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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
Inverse scattering problem      760
Inverse scattering problem, method      755
Inverse transform      435
Inverse transform, Fourier      443
Inverse transform, Fourier cosine      445
Inverse transform, Fourier sine      446
Inverse transform, Hankel      446
Inverse transform, Kontorovich — Lebedev      448
Inverse transform, Laplace      437
Inverse transform, Meijer      447
Inverse trigonometric functions      30
Inverse trigonometric functions integration formulas      34
Inverse trigonometric functions, arccosine      32
Inverse trigonometric functions, arccotangent      32
Inverse trigonometric functions, arcsine      31
Inverse trigonometric functions, arctangent      32
Inverse trigonometric functions, differentiation formulas      34
Inverse trigonometric functions, expansion in power series      34
inversion      178 422
Invertible linear operator      205
Invertible mapping      226
Invertible transformation      267
Involutive matrix      172
Involutory function      917 1423
Irrational numbers      4 5
Irreducible representation      231
Isolated point      371
Isolated singularity      413
Isometric correspondence      395
Isomorphic Euclidean spaces      194
Isomorphic groups      227
Isomorphic linear spaces      189
Isomorphic mapping of groups      227
Isomorphic unitary spaces      196
Isomorphism      226 227
Isomorphisms of linear spaces      188
Isoperimetric constraints      1002
Isoperimetric problem      1002
Isosceles trapezoid      54
Isosceles triangle      43 50
Isosceles triangle, base      50
Isosceles triangle, leg      50
Iterated integral      319
iterated kernel      822 832 838
Iteration axis      876
Iteration of function      907
Iteration process      858
Jacobi condition      998 1000 1004 1007
Jacobi condition, strengthened      1000 1004 1007
Jacobi elliptic functions      979
Jacobi equation      998 1004 1007
Jacobi method      217
Jacobi polynomials      986
Jacobi theorem      180
Jacobi theta functions      978
Jacobi — Mayer bracket      574
Jacobian      267 321
Jacobian determinant      321
Jensen equation      1436
Jensen inequality      15 245 297
Joining face of prism      61
Joint distribution function      1064
Joint distribution function of random variables      1057
Joint probability function      1059 1064
Jordan cell      182
Jordan form of matrix, canonical      182
Jordan lemma      417 436
Jump conditions      561 568 791
K-transform      449
Kernel of integral equation      801 825 829
Kernel of integral transform      435
Kernel of linear operator      205
Kernel with weak singularity      801 825 829
Kernel, degenerate      801 802 810 811 825 829
Kernel, difference      801 804 810 813 825 829 841
Kernel, Fredholm      825 829
Kernel, iterated      822 832
Kernel, logarithmic      801
Kernel, polar      801 825
Kernel, positive definite      837
kernel, symmetric      825 829
Khokhlov — Zabolotskaya equation      658
Klein — Gordon equation      625 1280
Kolmogorov distribution      1086
Kolmogorov test      1099
Kolmogorov theorem      1070
Kontorovich — Lebedev inversion formula      448
Kontorovich — Lebedev transform      448 449
Korteweg — de Vries equation      752 756 759 764 1327
Korteweg — de Vries equation, cylindrical      1328
Korteweg — de Vries equation, modified      1328
Kronecker delta, xxxii      
Kronecker product of matrices      175
Kronecker — Capelli theorem      198
Kth absolute moment      1044
Kth central moment      1043
Kth moment      1043
Kth sample central moment      1087
Kth sample moment      1087
Kummer convergence criterion for series      340
Kummer functions      956
Kummer series      956 1215
Kummer transformation      345 957
Kummer — Liouville transformation      475
kurtosis      1045
L'Hospital rules      254
L'Huiller equation      74
Lagrange equation      467
Lagrange function      270
Lagrange method      217
Lagrange multiplier      270
Lagrange multiplier rule      1002
Lagrange principle      1008
Lagrange problem      1008
Lagrange theorem      254
Lagrange — Charpit method      573
Lagrangian      767 993 1002 1006
Lagrangian, Bolza      1001
Lagrangian, Noetherian symmetry      768
Laguerre polynomials      957 982
Laguerre polynomials, generalized      983
Lalesco — Picard equation      1403
Lame coefficients      1196
Landen transformations      974 975
Laplace cascade method      600
Laplace equation, ODE      520
Laplace equation, PDE, three-dimensional      643
Laplace equation, PDE, two-dimensional      633 1282
Laplace integral      418 521 963
Laplace integral, general form      292
Laplace integral, special form      291
Laplace operator      272
Laplace theorem      177
Laplace transform      436 548 611 804 813 843 856
Laplace transform inverse      437
Laplace transform, convolution theorem      437
Laplace transform, for derivatives      611
Laplace transform, limit theorems      440
Laplace transform, properties      437
Laplace transform, solving linear problems for hyperbolic equations      614
Laplace transform, solving linear problems for parabolic equations      612
Laplace transform, tables      1157—1163
Laplace-type multiple integral      328
Large discriminant      108
Large numbers, strong law      1070
Large numbers, weak law      1069
Largest value of function      258
Lateral face of pyramid      63
Latitude      119
Laurent series      410 412
Lavrentiev regularization method      827
Law of conservation of mass      784
Law of Cosines      44
Law of cosines of angles      73
Law of cosines of sides      73
Law of Large Numbers      1069 1070
Law of Sines      44 73
Law of tangents      44
Law, commutative composition      225
Law, composition      225
Law, conservation      766
Law, conservation at discontinuity      561
Law, energy conservation      996
Law, weak of large numbers      1069
Laws, de Morgan      1032
Lax condition      792
Lax pair      755
Least common multiple      4
Least-squared error method      511
Least-squares method      509 1092
Left arm of hyperbola      101
Left coset      227
Left directrix of ellipse      99
Left directrix of hyperbola      102
Left focal radius      99 102
Left focus of ellipse      99
Left focus of hyperbola      102
Left half-plane      79
Left inverse matrix      171
Left rectangular Cartesian coordinate system      79
Left-hand limit      240
Leg of isosceles triangle      50
Leg of right triangle      50
Leg of trapezoid      54
Legendre condition      998 999 1004 1007
Legendre condition, strengthened      999 1004 1007
Legendre equation      1217—1219
Legendre function      962
Legendre function, associated      964 965
Legendre function, first kind, associated      965
Legendre function, modified associated      966
Legendre function, second kind      1217
Legendre function, second kind, associated      965
Legendre functions, Wronskians      967
Legendre polynomial, xxxi      962 1217
Legendre theorem      72
Legendre transformation      469 660
Legendre transformation with many variables      663
Leibnitz convergence criteria      341
Leibnitz convergence criterion for series      341
Leibnitz formula      256
Lemma, Jordan      417
Lemma, Neyman — Pearson      1097
Length of element      193
Length of segment      77
Length of vector      113
Level line      264 1014
Level, confidence      1093
Levi — Civita symbol      179
Levy solution      914
Lie group      730
Lie group of point transformations      730
Lienard equation      1225
Light rays, equation      1259
Likelihood equation      1092
Likelihood function      1092
Likelihood ratio      1097
Likelihood ratio test      1097
Limit of function      240 264
Limit of sequence      237
Limit theorems      1068 1069
Limit theorems, for Bernoulli process      1038
Limit theorems, for Laplace transform      440
Limit, first noteworthy      241
Limit, left-hand      240
Limit, lower of sequence      240
Limit, noteworthy second      241
Limit, partial of sequence      240
Limit, right-hand      240
Limit, upper of sequence      240
Limiting self-similar solution      675
Lindeberg central limit theorem      1071
Line in space      131
Line integral, first kind      329
Line integral, second kind      330 331
Line, deviation of point from line      93
Line, Euler      47
Line, level      264 1014
Line, Simpson      47
Line, support      1014
Line, tangent      251
Line, tangent to surface      388
Linear algebraic equation      157
Linear combination of column vectors      171
Linear combination of row vectors      171
Linear combination of vectors      188
Linear constant-coefficient partial differential equation      588
Linear difference homogeneous equation with constant coefficients      906
Linear eccentricity of ellipse      98
Linear eccentricity of hyperbola      102
Linear equation integral      801 810 824 829
Linear equation, algebraic      157
Linear equation, difference      881 885 889 1421 1425
Linear equation, difference, constant-coefficient      1409 1422 1426
Linear equation, ordinary differential      472 518 1213
Linear equation, partial differential, elliptic      592
Linear equation, partial differential, hyperbolic      592
Linear equation, partial differential, parabolic      591
Linear equations of mathematical physics      1267
Linear first-order ODE      457
Linear form      213
Linear functional      213
Linear functional equations      907 1414—1421 1438
Linear functional equations in one independent variable      1409
Linear group, general of dimension n      228
Linear harmonic oscillator      1277
Linear homogeneous difference equations      904
Linear homogeneous difference equations with constant coefficients      894 904
Linear homogeneous difference equations with variable coefficients      895 901
Linear homogeneous functional equations      910
Linear integral equations, first kind with constant limits of integration      824 1396—1400
Linear integral equations, first kind with variable limit of integration      801 1385—1390
Linear integral equations, second kind with constant limits of integration      829 1401—1408
Linear integral equations, second kind with variable limit of integration      810 1391—1395
Linear nonhomogeneous difference equations      906
Linear nonhomogeneous difference equations with constant coefficients      895 899
Linear nonhomogeneous difference equations with variable coefficients      896 902
Linear nonhomogeneous functional equations      912
Linear operator      204
Linear operator in matrix form      208
Linear operator injective      205
Linear operator invariant      211
Linear operator inverse      205
Linear operator invertible      205
Linear operator, canonical form      213
Linear operator, characteristic equation      211
Linear operator, determinant      209
Linear operator, kernel      205
Linear operator, matrix      208
Linear operator, nondegenerate      205
Linear operator, norm      204
Linear operator, range      205
Linear operator, rank      206
Linear operator, trace      209
Linear operators, product      205
Linear operators, sum      204
Linear ordinary differential equations      457 472—488 514—524 1212—1222
Linear ordinary differential equations, canonical form      473
Linear partial differential equations      553—650 1267—1298
Linear partial differential equations, canonical form      585—590
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