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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
Linear programming problem 1012 Linear programming problem, standard form 1013 Linear programming problem, symmetric 1013 Linear representation of group 230 Linear space 187 189 Linear space infinite-dimensional 189 Linear space of affine space, associated 189 Linear space, basis 189 Linear space, complex 188 Linear space, dimension 189 Linear space, elements 187 Linear space, linear transformation 204 Linear spaces, isomorphic 189 Linear spaces, isomorphisms 188 Linear span 190 Linear subspace 190 Linear subspace invariant under nonlinear operator 693 695 Linear superposition principle 594 Linear surface element 390 Linear systems of algebraic equations 197 Linear systems of ODEs 528 Linear systems of PDEs of general form 1374 Linear systems of two second-order PDEs 1341 Linear transformation 656 Linear transformation of linear space 204 Linear transformations, product 228 Linear-fractional mappings 422 Linearly dependent column vectors 171 Linearly dependent elements 188 Linearly dependent row vectors 171 Linearly independent column vectors 171 Linearly independent elements 188 Linearly independent row vectors 171 Linearly independent solutions of difference equation 882 Lines in space, theorem on arrangement 136 Lines, asymptotic 393 Lines, condition for two lines in space to meet 143 Lines, curvature 393 Lines, curvilinear 387 Lines, for system of ODEs 540 Lines, parallel 59 96 Lines, perpendicular 95 Lines, skew 59 Liouville equation 664 Liouville formula 473 518 Liouville theorem 403 414 Lipschitz condition 248 310 313 454 488 543 584 Lipschitz convergence criterion for Fourier series 358 Lipschitz criterion of uniform convergence of Fourier series 361 Lobachevsky convergence criterion for series 341 Lobachevsky equation 1444 Local maximum 257 Local maximum, point 269 Local minimum 257 Local minimum, point 269 Local theorem of de Moivre — Laplace 1038 Log-normal distribution 1042 Logarithm, xxxi 9 Logarithm, xxxi, common 9 Logarithm, xxxi, decadic 9 Logarithm, xxxi, natural, xxxi Logarithmic branch point 415 Logarithmic derivative of gamma function 949 954 Logarithmic function 22 Logarithmic function, graphs 22 Logarithmic function, properties 23 Logarithmic identity 9 Logarithmic integral 941 958 Logarithmic kernel 801 Logarithmic residue 416 Logarithmic spiral 86 Logarithms, natural 9 22 23 238 Logistic difference equation 875 longitude 119 Lorentz transformation 718 1278 Lower bound 235 Lower half-plane 79 Lower limit of sequence 240 Lower price of game 1025 Lower triangular matrix 168 Lyapunov central limit theorem 1071 Lyapunov function 549 Lyapunov stability 546 Lyapunov stable 546 Lyapunov theorem of asymptotic stability 549 Lyapunov theorem of stability 549 Macdonald function 953 Maclaurin formula 257 Maclaurin method 164 Maclaurin power series 352 Maclaurin series 353 Maclaurin — Cauchy integral criterion of convergence of series 339 Main diagonal 168 Major axis of ellipse 98 Majorant series 349 Many-valued function, branch 404 Mapping 226 Mapping invertible 226 Mapping, conformal 419 Mapping, groups 227 Mapping, groups, isomorphic 227 Mapping, linear-fractional 422 Mapping, onto set 226 Mapping, range 226 Mapping, schlicht 402 Marginal distribution function 1064 Marginal probability functions 1059 Markov inequality 1070 Markov process 1075 Markov property 1075 Mass of body of variable density 327 Mathematical induction 16 Mathematical model of transportation problem 1019 Mathematical physics equations, nonlinear 1301 Mathematical programming 1012 Mathematical programming, general problem 1012 Mathematical statistics 1081 Mathematical statistics, problems 1081 Mathieu equation 980 1221 Mathieu equation, modified 982 1220 Mathieu functions 980 1221 Mathieu functions, modified 982 Matrices 167 Matrices, commuting 169 Matrices, compatible size 169 Matrices, congruent 182 Matrices, conjunctive 183 Matrices, difference 169 Matrices, direct sum 175 Matrices, elementary 181 Matrices, elementary transformations 180 Matrices, equal 168 Matrices, equivalent 180 Matrices, Kronecker product 175 Matrices, multiplication 169 Matrices, similar 181 Matrices, subtraction 169 Matrices, sum 168 Matrices, unitary transformations 183 169 Matrix 167 Matrix decomposition 201 Matrix entry 167 Matrix entry, cofactor 176 Matrix index 182 Matrix infinite 167 Matrix inverse 171 Matrix inverse left 171 Matrix inverse right 171 Matrix involutive 172 Matrix of bilinear form 215 Matrix of linear operator 208 Matrix of linear system of algebraic equations, basic 197 Matrix of moments 1065 Matrix of sesquilinear form 214 Matrix of simple structure 182 Matrix, additively inverse 169 Matrix, adjoint 170 Matrix, adjugate 180 Matrix, antihermitian 168 Matrix, antisymmetric 168 Matrix, block 174 Matrix, canonical form 181 Matrix, canonical Jordan form 182 Matrix, characteristic 183 Matrix, characteristic equation 185 Matrix, characteristic polynomial 185 Matrix, complex conjugate 170 Matrix, correlation 1066 Matrix, covariance 1065 Matrix, defect 177 178 Matrix, determinant of order 2 175 Matrix, determinant of order 3 176 Matrix, determinant of order n 176 Matrix, diagonal 168 Matrix, dimension 167 Matrix, eigenvalue 183 Matrix, elementary transformation 199 Matrix, finite 167 Matrix, generalized permutation 168 Matrix, hermitian 168 Matrix, identity 168 Matrix, multiplication by scalar 169 Matrix, nilpotent 172 Matrix, nondegenerate 171 Matrix, nonsingular 171 Matrix, normal 171 Matrix, normal form 181 Matrix, null 167 Matrix, opposite 169 Matrix, orthogonal 170 Matrix, payoff 1024 Matrix, payoff, saddle point 1025 Matrix, rank 177 178 Matrix, real 171 Matrix, rectangular 177 Matrix, self-adjoint 168 Matrix, signature 182 Matrix, skew — Hermitian 168 Matrix, skew-symmetric 168 Matrix, spectrum 183 Matrix, square 168 176 Matrix, subdiagonal 168 Matrix, superdiagonal 168 Matrix, symmetric 168 Matrix, trace 171 Matrix, transforming 181 Matrix, triangular, lower 168 Matrix, triangular, strictly lower 168 Matrix, triangular, strictly upper 168 Matrix, unitary 171 Matrix, upper triangular 168 Matrix, Vandermonde 179 Matrix, zero 167 Maximin principle 1025 Maximum likelihood estimator 1092 Maximum Modulus Principle 403 Maximum of function, xxxi 257 Maximum principle, Pontryagin 1011 Maximum, conditional 270 Maximum, constrained 270 Maximum, local 257 Maximum, local weak 993 1001 1002 1006 Maximum, strong 1006 Maximum, strong local 994 Maximum, strong of functional 991 Maximum, weak of functional 991 Mean curvature 394 Mean value of function 318 325 Mean Value Theorems 295 Mean value theorems, for double integral 318 Mean value theorems, for triple integral 325 Mean values, general approach 13 Mean, functional 13 Mean, geometric 13 Mean, harmonic 13 Mean, sample 1087 Mean-square convergence 315 Mean-square deviation 1088 Mean-square regression 1063 1066 Median 1045 Median of trapezoid 54 Median of triangle 45 Mehler — Fock transform 449 Meijer inversion formula 447 Meijer transform 447 Meijer transform (K-transform) 449 Mellin transform 441 449 826 842 844 Mellin transform inverse 442 Mellin transform, properties 442 Mellin transform, tables 1187—1190 Menelaus theorem 49 Meromorphic function 414 Mertens theorem 343 Method integral transforms 611 Method of accelerated convergence in eigenvalue problems 513 Method of approximating kernel by degenerate one 844 Method of argument elimination, for functional equations 928 Method of differentiation for integral equations 857 866 Method of differentiation for ODEs 857 Method of differentiation in independent variables, for functional equations 925 Method of differentiation in parameter, for functional equations 922 Method of Euler polygonal lines 471 Method of functional separation of variables 697 Method of generalized separation of variables 681 Method of integral transforms 825 856 865 Method of integral transforms, for linear PDEs 611 Method of integral transforms, for nonlinear integral equations 856 865 Method of integration by differentiation 465 Method of inverse scattering problem 755 Method of least squares 509 849 1092 Method of least squares, for integral equations 849 Method of least squares, normal system 850 Method of least-squared error 511 Method of matched asymptotic expansions 506 Method of model solutions 818 Method of partitioning domain 511 Method of potentials 1021 Method of quadratures 808 823 Method of quadratures, for integral equations 808 823 852 861 870 Method of regular expansion in small parameter, for ODEs 470 501 Method of replacing kernel by degenerate kernel 844 Method of scaled parameters 502 Method of separation of variables 602 Method of separation of variables, for first-order PDEs 571 Method of separation of variables, for linear PDEs 602 Method of substituting particular values of independent arguments, for functional equations 926 Method of successive approximations 469 511 832 858 Method of symmetry reductions, classical 732 Method of symmetry reductions, direct 708 Method of symmetry reductions, nonclassical 732 747 Method of Taylor series expansion in independent variable, for ODEs 470 Method of two-scale expansions 504 Method of undetermined coefficients 17 277 Method of vanishing viscosity 564 580 Method, averaging 503 Method, backward substitution in Gaussian elimination 200 Method, bisection 261 Method, Bubnov — Galerkin, for integral equations 850 Method, Bubnov — Galerkin, for ODEs 509 Method, Budan — Fourier 166
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