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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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Nonorthogonal polynomials 988 Nonparametric hypothesis 1094 Nonpositive Hermitian operator 207 Nonpositive quadratic form 216 Nonpositive symmetric operator 207 Nonseparated by straight line points 97 Nonsingular extremal 995 Nonsingular matrix 171 Nonuniform convergence of functions 249 Norm 314 840 Norm of element 193 Norm of linear operator 204 normal 91 252 368 380 389 Normal curvature 392 Normal curvature vector 392 Normal direction 389 Normal distribution 1053 Normal form 473 Normal form of matrix 181 Normal fundamental system of solutions of homogeneous system 198 Normal hyperbolic equation 590 Normal matrix 171 Normal operator 207 Normal plane 380 382 Normal representation of quadratic form 218 Normal section 392 Normal subgroup 227 Normal system of method of least squares 850 Normal vector 124 Normal, positive sense 369 Normal, principal 381 Normal, to quadric 152 Normal, to second-order curve 111 Normal, to surface 153 Normalized cross-correlation function 1073 Normalized equation of plane 126 Normalized equation of straight line 91 Normed Euclidean space 193 Normed unitary space 195 Noteworthy limit, second 241 Null hypothesis 1094 Null matrix 167 Null subspace 190 Number axis 77 Number integer 3 Number of real roots of polynomial 165 Number, absolute value 8 Number, bernoulli 938 Number, complex 399 Number, complex conjugate 399 Number, composite 3 Number, e, base of natural logarithms, xxxi 9 22 23 Number, Euler 939 Number, even 3 Number, irrational 4 5 Number, modulus 8 Number, natural 3 Number, odd 3 Number, prime 3 Number, pure imaginary 399 Number, rational 4 5 Number, real 3 4 Number, “pi” Numerical eccentricity of ellipse 98 Numerical eccentricity of hyperbola 102 Numerical integration of differential equations 471 Numerical sequence 237 Numerical sequence, generating function 1047 Numerical series 337 1118 Numerical sum 1113 Obelisk 63 65 Oblate spheroid 144 Oblique asymptote 242 Oblique Cartesian coordinate system 79 Obtuse triangle 43 Octant 114 Odd function 236 odd number 3 Odd permutation 178 ODE see “Ordinary differential equation” One-dimensional Klein — Gordon equation 618 One-dimensional stochastic process 1072 One-parameter family of curves 377 One-parameter Lie group of point transformations 730 One-parameter solution 724 One-parameter transformation 716 One-sheeted hyperboloid 144 One-sheeted hyperboloid, imaginary semiaxis 144 One-sided derivative 252 One-sided limits 240 One-soliton solution 765 One-to-one mapping 226 Open interval 235 Open model of transportation problem 1020 Operations with asymptotic series 364 Operator 204 Operator infinitesimal 716 717 730 Operator invariant 717 731 Operator inverse 205 Operator, adjoint 206 Operator, bounded 204 Operator, characteristic value 209 Operator, differential, linear 591 592 Operator, differential, total 740 742 Operator, eigenvalue 209 Operator, eigenvector 209 Operator, hermitian 206 207 Operator, Hermitian negative 207 Operator, Hermitian nonnegative 207 Operator, Hermitian nonpositive 207 Operator, Hermitian positive 207 Operator, identity 204 Operator, Laplace, xxxii 272 Operator, linear 204 Operator, linear invertible 205 Operator, normal 207 Operator, opposite 205 Operator, orthogonal 207 Operator, reducible 205 Operator, root 207 Operator, second prolongation 720 Operator, self-adjoint 206 Operator, skew-Hermitian 206 Operator, skew-symmetric 207 Operator, symmetric 207 Operator, symmetric negative 207 Operator, symmetric nonnegative 207 Operator, symmetric nonpositive 207 Operator, symmetric positive 207 Operator, transpose 207 Operator, unitary 206 Operator, zero 204 Operators, commutator 755 Operators, differential of field theory 272 Operators, orthogonality condition 207 Opposite matrix 169 Opposite of real number 6 Optical property of ellipse 100 Optical property of hyperbola 103 Optical property of parabola 105 106 Optimal solution 1012 Optimal strategy 1024 Optimality principle, Bellman 1028 Order of associated element 213 Order of branch point 414 Order of homogeneity 1441 Order of pole 413 Order of zero of function 413 Ordinary differential equation, Abel of first kind 462 Ordinary differential equation, Abel of first kind, canonical form 463 Ordinary differential equation, Abel of second kind 464 Ordinary differential equation, Abel of second kind, canonical form 465 Ordinary differential equation, Airy 955 Ordinary differential equation, asymptotic solutions 477 Ordinary differential equation, autonomous 489 525 1207 1223 1225 Ordinary differential equation, Bernoulli 458 1207 Ordinary differential equation, Bessel 1216 Ordinary differential equation, Bessel, modified 1216 Ordinary differential equation, boundary value problems 480 Ordinary differential equation, Clairaut 467 Ordinary differential equation, Darboux 458 Ordinary differential equation, degenerate hypergeometric 1215 Ordinary differential equation, Duffing 501 Ordinary differential equation, Emden — Fowler 1223 Ordinary differential equation, Ermakov 1224 Ordinary differential equation, Euler 473 520 1216 Ordinary differential equation, exact, first-order 458 Ordinary differential equation, exact, second-order 491 Ordinary differential equation, first boundary value problem 480 Ordinary differential equation, Gaussian hypergeometric 960 1218 Ordinary differential equation, Green function 481 Ordinary differential equation, homogeneous, first-order 456 Ordinary differential equation, homogeneous, first-order, generalized 456 Ordinary differential equation, hypergeometric 960 1218 Ordinary differential equation, hypergeometric, degenerate 1215 Ordinary differential equation, Lagrange 467 Ordinary differential equation, Laplace 520 Ordinary differential equation, Legendre 1217—1219 Ordinary differential equation, Lienard 1225 Ordinary differential equation, linear 472 518 1213 Ordinary differential equation, linear, constant-coefficient 473 514 1213 Ordinary differential equation, linear, first-order 457 1207 Ordinary differential equation, linear, homogeneous 472 1212 Ordinary differential equation, linear, nonhomogeneous 473 Ordinary differential equation, linear, second-order 472 1212 Ordinary differential equation, Mathieu 980 1221 Ordinary differential equation, Mathieu, modified 982 1220 Ordinary differential equation, method of regular expansion in small parameter 470 Ordinary differential equation, method of Taylor series expansion in independent variable 470 Ordinary differential equation, mixed boundary value problem 480 Ordinary differential equation, Riccati 460 Ordinary differential equation, Riccati, general 461 462 1209 1210 Ordinary differential equation, Riccati, special 1208 Ordinary differential equation, second boundary value problem 480 Ordinary differential equation, second-order, linear 467 Ordinary differential equation, second-order, nonlinear 488 Ordinary differential equation, self-adjoint form 481 Ordinary differential equation, separable 456 1207 Ordinary differential equation, separated 456 Ordinary differential equation, third boundary value problem 480 Ordinary differential equation, Whittaker 960 Ordinary differential equations 453—550 1207—1228 Ordinary differential equations, admitting reduction of order 489 525 Ordinary differential equations, asymptotic solutions 522 Ordinary differential equations, boundary value problems 480 481 512 Ordinary differential equations, Cauchy problem 488 524 Ordinary differential equations, existence and uniqueness theorem 488 Ordinary differential equations, first-order 453—472 1207—1212 Ordinary differential equations, homogeneous 490 526 Ordinary differential equations, homogeneous, generalized 490 526 Ordinary differential equations, linear 457 472—488 514—524 1212—1222 Ordinary differential equations, linear of arbitrary order 514 Ordinary differential equations, linear with constant coefficients 514 Ordinary differential equations, linear, homogeneous 514 518 Ordinary differential equations, linear, nonhomogeneous 515 519 Ordinary differential equations, nonlinear 453—472 488—513 524—527 1223—1228 Ordinary differential equations, not solved for derivative 465 Ordinary differential equations, numerical methods 511 Ordinary differential equations, Painleve 495 Ordinary differential equations, second-order 472—514 1212—1228 Ordinary differential equations, solved for derivative 488 Ordinary differential equations, systems, nonlinear 542—550 Ordinate axis 78 Ordinate of point 79 115 Oriented area 83 Oriented surface 333 Origin in space 114 Origin of affine coordinate system 190 Origin on axis 77 Origin on plane 78 Orthocenter of triangle 46 Orthogonal complement of subspace 194 Orthogonal coordinates 1194 Orthogonal curvilinear systems of coordinate 1195 Orthogonal elements 193 Orthogonal elements of unitary space 195 Orthogonal group 229 Orthogonal matrix 170 Orthogonal operator 207 Orthogonal polynomials 982 Orthogonal projection 197 Orthogonal trajectory 379 Orthogonal transformation of matrix 182 Orthogonality condition for operators 207 Orthogonalization, Gram — Schmidt 194 Orthonormal basis in finite-dimensional Euclidean Orthonormal basis space 193 Orthonormal basis in finite-dimensional unitary space 195 Osculating circle 375 Osculating plane 381 Osculation, point 372 Ostrogradsky — Gauss theorem 334 Overdetermined systems of PDEs 770 771 Pade approximants 493 Painleve equations 495 Painleve test for nonlinear PDEs 748 Painleve transcendent 495 Painleve transcendent, fifth 499 Painleve transcendent, first 496 Painleve transcendent, fourth 498 Painleve transcendent, second 496 Painleve transcendent, sixth 499 Painleve transcendent, third 497 Painleve transcendental functions 495 Pair, Lax 755 parabola 104 Parabola in polar coordinates 107 Parabola with vertical axis 106 Parabola, canonical equation 104 Parabola, diameters 106 Parabola, directrix 105 Parabola, focal distance 105 Parabola, focal properties 105 Parabola, focal radius 105 Parabola, focus 105 Parabola, focus-directrix property 105 Parabola, optical property 105 106 Parabola, vertex 105 Parabolic coordinates 1203 Parabolic cylinder coordinates 1203 Parabolic cylinder function 967 Parabolic equation 585 590 Parabolic equation in narrow sense 590 Parabolic equation, boundary value problems 645 Parabolic equation, canonical form 586 Parabolic equation, Cauchy problem 615 Parabolic equation, linear 586 615—616 618—622 634 635 646 648 1267—1278 Parabolic equation, nonlinear 653 654 1301—1311 Parabolic point 394 Parabolic type of second-order curves 108 Paraboloid 145 224 Paraboloid of revolution 146 Paraboloid, elliptic 145 Paraboloid, hyperbolic 146 Paraboloidal cylinder 225 Parallel lines 59 Parallel planes 59 Parallel translation 220 Parallel translation of axes 79 Parallel vectors 113 Parallelepiped 61 62
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