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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
Quadratic mean 13 Quadratic mean of functions 297 Quadratic nonlinearity 865 Quadratic programming 1027 Quadrature formula 808 860 Quadrature method, for integral equations 852 861 870 Quadrature nodes 808 Quadric invariant 148 Quadric surfaces 143 Quadric, canonical equations 143 Quadric, canonical form 143 148 Quadric, classification 148 Quadric, general equation 148 Quadric, general theory 148 Quadric, semi-invariant 148 Quadrilaterals 52 quartile 1045 Quasidiagonal canonical form of matrix 182 Quasilinear equations in conservative form 567 Quasilinear partial differential equations 553 Quotient 155 Quotient group 227 Quotient of complex numbers 399 Raabe convergence criterion for series 339 Radian 24 Radiation conditions 1290 1291 Radical 8 Radius of convergence 351 Radius of convergence of power series 411 Radius of curvature 376 384 Radius of torsion 385 Radius, focal left 99 102 Radius, polar 80 Ramification point 414 Random event 1031 1032 Random sampling with replacement 1034 Random sampling without replacement 1033 Random sequence 1072 Random variable 1039 1057 Random variable initial moment 1060 1065 Random variable, bivariate 1060 Random variable, central moment 1065 Random variable, continuous 1040 1042 1064 Random variable, continuous bivariate 1059 Random variable, discrete 1039 1042 1064 Random variable, discrete bivariate 1058 Random variable, expected value 1042 Random variable, symmetric 1041 Random variable, symmetric about expected value 1041 Random variable, variance 1044 Random variables independent 1060 1067 Random variables, correlated 1061 Random variables, joint distribution function 1057 Random variables, uncorrelated 1061 Random vector 1057 Range of function 236 Range of linear operator 205 Range of mapping 226 Range, sample 1082 Rank of bilinear form 215 Rank of linear operator 206 Rank of matrix 178 Rank of quadratic form 216 Rankine — Hugoniot jump conditions 561 568 790 791 Rarefaction wave 559 785 1253 Rate, false negative 1096 Rate, false positive 1095 Ratio, common 11 Ratio, contraction 403 Ratio, dilatation 403 Ratio, likelihood 1097 Ratio, Romanovskii 1101 Ratio, Student 1090 Rational function 276 Rational numbers 4 5 Rational polynomial function 276 Rayleigh — Ritz principle 484 513 Real axis 235 401 Real axis of hyperbola 101 Real Euclidean space 192 Real linear space 188 Real matrix 171 Real number 3 4 Real number, multiplicative inverse 6 Real number, reciprocal 6 Real part 399 Real semiaxes of hyperbola 102 Real semiaxes of one-sheeted hyperboloid 144 Real semiaxes of two-sheeted hyperboloid 144 Real-valued function of real variable 236 Reciprocal (algebraic) equation 160 161 Reciprocal functional equation 919 Reciprocal of real number 6 Rectangle rule 315 808 Rectangle rule, for computation of integrals 315 Rectangular Cartesian coordinate system 78 114 Rectangular Cartesian coordinates on plane 78 Rectangular matrix, minor 177 Rectangular parallelepiped 62 Rectangular spherical triangle 72 Rectification, point 382 Rectifying plane 382 Reduced cost 1015 Reducible operator 205 Reducible representation 230 Reduction formulas 1145 Reduction formulas, for trigonometric functions 27 Reduction of central second-order curves to canonical form 110 Reduction of noncentral second-order curves to canonical form 110 Reduction of quadratic form to sum of squares 219 Reduction of square matrix to diagonal form 184 Reduction of square matrix to triangular form 184 Reflectance 760 Reflection coefficient 760 Reflection factor 760 Regime, blow-up 1303 1304 Regime, critical 1095 Regime, feasible 1012 Regression 1063 1066 Regression analysis 1105 Regression coefficient 1063 Regression function 1063 1066 Regression, mean-square 1063 1066 Regula falsi method 262 Regular arc 379 Regular extremal 995 Regular part of Laurent series 412 Regular point 367 379 387 Regular point of extremal 995 Regular point of generalized solution 580 Regular point of plane curve 367 Regular point of space curve 379 Regular polygon 55 Regular polygon, center 55 Regular polyhedron 65 Regular prism 62 Regular pyramid 64 Regular triangle 43 51 Regular value 829 834 Regularization methods for integral equations 827 Relation, Parseval for Fourier cosine transform 445 Relation, Parseval for Fourier sine transform 446 Relation, Parseval for Hankel transform 447 Relative extrema 991 Relative frequencies 1083 Relative frequency histogram 1086 Relative frequency of event 1083 Relative frequency polygon 1085 Remainder in Taylor formula in form of Cauchy 257 Remainder in Taylor formula in form of Lagrange 257 Remainder in Taylor formula in form of Peano 257 Remainder in Taylor formula in form of Schlomilch and Roche 257 Remainder in Taylor formula in integral form 257 Remainder of functional series 349 Remainder of series 337 Removable singularity 413 Renewal equation 1395 Representation basis 230 Representation invariant 230 Representation of group, completely reducible 231 Representation of quadratic form canonical 217 Representation of vector in terms of basis 189 Representation space 230 Representation, dimension 230 Representation, irreducible 231 Representation, reducible 230 Representation, triangular 201 Residual 847 1066 Residual standard deviation 1063 Residual variance 1066 1108 Residue 415 435 Residue, logarithmic 416 Resolvent 810 823 829 833 Resolvent of symmetric kernel 839 Resonance, Painleve test 749 Rhombus 53 Riccati difference equation 875 918 1428 1429 Riccati differential equation 460 Riccati differential equation, for system of PDEs 785 Riccati differential equation, general 461 462 1209 1210 Riccati differential equation, polynomial solutions 460 Riccati differential equation, reduction to canonical form 460 Riccati differential equation, reduction to second-order linear equation 461 Riccati differential equation, special 1208 Riemann function 628 629 783 Riemann integral 286 Riemann invariant 783 786 787 Riemann localization principle 358 Riemann problem 785 Riemann property 294 Riemann sum 286 Riemann Theorem 419 Riemann wave 782 Riemann — Schwarz theorem 426 Riemannian space 395 Right arm of hyperbola 101 Right circular cone 68 145 Right circular cylinder 66 Right coset 227 Right cylinder 66 Right directrix of ellipse 99 Right directrix of hyperbola 102 Right ellipsoid 145 Right focal radius 99 102 Right focus of ellipse 99 Right focus of hyperbola 102 Right half-plane 79 Right inverse matrix 171 Right prism 62 Right rectangular Cartesian coordinate system 79 right triangle 43 50 Right triangle, leg 50 Right-angled triangles 43 50 Right-hand limit 240 Right-hand side of integral equation 810 Right-handed trihedral 121 Rolle theorem 254 Romanovskii ratio 1101 Romanovskii statistic 1101 Romanovskii test 1101 Root mean square 13 Root of complex number 399 Root of equation 162 Root of multiplicity m 162 Root of operator 207 Root-finding algorithms for continuous functions 260 Root-mean-square deviation 1045 Rotation of axes 79 Rotation transformation 656 Rouche theorem 413 Round cylinder 66 Round cylinder, segment 67 Routh — Hurwitz criterion 167 Row expansion of determinant 176 Row vectors 167 Row vectors, linear combination 171 Row vectors, linearly dependent 171 Row vectors, linearly independent 171 Row, pivot 1016 Rows, basic 165 Rule of closing chain of vectors 113 Rule, Cramer 199 Rule, Lagrange multiplier 1002 Rule, parallelogram 113 Rule, rectangle 315 808 Rule, sigma 1054 Rule, Simpson 315 808 Rule, trapezoidal 315 808 Rule, triangle 113 176 Rule, Whitham, “equal areas” 562 Ruled surface 146 Rules, Neper 75 Rulings 146 Rulings of ruled surfaces 146 Runge — Kutta method 472 512 Saddle 536 Saddle point 394 Saddle point of payoff matrix 1025 Sample 1082 Sample, asymmetry coefficient 1088 Sample, central moment 1087 Sample, correlation 1104 Sample, distribution function 1084 Sample, excess coefficient 1088 Sample, function 1072 Sample, mean 1087 Sample, mean square deviation 1088 Sample, moment 1087 Sample, range 1082 Sample, size 1082 Sample, space 1031 Sample, variance 1088 Sample, variance adjusted 1088 Sampling, random with replacement 1034 Sampling, random without replacement 1033 Sapogov convergence criterion for series 340 Sarrus scheme 176 scalar 187 Scalar product 192 Scalar product of vectors 120 Scalar square 120 Scalar triple product of vectors 123 Scale segment 77 Scalene ellipsoid 144 Scalene triangle 43 Scaling transformation 656 676 923 Scattering data 761 Scheme, Bernoulli 1037 Scheme, Cole — Kevorkian 504 Scheme, Horner 156 Scheme, Sarrus 176 Scheme, Van der Pol — Krylov — Bogolyubov 503 Schlicht mapping 402 Schlomilch equation 1400 Schroder — Koenigs functional equation 911 Schrodinger equation with cubic nonlinearity 1309 Schrodinger equation with power-law nonlinearity 1310 Schrodinger equation, linear 1276 Schrodinger equation, nonlinear of general form 1311 Schwarz analytic continuation principle 426
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