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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 Scientists
Авторы: 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.
Organized in ascending order of complexity, the material is divided into two parts. The first part is a coherent survey of the most important definitions, formulas, equations, methods, and theorems. It covers arithmetic, elementary and analytic geometry, algebra, differential and integral calculus, special functions, calculus of variations, and probability theory. Numerous specific examples clarify the methods for solving problems and equations. The second part provides many in-depth mathematical tables, including those ofexact solutions of various types of equations.
This concise, comprehensive compendium of mathematical definitions, formulas, and theorems provides the foundation for exploring scientific and technological phenomena.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
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Год издания: 2006
Количество страниц: 600
Добавлена в каталог: 30.06.2008
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Предметный указатель
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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