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



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Название: Survey of Applicable Mathematics

Автор: Rektorys K. (ed.)

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1969

Количество страниц: 1369

Добавлена в каталог: 06.12.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Strophoid      189
Student's t-test      1273
Sturm — Liouville problem      806
Sturm's theorem      772 1171
Subnormal      162 339
Subsequences      377
Subset      83
Substantially singular point      347
Subtangent      162 339
Success, in Bernoulli experiment      1246—1247
Successive approximations, solving differential equations      1067—1069
Successive approximations, solving integral equations      1137
Summabilities of series      674
Supercritical damping      197
Superosculating circle      325
Superosculating curve      322
Supremum (l.u.b.)      43
Surface(s) of revolution      257
Surface(s), conical      262
Surface(s), contravariant and covariant vector, on      290
Surface(s), cuspidal edge      354
Surface(s), definition      247
Surface(s), differential calculus, applications to      657—661
Surface(s), discriminant      362
Surface(s), edge of regression      354
Surface(s), element of area      362
Surface(s), elliptic point of      363
Surface(s), envelope of 1-parameter family      356
Surface(s), equipotential      271
Surface(s), explicit equation of      344
Surface(s), finite piecewise smooth      343—344
Surface(s), first fundamental form      291 360—362
Surface(s), fundamental coefficients      362
Surface(s), Gaussian curvature      368
Surface(s), generator of      355 358
Surface(s), hyperbolic point of      363
Surface(s), integrals      638—645
Surface(s), integrals of first and second kinds      639—640
Surface(s), interior diameter      638
Surface(s), lines of curvature      369
Surface(s), mean curvature      368
Surface(s), non-developable      354
Surface(s), normal curvature      366
Surface(s), normal section radius of curvature      366
Surface(s), oriented      638
Surface(s), orthogonal conjugate net on      369
Surface(s), parabolic point of      363
Surface(s), parameters and parametric equations      344
Surface(s), regular points on      247
Surface(s), ruled      259
Surface(s), scalar on      290
Surface(s), scroll (skew surface)      354
Surface(s), second fundamental form      363—364
Surface(s), second order      247—257
Surface(s), shape with respect to tangent plane      363—364
Surface(s), simple finite piecewise smooth      604—605
Surface(s), singular points on      247
Surface(s), tensor on      287—292
Sylvester's law of inertia      105
Symbols O(g(x)), o(g(x))      414
Symmetric kernels of integral equations      816
Symmetric matrices      89
Symmetric operators      1018 1045
Symmetric problems      805
Systematic errors      1316
Tabular inaccuracy      1228 1243
Tabulation of 2-variable functions      1239—1242
Tangent and cotangent, integrals, containing      539—541
Tangent(s) to a conic      229—232
Tangent(s), developable (surface)      354
Tangent(s), direction, angle and length, in polar coordinates      338—339
Tangent(s), drawn to a curve from an arbitrary point      341
Tangent(s), length, in polar coordinates      339
Tangent(s), plane of a surface      349
Tangent(s), plane to a curve      310
Tangent(s), surface      354
Tangent(s), theorem      117
Tangent(s), vector field      287
Tangent(s), vector of a curve      270 304
Tangential vector of a surface      349
Taylor's formula      434
Taylor's formula for polynomial      61
Taylor's series      681—682 957—958
Taylor's theorem      434 439
Taylor's theorem, generalization for several variables      452—454
Temperature distribution, example using Laplace transform      1129—1130
Tensor(s) in space      284—287
Tensor(s) on a surface      287—292
Tensor(s), alternating      294
Tensor(s), calculus      280—296
Tensor(s), characteristic numbers of      296
Tensor(s), conjugate directions      295
Tensor(s), contravariant and covariant      285
Tensor(s), contravariant and covariant on a surface      287
Tensor(s), deformation      287 294
Tensor(s), first fundamental of a surface      290
Tensor(s), indicatrix of a point      295
Tensor(s), indices, lowering and raising of      293
Tensor(s), metric of a space      285
Tensor(s), metric of a surface      290
Tensor(s), quadratic      285
Tensor(s), second fundamental, of a surface      291
Tensor(s), symmetric and skew-symmetric      293—294
Tensor(s), symmetric quadratic      292—297
Term-by-term differentiation      669 673 955
Term-by-term integration      668 672 955
Theoretical regression function and curve      1287
Tillot inequality      1169
Total differential      447—450
Tractrix      185
Trajectories to solutions of differential equations      761—762
Transcendent curve      301
Transcendental branch point of logarithmic function      967
Transcendental equations, numerical solution of      1168—1182
Transcendental functions      402 488 541—548
Transcendental real numbers      43
Transformation matrix of coordinate systems      281
Transformations of differential expressions into polar, cylindrical and spherical coordinates      472—476
Transformations, affine      227—229
Transformations, congruent, of cartesian coordinates in a plane      224—225
Transformations, mapping      84 455—458
Transformations, projective in a plane      228—229
transforms      see "Integral transforms"
Transient oscillations      200
Translation, cartesian coordinate system      236
Transparency used in nomography      1210—1213
Transparency used in nomography, positional contacts      1210
Transparency used in nomography, symbolic key (structural formula)      1211
Transparency used in nomography, transformation formulae      1212
Transversality conditions of variational problem      1039
Transverse vibrations of a rod, differential equations      853—854
Trapezoidal rule for definite integrals      593
Trefftz method for boundary value problems      1056—1058
Triangle(s), area of      207
Triangle(s), centroid of      238
Triangle(s), formulae for geometrical elements of      133—134
Triangle(s), general (scalene)      116
Triangle(s), general (scalene), formulae for determining      117—120
Triangle(s), general (scalene), fundamental and further relations      117—118
Triangle(s), general (scalene), solution      118—120
Triangle(s), geometrical formulae      133—134
Triangle(s), inequality      46 48
Triangle(s), spherical      120
Trigonometric equations      115—116
Trigonometric Fourier series      702—720
Trigonometric functions of same angle, relations among      109—113
Trigonometric functions, addition formulae      112—113
Trigonometric functions, behaviour of      109
Trigonometric functions, definitions of      108—109
Trigonometric functions, difference of      114
Trigonometric functions, expansions into series      684—685
Trigonometric functions, half-angle formulae      112—113
Trigonometric functions, higher powers of      114
Trigonometric functions, inverse      124—128
Trigonometric functions, multiple-angle formulae      112—113
Trigonometric functions, powers of      114
Trigonometric functions, product of      114
Trigonometric functions, relations between      130
Trigonometric functions, signs in individual quadrants      110
Trigonometric functions, sum of      114—115
Trigonometric functions, values for some special angles      111
Trigonometry, plane      116—120
Trigonometry, spherical      120—124
Triple integrals      618—622
Triple integrals, improper      623—628
Triple integrals, method of substitution for      621
Triple scalar product of three vectors      268
Trochoid      165
Tube, volume and moment of inertia      146
Twisted curve      301
Ultrahyperbolic equation      883
Umbilic, umbilical point      368—369
Undamped forced vibrations, differential equations      843
Undamped oscillations, forced, curves of      195—196
Undamped oscillations, free, curves of      194—195
Undetermined coefficients, Lagrange's method of      480—481
Uniform convergence, sequences with variable terms      666 954
Uniform convergence, series with variable terms      671 954
Uniformly bounded sequence      667—668
Uniformly convergent integral      574—575
Union of sets      83
Uniqueness of solution of problems in ordinary differential equations      731—738
Uniqueness of solution of problems in partial differential equations      887 904 906 910
Unit (tangent) vector of a curve      270 304
Univalent (simple) function in a region O      943
Unsubstantially singular point of a curve, or surface      299 347
Upper integral of Darboux sums      550
Van der Pol's equation      1097
Variables, Functions of 2 or more      440—485
Variables, separation for solving differential equation      739—741
Variance      1279
Variation coefficient      1266
Variation coefficient of parameters      780
Variational (direct) methods      1045—1064
Variational (direct) methods for eigenvalue problems in ordinary differential equations      1090—1093
Variational (direct) methods in conformal mapping      986—989
Vector(s) in 3-dimensional space      263
Vector(s) in algebra      62—63
Vector(s) of acceleration, components of      314
Vector(s) on a surface      289—292
Vector(s), 2- and 3-dimensional      206
Vector(s), absolute value      265
Vector(s), algebra      62—63 263—269
Vector(s), analysis      269—279
Vector(s), circulation along closed curve      276
Vector(s), collinear (parallel) and coplanar      265
Vector(s), complex      62
Vector(s), components, coordinates of      62 263
Vector(s), conformably collinear (parallel)      265—266
Vector(s), contravariant and covariant      280—285
Vector(s), cross product      267
Vector(s), curvilinear and surface integrals      276—279
Vector(s), derivative      269
Vector(s), direction angles, direction cosines      266
Vector(s), dot product of      266
Vector(s), equation of a straight line      243
Vector(s), field      269
Vector(s), field, divergence and curl      272—276
Vector(s), field, irrotational      273
Vector(s), field, solenoidal (sourceless)      272
Vector(s), flux of      278
Vector(s), inner product      266
Vector(s), laws      62 264
Vector(s), length or magnitude      206 265
Vector(s), linearly dependent or independent      62—63
Vector(s), magnitude, norm, modulus      265
Vector(s), mixed product      268
Vector(s), n-component (n-coordinate)      62
Vector(s), non-coplanar in space      281
Vector(s), notation for Stokes, Gauss and Green theorems      277—279
Vector(s), outer product      267
Vector(s), principal normal (unit)      270
Vector(s), product      264 267
Vector(s), rank of a system of      63
Vector(s), real      62
Vector(s), scalar product of      266
Vector(s), signs and notation      30—31
Vector(s), space      1001—1003
Vector(s), space, n-dimensional      62
Vector(s), triple product      268
Vector(s), vector product      267
Vector(s), zero or null      62 263
Vibrating string equation      1098—1102
Virtual cone      254
Virtual quadric      256
Virtual sphere      247
Void set      83
Volterra integral equations      934—936
Volumes, formulae      142—149 653—657
Wallis's product      381 396
Wave equation      901—907
Weakly nonlinear oscillator      1095—1097
Weierstrass, M-test      671—672 954
Weierstrass, theorem      408 954—955
Weight function      697
Weighted average, weighted variance      1267
Weingarten, fundamental equation for surfaces      371
Well posed problems      866
Work done by force moving along a given curve      661
Wronskian determinant      776—777
Z-nomogram      1201
Zero, divisors      86
Zero, vector      63 263
Zeta function      672
1 2 3 4 5 6 7 8 9
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