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Polyanin A., Manzhirov A.V. — Handbook of Mathematics for Engineers and Scientists
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.


Язык: en

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

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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