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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
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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