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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
Solution, special functional separable 697 Solution, stable generalized 569 Solution, traveling-wave 554 667 775 790 796 Solution, trivial 197 Solution, unstable 546 Solution, viscosity 564 Solution, weak 563 Solutions of homogeneous system, fundamental system 198 Solutions, fundamental system 477 478 522 523 Solutions, linearly independent of difference equation 882 Sommerfeld conditions 1288 1289 Source 536 538 Source, spiral 537 Space curves 379 Space of elementary events 1031 Space, affine 189 190 Space, Banach 196 Space, complete 196 Space, continuous curve 123 Space, continuous surface 123 Space, coordinate axes 114 Space, coordinate system 114 Space, curve 120 Space, Euclidean 192 193 Space, Euclidean, complex 195 Space, Euclidean, real 192 Space, Hilbert 196 Space, linear 187—189 Space, linear infinite-dimensional 189 Space, linear, complex 188 Space, linear, real 188 Space, metric 196 Space, normed 195 Space, probability 1032 Space, probability, discrete 1033 Space, representation 230 Space, sample 1031 Space, surface 119 120 Space, unitary 195 Space, vector 187 Spaces, Euclidean isomorphic 194 Spaces, linear isomorphic 189 Spaces, unitary isomorphic 196 Span, linear 190 Special Cauchy criterion 341 Special form, Laplace integral 291 Special functional separable solution 697 Special functions 939—990 Special linear group 228 Special orthogonal group 229 Special Riccati equation 1208 Special right-hand side 815 Specific Euclidean space 192 Specificity test 1095 Spectra of square matrices 183 Spectral decomposition of Hermitian operator 212 Spectral decomposition of normal operator 212 Spectral density 1075 Spectral function of stationary process 1075 Spectrum of matrix 183 Sphere 68 224 Sphere, diameter 69 Sphere, unit 220 Spherical biangles 71 Spherical cap 69 Spherical coordinates, xxxi 118 119 1199 Spherical excess 72 Spherical geometry 70 Spherical sector 69 Spherical segment 69 Spherical segment, base 69 Spherical triangle 71 72 Spherical triangle, rectangular 72 Spherical triangle, vertices 71 Spherical zone 69 Spheroid 144 Spheroid, oblate 144 Spheroid, prolate 144 Spiral of Archimedes 85 Spiral point, stable 537 Spiral point, unstable 537 Spiral sink 537 Spiral source 537 Spiral, hyperbolic 86 368 Spiral, logarithmic 86 Splitting in derivatives 719 Splitting method 704 Square integrable function 314 Square matrix 168 Square matrix, minor 176 Square matrix, trace 171 Square system of linear algebraic equations 197 Square, scalar 120 Stability condition 568 Stability condition, for generalized solution 568 Stability property 1055 Stability theory 546 Stability, asymptotic 546 Stability, Lyapunov 546 Stable focus 537 Stable generalized solutions 569 Stable node 535 538 Stable spiral point 537 Standard deviation 1045 Standard form of linear programming problem 1013 Stationary equation, heat (diffusion) with nonlinear source 1320 Stationary equation, heat (diffusion), anisotropic 1323 Stationary equation, Khokhlov — Zabolotskaya 1322 Stationary point 220 269 545 Stationary process, spectral function 1075 Stationary stochastic process 1074 Stationary stochastic process in narrow sense 1074 Stationary stochastic process in wide sense 1074 Stationary value of function 220 Statistic 1084 Statistic, Cochran 1104 Statistic, complete 1090 Statistic, Romanovskii 1101 Statistic, sufficient 1090 Statistical estimation 1088 Statistical estimator 1088 1090 Statistical hypothesis 1094 Statistical hypothesis, simple 1096 Statistical series 1082 1083 Statistical test 1095 Statistical transformations 1082 Statistically independent events 1036 Steady transonic gas flow 1324 Steklov inequality 297 Step method 884 885 889 893 919 Stewart theorem 48 Stieltjes integral 312 Stieltjes integral sum 312 Stirling formula 944 Stochastic process in narrow sense 1074 Stochastic process in wide sense 1074 Stochastic process with continuous time 1072 Stochastic process with discrete time 1072 Stochastic process, differentiation 1073 Stochastic process, multidimensional 1072 Stochastic process, stationary 1074 Stochastic process, vector 1072 Stochastic processes 1071—1073 Stochastic processes, complex 1073 Stokes theorem 334 Straight line in polar coordinates 92 Straight line in projections in space 133 Straight line in space 59 Straight line in space, general equation 132 Straight line intercept-intercept equation 91 Straight line, direction coefficients 131 Straight line, general equation 90 Straight line, normalized equation 91 Straight line, on plane 89 Straight line, slope 89 Straight line, slope-intercept equation 89 Strategy 1024 Strategy, mixed 1025 Strategy, optimal 1024 Stream function 1297 Strengthened Jacobi condition 1000 1004 1007 Strengthened Legendre condition 999 1004 1007 Stress function, Airy 1297 Strictly concave function 245 Strictly convex function 245 Strictly hyperbolic system 781 790 Strictly lower triangular matrix 168 Strictly upper triangular matrix 168 Strong Law of Large Numbers 1070 Strong local minimum 994 Strong maximum 1006 Strong maximum of functional 991 Strong minimum 1006 Strong minimum of functional 991 Strong neighborhood 991 Struve function 448 449 Student distribution 1056 Student ratio 1090 Student t-distribution 1056 Sturges formula 1083 Sturm comparison theorem on zeros of solutions 487 Sturm method 166 Sturm — Liouville problem 482 621 622 625 626 633 Subdiagonal matrix 168 Subgroup 227 Subgroup, compact 229 Subgroup, continuous 228 Subgroup, discrete 228 Subgroup, finite 228 Subgroup, normal 227 Submodulus set 907 Subsequence 238 Subspace invariant 205 Subspace invariant of representation 230 Subspace of linear spaces 190 Subspace, improper 190 Subspace, linear 190 Subspace, null 190 Subspace, orthogonal complement 194 Subspace, proper 190 Subspaces intersection 190 Subspaces, direct sum 189 Subspaces, sum 189 Substitution, canonical 465 Substitution, Euler 280 Substitution, trigonometric 280 Substitution, trigonometric versatile 282 Subtraction of asymptotic series 364 Subtraction of hyperbolic functions 37 Subtraction of inverse hyperbolic functions 41 Subtraction of inverse trigonometric functions 33 Subtraction of matrices 169 Subtraction of trigonometric functions 28 Successive approximation method for integral equations 822 833 858 867 Successive approximation method for ODEs 469 511 Sufficient conditions of extremum 269 Sufficient estimators 1090 Sufficient statistic 1090 Sum integral 286 317 Sum of complex numbers 399 Sum of elements of linear space 187 Sum of linear operators 204 Sum of matrices 168 Sum of polynomials 155 Sum of series 337 Sum of subspaces 190 Sum of vectors 113 Sum, Cauchy — Riemann 286 Sum, partial of series 337 Sum, Stieltjes integral 312 Summation index 12 Summation, formulas for trigonometric series 362 Sums involving hyperbolic functions 1116 Sums involving trigonometric functions 1117 Sums, functional, finite 1116 Sums, numerical, finite 1113—1116 Superdiagonal matrix 168 Superposition principle 519 880 883 Superposition principle, for homogeneous system 528 539 Superposition principle, for nonhomogeneous system 541 Support line 1014 Supremum, xxxi Sure event 1031 Surface in Cartesian coordinate system 119 Surface in space 119 120 123 Surface intrinsic geometry 391 Surface of constant curvature 394 Surface, center 143 151 Surface, central 143 Surface, conical 67 Surface, continuous in space 123 Surface, cylindrical 65 Surface, first quadratic form 390 Surface, minimal 394 770 Surface, normal 153 Surface, oriented 333 Surface, parametrized 387 Surface, ruled 146 Surface, second quadratic form 392 Surface, tangent line 388 Sylvester criterion 219 Sylvester inequality 178 Sylvester theorem 187 Symbol, Levi — Civita 179 Symbols of order O and o 243 Symbols, Christoffel of first kind 396 Symbols, Christoffel of second kind 396 Symmetric bilinear form 214 Symmetric integral equation 835 Symmetric kernel 825 829 Symmetric linear programming problem 1013 Symmetric matrix 168 Symmetric multilinear form 215 Symmetric operator 207 Symmetric operator, nonnegative 207 Symmetric operator, nonpositive 207 Symmetric polyhedral angles 61 Symmetric random variable 1041 Symmetries, differential equations 716 Symmetries, nonclassical 733 Symmetries, nonlinear second-order equations 719 Symmetry 422 Symmetry principle 426 Symmetry reductions, based on generalized Symmetry reductions, separation of variables 712 Symmetry reductions, classical method 732 Symmetry reductions, direct method 708 Symmetry reductions, nonclassical method 732 747 System incomplete of eigenfunctions 836 System, algebraic equations, linear 197 System, characteristic 553 System, characteristic values 836 System, Clairaut 1238 System, conservation laws 780 System, eigenfunctions 836 System, eigenfunctions, complete 836 System, Ermakov generalized 1240 System, first-order linear homogeneous ODEs 528 529 System, first-order ordinary differential equations 1227 System, Fredholm integral equations of second kind 854 System, general form, autonomous 1238
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