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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
ed2k: ed2k stats
Год издания: 2006
Количество страниц: 600
Добавлена в каталог: 30.06.2008
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Предметный указатель
Criterion, second convergence 338
Criterion, special Cauchy 341
Criterion, Sylvester 219
Criterion, Weierstrass convergence 349
Critical region 1095
Cross product of vectors 121
Cross-correlation function 1072
Cross-covariance function 1072
cube 62
Cubic equation 158
Cumulative distribution function 1039
Cumulative distribution function, conditional 1062
Cumulative frequency 1084
Cumulative relative frequency 1084
Curl 331
Curl of vector field 331 334
Curvature 376 384
Curvature of curve on surface 392
Curvature of plane curves 376
Curvature of space curves 384
Curvature, center 375
Curvature, circle 375
Curvature, extrinsic 394
Curvature, Gaussian 394
Curvature, geodesic 392
Curvature, lines 393
Curvature, mean 394
Curvature, normal 392 394
Curvature, radius 376 384
Curvature, vector 383
Curve in space 120 123
Curve, discriminant 378
Curve, intrinsic equations 388
Curve, on plane 84
Curve, parabolic type of second-order 108
Curve, second-order 107
Curve, second-order in space 119 123
Curve, second-order, on plane 84
Curve, second-order, on plane algebraic 87
Curves, parametric 387
Curvilinear coordinates 387
Curvilinear coordinates, on surface 387
Curvilinear integral 329
Curvilinear lines 387
Cusp, first kind 372
Cusp, second kind 372
CYCLE 1022
Cyclic functional equation 920
Cyclic groups 229
Cylinder 65 66
Cylinder, base 65
Cylinder, central 225
Cylinder, function 947
Cylinder, paraboloidal 225
Cylinder, right 66
Cylinder, right circular 66
Cylinder, round 66
Cylinder, segment 67
Cylinder, truncated 66
Cylindrical coordinates, xxxi 118 1198
Cylindrical function 947 1214
Cylindrical Korteweg — de Vries equation 1328
Cylindrical surface 65
Cylindrical tube 67
D'Alembert (Gauss) formulas 73
D'Alembert convergence criterion for series 338
D'Alembert equation 1443
D'Alembert formula 1278
D'Alembert method 533
D'Alembert solution for wave equation 600
D'Alembert — Euler conditions 402
Damped vibrations 1213
Darboux equation 458
Darboux vector 386
de Moivre formula 30 400
De Morgan laws 1032
Death process 1077
Decadic logarithm 9
decile 1045
Decomposition of matrices 173 201
Decomposition, theorems 208 1055
Decomposition, triangular 180
Decreasing function 236
Decreasing sequence 238
Defect of matrix 178
Definite integral 286 1147
Definite integral, geometric applications 299
Definite integral, geometric meaning 287
Definite integral, physical applications 299
Definite integral, properties 287
Definite integrals involving exponential functions 1150
Definite integrals involving hyperbolic functions 1152
Definite integrals involving logarithmic functions 1152
Definite integrals involving trigonometric functions 1153
Degenerate bilinear form 215
Degenerate hypergeometric equation 1215
Degenerate hypergeometric function, xxxii 956
Degenerate hypergeometric function, xxxii, Wronskian 958
Degenerate kernel 801 802 810 811 825 829
Degenerate matrix 178
Degenerate Quadratic Form 216
Density multiplication theorem 1062
Density, spectral 1075
Dependent variable 236
Derivation formulas 396
Derivative 250
Derivative of function 402
Derivative of polynomial 157
Derivative, basic elementary functions 252
Derivative, directional 267 268
Derivative, geometrical meaning 251
Derivative, higher-order 255
Derivative, one-sided 252
Derivative, partial 264
Derivative, physical meaning 251
Derivative, total 265
Descartes theorem 165
Descartes — Euler solution 160
Descartes, Folium 374
Descending Landen transformation 974
Determinant 175
Determinant, Casoratti 901
Determinant, column expansion 176
Determinant, Gram 193
Determinant, Jacobian 321
Determinant, linear operator 209
Determinant, order 2 175
Determinant, order 3 176
Determinant, order n 176
Determinant, product of matrices 179
Determinant, properties 176
Determinant, row expansion 176
Determinant, sum of matrices 179
Determinant, Vandermonde 179
Determinant, Wronskian 473 482 518 539
Determined system of linear algebraic equations 197
Deviation of point from line 93
Deviation of point from plane 141
Deviation, residual standard 1063
Deviation, root-mean-square 1045
Deviation, sample 1088
Deviation, standard 1045
Diagonal matrix 168
Diagonal, main 168
Diagonal, secondary 168
Diameter 151
Diameter of circle 56
Diameter of ellipse 100
Diameter of hyperbola 104
Diameter of parabola 106
Diameter of second-order curve 108
Diameter of set 317
Diameter of sphere 69
Diameter, conjugate to chords 108
Diameter, conjugate to family of planes 151
Diameter, partition 317
Diameter, principal of ellipse 100
Diameter, principal of hyperbola 104
Diameter, principal of parabola 106
Diameters, conjugate 151
Diameters, conjugate of ellipse 100
Diameters, conjugate of hyperbola 104
Dido problem 1003
Diet problem 1012
Difference equation 889 1409 1422 1425—1426
Difference equation in integer argument 873
Difference equation, characteristic 881
Difference equation, general solution 874 884
Difference equation, linear homogeneous 881 885 889 906 904
Difference equation, linear homogeneous, first-order 873
Difference equation, linear homogeneous, second-order 877 1421
Difference equation, linear nonhomogeneous 883 890—893
Difference equation, linear nonhomogeneous, constant-coefficient, first-order 1411
Difference equation, linear nonhomogeneous, constant-coefficient, nth-order 1427
Difference equation, linear nonhomogeneous, constant-coefficient, second-order 1422
Difference equation, linear nonhomogeneous, first-order 873
Difference equation, linear nonhomogeneous, nth-order 1426
Difference equation, linear nonhomogeneous, second-order 879 880 1421
Difference equation, linear, constant-coefficient 873 877
Difference equation, linear, higher-order 1425
Difference equation, linear, second-order 877 1421
Difference equation, linearly independent solutions 882
Difference equation, logistic 875
Difference equation, nonlinear 884
Difference equation, nonlinear, first-order 873
Difference equation, Riccati 875 918
Difference kernel 801 804 810 813 825 829 841
Difference of complex numbers 399
Difference of events 1031
Difference of matrices 169
Difference of polynomials 155
Difference of vectors 113 188
Difference, common 11
Difference, finite 884
Differentiable function 251
Differential 250 251 265
Differential constraint 737 1009 1010
Differential constraint, first-order 739
Differential constraint, second-order 744
Differential constraints method 737
Differential equation, Abel of first kind 462
Differential equation, Abel of first kind, canonical form 463
Differential equation, Abel of second kind 464
Differential equation, Abel of second kind, canonical form 465
Differential equation, Airy 955
Differential equation, autonomous 1207 1223 1225
Differential equation, axisymmetric steady hydrodynamic boundary layer 712
Differential equation, Bernoulli 458 1207
Differential equation, Bessel 1216
Differential equation, Bessel, modified 1216
Differential equation, biharmonic 1297
Differential equation, biharmonic, homogeneous 1297
Differential equation, biharmonic, nonhomogeneous 1298
Differential equation, Born — Infeld 659
Differential equation, Boussinesq 709 1332
Differential equation, Burgers 664 666 751 1307
Differential equation, Burgers — Korteweg — de Vries, generalized 709
Differential equation, Burgers, radial symmetric case 1307
Differential equation, characteristic, for system of ODEs 529
Differential equation, Clairaut 467 572 1262
Differential equation, Darboux 458
Differential equation, degenerate hypergeometric 1215
Differential equation, diffusion boundary layer 1276
Differential equation, diffusion, nonlinear with cubic source 753
Differential equation, Duffing 501
Differential equation, elliptic 585 588 590 1284
Differential equation, Emden — Fowler 1223
Differential equation, Ermakov 1222
Differential equation, Euler 473 520 994 998 1216
Differential equation, evolution, second-order 739
Differential equation, exact, first-order 458
Differential equation, exact, second-order 491
Differential equation, Fisher 1299
Differential equation, Fitzhugh — Nagumo 1302
Differential equation, free oscillations 1213
Differential equation, gas dynamics 558
Differential equation, Gaussian hypergeometric 960 1218
Differential equation, generalized homogeneous 526
Differential equation, Hamilton — Jacobi 576
Differential equation, heat with axial symmetry 1270
Differential equation, heat with central symmetry 1272
Differential equation, heat, linear 585 1267
Differential equation, heat, linear, nonhomogeneous 1268
Differential equation, heat, nonlinear 1318
Differential equation, heat, stationary anisotropic 1323
Differential equation, heat, stationary with nonlinear source 1320
Differential equation, Helmholtz 1289
Differential equation, Helmholtz, three-dimensional 600
Differential equation, Helmholtz, two-dimensional 599
Differential equation, homogeneous 526 591 592 810 829 834 1207 1224
Differential equation, homogeneous, generalized 1210 1224
Differential equation, hyperbolic 585 587 590
Differential equation, hyperbolic, first canonical form 587
Differential equation, hyperbolic, normal 590
Differential equation, hyperbolic, second canonical form 587
Differential equation, hypergeometric 960 1218
Differential equation, hypergeometric, degenerate 1215
Differential equation, Jacobi 998 1004 1007
Differential equation, Khokhlov — Zabolotskaya 658
Differential equation, Khokhlov — Zabolotskaya, stationary 1322
Differential equation, Klein — Gordon 618 625 1280
Differential equation, Klein — Gordon, linear 625
Differential equation, Klein — Gordon, nonlinear 702 1315
Differential equation, Klein — Gordon, two-dimensional 618
Differential equation, Korteweg — de Vries 752 756 759 1327
Differential equation, Korteweg — de Vries, cylindrical 1328
Differential equation, Korteweg — de Vries, modified 1328
Differential equation, Lagrange 467
Differential equation, Laplace, ODE 520
Differential equation, Laplace, three-dimensional, PDE 643
Differential equation, Laplace, two-dimensional, PDE 585 633 1284
Differential equation, Legendre 1217—1219
Differential equation, Lienard 1225
Differential equation, light rays 1259
Differential equation, linear homogeneous, second order 1212
Differential equation, linear, constant-coefficient, second-order 473 1213
Differential equation, Liouville 664
Differential equation, Mathieu 980 1221
Differential equation, Mathieu modified 982 1220
Differential equation, minimal surfaces 770
Differential equation, model of gas dynamics 1254
Differential equation, Monge — Ampere 1326
Differential equation, Monge — Ampere, homogeneous 668 1326
Differential equation, Monge — Ampere, nonhomogeneous 1326
Differential equation, Newell — Whitehead 733
Differential equation, ordinary 453—550 1207—1228
Differential equation, Painleve 495
Differential equation, parabolic 585 586 590
Differential equation, parabolic in narrow sense 590
Differential equation, partial 553—798 1247—1382
Differential equation, Pfaffian 772 773
Differential equation, Poisson 1287
Differential equation, Poisson, three-dimensional 599
Differential equation, Poisson, two-dimensional 599
Differential equation, Riccati 460
Differential equation, Riccati, general 461 462 1209 1210
Differential equation, Riccati, special 1208
Differential equation, Schrodinger of general form 1311
Differential equation, Schrodinger with cubic nonlinearity 1309
Differential equation, Schrodinger with power-law nonlinearity 1310
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