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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
Method, characteristics, generalized classical      582
Method, Clarkson — Kruskal direct      708—710
Method, Cole — Kevorkian      504
Method, collocation      509 523 847 848 860
Method, collocation, convergence theorem      524
Method, collocation, for integral equations      847 848
Method, collocation, for ODEs      509 523
Method, D'Alembert      533
Method, D'Alembert, for nonhomogeneous higher-order linear systems      533
Method, differential constraints      737
Method, estimation      1091
Method, false position      262
Method, Fourier      602
Method, Galerkin      508
Method, Gaussian elimination, backward substitution      200
Method, Jacobi      217
Method, Lagrange      217
Method, Lagrange — Charpit      573
Method, Laplace cascade      600
Method, Lavrentiev regularization      827
Method, least squares      509 1092
Method, least-squared error      511
Method, Lindstedt — Poincare      502
Method, Maclaurin      164
Method, mathematical induction      16
Method, minimal cost      1020
Method, modified Newton — Kantorovich      859 868
Method, moments      509 1091
Method, Newton      164
Method, Newton — Kantorovich      859 868
Method, Newton — Raphson      262
Method, parametric for defining curve      123
Method, parametric for defining surface      123
Method, penalty function      1027
Method, perturbation      499
Method, Picard      469
Method, projection      508
Method, quadrature      861
Method, quadrature, for integral equations      870
Method, quadric      148
Method, regula falsi      262
Method, regularization, for integral equations      827
Method, Runge — Kutta      472 512
Method, shooting      512
Method, similarity      669
Method, simplex      1014
Method, single-step of second-order approximation      471
Method, splitting      704
Method, step      884 885 889 893 919
Method, Sturm      166
Method, successive approximation      822 833 858 867
Method, summation of series      344
Method, Tikhonov regularization      828
Method, Titov — Galaktionov      693
Method, Van der Pol — Krylov — Bogolyubov      503
Methods of defining function      236
Methods of integral transforms      841
Methods, numerical for ODEs      511 512
Methods, perturbation      499—507
Methods, projection      508
Metric space      196
Metric tensor      1193
Metric tensor components      1195
Meusnier theorem      392
Midline      44
Minimal cost method      1020
Minimal polynomial      186
Minimal surface      394 770
Minimality of variance of estimator      1090
Minimax principle      1025
Minimax property      210
Minimax theorem, for antagonistic two-person zero-sum games      1026
Minimax theorem, von Neumann      1026
Minimum of function, xxxi      257
Minimum, conditional      270
Minimum, constrained      270
Minimum, local      257
Minimum, local, strong      994
Minimum, local, weak      993 1001 1002 1006
Minimum, strong      1006
Minimum, strong of functional      991
Minimum, weak of functional      991
Minkowski inequality for finite sums      14
Minkowski inequality for integrals      296
Minkowski inequality for series      343
Minkowski inequality for vectors      121 193
Minor      177
Minor axis of ellipse      98
Minor of rectangular matrix      177
Minor of square matrix      176
Minor, basic      178
Minor, cofactor      177
Minor, first kind      177
Minor, second kind      177
Mixed boundary value problem      480 593
Mixed boundary value problem, for hyperbolic equations      627
Mixed boundary value problem, for PDEs      593
Mixed strategy      1025
Mixed strategy, game price      1026
Mode of continuous probability distribution      1045
Mode of discrete probability distribution      1045
Model equation of gas dynamics      558 1254
Model of transportation problem      1020
Model of transportation problem, closed      1020
Modified associated Legendre functions      966
Modified Bessel equation      1216
Modified Bessel functions      953
Modified Bessel functions, first kind, xxxi      953 1216
Modified Bessel functions, second kind, xxxi      953 1216
Modified Korteweg — de Vries equation      759
Modified Mathieu equation      982 1220
Modified Mathieu functions      982
Modified Newton — Kantorovich method      859 868
Modified reciprocal equation      160
Modulus of complex number, xxxii      400
Modulus of real number, xxx      8
Modulus of vector, xxx      
Modulus set      907
Modulus, complementary      971
Modulus, elliptic      971
Mollweide formulas      44
moment      1043
Moment initial of multivariate random variable      1065
Moment initial of two-dimensional random variable      1060
Moment method      509
Moment of multivariate random variable      1065
Moment of two-dimensional random variable      1060
Moment, absolute      1044
Moment, central      1043
Moment, central of n-dimensional random variable      1065
Moment, cth absolute      1044
Moment, cth central      1043
Moment, cth sample, central      1087
Moment, fcth sample      1087
Moment, sample      1087
Moment, sample, central      1087
Moment-generating function      1047
Moments of inertia of body      327
Moments of inertia of flat plate      324
Momentum conservation law      996
Monge — Ampere equation      654 1326
Monge — Ampere equation, homogeneous      668 1326
Monotone function      236
Monotone sequence      238
Morera theorem      410
Morley theorem      49
Morse potential      1278
Motion of mass point      87
Movable critical points      495
Movable singularities of solutions of ordinary differential equations      494
Moving trihedral      382
Moving trihedral of curve      382
Multidimensional stochastic process      1072
Multifactor analysis of variance      1108
Multilinear form      215
Multilinear form, skew-symmetric      215
Multilinear form, symmetric      215
Multimodal distribution      1045
Multiple correlation coefficient      1066
Multiple integral      328
Multiple integral, asymptotic formulas      328
Multiple integration      289
Multiple, common least      4
Multiplication index      12
Multiplication of asymptotic series      364
Multiplication of matrices      169
Multiplication of matrix by scalar      169
Multiplication of polynomials      155
Multiplication of real numbers      6
Multiplication of series      343
Multiplicative inverse of real number      6
Multiplicative separable solution      571 596 678
Multiplicity of eigenvalue, algebraic      184 209
Multiplicity of eigenvalue, geometric      209
Multiplier, Lagrange      270
Multiply connected domain      409
Multivalued function      236 402
Multivariate random variable initial moment      1065
Multivariate random variable, moment      1065
N-dimensional coordinate space      188
N-dimensional distribution, generalized variance      1065
N-dimensional ellipsoid      224
N-dimensional Fourier transform      445
N-dimensional linear space      189
n-dimensional random variable      1065
N-dimensional random vector      1057
N-fold singular point      371
N-person game      1024
N-sided pyramid      63
N-soliton solution      765
N-soliton solution, Korteweg — de Vries equation      764
Nagel point      47
Napierian base      23
Natural logarithm, xxxi      9 22 23 238
Natural logarithm, xxxi, base      9 23
Natural number      3
Natural trihedral      382
Necessary condition for extremum      269 1002 1006 1009
Necessary condition for solvability of Neumann problem      429
Negative binomial distribution      1050
Negative definite quadratic form      216
Negative Hermitian operator      207
Negative index of inertia of quadratic form      218
Negative symmetric operator      207
Neighborhood of point at infinity      402
Neighborhood of point on complex plane      402
Neighborhood, first-order      991
Neighborhood, strong      991
Neighborhood, weak      991
Neighborhood, zero-order      991
Neper analogs      73
Neper rules      75
Net, coordinate      387
Neumann function      947
Neumann problem      429
Neumann problem, for elliptic equations      593 1330
Neumann problem, necessary condition for solvability      429
Neumann series      823 833
Neutral element      225
Newell — Whitehead equation      733
Newton method      164
Newton — Kantorovich method      859 868
Newton — Leibniz formula      288
Newton — Leibniz formula, for function of complex variable      408
Newton — Raphson method      262
Neyman — Fisher theorem      1090
Neyman — Pearson lemma      1097
Nilpotent matrix      172
Nine-point circle      49
Node      372
Node interpolation      808
Node, Chebyshev      523
Node, quadrature      808
Node, stable      535 538
Node, unstable      536
Noetherian symmetry      767
Noetherian symmetry of Lagrangian      768
Nonbasic variable      1015
Nonclassical method of symmetry reductions      732 747
Nonclassical symmetries      733
Nondecreasing function      236
Nondegenerate bilinear form      215
Nondegenerate linear operator      205
Nondegenerate matrix      171
Nondegenerate quadratic form      216
Nonhomogeneous biharmonic equation      1298
Nonhomogeneous first-order constant-coefficient linear difference equation      1411
Nonhomogeneous higher-order linear systems, D'Alembert method      533
Nonhomogeneous integral equation      810 829
Nonhomogeneous linear boundary value problems      620 624
Nonhomogeneous linear difference equations      882
Nonhomogeneous linear ODEs      474 515
Nonhomogeneous linear PDEs      598
Nonhomogeneous Monge — Ampere equation      1326
Nonhomogeneous nth-order constant-coefficient linear difference equation      1427
Nonhomogeneous nth-order linear difference equation      1426
Nonhomogeneous second-order constant-coefficient linear difference equation      1422
Nonhomogeneous second-order linear difference equation      1421
Nonhomogeneous system of linear algebraic equations      197
Nonhomogeneous system of linear first-order ODEs      531 540
Nonhomogeneous system, superposition principle      541
Nonincreasing function      236
Nonlinear difference equation      884 918 1428
Nonlinear difference equation of general form      1437
Nonlinear diffusion equation with cubic source      753
Nonlinear elliptic equations      1318
Nonlinear first-order partial differential equation with two independent variables      570
Nonlinear functional equation      1443
Nonlinear functional equation in one independent variable      1428
Nonlinear functional equation, power series solution      922
Nonlinear heat equation      1301 1318
Nonlinear heat equation in radial symmetric case      1307
Nonlinear integral equations      856
Nonlinear integral equations with constant integration limits      856 863
Nonlinear integral equations with degenerate kernels      863
Nonlinear integral equations with variable integration limit      856
Nonlinear Klein — Gordon equation      702 1315
Nonlinear mathematical physics equations      1301
Nonlinear nth-order difference equation      919
Nonlinear operator      693 695
Nonlinear ordinary differential equations      453—472 488—513 524—527
Nonlinear ordinary differential equations, systems      542—550
Nonlinear partial differential equations      570—584 653—779 1301—1335
Nonlinear partial differential equations, systems      780—798 1343—1382
Nonlinear programming      1027
Nonlinear programming, problem      1027
Nonlinear Schrodinger equation      759 1307
Nonlinear systems of first-order ODEs      1239
Nonlinear systems of ODEs      542—550 1239 1244
Nonlinear systems of PDEs      780—798 1343—1382
Nonlinear systems of PDEs of general form      1374—1384
Nonlinear systems of second-order ODEs      1240
Nonlinear systems of two first-order PDEs      1337
Nonlinear systems of two second-order PDEs      1343
Nonlinear Urysohn integral equation      856
Nonlinear Volterra integral equation      856 858 860 861
Nonlinear wave equations      723 1312—1317
Nonnegative Hermitian operator      207
Nonnegative quadratic form      216
Nonnegative symmetric operator      207
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
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