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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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Предметный указатель
Method, characteristics, generalized classical 582 Method, Clarkson — Kruskal direct 708—710 Method, Cole — Kevorkian 504 Method, collocation 509 523 847 848 860 Method, collocation, convergence theorem 524 Method, collocation, for integral equations 847 848 Method, collocation, for ODEs 509 523 Method, D'Alembert 533 Method, D'Alembert, for nonhomogeneous higher-order linear systems 533 Method, differential constraints 737 Method, estimation 1091 Method, false position 262 Method, Fourier 602 Method, Galerkin 508 Method, Gaussian elimination, backward substitution 200 Method, Jacobi 217 Method, Lagrange 217 Method, Lagrange — Charpit 573 Method, Laplace cascade 600 Method, Lavrentiev regularization 827 Method, least squares 509 1092 Method, least-squared error 511 Method, Lindstedt — Poincare 502 Method, Maclaurin 164 Method, mathematical induction 16 Method, minimal cost 1020 Method, modified Newton — Kantorovich 859 868 Method, moments 509 1091 Method, Newton 164 Method, Newton — Kantorovich 859 868 Method, Newton — Raphson 262 Method, parametric for defining curve 123 Method, parametric for defining surface 123 Method, penalty function 1027 Method, perturbation 499 Method, Picard 469 Method, projection 508 Method, quadrature 861 Method, quadrature, for integral equations 870 Method, quadric 148 Method, regula falsi 262 Method, regularization, for integral equations 827 Method, Runge — Kutta 472 512 Method, shooting 512 Method, similarity 669 Method, simplex 1014 Method, single-step of second-order approximation 471 Method, splitting 704 Method, step 884 885 889 893 919 Method, Sturm 166 Method, successive approximation 822 833 858 867 Method, summation of series 344 Method, Tikhonov regularization 828 Method, Titov — Galaktionov 693 Method, Van der Pol — Krylov — Bogolyubov 503 Methods of defining function 236 Methods of integral transforms 841 Methods, numerical for ODEs 511 512 Methods, perturbation 499—507 Methods, projection 508 Metric space 196 Metric tensor 1193 Metric tensor components 1195 Meusnier theorem 392 Midline 44 Minimal cost method 1020 Minimal polynomial 186 Minimal surface 394 770 Minimality of variance of estimator 1090 Minimax principle 1025 Minimax property 210 Minimax theorem, for antagonistic two-person zero-sum games 1026 Minimax theorem, von Neumann 1026 Minimum of function, xxxi 257 Minimum, conditional 270 Minimum, constrained 270 Minimum, local 257 Minimum, local, strong 994 Minimum, local, weak 993 1001 1002 1006 Minimum, strong 1006 Minimum, strong of functional 991 Minimum, weak of functional 991 Minkowski inequality for finite sums 14 Minkowski inequality for integrals 296 Minkowski inequality for series 343 Minkowski inequality for vectors 121 193 Minor 177 Minor axis of ellipse 98 Minor of rectangular matrix 177 Minor of square matrix 176 Minor, basic 178 Minor, cofactor 177 Minor, first kind 177 Minor, second kind 177 Mixed boundary value problem 480 593 Mixed boundary value problem, for hyperbolic equations 627 Mixed boundary value problem, for PDEs 593 Mixed strategy 1025 Mixed strategy, game price 1026 Mode of continuous probability distribution 1045 Mode of discrete probability distribution 1045 Model equation of gas dynamics 558 1254 Model of transportation problem 1020 Model of transportation problem, closed 1020 Modified associated Legendre functions 966 Modified Bessel equation 1216 Modified Bessel functions 953 Modified Bessel functions, first kind, xxxi 953 1216 Modified Bessel functions, second kind, xxxi 953 1216 Modified Korteweg — de Vries equation 759 Modified Mathieu equation 982 1220 Modified Mathieu functions 982 Modified Newton — Kantorovich method 859 868 Modified reciprocal equation 160 Modulus of complex number, xxxii 400 Modulus of real number, xxx 8 Modulus of vector, xxx Modulus set 907 Modulus, complementary 971 Modulus, elliptic 971 Mollweide formulas 44 moment 1043 Moment initial of multivariate random variable 1065 Moment initial of two-dimensional random variable 1060 Moment method 509 Moment of multivariate random variable 1065 Moment of two-dimensional random variable 1060 Moment, absolute 1044 Moment, central 1043 Moment, central of n-dimensional random variable 1065 Moment, cth absolute 1044 Moment, cth central 1043 Moment, cth sample, central 1087 Moment, fcth sample 1087 Moment, sample 1087 Moment, sample, central 1087 Moment-generating function 1047 Moments of inertia of body 327 Moments of inertia of flat plate 324 Momentum conservation law 996 Monge — Ampere equation 654 1326 Monge — Ampere equation, homogeneous 668 1326 Monotone function 236 Monotone sequence 238 Morera theorem 410 Morley theorem 49 Morse potential 1278 Motion of mass point 87 Movable critical points 495 Movable singularities of solutions of ordinary differential equations 494 Moving trihedral 382 Moving trihedral of curve 382 Multidimensional stochastic process 1072 Multifactor analysis of variance 1108 Multilinear form 215 Multilinear form, skew-symmetric 215 Multilinear form, symmetric 215 Multimodal distribution 1045 Multiple correlation coefficient 1066 Multiple integral 328 Multiple integral, asymptotic formulas 328 Multiple integration 289 Multiple, common least 4 Multiplication index 12 Multiplication of asymptotic series 364 Multiplication of matrices 169 Multiplication of matrix by scalar 169 Multiplication of polynomials 155 Multiplication of real numbers 6 Multiplication of series 343 Multiplicative inverse of real number 6 Multiplicative separable solution 571 596 678 Multiplicity of eigenvalue, algebraic 184 209 Multiplicity of eigenvalue, geometric 209 Multiplier, Lagrange 270 Multiply connected domain 409 Multivalued function 236 402 Multivariate random variable initial moment 1065 Multivariate random variable, moment 1065 N-dimensional coordinate space 188 N-dimensional distribution, generalized variance 1065 N-dimensional ellipsoid 224 N-dimensional Fourier transform 445 N-dimensional linear space 189 n-dimensional random variable 1065 N-dimensional random vector 1057 N-fold singular point 371 N-person game 1024 N-sided pyramid 63 N-soliton solution 765 N-soliton solution, Korteweg — de Vries equation 764 Nagel point 47 Napierian base 23 Natural logarithm, xxxi 9 22 23 238 Natural logarithm, xxxi, base 9 23 Natural number 3 Natural trihedral 382 Necessary condition for extremum 269 1002 1006 1009 Necessary condition for solvability of Neumann problem 429 Negative binomial distribution 1050 Negative definite quadratic form 216 Negative Hermitian operator 207 Negative index of inertia of quadratic form 218 Negative symmetric operator 207 Neighborhood of point at infinity 402 Neighborhood of point on complex plane 402 Neighborhood, first-order 991 Neighborhood, strong 991 Neighborhood, weak 991 Neighborhood, zero-order 991 Neper analogs 73 Neper rules 75 Net, coordinate 387 Neumann function 947 Neumann problem 429 Neumann problem, for elliptic equations 593 1330 Neumann problem, necessary condition for solvability 429 Neumann series 823 833 Neutral element 225 Newell — Whitehead equation 733 Newton method 164 Newton — Kantorovich method 859 868 Newton — Leibniz formula 288 Newton — Leibniz formula, for function of complex variable 408 Newton — Raphson method 262 Neyman — Fisher theorem 1090 Neyman — Pearson lemma 1097 Nilpotent matrix 172 Nine-point circle 49 Node 372 Node interpolation 808 Node, Chebyshev 523 Node, quadrature 808 Node, stable 535 538 Node, unstable 536 Noetherian symmetry 767 Noetherian symmetry of Lagrangian 768 Nonbasic variable 1015 Nonclassical method of symmetry reductions 732 747 Nonclassical symmetries 733 Nondecreasing function 236 Nondegenerate bilinear form 215 Nondegenerate linear operator 205 Nondegenerate matrix 171 Nondegenerate quadratic form 216 Nonhomogeneous biharmonic equation 1298 Nonhomogeneous first-order constant-coefficient linear difference equation 1411 Nonhomogeneous higher-order linear systems, D'Alembert method 533 Nonhomogeneous integral equation 810 829 Nonhomogeneous linear boundary value problems 620 624 Nonhomogeneous linear difference equations 882 Nonhomogeneous linear ODEs 474 515 Nonhomogeneous linear PDEs 598 Nonhomogeneous Monge — Ampere equation 1326 Nonhomogeneous nth-order constant-coefficient linear difference equation 1427 Nonhomogeneous nth-order linear difference equation 1426 Nonhomogeneous second-order constant-coefficient linear difference equation 1422 Nonhomogeneous second-order linear difference equation 1421 Nonhomogeneous system of linear algebraic equations 197 Nonhomogeneous system of linear first-order ODEs 531 540 Nonhomogeneous system, superposition principle 541 Nonincreasing function 236 Nonlinear difference equation 884 918 1428 Nonlinear difference equation of general form 1437 Nonlinear diffusion equation with cubic source 753 Nonlinear elliptic equations 1318 Nonlinear first-order partial differential equation with two independent variables 570 Nonlinear functional equation 1443 Nonlinear functional equation in one independent variable 1428 Nonlinear functional equation, power series solution 922 Nonlinear heat equation 1301 1318 Nonlinear heat equation in radial symmetric case 1307 Nonlinear integral equations 856 Nonlinear integral equations with constant integration limits 856 863 Nonlinear integral equations with degenerate kernels 863 Nonlinear integral equations with variable integration limit 856 Nonlinear Klein — Gordon equation 702 1315 Nonlinear mathematical physics equations 1301 Nonlinear nth-order difference equation 919 Nonlinear operator 693 695 Nonlinear ordinary differential equations 453—472 488—513 524—527 Nonlinear ordinary differential equations, systems 542—550 Nonlinear partial differential equations 570—584 653—779 1301—1335 Nonlinear partial differential equations, systems 780—798 1343—1382 Nonlinear programming 1027 Nonlinear programming, problem 1027 Nonlinear Schrodinger equation 759 1307 Nonlinear systems of first-order ODEs 1239 Nonlinear systems of ODEs 542—550 1239 1244 Nonlinear systems of PDEs 780—798 1343—1382 Nonlinear systems of PDEs of general form 1374—1384 Nonlinear systems of second-order ODEs 1240 Nonlinear systems of two first-order PDEs 1337 Nonlinear systems of two second-order PDEs 1343 Nonlinear Urysohn integral equation 856 Nonlinear Volterra integral equation 856 858 860 861 Nonlinear wave equations 723 1312—1317 Nonnegative Hermitian operator 207 Nonnegative quadratic form 216 Nonnegative symmetric operator 207
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