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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
General solution of linear hyperbolic equations      600—602
General solution of linear ODEs      472 514 518
General solution of ODEs      453 488
General square system of linear algebraic equations      199
General system of m linear algebraic equations with n unknown quantities      203
Generalized Abel equation      806
Generalized Abel equation of second kind      1393
Generalized Burgers — Korteweg — de Vries equation      709
Generalized Cauchy problem      627
Generalized Chebyshev inequalities      15
Generalized classical method of characteristics      582
Generalized Dirichlet problem      428
Generalized Ermakov criterion of convergence of series      340
Generalized Ermakov system      1242
Generalized Gauss equation      1445
Generalized homogeneous equation      490 526 1210 1224
Generalized Jensen equation      1449
Generalized Jensen inequalities      246
Generalized Laguerre polynomials      983
Generalized permutation matrix      168
Generalized reciprocal equation      160
Generalized self-similar solution      677
Generalized separable solution      681 682
Generalized separation of variables      681
Generalized similarity reduction      746
Generalized solution      563
Generalized solution of first-order PDE      563 568
Generalized solution, Hopf formula      565
Generalized solution, regular point      580
Generalized solution, singular point      580
Generalized solution, stable      569
Generalized telegraph equation      626
Generalized traveling-wave solution      697
Generalized triangle inequality      343
Generalized variance of n-dimensional distribution      1065
Generalized viscosity solutions      579 580
Generating function      815 1047
Generating function of numerical sequence      1047
Generator      65 67
Generator infinitesimal      717
Generator, group      717 730
Generic term of sequence      237
Generic term of series      337
Geodesic arc      70
Geodesic curvature      392
Geodesic curvature vector      392
Geometric definition of nondegenerate second-order curve      111
Geometric distribution      1048
Geometric mean      13
Geometric mean of functions      297
Geometric multiplicity of eigenvalue      209
Geometric probability      1034
Geometric programming      1027
Geometric progression      11
Geometric sequence      11
Geometric series      11
Geometry intrinsic of surface      391
Geometry, analytic      77
Geometry, differential      367
Geometry, spherical      70
Gergonne point      47
Goodness-of-fit tests      1098 1101
Gorge ellipse      145
Goursat problem      592 629
Gram determinant      193
Gram — Schmidt orthogonalization      194
Graph of function      84 236
Gravitational field potential      328
Great circle      68 70
Great circle, spherical geometry      70
Greatest common divisor      4
Green first identities      335
Green formula      428
Green function      428 623 631 633—637
Green function for elliptic equations      631—634 637
Green function for hyperbolic equations      623—625 636
Green function for linear ordinary differential equation      481
Green function for parabolic equations      618—622 635
Green function in terms of infinite series      639
Green function, admitting incomplete separation of variables      640
Green second identities      335
Green theorem      335
Group analysis of differential equations      716
Group element, character      231
Group generator      717 730 732
Group invariant      731
Group of derivation formulas, second      396
Group of events, complete      1031
Group of incompatible events, complete      1032
Group of leading terms of equation      220
Group of linear transformations      228
Group of mirror symmetry      229
Group of modulo 2 residues      226
Group of orthogonal transformations      229
Group theory      225
Group, abelian      226
Group, automorphism      227
Group, commutative      226
Group, completely reducible representation      231
Group, conjugate element      231
Group, continuous point      730
Group, equivalent representations      230
Group, faithful representation      230
Group, Lie      730
Group, linear representation      230
Group, orthogonal      229
Group, quotient      227
Group, special linear      228
Group, special orthogonal      229
Group, trivial representation      230
Groups, basic properties      225
Groups, cyclic      229
Groups, isomorphic      227
Groups, permutation      226
Groups, unitary      229
Growth exponent      436
Half-plane, left      79
Half-plane, lower      79
Half-plane, right      79
Half-plane, upper      79
Half-side theorem      73
Hamilton operator      272
Hamilton — Jacobi equation      576
Hamiltonian      576
Hankel functions      952
Hankel transform      446 449 1400
Hardy transform      449
Harmonic function      404
Harmonic mean      13
Harmonic mean of functions      297
Harmonic series      339
Hartley transform      449
Heat equation with axial symmetry      1270
Heat equation with central symmetry      1272
Heat equation, linear      585 1267
Heat equation, linear, nonhomogeneous      1268
Heat equation, nonlinear      1318
Heat equation, stationary with nonlinear source      1320
Heat equation, stationary, anisotropic      1323
Heaviside unit step function      618
Helmholtz equation      1289
Hermite functions      986
Hermite polynomials, xxxi      957 958 985
Hermitian matrix      168
Hermitian operator      206
Hermitian operator, negative      207
Hermitian operator, nonnegative      207
Hermitian operator, nonpositive      207
Hermitian operator, positive      207
Heron formula      48
Higher-order derivatives of elementary functions      255
Higher-order linear difference equations      1425
Hilbert boundary value problem      432
Hilbert example      997
Hilbert space      196
Hilbert transform      449 1396 1400
Hilbert — Privalov boundary value problem      432
Hilbert — Schmidt theorem      837
histogram      1086
Histogram, frequency      1086
Histogram, relative frequency      1086
Hodograph transformation for gas dynamic system      784
Hodograph transformation for ODEs      455
Hodograph transformation for PDEs      657 658
Holder condition      310 430
Holder constant      310
Holder exponent      310
Holder inequality      14 297 343
Holder — Jensen inequality      15
Homogeneity, order      1441
Homogeneous boundary condition      591
Homogeneous equations, linear difference      881 885 889 1421 1425
Homogeneous equations, linear difference, constant-coefficient      1409 1422 1426
Homogeneous equations, linear integral      810 829 834
Homogeneous equations, ordinary differential      456 490 526 1207 1224
Homogeneous equations, ordinary differential, generalized      457 490 526 1224
Homogeneous equations, ordinary differential, linear      472 514
Homogeneous equations, partial differential, elliptic      592
Homogeneous equations, partial differential, hyperbolic      592
Homogeneous equations, partial differential, parabolic      591
Homogeneous function      1441
Homogeneous initial condition      591
Homogeneous linear algebraic system      203
Homogeneous linear algebraic system, general solution      203
Homogeneous linear integral equation      810 829
Homogeneous linear ODEs      472 514
Homogeneous linear ODEs of higher-order ODEs      532
Homogeneous Monge — Ampere equation      668 1326
Homogeneous system of linear algebraic equations      197
Homogeneous system of linear ODEs      539
Homogeneous system of linear ODEs, superposition principle      528 539
Homomorphic image      226
Homomorphisms      226
Hopf formula for generalized solution      565
Hopf — Cole transformation      666 1308
Horner scheme      156
Hurwitz functions      893
Hyperbola      101
Hyperbola in polar coordinate system      104
Hyperbola, arm      101
Hyperbola, asymptotes      101
Hyperbola, canonical equation      101
Hyperbola, center      102
Hyperbola, conjugate diameters      104
Hyperbola, diameter      104
Hyperbola, directrix      102
Hyperbola, eccentricity      102
Hyperbola, equilateral      101
Hyperbola, focal axis      101
Hyperbola, focal distance      102
Hyperbola, focal parameter      102
Hyperbola, focal properties      102
Hyperbola, focus      102
Hyperbola, focus-directrix property      103
Hyperbola, imaginary axis      101
Hyperbola, imaginary semiaxis      102
Hyperbola, left arm      101
Hyperbola, left directrix      102
Hyperbola, left focus      102
Hyperbola, linear eccentricity      102
Hyperbola, numerical eccentricity      102
Hyperbola, optical property      103
Hyperbola, parameter      102
Hyperbola, real semiaxes      102
Hyperbola, right arm      101
Hyperbola, right directrix      102
Hyperbola, right focus      102
Hyperbola, vertex      102
Hyperbolic arccosine, xxx      
Hyperbolic arccotangent, xxx      
Hyperbolic arcsine, xxx      
Hyperbolic arctangent, xxx      
Hyperbolic cosine, xxx      35
Hyperbolic cotangent, xxx      35
Hyperbolic equation, boundary value problems      623
Hyperbolic equation, canonical form      587
Hyperbolic equation, first canonical form      587
Hyperbolic equation, second canonical form      587
Hyperbolic equations      585 590 647 648 742
Hyperbolic equations, Cauchy problem      617
Hyperbolic equations, linear      587 617 623—630 636 647 648 1278—1284
Hyperbolic equations, nonlinear      653 654 1312—1317
Hyperbolic functions      34
Hyperbolic functions integration formulas      38
Hyperbolic functions inverse      39
Hyperbolic functions of half argument      38
Hyperbolic functions of multiple argument      38
Hyperbolic functions, addition formulas      36
Hyperbolic functions, differentiation formulas      38
Hyperbolic functions, expansion in power series      39
Hyperbolic functions, properties      36
Hyperbolic paraboloid      146
Hyperbolic point      394 536
Hyperbolic sine, xxxi      35
Hyperbolic spiral      86 368
Hyperbolic system of PDEs      781 790
Hyperbolic tangent, xxxi      35
Hyperbolic type of second-order curves      108
Hyperboloid      144 224
Hyperboloid of revolution      145
Hyperboloid, one-sheeted      144
Hyperboloid, real semiaxes      144
Hyperboloid, two-sheeted      144
Hypergeometric distribution      1049
Hypergeometric equation      960 1218
Hypergeometric equation, degenerate      1215
Hypergeometric functions      960
Hypergeometric series      960 1218
Hypersurface      220
Hypersurface, center      222
Hypersurface, central      222
Hypersurface, noncentral      224
Hypersurface, semiaxis      223
Hypotenuse      50 72
Hypothesis      1094
Hypothesis, alternative      1094
Hypothesis, composite      1094
Hypothesis, nonparametric      1094
Hypothesis, null      1094
Hypothesis, parametric      1094
Hypothesis, simple      1094
hypothesis, statistical      1094
Identity matrix      168
Identity operator      204
Identity, Abel      902
Identity, Parseval      361
Image, homomorphic      226
Imaginary axis      401
Imaginary axis of hyperbola      101
Imaginary ellipsoid      224
Imaginary part      399
Imaginary semiaxis of hyperbola      102
Imaginary semiaxis of one-sheeted hyperboloid      144
Imaginary semiaxis of two-sheeted hyperboloid      144
Imaginary unit      399
Impossible event      1031
Improper integral      301
Improper integrals involving logarithmic functions      305
Improper integrals involving power functions      304
Improper integrals involving trigonometric functions      305
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