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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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Commuting matrices 169 Compact subgroup 229 Compatibility conditions for PDEs 738 740 742 744 Compatibility conditions for systems of linear equations 757 Compatibility conditions of initial and boundary conditions 607 609 Compatible size of matrices 169 Complementary error function, xxx 939 958 Complementary event 1031 Complementary modulus 971 Complete cubic equation 159 Complete elliptic integral 969 Complete elliptic integral, first kind 969 Complete elliptic integral, second kind 969 Complete equation of plane see “General equation of plane” Complete group of events 1031 Complete group of incompatible events 1032 Complete integral 570 Complete space 196 Complete statistic 1090 Complete system of eigenfunctions 836 Completely integrable 773 Completely reducible representation of group 231 Complex conjugate matrix 170 Complex Euclidean space 195 Complex linear space 188 Complex number 399 Complex number, argument 400 Complex number, conjugate 399 Complex number, exponential form 405 Complex number, geometric interpretation 399 Complex number, modulus 400 Complex number, root 399 Complex number, trigonometric form 400 Complex numbers, difference 399 Complex numbers, equal 399 Complex numbers, product 399 Complex numbers, quotient 399 Complex numbers, sum 399 Complex plane 401 Complex plane, domain 401 Complex plane, extended 402 Complex separation of variables 679 Complex stochastic processes 1073 Components, metric tensor 1195 Composite function 237 265 Composite hypothesis 1094 Composite number 3 composition 225 Composition law 225 Compound percentage 7 Concave function 245 Condition initial homogeneous 591 Condition invariance 720 732 Condition invariant surface 732 Condition, boundary 484 591 592 Condition, boundary of first kind 484 Condition, boundary of second kind 485 Condition, boundary of third kind 486 Condition, first-order necessary for extremum 994 Condition, Holder 310 430 Condition, Jacobi 998 1000 1004 1007 Condition, Jacobi, strengthened 1000 1004 1007 Condition, jump 561 Condition, Lax 792 Condition, Legendre 998 999 1004 1007 Condition, Legendre, strengthened 999 1004 1007 Condition, line and plane to be parallel 140 Condition, line and plane to be perpendicular 140 Condition, line to be entirely contained in plane 140 Condition, Lipschitz 248 310 313 543 Condition, necessary of extremum 269 Condition, planes to be parallel 138 Condition, planes to be perpendicular 138 Condition, planes to coincide 138 Condition, stability for generalized solution 568 Condition, straight lines to be parallel on plane 96 Condition, straight lines to be perpendicular on plane 95 Condition, straight lines to coincide on plane 96 Condition, three points to be collinear 93 Condition, transversality 577 Condition, two lines in space to meet 143 Condition, two lines to be parallel in space 135 Condition, two lines to be perpendicular in space 136 Condition, two planes to be parallel 138 Condition, two planes to be perpendicular 138 Condition, unitarity 206 Condition, vectors to be parallel 122 Condition, vectors to be perpendicular 122 Condition, Weierstrass 998 Conditional convergence 342 Conditional cumulative distribution function 1062 Conditional distribution 1062 Conditional expectation 1063 1066 Conditional extremum of function 271 Conditional minimum 270 Conditional probability 1035 Conditionally convergent series 342 Conditions, Cauchy — Riemann 402 Conditions, compatibility for PDEs 738 740 742 744 Conditions, compatibility for systems of linear equations 757 Conditions, compatibility of initial and boundary conditions 607 609 Conditions, d'Alembert — Euler 402 Conditions, Dirichlet 357 Conditions, evolutionary 792 Conditions, existence of extremum 258 Conditions, extremum of function of two variables 269 Conditions, radiation 1290 Conditions, Sommerfeld 1290 1291 Conditions, sufficient of extremum 269 Conditions, transversality 1001 Conditions, Weierstrass — Erdmann 997 999 Cone 67 68 145 Cone, asymptotic 144 Cone, frustum 68 Cone, right circular 68 145 Confidence boundary 1081 Confidence interval 1093 Confidence level 1093 Conformal mapping 419 Congruence transformation 182 Congruent matrices 182 Congruent polyhedral angles 61 Congruent transformation 182 Conic point 391 Conic point of surface 391 Conical coordinates 1202 Conical surface 67 Conjugate complex number 399 Conjugate diameters 151 Conjugate diameters of ellipse 100 Conjugate diameters of hyperbola 104 Conjugate element of group 231 Conjugate matrix 170 Conjugate point 998 1000 1004 1007 Conjunctive matrices 183 Conjunctive transformation 183 Conservation law 564 766 996 Conservation law at discontinuity 561 Conservation law for PDEs 766 Consistency condition for general linear system 198 Consistency of estimator 1089 Consistent system of linear algebraic equations 197 Constant, Euler, xxx 944 949 958 Constant, Holder 310 Constant, separation 678 Constrained maximum 270 Constrained minimum 270 Constraint 270 Constraint, differential 737 738 1009 1010 Constraint, differential, first-order 739 Constraint, differential, secod-order 744 Constraint, isoperimetric 1002 Contact transformation for ordinary differential equations 468 Contact transformation for partial differential equations 660 Continuation, direct analytic 418 Continuity equation 784 Continuity theorem for characteristic functions 1067 Continuous bivariate random variable 1059 Continuous curve in space 123 Continuous distributions 1051 Continuous function 243 Continuous function of bounded variation 249 Continuous point group 730 Continuous probability distribution, mode 1045 Continuous random variable 1040 1064 Continuous random variable, expectation 1042 Continuous subgroups 228 Continuous surface in space 123 Contraction ratio 403 Control 1010 Controlled process, admissible 1010 Convergence criteria infinite products 347 Convergence criteria, arbitrary series 341 Convergence criteria, series with positive terms 338 Convergence criterion, Abel 341 Convergence criterion, Abel — Dini 341 Convergence criterion, Bertrand 340 Convergence criterion, Bugaev 341 Convergence criterion, D'Alembert 338 Convergence criterion, Dini 341 Convergence criterion, Dirichlet 342 Convergence criterion, Dirichlet — Jordan 358 361 Convergence criterion, Ermakov 340 Convergence criterion, Gauss 339 Convergence criterion, generalized Ermakov 340 Convergence criterion, Kummer 340 Convergence criterion, Lipschitz 358 Convergence criterion, Lobachevsky 341 Convergence criterion, Maclaurin — Cauchy 339 Convergence criterion, Raabe 339 Convergence criterion, Sapogov 340 Convergence criterion, Weierstrass 349 Convergence domain of series 348 Convergence in distribution 1069 Convergence in mean 1068 Convergence in probability 1068 Convergence radius of power series 350 411 Convergence theorem, collocation method 524 Convergence with probability 1 1068 Convergence, almost sure 1068 Convergence, mean-square 315 Convergence, nonuniform 249 Convergence, pointwise 249 Convergence, uniform 249 Convergence, weak 1069 Convergent infinite products 346 Convergent sequence 237 238 Convergent Series 337 338 Convex function 245 Convex polygon 51 Convex polyhedron 61 Convex programming 1027 Convolution theorem 437 444 Convolution theorem, Fourier transform 444 Convolution theorem, Laplace transform 437 Convolution-type equation 825 829 Coordinate axes in space 114 Coordinate axes on plane 78 Coordinate functions 847 851 Coordinate net 387 Coordinate of point on axis 77 Coordinate space 188 Coordinate system in space 114 Coordinate system, affine 190 Coordinate system, left rectangular Cartesian 79 Coordinate system, oblique Cartesian 79 Coordinate system, on axis 77 Coordinate system, on plane 78 Coordinate system, polar 80 Coordinate system, rectangular Cartesian 78 114 Coordinate system, right rectangular Cartesian 79 Coordinate vectors 388 Coordinates, bicylindrical 326 1204 Coordinates, bipolar 1204 Coordinates, Cartesian in plane 79 Coordinates, Cartesian in space 115 Coordinates, center of mass of body 327 Coordinates, center of mass of flat plate 324 Coordinates, conical 1202 Coordinates, current 84 Coordinates, curvilinear 387 Coordinates, cylindrical, xxxi 118 326 1198 Coordinates, element 188 189 Coordinates, ellipse canonical 98 Coordinates, elliptic 1202 Coordinates, elliptic cylinder 1202 Coordinates, first prolongation 718 Coordinates, Gaussian 387 Coordinates, general orthogonal curvilinear 1196 Coordinates, hyperbola canonical 101 Coordinates, line 77 Coordinates, oblate ellipsoid of revolution 1200 Coordinates, orthogonal 1196 Coordinates, parabola canonical 104 Coordinates, parabolic 1203 Coordinates, parabolic cylinder 1203 Coordinates, plane 78 Coordinates, point 79 115 Coordinates, polar 80 1198 Coordinates, second prolongation 718 Coordinates, spherical, xxxi 119 326 1199 Coordinates, toroidal 326 1205 Coplanar vectors 113 Correlated random variables 1061 Correlation, function 1072 Correlation, matrix 1066 Correlation, random variables 1061 Correlation, sample 1104 Correlation, two random variables 1061 Correspondence, isometric 395 Cosecant, xxx 24 Coset 227 Coset, left 227 Coset, right 227 Cosine 24 25 Cosine integral 942 Cost, reduced 1015 Cotangent, xxx 24 26 Countable set 3 Counterexample 17 Covariance 1060 1061 Covariance of two random variables 1061 Covariance, matrix 1065 Cramer rule 199 Cramer — Rao efficient unbiased estimator 1089 Cramer — Rao inequality 1089 Criterion, Cauchy convergence for series 339 Criterion, Dini convergence for series 341 Criterion, Dirichlet convergence 342 350 Criterion, Dirichlet — Jordan convergence for Fourier series 358 361 Criterion, Ermakov convergence for series 340 Criterion, first comparison 338 Criterion, Gauss convergence for series 339 Criterion, Kummer convergence for series 340 Criterion, Leibnitz convergence for series 341 Criterion, Lipschitz convergence for series 358 361 Criterion, Lobachevsky convergence for series 341 Criterion, Maclaurin — Cauchy convergence for series 339 Criterion, Routh — Hurwitz 167 Criterion, Sapogov convergence for series 340
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