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| Rektorys K. — Survey of applicable mathematics |
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| Предметный указатель |
"Del" operator 272
 -region 988-9
 -component (-coordinate) complex vector 62
-dimensional vector space 62
 -quantile 1251
 -integrability see Riemann
 -neighbourhood of a point 442
1-parameter family of plane curves, envelopes of 330-4
1-parameter family of plane curves, envelopes of, of surfaces, envelopes of 355
2 or more variables, functions of 440-85
2 or more variables, functions of, extremes 476-84
2 or more variables, functions of, introduction of new variables, transformations 470-6
2 or more variables, functions of, survey of important formulae 484-5
Abel's identity 777
Abel's identity, integral equation 937
Abel's identity, summability of a series 674
Abel's identity, tests for convergence of a series 388
Abel's identity, theorem of power series 676 956
Abelian groups 85
Absolute accuracy, absolute error, of a scale 1186-7
Absolute and relative errors (approximate numbers) 1242
Absolute value, of a complex number 48
Absolute value, of a real number 46
Absolute value, of a vector 265
Acceleration, vector of, components 314
Accumulation point 378 994
Adams method of solving differential equations by extrapolation 1076-80
Adams method of solving differential equations by interpolation 1050-2
Addition of tensors 292
Addition of trigonometric functions, formulae 112-3
Addition of vectors 263-4
Addition theorem for expectations 1259
Addition theorem for variances 1261
Adjoined equations 802 914
Adjoined equations, system of coordinates 234
Adjustment of data by method of least squares 1317-20
Admissible parameter 302
Affine ratio and transformations 227-9
Airy's function, biharmonic equation for 912-3
Airy's function, in problems of elasticity 943
Algebra, fundamental theorem of 59
Algebra, signs and notations 27-29
Algebraic branch point 967
Algebraic curves 187-94 301 327
Algebraic equations, Numerical solution of 1168-82
Algebraic equations, of higher degree 75-77
Algebraic equations, Quadratic, cubic, biquadratic 77-79
Algebraic real numbers 43
Alignment nomograms 1195-210
Alignment nomograms, anamorphosis, conditions of 1196
Alignment nomograms, binary field 1207-8
Alignment nomograms, grouped 1207
Alignment nomograms, skeleton 1204-6
Almost uniform convergence 954
Alternating series 388
Alternating tensor 294
Alternative distribution 1255
Amplitude of a complex number 49
Amplitude of a sine curve 194
Analytic function of a complex variable 941
Analytic geometry, plane 205-32
Analytic geometry, solid 233-262
Anamorphosis of collinear nomogram 1196
Anchor ring, equation of 258
And multidimensional 1135-6
Angle(s), between 2 curves 342
Angle(s), between 2 planes 240
Angle(s), between 2 straight lines 212-5 246
Angle(s), between a line and a plane 246
Angle(s), bisectors of 216
Angle(s), circular measure and degrees 107-8
Angle(s), of contingence 316
Angle(s), trigonometric functions of 109-11
Angular frequency 194
Annuloid, volume, surface area, moment of inertia 149
Aperiodic motions 197
Applications of integral calculus in geometry and physics 645-665
Approximate expressions 436-8
Approximate numbers, arithmetic operations with 1242-4
Approximate tests of significance 1276
Approximation(s), approximate methods in boundary value problems 1045-64 1083-90 1109-24
Approximation(s), curve constructions 203-4
Approximation(s), eigenvalue problems 1090 5 1054 1059
Approximation(s), first and higher, to various functions 437-8
Approximation(s), Fredholm's integral equations 1137-45
Approximation(s), of a function by a polynomial 408
Approximation(s), periodic solutions 1095-7
Approximation(s), successive, method of, for integral equations 1137-8
Approximation(s), successive, method of, for ordinary differential equations 1067
Archimedes's spiral 173
Archimedes's spiral, constructions and theorems 174-5
Archimedes's spiral, equation in polar coordinates 174
Arcsin, arccos, arctan, arccot functions 124-8
Areas of plane figures, formulae for 133-42
Areas of plane figures, integral calculus 651-2
Argand diagram 48
Argument(s), calculation by interpolation 1237
Argument(s), calculation by interpolation, by 'regula falsi' method 1179 1237
Argument(s), equidistant (equal) 1225
Argument(s), of a complex number 49
Argument(s), of a function 397
Arithmetic and Algebra 39-106
Arithmetic, mean 1265
Arithmetic, operations with approximate numbers 1242-4
Arithmetic, sequences 54
Arsinh, arcosh, artanh, arcoth functions 130-2
Arzela's (or Ascoli's) theorem 668
Associative law 85
Associative law, vectors 264
Associative rings 85
Astroid 172
Asymptotes of hyperbola 159
Asymptotes of plane curves 326-30
Asymptotes of plane curves, in polar coordinates 340-1
Asymptotic behaviour of integrals of differential equations 771
Asymptotic cone of 2 hyperboloids 252
Asymptotic curve (or line) on a surface 370
Asymptotic directions on a surface 364
Asymptotic expansions of series 688-90
Asymptotic point of a curve 176
Axes of coordinates 205
Axial pencil of planes 241
Axioms, for addition and multiplication, groups, rings 85 86
Axioms, of the metric 997
Back substitution 1146
Backward differences 1226-7
Banach fixed-point theorem 1008
Banach space 1003-4
Banachiewicz's method 1151
Basic argument 1225
Basic uniform (regular) scale 1184
Bernoulli and Whittaker method 1172-3
Bernoulli coefficients 549
Bernoulli differential equation 746-7
Bernoulli experiment 1246
Bernoulli lemniscate 189-90
Bernoulli theorem 1262
Bertrand curves 334
Bessel central-difference interpolation formula 1233
Bessel differential equation 717 846
Bessel differential equation, modified 847
Bessel equation 717 790 796 846
Bessel functions 716-21
Bessel functions, of orders zero and one 718
Bessel functions, of second kind 721 797
Bessel functions, of third kind 721
Bessel inequality 699 1005
Bessel interpolation formula 1233-4
beta function 587
Biharmonic equation for Airy's function 912-3
| Binary field in nomogram 1207-8
Binomial distribution 1255-6
Binomial equations 80-81
Binomial integrals, reduction formulae for 528
Binomial series 682-3
Binomial theorem and coefficients 57-58
Binormal (unit vector) to a curve 307-8
Biquadratic equations, solution, algebraic 80
Biquadratic equations, solution, by factorization 79
Bisectors of angles between 2 straight lines 215-6
Bisectors of angles of triangle 118
Bolzano - Cauchy condition 375 383 410
Bolzano - Cauchy condition, improper integrals 560 567
Bolzano - Cauchy condition, of uniform convergence 666 671
Bolzano - Weierstrass theorem 378
Boundary point of a set 995
Boundary properties in conformal mapping 985-6
Boundary value problems of ordinary differential equations 1083-90
Boundary value problems of ordinary differential equations, applicability and choice of methods 1089
Boundary value problems of ordinary differential equations, approximate solution by collocation method 1086
Boundary value problems of ordinary differential equations, approximate solution by direct methods 1086-7
Boundary value problems of ordinary differential equations, approximate solution by finite difference method 1084-6
Boundary value problems of ordinary differential equations, approximate solution by least squares method 1086-7
Boundary value problems of ordinary differential equations, approximate solution by perturbation method 1088-9
Boundary value problems of ordinary differential equations, approximate solution by successive approximations 1088
Boundary value problems of ordinary differential equations, reduction to initial value problems 1083-4
Boundary value problems of partial differential equations 860
Boundary value problems of partial differential equations, approximate solution, direct methods 1045-64
Boundary value problems of partial differential equations, approximate solution, finite difference method 1113-23
Boundary value problems of partial differential equations, approximate solution, Galerkin, Kantorovitch, Ritz and Trefftz methods 1052-61
Boundary value problems of partial differential equations, approximate solution, least squares method 1086-8
Boundary value problems of partial differential equations, approximate solution, product method 1098-1108
Boundary value problems of partial differential equations, approximate solution, transformation to finding the minimum of a quadratic functional 1045-6
Boundary value problems of partial differential equations, approximate solution, variational methods 1045-64
Boundary-correspondence principle 981
Bounded diameter 151
Bounded operator 1013
Bounded sequence 377
Bounded variation, functions of 408-9
Bounds of real numbers 43
Brachistochrone problem 1027-9
Branch points of infinite and finite order 967
Branches of a hyperbola 157
Budan - Fourier theorem 1171
Bundle of planes 242
Calculus of variations 1020-44
Calculus of variations,  -neighbourhood of order  of a curve 1021
Calculus of variations, brachistochrone problem 1027-9
Calculus of variations, categories of problems, "movable (free) ends of admissible curves" 1037-40
Calculus of variations, categories of problems, elementary 1020-9
Calculus of variations, categories of problems, functionals depending on a function of variables 1034-7
Calculus of variations, categories of problems, simplest case of izoperimetric problem 1040-4
Calculus of variations, curves of the -th class 1020-1
Calculus of variations, distance of order between 2 curves 1020
Calculus of variations, Euler - Poisson equation 1033
Calculus of variations, Euler equation and special cases 1026
Calculus of variations, formulation of individual problems 1021 30 1032 1036-7 1037-8 1041
Calculus of variations, isoperimetric problem 1041
Calculus of variations, necessary conditions for extrema in problems of calculus of variations 1025-6 1030-1 1032 4 1036 1038 41 1041 4
Calculus, differential 397-485
Calculus, integral 486-665
Calculus, operational 1025 36
Calculus, tensor 280-96
Calculus, vector 263-79
Cardioid 170-1
Cartesian coordinates in plane geometry 205
Cartesian coordinates in plane geometry, congruent transformations 224-5
Cartesian coordinates in plane geometry, relations with polar coordinates 217-8
Cartesian coordinates in solid geometry 233
Cartesian coordinates in solid geometry, relations with cylindrical and spherical coordinates 235
Cartesian coordinates in solid geometry, singular points 236
Cartesian coordinates in solid geometry, transformation by translation and by rotation and reflection 236-7
Cartesian product of sets 83
Cask volume formulae 149
Cassinian ovals 189
Catenaries (chainettes) 183-6
Catenaries (chainettes), constant strength 185-6
Catenaries (chainettes), general 183-5
Catenaries (chainettes), involute of (called tractrix) 185
Cauchy canonical form (nomography) 1193 1197
Cauchy canonical form (nomography), mapped by a lattice nomogram 1193
Cauchy canonical form (nomography), transformation of nomographic order 1197-8
Cauchy continuity definition 404 5
Cauchy form of Taylor's theorem 435
Cauchy inequality 46 571
Cauchy integral formula and theorem 946 8
Cauchy integrals, type of 949 53
Cauchy method 875
Cauchy principal value of integral 562 582
Cauchy problem 860-1
Cauchy problem, generalized 863
Cauchy problem, in hyperbolic and parabolic equations 901 907
Cauchy problem, special 860-1
Cauchy problem, uniqueness and well-posed nature, in hyperbolic and parabolic equations 904 909
Cauchy problem, using complete integral 873-4
Cauchy product of series 392
Cauchy root tests for convergence of series 385
Cauchy sequence 999
Cauchy theorem 387 952
Cauchy-Dirichlet formula 762
Cauchy-Riemann integrals 551
Cauchy-Riernann equations 941-2
Cauchy-Schwarz inequality 571
Central dispersions theory 774
Central-difference interpolation formulae 1230-6
Centre of curvature 324 339
Centre of curvature, construction for cyclic curves 174
Centre of gravity, curves in space 649
Centre of gravity, plane curves 648
Centre of gravity, plane figures 649
Centre of gravity, solids 656
Centre of gravity, surfaces 660
Centroids, plane figures 133 42
Centroids, solids 142 9
Ces ro summable series 392
Chain rule 420
Chainettes see Catenaries
Chance errors 1316
Change of order of differentiation 446
Characteristic curve of a family 357
Characteristic equation 782
Characteristic exponent 775
Characteristic matrix of a Jordan block 98-100
Characteristic matrix of a square matrix 97
Characteristic polynomial of a matrix, eigenvalues or characteristic zeros or numbers 97 100
Characteristic value in eigenvalue problem 97 804 913 920 1016
Characteristics and characteristic directions 863
Chasles's Theorem 359
Chebyshev approximate formula for definite integrals 594 5
Chebyshev inequality 1252
Chebyshev polynomials 728 848
Choleski's method 1151
circle 151-2 219-20
Circle, circumscribed on triangle 118
Circle, conchoid of a 191
Circle, constructions of 150-1
Circle, diameter, bounded and conjugate 151
Circle, equation of 219
Circle, equation of, in polar coordinates 220
Circle, formulae for geometrical elements of 137-9
Circle, inscribed in triangle 118
Circle, involute of 172-3
Circle, Involute of, curtate and prolate 173
Circle, of curvature 323 4
Circle, parametric equations of 219 20
Circle, rectification of, Kocha nski's and Sobotka's 151-2
Circle, superosculating 325
Circle, Thalet's 151
Circular cask, volume formula 149
Circular frequency 194
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