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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
Differential equation, Schrodinger, linear 1276 Differential equation, Schrodinger, nonlinear 759 1309 Differential equation, separable 456 1207 Differential equation, separated 456 Differential equation, sine — Gordon 1314 Differential equation, sinh — Gordon 1314 Differential equation, steady transonic gas flow 1324 Differential equation, telegraph 1284 Differential equation, telegraph, generalized 626 Differential equation, thermal boundary layer 1276 Differential equation, transonic gas flow 1324 Differential equation, ultrahyperbolic 590 Differential equation, vibration of string 1278 Differential equation, vibration with axial symmetry 1282 Differential equation, vibration with central symmetry 1283 Differential equation, wave 585 1278 Differential equation, wave, nonlinear 723 1312—1317 Differential equation, wave, three-dimensional 618 Differential equation, wave, two-dimensional 618 Differential equation, Whittaker 960 Differential geometry 367 Differential operator, linear 591 592 Differential operator, total 740 742 Differential operators of field theory 272 Differential substitution 666 Differential, higher-order 255 Differentiation 266 Differentiation method for PDEs 700 Differentiation of implicit function 266 Differentiation of stochastic process 1073 Differentiation, rules 253 Digamma function 944 949 Dihedral angle 60 Dihedral angle, edge 60 Dihedral angle, face 60 Dilatation ratio 403 Dimension of affine space 190 Dimension of linear space 189 Dimension of matrix 167 Dimension of representation 230 Dini convergence criterion for series 341 Dini formula 429 Dini integral 1287 Diocles cissoid 372 Dirac delta function 599 Direct analytic continuation 418 Direct method of symmetry reductions 708 Direct scattering problem 760 Direct sum of subspaces 191 Direct sum of two matrices 175 Directed segment 77 Direction coefficients of straight line 131 Direction cosine of segment 116 Direction, principal of second-order curve 109 Directional derivative 267 268 Directrix 65 67 Directrix of ellipse 99 Directrix of hyperbola 102 Directrix of parabola 105 Dirichlet conditions 357 Dirichlet convergence criteria 341 342 Dirichlet criterion of uniform convergence of functional series 350 Dirichlet problem 427 428 Dirichlet problem, for elliptic equations 593 1330 Dirichlet theorem 295 358 Dirichlet theorem, representation of function by Fourier series 357 Dirichlet — Jordan convergence criterion for Fouri series 358 361 Dirichlet — Mehler integral 963 Discontinuity, conservation law 561 Discontinuous solutions of quasilinear equations 558 Discrete bivariate random variable 1058 Discrete probability distribution 1045 Discrete probability space 1033 Discrete random variable 1039 1064 Discrete random variable, expectation 1042 1063 Discrete subgroups 228 Discriminant curve 378 Discriminant of algebraic equation 163 Discriminant, large 108 Discriminant, small 108 Disk 56 97 Dispersion equation 532 596 Distance between elements 193 195 Distance between lines in space 142 Distance between parallel lines 96 Distance between points on axis 78 Distance between points on plane 81 Distance between two parallel planes 142 Distance from point to line in space 142 Distance from point to plane 141 Distance from point to straight line 93 Distance shortest 70 Distribution function, empirical 1084 Distribution function, joint 1064 Distribution function, marginal 1064 Distribution function, multivariate random variable 1064 Distribution function, two-dimensional random vector 1057 Distribution polygon 1085 Distribution, bimodal 1045 Distribution, binomial 1037 1047 Distribution, Cauchy 1054 Distribution, chi-square 1054 Distribution, conditional 1062 Distribution, continuous 1051 Distribution, convergence 1069 Distribution, exponential 1052 Distribution, Fisher — Snedecor 1086 Distribution, geometric 1048 Distribution, hypergeometric 1049 Distribution, Kolmogorov 1086 Distribution, log-normal 1042 Distribution, multimodal 1045 Distribution, negative binomial 1050 Distribution, normal 1053 Distribution, Poisson 1050 Distribution, Student 1056 Distribution, uniform 1051 Distribution, unimodal 1045 Divergence 334 Divergence theorem 334 Divergent infinite products 346 Divergent integral 301 Divergent series 337 Divisibility tests 3 Division of asymptotic series 364 Division of asymptotic series of polynomials 155 Division of asymptotic series of segment in given ratio 82 Divisor, greatest common 4 Domain, boundary 401 Domain, boundary of attraction of fixed point 877 Domain, boundary of function 236 Domain, boundary, closed 402 Domain, boundary, formula for calculation of volume 327 Domain, boundary, multiply connected 409 Domain, boundary, on complex plane 401 Domain, boundary, simply connected 409 Double factorial 10 Double integral 317 Double integral, change of variables 321 Double integral, estimation theorem 318 Double integral, geometric applications 321 Double integral, geometric meaning 317 Double integral, mean value theorem 318 Double integral, physical applications 321 Double integral, properties 317 Double point 371 Dual linear programming problem 1017 Duality theorem, second 1018 Duffing equation 501 Duhamel integral 516 Duhamel principle 646 Duhamel principle, first 646 Duhamel principle, second 648 Dynamic programming 1027 Eccentricity of ellipse 98 Eccentricity of hyperbola 102 Edge of dihedral angle 60 Edge of polygon 51 Edge of polyhedral angle 61 Edge of polyhedron 61 Edge of trihedral angle 60 Efficient unbiased estimator 1089 Eigenfunction 482 604 605 829 Eigenfunction integral equation 835 Eigenfunctions, Fredholm integral equation 829 Eigenfunctions, incomplete system 836 Eigenfunctions, system 836 Eigenvalue 183 482 605 829 Eigenvalue problem 604 Eigenvalue problem, for linear ordinary differential equations 482 Eigenvalues, algebraic multiplicity 209 Eigenvalues, geometric multiplicity 209 Eigenvalues, linear operator 211 209 Eigenvalues, matrix 183 Eigenvalues, operator 209 Eigenvector, linear operator 209 Eigenvector, matrix 184 Elastic rods, transverse vibration 1294 Electronic mathematical resources 1451 Element inverse 225 Element, admissible 1009 Element, conjugate of group 231 Element, coordinates 188 189 Element, length 193 Element, neutral 225 Element, norm 193 Element, probability 1040 Element, surface linear 390 Elementary event 1031 Elementary events space 1031 Elementary functions 19—41 Elementary geometry 43 Elementary matrices 181 Elementary symmetric functions 163 Elementary transformation of matrix 180 199 Elementary transformation of system of linear equations 199 Elements of linear space 187 Elements, linearly dependent 188 Elements, linearly independent 188 Elements, orthogonal 193 ellipse 98 Ellipse in polar coordinate system 101 Ellipse, canonical equation 98 Ellipse, center 99 Ellipse, conjugate diameters 100 Ellipse, diameter 100 Ellipse, directrix 99 Ellipse, eccentricity 98 Ellipse, focal axis 99 Ellipse, focal distance 98 Ellipse, focal parameter 98 Ellipse, focal property 99 Ellipse, focus-directrix property 100 Ellipse, gorge 145 Ellipse, left directrix 99 Ellipse, left focus 99 Ellipse, linear eccentricity 98 Ellipse, minor axis 98 Ellipse, numerical eccentricity 98 Ellipse, optical property 100 Ellipse, parameter 98 Ellipse, right directrix 99 Ellipse, right focus 99 Ellipse, semimajor axis 98 Ellipse, semiminor axis 98 Ellipse, throat 145 Ellipse, vertex 99 Ellipsoid 143 224 Ellipsoid, imaginary 224 Ellipsoid, right 145 Ellipsoid, scalene 144 Ellipsoid, semiaxis 143 Ellipsoid, triaxial 144 Elliptic coordinates 1202 Elliptic equation 585 590 642 972 1284 Elliptic equation, canonical form 588 Elliptic equation, first boundary value problem 633 643 644 Elliptic equation, fundamental solution 642 Elliptic equation, mixed boundary value problem 644 Elliptic equation, second boundary value problem 633 643 644 Elliptic equation, third boundary value problem 643 644 Elliptic equations, boundary value problems 631 643 644 Elliptic equations, linear 588 609—611 631—633 637 1284—1298 Elliptic equations, nonlinear 653 654 318—1334 Elliptic integral 969 Elliptic integral incomplete 970 Elliptic integral, complete 969 Elliptic integral, first kind 970 Elliptic integral, second kind 970 Elliptic integral, third kind 971 Elliptic modulus 971 Elliptic paraboloid 145 Elliptic point 394 Emden — Fowler equation 1223 Empirical distribution, function 1084 Empirical distribution, variance 1088 Energy conservation law 996 Entire axis 825 826 841 Entire function 414 Entry, pivot 1016 Envelope 377 Envelope of family of curves 377 Equal complex numbers 399 Equal matrices 168 Equal polynomials 155 Equation incomplete of plane 124 Equation information theory, basic 1440 Equation intercept of plane 125 Equation intercept-intercept of straight line 91 Equation involutory functions 1423 Equation with difference kernel integral 825 829 Equation with quadratic nonlinearity 865 Equation with weak singularity of second kind 829 Equation, Abel differential, first kind 462 Equation, Abel differential, first kind, canonical form 463 Equation, Abel differential, second kind 464 Equation, Abel differential, second kind, canonical form 465 Equation, Abel functional 914 Equation, Abel integral 1385 Equation, Abel integral, generalized 806 1386 Equation, Abel integral, second kind 1392 Equation, Abel integral, second kind, generalized 1393 Equation, Airy 955 Equation, algebraic 162 Equation, algebraic, binomial 161 Equation, algebraic, fourth — degree 159 Equation, algebraic, linear 157 Equation, algebraic, nth — degree 162 Equation, algebraic, quadratic 158 Equation, algebraic, reciprocal 160 161 Equation, algebraic, reciprocal, modified 160 Equation, autonomous 1207 1223 1225 Equation, axisymmetric steady hydrodynamic boundary layer 712 Equation, Babbage 917 1416 1423 Equation, Bernoulli 1207 Equation, Bessel 1216 Equation, Bessel, modified 1216 Equation, biharmonic 1297 Equation, biharmonic, homogeneous 1297 Equation, biharmonic, nonhomogeneous 1298
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