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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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Inverse scattering problem 760 Inverse scattering problem, method 755 Inverse transform 435 Inverse transform, Fourier 443 Inverse transform, Fourier cosine 445 Inverse transform, Fourier sine 446 Inverse transform, Hankel 446 Inverse transform, Kontorovich — Lebedev 448 Inverse transform, Laplace 437 Inverse transform, Meijer 447 Inverse trigonometric functions 30 Inverse trigonometric functions integration formulas 34 Inverse trigonometric functions, arccosine 32 Inverse trigonometric functions, arccotangent 32 Inverse trigonometric functions, arcsine 31 Inverse trigonometric functions, arctangent 32 Inverse trigonometric functions, differentiation formulas 34 Inverse trigonometric functions, expansion in power series 34 inversion 178 422 Invertible linear operator 205 Invertible mapping 226 Invertible transformation 267 Involutive matrix 172 Involutory function 917 1423 Irrational numbers 4 5 Irreducible representation 231 Isolated point 371 Isolated singularity 413 Isometric correspondence 395 Isomorphic Euclidean spaces 194 Isomorphic groups 227 Isomorphic linear spaces 189 Isomorphic mapping of groups 227 Isomorphic unitary spaces 196 Isomorphism 226 227 Isomorphisms of linear spaces 188 Isoperimetric constraints 1002 Isoperimetric problem 1002 Isosceles trapezoid 54 Isosceles triangle 43 50 Isosceles triangle, base 50 Isosceles triangle, leg 50 Iterated integral 319 iterated kernel 822 832 838 Iteration axis 876 Iteration of function 907 Iteration process 858 Jacobi condition 998 1000 1004 1007 Jacobi condition, strengthened 1000 1004 1007 Jacobi elliptic functions 979 Jacobi equation 998 1004 1007 Jacobi method 217 Jacobi polynomials 986 Jacobi theorem 180 Jacobi theta functions 978 Jacobi — Mayer bracket 574 Jacobian 267 321 Jacobian determinant 321 Jensen equation 1436 Jensen inequality 15 245 297 Joining face of prism 61 Joint distribution function 1064 Joint distribution function of random variables 1057 Joint probability function 1059 1064 Jordan cell 182 Jordan form of matrix, canonical 182 Jordan lemma 417 436 Jump conditions 561 568 791 K-transform 449 Kernel of integral equation 801 825 829 Kernel of integral transform 435 Kernel of linear operator 205 Kernel with weak singularity 801 825 829 Kernel, degenerate 801 802 810 811 825 829 Kernel, difference 801 804 810 813 825 829 841 Kernel, Fredholm 825 829 Kernel, iterated 822 832 Kernel, logarithmic 801 Kernel, polar 801 825 Kernel, positive definite 837 kernel, symmetric 825 829 Khokhlov — Zabolotskaya equation 658 Klein — Gordon equation 625 1280 Kolmogorov distribution 1086 Kolmogorov test 1099 Kolmogorov theorem 1070 Kontorovich — Lebedev inversion formula 448 Kontorovich — Lebedev transform 448 449 Korteweg — de Vries equation 752 756 759 764 1327 Korteweg — de Vries equation, cylindrical 1328 Korteweg — de Vries equation, modified 1328 Kronecker delta, xxxii Kronecker product of matrices 175 Kronecker — Capelli theorem 198 Kth absolute moment 1044 Kth central moment 1043 Kth moment 1043 Kth sample central moment 1087 Kth sample moment 1087 Kummer convergence criterion for series 340 Kummer functions 956 Kummer series 956 1215 Kummer transformation 345 957 Kummer — Liouville transformation 475 kurtosis 1045 L'Hospital rules 254 L'Huiller equation 74 Lagrange equation 467 Lagrange function 270 Lagrange method 217 Lagrange multiplier 270 Lagrange multiplier rule 1002 Lagrange principle 1008 Lagrange problem 1008 Lagrange theorem 254 Lagrange — Charpit method 573 Lagrangian 767 993 1002 1006 Lagrangian, Bolza 1001 Lagrangian, Noetherian symmetry 768 Laguerre polynomials 957 982 Laguerre polynomials, generalized 983 Lalesco — Picard equation 1403 Lame coefficients 1196 Landen transformations 974 975 Laplace cascade method 600 Laplace equation, ODE 520 Laplace equation, PDE, three-dimensional 643 Laplace equation, PDE, two-dimensional 633 1282 Laplace integral 418 521 963 Laplace integral, general form 292 Laplace integral, special form 291 Laplace operator 272 Laplace theorem 177 Laplace transform 436 548 611 804 813 843 856 Laplace transform inverse 437 Laplace transform, convolution theorem 437 Laplace transform, for derivatives 611 Laplace transform, limit theorems 440 Laplace transform, properties 437 Laplace transform, solving linear problems for hyperbolic equations 614 Laplace transform, solving linear problems for parabolic equations 612 Laplace transform, tables 1157—1163 Laplace-type multiple integral 328 Large discriminant 108 Large numbers, strong law 1070 Large numbers, weak law 1069 Largest value of function 258 Lateral face of pyramid 63 Latitude 119 Laurent series 410 412 Lavrentiev regularization method 827 Law of conservation of mass 784 Law of Cosines 44 Law of cosines of angles 73 Law of cosines of sides 73 Law of Large Numbers 1069 1070 Law of Sines 44 73 Law of tangents 44 Law, commutative composition 225 Law, composition 225 Law, conservation 766 Law, conservation at discontinuity 561 Law, energy conservation 996 Law, weak of large numbers 1069 Laws, de Morgan 1032 Lax condition 792 Lax pair 755 Least common multiple 4 Least-squared error method 511 Least-squares method 509 1092 Left arm of hyperbola 101 Left coset 227 Left directrix of ellipse 99 Left directrix of hyperbola 102 Left focal radius 99 102 Left focus of ellipse 99 Left focus of hyperbola 102 Left half-plane 79 Left inverse matrix 171 Left rectangular Cartesian coordinate system 79 Left-hand limit 240 Leg of isosceles triangle 50 Leg of right triangle 50 Leg of trapezoid 54 Legendre condition 998 999 1004 1007 Legendre condition, strengthened 999 1004 1007 Legendre equation 1217—1219 Legendre function 962 Legendre function, associated 964 965 Legendre function, first kind, associated 965 Legendre function, modified associated 966 Legendre function, second kind 1217 Legendre function, second kind, associated 965 Legendre functions, Wronskians 967 Legendre polynomial, xxxi 962 1217 Legendre theorem 72 Legendre transformation 469 660 Legendre transformation with many variables 663 Leibnitz convergence criteria 341 Leibnitz convergence criterion for series 341 Leibnitz formula 256 Lemma, Jordan 417 Lemma, Neyman — Pearson 1097 Length of element 193 Length of segment 77 Length of vector 113 Level line 264 1014 Level, confidence 1093 Levi — Civita symbol 179 Levy solution 914 Lie group 730 Lie group of point transformations 730 Lienard equation 1225 Light rays, equation 1259 Likelihood equation 1092 Likelihood function 1092 Likelihood ratio 1097 Likelihood ratio test 1097 Limit of function 240 264 Limit of sequence 237 Limit theorems 1068 1069 Limit theorems, for Bernoulli process 1038 Limit theorems, for Laplace transform 440 Limit, first noteworthy 241 Limit, left-hand 240 Limit, lower of sequence 240 Limit, noteworthy second 241 Limit, partial of sequence 240 Limit, right-hand 240 Limit, upper of sequence 240 Limiting self-similar solution 675 Lindeberg central limit theorem 1071 Line in space 131 Line integral, first kind 329 Line integral, second kind 330 331 Line, deviation of point from line 93 Line, Euler 47 Line, level 264 1014 Line, Simpson 47 Line, support 1014 Line, tangent 251 Line, tangent to surface 388 Linear algebraic equation 157 Linear combination of column vectors 171 Linear combination of row vectors 171 Linear combination of vectors 188 Linear constant-coefficient partial differential equation 588 Linear difference homogeneous equation with constant coefficients 906 Linear eccentricity of ellipse 98 Linear eccentricity of hyperbola 102 Linear equation integral 801 810 824 829 Linear equation, algebraic 157 Linear equation, difference 881 885 889 1421 1425 Linear equation, difference, constant-coefficient 1409 1422 1426 Linear equation, ordinary differential 472 518 1213 Linear equation, partial differential, elliptic 592 Linear equation, partial differential, hyperbolic 592 Linear equation, partial differential, parabolic 591 Linear equations of mathematical physics 1267 Linear first-order ODE 457 Linear form 213 Linear functional 213 Linear functional equations 907 1414—1421 1438 Linear functional equations in one independent variable 1409 Linear group, general of dimension n 228 Linear harmonic oscillator 1277 Linear homogeneous difference equations 904 Linear homogeneous difference equations with constant coefficients 894 904 Linear homogeneous difference equations with variable coefficients 895 901 Linear homogeneous functional equations 910 Linear integral equations, first kind with constant limits of integration 824 1396—1400 Linear integral equations, first kind with variable limit of integration 801 1385—1390 Linear integral equations, second kind with constant limits of integration 829 1401—1408 Linear integral equations, second kind with variable limit of integration 810 1391—1395 Linear nonhomogeneous difference equations 906 Linear nonhomogeneous difference equations with constant coefficients 895 899 Linear nonhomogeneous difference equations with variable coefficients 896 902 Linear nonhomogeneous functional equations 912 Linear operator 204 Linear operator in matrix form 208 Linear operator injective 205 Linear operator invariant 211 Linear operator inverse 205 Linear operator invertible 205 Linear operator, canonical form 213 Linear operator, characteristic equation 211 Linear operator, determinant 209 Linear operator, kernel 205 Linear operator, matrix 208 Linear operator, nondegenerate 205 Linear operator, norm 204 Linear operator, range 205 Linear operator, rank 206 Linear operator, trace 209 Linear operators, product 205 Linear operators, sum 204 Linear ordinary differential equations 457 472—488 514—524 1212—1222 Linear ordinary differential equations, canonical form 473 Linear partial differential equations 553—650 1267—1298 Linear partial differential equations, canonical form 585—590
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