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Rektorys K. (ed.) — Survey of Applicable Mathematics
Rektorys K. (ed.) — Survey of Applicable Mathematics



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Íàçâàíèå: Survey of Applicable Mathematics

Àâòîð: Rektorys K. (ed.)

Àííîòàöèÿ:

This major two-volume handbook is an extensively revised, updated second edition of the highly praised Survey of Applicable Mathematics, first published in English in 1969.
The thirty-seven chapters cover all the important mathematical fields of use in applications: algebra, geometry, differential and integral calculus, infinite series, orthogonal systems of functions, Fourier series, special functions, ordinary differential equations, partial differential equations, integral equations, functions of one and several complex variables, conformal mapping, integral transforms, functional analysis, numerical methods in algebra and in algebra and in differential boundary value problems, probability, statistics, stochastic processes, calculus of variations, and linear programming. All proofs have been omitted. However, theorems are carefully formulated, and where considered useful, are commented with explanatory remarks. Many practical examples are given by way of illustration. Each of the two volumes contains an extensive bibliography and a comprehensive index.
Together these two volumes represent a survey library of mathematics which is applicable in many fields of science, engineering, economics, etc.
For researchers, students and teachers of mathematics and its applications.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1969

Êîëè÷åñòâî ñòðàíèö: 1369

Äîáàâëåíà â êàòàëîã: 06.12.2013

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Improper integrals, double and triple      623—628
Improper integrals, involving a parameter      572—579
Indefinite integrals      486
Indefinite integrals, tables of irrational functions      516—529
Indefinite integrals, tables of rational functions      508—516
Indefinite integrals, tables of transcendental functions      541—548
Indefinite integrals, tables of transcendental functions, exponential      543—544
Indefinite integrals, tables of transcendental functions, hyperbolic      541—542
Indefinite integrals, tables of transcendental functions, inverse hyperbolic      548
Indefinite integrals, tables of transcendental functions, logarithmic      544—546
Indefinite integrals, tables of trigonometric functions containing, cosine      532—535
Indefinite integrals, tables of trigonometric functions containing, sine and cosine      535—539
Indefinite integrals, tables of trigonometric functions containing, sine only      529—532
Indefinite integrals, tables of trigonometric functions containing, tangent and cotangent      539—541
Indefinite integrals, tables, remarks      548—549
Independent variable      397
Indicatrix of Dupin      368
Indicial equation      793
Inequalities between real numbers      44—46
Inequalities, basic rules of      41
Inequalities, Cauchy's, Hoelder's, Minkowski's      46—47
Inertia, Sylvester's law of      105
Infimum (g.l.b.)      43
Infinite products      395—396
Infinite series of constant terms      381—395
Infinite series of constant terms, Convergence      381
Infinite series of constant terms, important formulae      392—395
Infinite series of constant terms, multiplication or product      391—392
Infinite series of functions      670—690
Initial line (polar coordinates)      216
Initial point of vector      264
Initial value problems in ordinary differential equations, applicability of different methods      1082—1083
Initial value problems in ordinary differential equations, notation      1065—1067
Initial value problems in ordinary differential equations, solution by Adams extrapolation      1076—1080
Initial value problems in ordinary differential equations, solution by Adams interpolation      1080—1082
Initial value problems in ordinary differential equations, solution by expansion in a power series      1069—1071
Initial value problems in ordinary differential equations, solution by perturbation method      1071—1073
Initial value problems in ordinary differential equations, solution by polygon method      1073—1075
Initial value problems in ordinary differential equations, solution by Runge — Kutta method      1075—1076
Initial value problems in ordinary differential equations, solution by successive approximations      1067—1069
inner product of functions      694—695
Inner product of vectors      266
Integers      41
Integrability of some systems      912
Integrability, Lebesgue (L) and Riemann (R) distinguished      596
Integral calculus of functions of 1 variable      486—601
Integral calculus of functions of 1 variable, approximate evaluation of definite integrals      592—595
Integral calculus of functions of 1 variable, basic integrals      486—489
Integral calculus of functions of 1 variable, definite integrals      550
Integral calculus of functions of 1 variable, definite integrals, table      579—584
Integral calculus of functions of 1 variable, indefinite integrals      486
Integral calculus of functions of 1 variable, indefinite integrals, table      508—549
Integral calculus of functions of 1 variable, integrals involving a parameter      572—579
Integral calculus of functions of 1 variable, integrals that can be rationalized      501—508
Integral calculus of functions of 1 variable, Lebesgue and Stieltjes integration      595—600
Integral calculus of functions of 1 variable, methods of integration      489—495
Integral calculus of functions of 1 variable, rational functions      495—500
Integral calculus of functions of 1 variable, Riemann (Cauchy — Riemann) integration      550
Integral calculus of functions of 1 variable, series expansions      588—592
Integral calculus of functions of 1 variable, survey of some important formulae      600—601
Integral calculus of functions of 2 or more variables      602—665
Integral calculus of functions of 2 or more variables, basic definitions and notation      602—605
Integral calculus of functions of 2 or more variables, surface integrals      638—645
Integral calculus of functions of 2 or more variables, survey of some important formulae      663—664
Integral calculus, applications in geometry and physics      645—663
Integral calculus, work done by a force moving along a curve      661
Integral curve      733
Integral equations      917—937
Integral equations in conformal mapping      989—991
Integral equations of first kind      936—937
Integral equations of Fredholm type      918
Integral equations of second kind      918
Integral equations of Volterra type      934—936
Integral equations with Cauchy kernel      934
Integral equations with degenerate kernels      923—925
Integral equations with Hilbert kernel      933
Integral equations with symmetric kernels      926—928
Integral equations with weak singularities      932—934
Integral test for convergence of a series      386
Integral transforms 1-dimensional finite      1136
Integral transforms 2- and multidimensional      1135—1136
Integral transforms, applications      1128—1130
Integral transforms, Fourier, Hankel, Laplace, Laplace — Carson, Mellin      1125
Integral transforms, fundamentally important results      1130—1135
Integral transforms, grammar for Laplace transforms      1134
Integral transforms, Laplace, applied to solving differential equations      1128—1130
Integral, curvilinear along a curve in space      633
Integral-valued random variables      1255—1257
Integrals of a differential equation      731
Integrals of Cauchy's type      949—953
Integrals of functions of complex variables      943—948
Integrals, able to be rationalized      501—508
Integrals, convergent and divergent      560
Integrals, curvilinear      628—637
Integrals, definite      550 605 618
Integrals, Definite, table      579—584
Integrals, double      605—618
Integrals, elliptic      589—592
Integrals, hyperelliptic      589
Integrals, improper      560—571 623—628
Integrals, indefinite      486
Integrals, Indefinite, table      508—549
Integrals, involving a parameter      572—579
Integrals, Legendre      590
Integrals, particular      731—732
Integrals, series expansions      588—592
Integrals, singular      737 871
Integrals, surface      638—645
Integrals, triple      618—628
Integrating factor in differential equation      750—751
Integration by differentiation with respect to a parameter      493—494 572
Integration by parts      489—490 557
Integration by substitution      491—493 558 615 621
Integration in an infinite interval      565
Integration of Fourier series      711—716
Integration of rational functions      495—500
Integration of series with variable terms (term-by-term integration)      672—673
Integration, Cauchy — Riemann      550
Integration, graphical      1214
Integration, Lebesgue      596
Integration, Riemann      550
Integration, Stieltjes      598
Intercepts on axes of coordinates      208
Interchange of limit and differentiation (integration)      668—669 672—673 678—679
Interior diameter of surface      638
Interpolation      1220—1244
Interpolation, applications to approximate solution of equations      1237—1239
Interpolation, arithmetic operations with approximate numbers      1242—1244
Interpolation, basic arguments      1225
Interpolation, Bessel formula      1233—1234
Interpolation, central-difference formulae      1230—1236
Interpolation, divided differences      1221—1222
Interpolation, double linear interpolation      1240—1242
Interpolation, equidistant (equal) arguments formula      1227—1229
Interpolation, Everett formula      1234—1236
Interpolation, Everett formula, written in Horner form      1235
Interpolation, Gauss's formula      1231—1232
Interpolation, general formulae      1220 1222—1225
Interpolation, general formulae, Lagrange's      1222—1223
Interpolation, general formulae, Newton's      1223—1225
Interpolation, iterative method      1237—1239
Interpolation, linear interpolation      1236—1237
Interpolation, regula falsi      1237
Interpolation, statement of the problem      1220
Interpolation, step of argument, step of table      1225
Interpolation, Stirling interpolation formula      1232—1233
Interpolation, tabular inaccuracy      1228—1229 1243
Interpolation, tabulation of functions of 2 variables      1239—1242
Intersection of 2 straight lines      210—211
Intersection of sets      83
Intersection of straight line with circle      220
Intervals (open, closed, infinite, ...)      397
Invariants      253 792
Inverse functions      400
Inverse functions, hyperbolic      130—132
Inverse functions, trigonometric      124—128
Inversion of a permutation      55
Involute of a catenary      185
Involute of a circle, construction and theorems      172—174
Involute of a curve      335—338
Involute, curtate and prolate      173
Irrational numbers      43
Irregular nets      1112
Irrotational vector field      273
Isoclines method of solving differential equations      1217—1218
Isogonal trajectories      762
Isogonal trajectories of a 1-parameter family of curves      342—343
Isoperimetric problems      1041
Iterative methods for calculation of eigenvalues of a matrix      1161—1164
Iterative methods of interpolation      1237—1239
Iterative methods, general, for solving algebraic and transcendental equations      1179—1180
Jacobi(an) determinants      456—458
Jacobi(an) elliptic functions      591—592
Jacobi(an) matrix      1180
Jacobi(an) polynomials      727—728
Jensen inequality      1252
Jordan block, matrix      98—99
Jordan curve      603
Jordan region      603
Joukowski aerofoils      979
Kantorovitch method for boundary value problems      1054—1056
Kelvin method of solving differential equations graphically      1218—1219
Kernel replacement      1141
Kirchhoff's formula      902
Kneser's theorem      773
Kochanski's rectification of circle      151—152
Kovalewski's theorem      862
Kronecker delta      282
Kuepper's conoid      262
L and R integration      596
l'Hospital's rule      380
l.u.b. (least upper bound)      43
Lagrange differential equation      757—758
Lagrange form of Taylor's theorem      435
Lagrange identity      268
Lagrange inequality      1169
Lagrange interpolation formula      1222—1223
Lagrange mean-value theorem      425—426
Lagrange method of undetermined coefficients (multipliers)      480—481
Lagrange — Charpit solution of Cauchy problem in 2 variables      875—876
Laguerre polynomials      728—729
Laplace differential equation      884
Laplace differential equation, Dirichlet problem in      886
Laplace differential equation, Neumann problem in      886
Laplace Integral transform      1125—1145
Laplace operator in vector analysis      275
Laplace transform      1125—1128
Laplace transform, applications to solving differential equations      1128—1130
Laplace — Gauss integral      580 589
Laplacian operator, properties      275
Large numbers, law of      1261—1262
Lattice nomograms      1189—1195
Latus rectum      218
Laurent series      958—961
Laurent series, essential singularity      960
Law of growth      200
Law of Large Numbers      1261—1262
Least squares method      1285—1321
Least squares method, adjustment of data by      1317—1320
Least squares method, best linear unbiassed estimates      1303—1304
Least squares method, best linear unbiassed estimates, variances and covariances      1306
Least squares method, boundary value problems      1061—1062
Least squares method, Calculus of observations      1315—1321
Least squares method, defining equations      1301
Least squares method, defining equations, matrix of rank smaller than p      1314—1315
Least squares method, defining equations, parameters restricted by linear constraints      1309—1310
Least squares method, Gauss — Markov theorem      1304
Least squares method, general problems      1301
Least squares method, normal distribution of random variables      1308—1309
Least squares method, normal equations      1304
Least squares method, parametric function      1303—1304
Least squares method, principle      1285—1288
Least squares method, residual sum of squares      1287
Least squares method, signs and notation      35—36
Least squares method, standard error estimates      1306—1307
Least squares method, standard error estimates, unconditioned observations      1319
Least squares method, weights      1310—1314
Least upper bound (l.u.b.)      43
Lebesgue and Riemann integration distinguished      596
Lebesgue and Stieltjes integration      595—600
Left-handed coordinate systems      234
Legendre differential equation      722 848
Legendre elliptic functions      591—592
Legendre integrals      590
Legendre polynomials      722—726 849
Lehmer's process      1175—1176
Leibniz rule for convergence of series      388
Leibniz rule for derivatives      422
Lemniscate of Bernoulli      189—190
Length of a vector      206
Length, integral calculus for curves in space      649
Length, integral calculus for plane curves      647
Level surfaces of scalar field      270
Liapunov theory      827—828
Liapunov type of surfaces      894
Liebmann iteration method      1121
Limacon of Pascal      191—192
Limit point      994
Limiting processes under the differentiation sign      669
Limiting processes under the integral sign      668—669
Limiting processes, interchange of      668
Limits      374 409—415 442 940
Limits of composite functions      410—411
Limits, from right or left      409—410
Limits, important      380—381
Limits, infinite      411—413
Line segment, division in a given ratio      207
Linear algebraic equations, equivalent systems      70—71
Linear algebraic equations, numerical methods of solving systems of      1146—1160
Linear concepts in solid analytic geometry      237—247
Linear differential equations      743 775
Linear differential equations of n-th order      775—780
Linear differential equations of second order with variable coefficients      790—798
Linear differential equations of second order with variable coefficients, oscillatory solutions      771
Linear differential equations, characteristic exponent      775
Linear differential equations, discontinuous solutions      798—801
Linear differential equations, Euler      784—785
Linear differential equations, Fuchsian type      793
Linear differential equations, fundamental equation      793—795
Linear differential equations, fundamental system of      778
Linear differential equations, homogeneous      743
Linear differential equations, homogeneous, corresponding to nonhomogeneous      776
Linear differential equations, homogeneous, periodic solutions to      774—775
Linear differential equations, homogeneous, with constant coefficients      782—786
Linear differential equations, indicial equation      793
Linear differential equations, nonhomogeneous      780—782
Linear differential equations, nonhomogeneous, with constant coefficients      786—790
Linear equations, algebraic, definition and properties      70—71
Linear equations, algebraic, definition and properties, solution without using determinants      71—73
Linear equations, algebraic, definition and properties, solution, using determinants      74—75
Linear function of a random variable      1254
Linear interpolation      1236—1237
Linear manifold      1002
Linear operator      1009
Linear regression functions      1288—1291
Linear segment division in a given ratio      207
Linear space      1001—1003
Lines of curvature on a surface      369
Lines of force      271
Liouville's formula      777
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