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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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General solution of linear hyperbolic equations 600—602 General solution of linear ODEs 472 514 518 General solution of ODEs 453 488 General square system of linear algebraic equations 199 General system of m linear algebraic equations with n unknown quantities 203 Generalized Abel equation 806 Generalized Abel equation of second kind 1393 Generalized Burgers — Korteweg — de Vries equation 709 Generalized Cauchy problem 627 Generalized Chebyshev inequalities 15 Generalized classical method of characteristics 582 Generalized Dirichlet problem 428 Generalized Ermakov criterion of convergence of series 340 Generalized Ermakov system 1242 Generalized Gauss equation 1445 Generalized homogeneous equation 490 526 1210 1224 Generalized Jensen equation 1449 Generalized Jensen inequalities 246 Generalized Laguerre polynomials 983 Generalized permutation matrix 168 Generalized reciprocal equation 160 Generalized self-similar solution 677 Generalized separable solution 681 682 Generalized separation of variables 681 Generalized similarity reduction 746 Generalized solution 563 Generalized solution of first-order PDE 563 568 Generalized solution, Hopf formula 565 Generalized solution, regular point 580 Generalized solution, singular point 580 Generalized solution, stable 569 Generalized telegraph equation 626 Generalized traveling-wave solution 697 Generalized triangle inequality 343 Generalized variance of n-dimensional distribution 1065 Generalized viscosity solutions 579 580 Generating function 815 1047 Generating function of numerical sequence 1047 Generator 65 67 Generator infinitesimal 717 Generator, group 717 730 Generic term of sequence 237 Generic term of series 337 Geodesic arc 70 Geodesic curvature 392 Geodesic curvature vector 392 Geometric definition of nondegenerate second-order curve 111 Geometric distribution 1048 Geometric mean 13 Geometric mean of functions 297 Geometric multiplicity of eigenvalue 209 Geometric probability 1034 Geometric programming 1027 Geometric progression 11 Geometric sequence 11 Geometric series 11 Geometry intrinsic of surface 391 Geometry, analytic 77 Geometry, differential 367 Geometry, spherical 70 Gergonne point 47 Goodness-of-fit tests 1098 1101 Gorge ellipse 145 Goursat problem 592 629 Gram determinant 193 Gram — Schmidt orthogonalization 194 Graph of function 84 236 Gravitational field potential 328 Great circle 68 70 Great circle, spherical geometry 70 Greatest common divisor 4 Green first identities 335 Green formula 428 Green function 428 623 631 633—637 Green function for elliptic equations 631—634 637 Green function for hyperbolic equations 623—625 636 Green function for linear ordinary differential equation 481 Green function for parabolic equations 618—622 635 Green function in terms of infinite series 639 Green function, admitting incomplete separation of variables 640 Green second identities 335 Green theorem 335 Group analysis of differential equations 716 Group element, character 231 Group generator 717 730 732 Group invariant 731 Group of derivation formulas, second 396 Group of events, complete 1031 Group of incompatible events, complete 1032 Group of leading terms of equation 220 Group of linear transformations 228 Group of mirror symmetry 229 Group of modulo 2 residues 226 Group of orthogonal transformations 229 Group theory 225 Group, abelian 226 Group, automorphism 227 Group, commutative 226 Group, completely reducible representation 231 Group, conjugate element 231 Group, continuous point 730 Group, equivalent representations 230 Group, faithful representation 230 Group, Lie 730 Group, linear representation 230 Group, orthogonal 229 Group, quotient 227 Group, special linear 228 Group, special orthogonal 229 Group, trivial representation 230 Groups, basic properties 225 Groups, cyclic 229 Groups, isomorphic 227 Groups, permutation 226 Groups, unitary 229 Growth exponent 436 Half-plane, left 79 Half-plane, lower 79 Half-plane, right 79 Half-plane, upper 79 Half-side theorem 73 Hamilton operator 272 Hamilton — Jacobi equation 576 Hamiltonian 576 Hankel functions 952 Hankel transform 446 449 1400 Hardy transform 449 Harmonic function 404 Harmonic mean 13 Harmonic mean of functions 297 Harmonic series 339 Hartley transform 449 Heat equation with axial symmetry 1270 Heat equation with central symmetry 1272 Heat equation, linear 585 1267 Heat equation, linear, nonhomogeneous 1268 Heat equation, nonlinear 1318 Heat equation, stationary with nonlinear source 1320 Heat equation, stationary, anisotropic 1323 Heaviside unit step function 618 Helmholtz equation 1289 Hermite functions 986 Hermite polynomials, xxxi 957 958 985 Hermitian matrix 168 Hermitian operator 206 Hermitian operator, negative 207 Hermitian operator, nonnegative 207 Hermitian operator, nonpositive 207 Hermitian operator, positive 207 Heron formula 48 Higher-order derivatives of elementary functions 255 Higher-order linear difference equations 1425 Hilbert boundary value problem 432 Hilbert example 997 Hilbert space 196 Hilbert transform 449 1396 1400 Hilbert — Privalov boundary value problem 432 Hilbert — Schmidt theorem 837 histogram 1086 Histogram, frequency 1086 Histogram, relative frequency 1086 Hodograph transformation for gas dynamic system 784 Hodograph transformation for ODEs 455 Hodograph transformation for PDEs 657 658 Holder condition 310 430 Holder constant 310 Holder exponent 310 Holder inequality 14 297 343 Holder — Jensen inequality 15 Homogeneity, order 1441 Homogeneous boundary condition 591 Homogeneous equations, linear difference 881 885 889 1421 1425 Homogeneous equations, linear difference, constant-coefficient 1409 1422 1426 Homogeneous equations, linear integral 810 829 834 Homogeneous equations, ordinary differential 456 490 526 1207 1224 Homogeneous equations, ordinary differential, generalized 457 490 526 1224 Homogeneous equations, ordinary differential, linear 472 514 Homogeneous equations, partial differential, elliptic 592 Homogeneous equations, partial differential, hyperbolic 592 Homogeneous equations, partial differential, parabolic 591 Homogeneous function 1441 Homogeneous initial condition 591 Homogeneous linear algebraic system 203 Homogeneous linear algebraic system, general solution 203 Homogeneous linear integral equation 810 829 Homogeneous linear ODEs 472 514 Homogeneous linear ODEs of higher-order ODEs 532 Homogeneous Monge — Ampere equation 668 1326 Homogeneous system of linear algebraic equations 197 Homogeneous system of linear ODEs 539 Homogeneous system of linear ODEs, superposition principle 528 539 Homomorphic image 226 Homomorphisms 226 Hopf formula for generalized solution 565 Hopf — Cole transformation 666 1308 Horner scheme 156 Hurwitz functions 893 Hyperbola 101 Hyperbola in polar coordinate system 104 Hyperbola, arm 101 Hyperbola, asymptotes 101 Hyperbola, canonical equation 101 Hyperbola, center 102 Hyperbola, conjugate diameters 104 Hyperbola, diameter 104 Hyperbola, directrix 102 Hyperbola, eccentricity 102 Hyperbola, equilateral 101 Hyperbola, focal axis 101 Hyperbola, focal distance 102 Hyperbola, focal parameter 102 Hyperbola, focal properties 102 Hyperbola, focus 102 Hyperbola, focus-directrix property 103 Hyperbola, imaginary axis 101 Hyperbola, imaginary semiaxis 102 Hyperbola, left arm 101 Hyperbola, left directrix 102 Hyperbola, left focus 102 Hyperbola, linear eccentricity 102 Hyperbola, numerical eccentricity 102 Hyperbola, optical property 103 Hyperbola, parameter 102 Hyperbola, real semiaxes 102 Hyperbola, right arm 101 Hyperbola, right directrix 102 Hyperbola, right focus 102 Hyperbola, vertex 102 Hyperbolic arccosine, xxx Hyperbolic arccotangent, xxx Hyperbolic arcsine, xxx Hyperbolic arctangent, xxx Hyperbolic cosine, xxx 35 Hyperbolic cotangent, xxx 35 Hyperbolic equation, boundary value problems 623 Hyperbolic equation, canonical form 587 Hyperbolic equation, first canonical form 587 Hyperbolic equation, second canonical form 587 Hyperbolic equations 585 590 647 648 742 Hyperbolic equations, Cauchy problem 617 Hyperbolic equations, linear 587 617 623—630 636 647 648 1278—1284 Hyperbolic equations, nonlinear 653 654 1312—1317 Hyperbolic functions 34 Hyperbolic functions integration formulas 38 Hyperbolic functions inverse 39 Hyperbolic functions of half argument 38 Hyperbolic functions of multiple argument 38 Hyperbolic functions, addition formulas 36 Hyperbolic functions, differentiation formulas 38 Hyperbolic functions, expansion in power series 39 Hyperbolic functions, properties 36 Hyperbolic paraboloid 146 Hyperbolic point 394 536 Hyperbolic sine, xxxi 35 Hyperbolic spiral 86 368 Hyperbolic system of PDEs 781 790 Hyperbolic tangent, xxxi 35 Hyperbolic type of second-order curves 108 Hyperboloid 144 224 Hyperboloid of revolution 145 Hyperboloid, one-sheeted 144 Hyperboloid, real semiaxes 144 Hyperboloid, two-sheeted 144 Hypergeometric distribution 1049 Hypergeometric equation 960 1218 Hypergeometric equation, degenerate 1215 Hypergeometric functions 960 Hypergeometric series 960 1218 Hypersurface 220 Hypersurface, center 222 Hypersurface, central 222 Hypersurface, noncentral 224 Hypersurface, semiaxis 223 Hypotenuse 50 72 Hypothesis 1094 Hypothesis, alternative 1094 Hypothesis, composite 1094 Hypothesis, nonparametric 1094 Hypothesis, null 1094 Hypothesis, parametric 1094 Hypothesis, simple 1094 hypothesis, statistical 1094 Identity matrix 168 Identity operator 204 Identity, Abel 902 Identity, Parseval 361 Image, homomorphic 226 Imaginary axis 401 Imaginary axis of hyperbola 101 Imaginary ellipsoid 224 Imaginary part 399 Imaginary semiaxis of hyperbola 102 Imaginary semiaxis of one-sheeted hyperboloid 144 Imaginary semiaxis of two-sheeted hyperboloid 144 Imaginary unit 399 Impossible event 1031 Improper integral 301 Improper integrals involving logarithmic functions 305 Improper integrals involving power functions 304 Improper integrals involving trigonometric functions 305
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