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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
Equation, bilinear functional 930 1446
Equation, binomial algebraic 161
Equation, biquadratic 159
Equation, Born — Infeld 659
Equation, Boussinesq 709 1332
Equation, Burgers 664 666 751 1307
Equation, Burgers — Korteweg — de Vries, generalized 709
Equation, Burgers, radial symmetric case 1307
Equation, Cantor first 1442
Equation, Cantor second 1449
Equation, Carleman 1399
Equation, Cauchy 1438
Equation, Cauchy exponential 1443
Equation, Cauchy logarithmic 1439
Equation, Cauchy power 1444
Equation, characteristic 514 654
Equation, characteristic of linear operator 211
Equation, characteristic of matrix 185
Equation, characteristic of quadratic form 150
Equation, characteristic, for difference equation 881
Equation, characteristic, for system of ODEs 529
Equation, circle, canonical 97
Equation, circle, parametric 98
Equation, Clairaut 572 1262
Equation, complete of plane 124
Equation, continuity 784
Equation, convolution-type of first kind 825
Equation, convolution-type of second kind 829
Equation, cubic incomplete 158
Equation, cubic, complete 159
Equation, curve, on plane 84
Equation, cyclic functional 920
Equation, D'Alembert 1441
Equation, damped vibrations 1213
Equation, Darboux 458
Equation, diffusion boundary layer 1276
Equation, diffusion, linear see “Heat equation”
Equation, diffusion, nonlinear with cubic source 753
Equation, diffusion, stationary anisotropic 1323
Equation, dispersion 532 596
Equation, Duffing 501
Equation, ellipse, canonical 98
Equation, elliptic 585 588 590 1284
Equation, Emden — Fowler 1223
Equation, Ermakov 1224
Equation, Euler 473 994 1216
Equation, Euler — Darboux 602
Equation, Euler — Lagrange 767
Equation, Euler — Poisson 1006
Equation, evolution, second-order 739
Equation, exact, first-order ODE 458
Equation, exact, second-order ODE 491
Equation, family 377
Equation, Fisher 1301
Equation, Fitzhugh — Nagumo 1302
Equation, Fredholm of first kind 825
Equation, Fredholm of second kind 829
Equation, free oscillations 1213
Equation, functional see “Functional equation”
Equation, functional differential 682 684 688
Equation, gas dynamics model 558
Equation, Gauss 1445
Equation, Gauss, generalized 1445
Equation, Gaussian hypergeometric 960 1218
Equation, Gel'fand — Levitan — Marchenko integral 1328 1333
Equation, general of plane 124
Equation, general of second-order hypersurface 220
Equation, general of straight line in space 132
Equation, general of straight line on plane 90
Equation, Hamilton — Jacobi 576
Equation, heat 585 672 680 698 728 1267
Equation, heat, nonhomogeneous 1268
Equation, heat, stationary anisotropic 1323
Equation, heat, stationary with nonlinear source 1320
Equation, Helmholtz 1289
Equation, Helmholtz, three-dimensional 600
Equation, Helmholtz, two-dimensional 599
Equation, homogeneous 591 592 810 829 834 1207 1224
Equation, homogeneous function 1441
Equation, homogeneous, generalized 1210 1224
Equation, hyperbola, canonical 101
Equation, hyperbolic 585 587 590
Equation, hyperbolic, first canonical form 587
Equation, hyperbolic, normal 590
Equation, hyperbolic, second canonical form 587
Equation, hypergeometric 960 1218
Equation, hypergeometric, degenerate 1215
Equation, Jacobi 998 1004 1007
Equation, Jensen 1438
Equation, Jensen, generalized 1449
Equation, Khokhlov — Zabolotskaya 658
Equation, Khokhlov — Zabolotskaya, stationary 1322
Equation, Klein — Gordon 618 625 1280
Equation, Klein — Gordon, linear 625
Equation, Klein — Gordon, nonlinear 702 1315
Equation, Klein — Gordon, two-dimensional 618
Equation, Kolmogorov, backward 1076
Equation, Kolmogorov, forward 1076
Equation, Korteweg — de Vries 752 756 759 1327
Equation, Korteweg — de Vries, cylindrical 1328
Equation, Korteweg — de Vries, modified 1328
Equation, L'Huiller 74
Equation, Lalesco — Picard 1403
Equation, Laplace, ODE 520
Equation, Laplace, three-dimensional, PDE 643
Equation, Laplace, two-dimensional, PDE 585 633 1284
Equation, Legendre 1217—1219
Equation, Lienard 1225
Equation, light rays 1259
Equation, likelihood 1092
Equation, line in projections 133
Equation, linear integral 801 810 824 829
Equation, linear, algebraic 157
Equation, linear, constant-coefficient, ODE 473 514 1213
Equation, linear, constant-coefficient, PDE 588
Equation, linear, first-order, ODE 457
Equation, linear, nonhomogeneous, ODE 473
Equation, linear, ODE 472 518 1213
Equation, linear, PDE 585 591 592
Equation, Liouville 664
Equation, Lobachevsky 1444
Equation, logarithmic Cauchy 1439
Equation, logistic 875
Equation, Mathieu 980 1221
Equation, Mathieu, modified 982 1220
Equation, minimal surfaces 770
Equation, model of gas dynamics 1254
Equation, Monge — Ampere 1326
Equation, Monge — Ampere, homogeneous 668 1326
Equation, Monge — Ampere, nonhomogeneous 1326
Equation, Newell — Whitehead 733
Equation, noncentral hypersurface, canonical 224
Equation, normal 252
Equation, normal to surface 153
Equation, normalized of plane 126
Equation, normalized of straight line 91
Equation, on entire axis 825 826 841
Equation, on semiaxis 826 842
Equation, one-dimensional vibration with central symmetry 1281
Equation, Painleve 495
Equation, parabola, canonical 104
Equation, parabolic 585 586 590
Equation, parabolic in narrow sense 590
Equation, parametric of curve on plane 87
Equation, parametric of line in space 131
Equation, parametric of plane 125
Equation, pencil of planes 131
Equation, pencil of straight lines 92
Equation, Pexider 925 1440
Equation, Pfaffian 772 773
Equation, plane passing through line of intersection of planes 131
Equation, plane passing through point and parallel to another plane 127
Equation, plane passing through point and parallel to two straight lines 129
Equation, plane passing through three points 127
Equation, plane passing through two points and parallel to line 128
Equation, Poisson 1285
Equation, Poisson, three-dimensional 599
Equation, Poisson, two-dimensional 599
Equation, quadratic 158
Equation, reciprocal, algebraic 160 161
Equation, reciprocal, algebraic, generalized 160
Equation, reciprocal, algebraic, modified 160
Equation, reciprocal, functional 919
Equation, renewal 1395
Equation, Riccati 460
Equation, Riccati difference 875 918 1428 1429
Equation, Riccati, general, differential 461 462 1207 1210
Equation, Riccati, special, differential 1208
Equation, right-hand side 801 825 829
Equation, root 162
Equation, Schlomilch 1400
Equation, Schroder — Koenigs 911
Equation, Schrodinger of general form 1311
Equation, Schrodinger with cubic nonlinearity 1309
Equation, Schrodinger with power-law nonlinearity 1310
Equation, Schrodinger, linear 1276
Equation, Schrodinger, nonlinear 759 1309
Equation, self-similar solutions 1442
Equation, separable 456 1207
Equation, separated 456
Equation, Sine — Gordon 1314
Equation, sinh — Gordon 1314
Equation, skew self-distributivity 1449
Equation, slope-intercept of straight line 89
Equation, steady transonic gas flow 1324
Equation, straight line in polar coordinates 92
Equation, straight line in projections in space 133
Equation, straight line in space, canonical 132
Equation, straight line passing through given point on plane, canonical 90
Equation, straight line passing through point and perpendicular to plane 134
Equation, straight line passing through two given points 90 134
Equation, straight line passing through two given points on plane, canonical 90
Equation, surface 386
Equation, surface in space 119
Equation, tangent line 251
Equation, tangent plane 268
Equation, tangent plane to surface 152
Equation, telegraph 1284
Equation, telegraph, generalized 626
Equation, thermal boundary layer 1276
Equation, transonic gas flow 1324
Equation, transposed 825 829 834
Equation, traveling wave 1441
Equation, Tricomi integral 1403
Equation, ultrahyperbolic 590
Equation, Urysohn integral, nonlinear 856
Equation, Urysohn with degenerate kernel 863 864
Equation, vibration of string 1278
Equation, vibration with axial symmetry 1282
Equation, Volterra integral of first kind 801 807
Equation, Volterra integral of second kind 807 810
Equation, Volterra integral, nonlinear 856 858—861
Equation, Volterra with quadratic nonlinearity 856
Equation, wave 585 1278
Equation, wave, nonlinear 723 1312—1317
Equation, wave, three-dimensional 618
Equation, wave, two-dimensional 618
Equation, Whittaker 960
Equation, Wiener — Hopf of first kind 825 1401
Equation, Wiener — Hopf of second kind 829 1406
Equations integral 801—871 1385—1406
Equations integral, linear 801—855 1385—1406
Equations integral, linear of second kind with constant limits of integration 824 829
Equations integral, nonlinear 856—871
Equations intrinsic of curve 388
Equations, admitting variational formulation 767
Equations, autonomous 525
Equations, Bellman 1028
Equations, center of hypersurface 222
Equations, difference 871—907
Equations, elliptic, linear 588 609—611 631—633 637 1284—1298
Equations, elliptic, nonlinear 653 654 318—1334
Equations, Fredholm integral of second kind 854
Equations, functional, linear 907—917
Equations, hyperbolic, linear 587 617 623—630 636 647 648 1278—1284
Equations, hyperbolic, nonlinear 653 654 1312—1317
Equations, motion of mass point 87
Equations, ordinary differential 453—550 1207—1228
Equations, Painleve 495
Equations, parabolic, linear 586 615—616 618—622 634 635 646 648 1267—1278
Equations, parabolic, nonlinear 653 654 1301—1311
Equations, partial differential 553—798 1247—1382
Equations, pencil 92
Equations, reaction-diffusion type 796
Equations, straight line on plane parametric 91
Equations, straight lines on plane 89
Equilateral hyperbola 101
Equilateral triangle 43 50 51
Equilibrium point of autonomous system 545
Equilibrium points of two-dimensional linear systems 534
Equilibrium solution 874 884
Equivalence transformation 180
Equivalent events 1031
Equivalent infinitely small functions 243
Equivalent matrices 180
Equivalent representations of group 230
Ermakov convergence criterion for series 340
Ermakov equation 1224
Error function, xxxi 939 957 1267
Essential singularity 413
Estimation theorem for double integral 318
Estimation theorem for triple integral 325
Estimator 1088
Estimator interval 1088 1093
Estimator, asymptotically unbiased 1089
Estimator, consistent 1089
Estimator, maximum likelihood 1092
Estimator, minimality of variance 1090
Estimator, statistical 1088
Estimator, unbiased 1089
Euclidean space 192
Euclidean space, isomorphic 194
Euclidean space, normed 193
Euler constant, xxx 944 949 958
Euler differential equations 998
Euler equation, calculus of variations 994
Euler equation, ODE 473 520 1216
Euler formula 30 405 944
Euler line 47
Euler numbers 939
Euler polynomials 989
Euler substitutions 280
Euler system of ODEs 542
Euler theorem 61 393
Euler transform of first kind 449
Euler transform of second kind 450
Euler transformation 661
Euler triangles 71
Euler — Darboux equation 602
Euler — Fourier formulas 358
Euler — Lagrange equation 767
Euler — Lagrange Theorem 1009
Euler — Poisson equation 1006
Even function 236
Even number 3
Even permutation 178
Event 1031
Event, complementary 1031
Event, elementary 1031
Event, favorable 1031
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