 Problem, Riemann 785 Problem, simplest of calculus of variations 993 Problem, Sturm — Liouville 482 621 622 625 626 Problem, terminal value 580 583 584 Problem, third boundary value 593 Problem, transportation 1019 Problem, transportation balanced 1020 Problem, two-body 1258 Problems for elliptic equations 637 643 644 Problems for hyperbolic equations 607 636 Problems for parabolic equations 605 634 Problems of mathematical physics 590 Problems of mathematical statistics 1081 Process, Bernoulli 1037 Process, birth — death 1077 Process, iteration 858 Process, Markov 1075 Process, optimal in strong sense 1010 Process, point simplest 1076 Process, Poisson 1076 Process, pure birth 1077 Process, pure death 1077 Process, stationary 1075 Process, stochastic 1071 1073 1074 Process, stochastic multidimensional 1072 Process, stochastic one-dimensional 1072 Process, stochastic stationary in narrow sense 1074 Process, stochastic stationary in wide sense 1074 Process, stochastic vector 1072 Process, stochastic with continuous time 1072 Process, stochastic with discrete time 1072 Process, Wiener 1086 Product inner 192 314 840 Product of complex numbers 399 Product of linear operators 203 Product of linear transformations 227 Product of matrices 157 Product of matrix by scalar 157 Product of polynomials 155 Product of real numbers 6 Product of scalar and linear operator 203 Product of scalar and vector 187 Product of subsets of group 227 Product of vector by number 113 Product, Kronecker of matrices 175 Product, mix problem 1012 Product, scalar 192 Product, scalar of vectors 120 Product, scalar triple of vectors 123 Product, triple cross of vectors 122 Products of hyperbolic functions 37 Products of trigonometric functions 28 Programming, convex 1027 Programming, dynamic 1027 Programming, geometric 1027 Programming, quadratic 1027 Progression 1113 1118 Progression, arithmetic 11 Progression, geometric 11 Projection 212 Projection methods 508 Projection of vector onto axis 114 Projection, on segment 81 Projection, orthogonal 197 Projections, theorem 44 Prolate spheroid 144 Prolongation of group generator 732 Prolongation of operator, second 720 Proof by contradiction 15 Proof by counterexample 17 Proper orthogonal transformations 229 Proper subspace 190 Properties of limits 240 Property, Markov 1075 Property, minimax 210 Property, optical of ellipse 100 Property, optical of hyperbola 103 Property, optical of parabola 106 Property, stability 1055 proportions 7 Psi function 944 Ptolemy theorem 52 Puiseux power series 415 Pure birth process 1077 Pure imaginary complex number 399 Pyramid 63 Pyramid, altitude 63 Pyramid, apex 63 Pyramid, apothem 64 Pyramid, base 63 Pyramid, frustum 64 Pyramid, lateral face 63 Pyramid, triangular 63 Pythagorean Theorem 50 193 Quadrant 79 Quadratic equation 158 Quadratic form 216 840 Quadratic form in Euclidean space 219 Quadratic form in finite-dimensional linear space 216 Quadratic form index of inertia 218 Quadratic form, alternating 216 Quadratic form, canonical representation 217 Quadratic form, characteristic 150 Quadratic form, characteristic equation 150 Quadratic form, degenerate 216 Quadratic form, extremal properties 220 Quadratic form, negative definite 216 Quadratic form, negative index of inertia 218 Quadratic form, nondegenerate 216 Quadratic form, nonnegative 216 Quadratic form, nonpositive 216 Quadratic form, normal representation 218 Quadratic form, positive definite 216 Quadratic form, positive index of inertia 218 Quadratic form, rank 216 Quadratic form, second of surface 392 Quadratic form, signature 218 Quadratic functional 992 Quadratic functional, positive definite 993 Quadratic functional, strongly positive 993
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