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| Rektorys K. — Survey of applicable mathematics |
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| Предметный указатель |
Finite difference method, basic theorems 1123-4
Finite difference method, boundary conditions, formulation containing derivatives 1118
Finite difference method, boundary conditions, formulation not containing derivatives 1117
Finite difference method, boundary value problems for ordinary differential equations 1084-6
Finite difference method, Dirichlet problem 1119-23
Finite difference method, eigenvalue problems for ordinary differential equations 1904-5
Finite difference method, error estimates 1119
Finite difference method, formulae for differential operators 1113-7
Finite difference method, nets, principal types 1112-3
Finite difference method, nets, refinement 1113
First and second curvatures 315-9
First and second integral mean value theorems 554
First integrals (differential equations) 766 828
Fitting of curves to empirical data 1285-1301
Fitting of curves to empirical data, linear regression function 1288-91
Fitting of curves to empirical data, linear regression function, with several independent variables 1297-9
Fitting of curves to empirical data, nonlinear regression functions 1299-1301
Fitting of curves to empirical data, principle of least squares 1285-8
Fixed polhode 165
Floquet's theorem 774
Flow round an obstacle 980-1
Flux of a vector, physical meaning 278
Focal radius of a hyperbola 157
Focus of an ellipse 221
Focus of an ellipse, of a parabola 223
Folium of Descartes 188-9
Forced oscillations, damped 199-200
Forced oscillations, undamped 195-6
Forward differences 1226-7
Fourier - Bessel expansion 720-1
Fourier coefficients 698 703 1005
Fourier integral 713
Fourier integral transform 1125
Fourier method, partial differential equations 1098-1108
Fourier series 702-20
Fourier series, differentiation and integration of 711-2
Fourier series, expansions of some important functions 707-11
Fourier series, generalized 698
Fourier series, harmonic analysis 714-6
Fourier series, in 2
Fourier series, in complex form 711
Fourier series, pointwise convergence 702-3
Fourier series, trigonometric 702-20
Fourier transforms 1125
Fourier transforms,  -dimensional 1136
Fredholm's alternative 920 1016
Fredholm's equation 917
Fredholm's integral equations 917
Fredholm's integral equations, approximate determination of first eigenvalue 1142-5
Fredholm's integral equations, approximate solutions by Galerkin's method of moments 1141-2
Fredholm's integral equations, approximate solutions by reduction to linear algebraic equations system 1138-41
Fredholm's integral equations, approximate solutions by replacement of kernel by degenerate kernel 1141
Fredholm's integral equations, approximate solutions by Ritz's method 1142-5
Fredholm's integral equations, approximate solutions by successive approximations (iterations) 1137-8
Fredholm's integral equations, with symmetric kernels 928
Free oscillations 194 196
Free vectors 264
Frenet formulae 308-9
frequencies 1266-7
Frequencies, cumulated in probit scale 1272
Fresnel's integrals 582 589
Frobenius's theorem 71
Fuchsian, differential equations 793
Functional analysis 997-1019
Functional determinants 456-7
Functionals in metric spaces 1007
Functionals, maximum and minimum along a curve 1022
Functionals, quadratic, minimum of 1045
Functions of a complex variable 938-70
Functions of a Complex variable, analytic 941
Functions of a Complex variable, analytic, continuation of 968
Functions of a Complex variable, analytic, natural domain of 969
Functions of a Complex variable, Cauchy - Riemann equations 941-2
Functions of a Complex variable, Cauchy type of integrals 949-53
Functions of a Complex variable, derivative 941-2
Functions of a Complex variable, fundamental concepts 938-43
Functions of a Complex variable, holomorphic (regular) 941-2
Functions of a Complex variable, integrals of 943-8
Functions of a Complex variable, limit and continuity 940
Functions of a Complex variable, Liouville's theorem 961
Functions of a Complex variable, Logarithmic 965-70
Functions of a Complex variable, Plemelj formulae 951
Functions of a Complex variable, regular 941-2
Functions of a Complex variable, residue theorem and its applications 962-5
Functions of a Complex variable, series 953-61
Functions of a Complex variable, series, Laurent's 958-61
Functions of a Complex variable, series, Taylor's 957-8
Functions of a Complex variable, univalent (simple) in a domain 943
Functions, algebraic 402
Functions, analytic 941
Functions, approximation 436-8
Functions, bounded 404
Functions, composite 399 441
Functions, composite, differentiation of 420 450-2
Functions, concave, convex 429
Functions, continuity of 404 442
Functions, continuously extensible 443
Functions, decomposition of 400
Functions, decreasing 428
Functions, dependence of 458-61
Functions, derivatives 415-22
Functions, domain of definition of 397-8 440
Functions, elementary 402
Functions, elementary, and higher transcendental 403
Functions, equicontinuous 668
Functions, erf  , erfc 589
Functions, even and odd 404
Functions, exponential 403
Functions, graphical representation 432
Functions, Green's 811 892
Functions, holomorphic 941
Functions, homogeneous, Euler's theorem 454-5
Functions, hyperbolic 128-30
Functions, implicit 461 468
Functions, important formulae 438-9 484-5
Functions, increasing 428
Functions, inverse 400
Functions, inverse, hyperbolic 130-2
Functions, investigation of 431-4
Functions, limits of 409-15
Functions, limits of, computation by l'Hospital's rule 426-8
Functions, linear combination of 460
Functions, linearly dependent, independent 460
Functions, local dependency of 460
Functions, mean-value theorem 452-4
Functions, meromorphic 960
Functions, monotonic 429
Functions, new variables, introduction and transformations 470-6
Functions, normed (normalized) 695
Functions, normed (normalized), with weight function 697
Functions, odd and even 404
Functions, of 2 or more variables, extremes 476-84
Functions, of 2 or more variables, important formulae 484-5
Functions, of 2 or more variables, introduction of new variables 470-6
Functions, of a complex variable 938-70 440-85; of
Functions, of bounded variation 408
Functions, of type B 603 605
Functions, piecewise smooth in a region 443
Functions, points of inflexion 429
Functions, rational 402
Functions, real 397
Functions, Regression 1288-91
Functions, regular 941
Functions, relative (local) maximum and minimum 430 476
Functions, smooth 417
Functions, square integrable 691
Functions, stationary points 431
Functions, transcendental 402-4
Functions, type B in a region 605
Functions, uniformly bounded 666
| Functions, vanishing at infinity 885
Fundamental sequence 999
Fundamental sequence, solutions of Laplace and heat conduction equations 892 908
Fundamental sequence, system 778 819
g.l.b. (greatest lower bound) 43
Galerkin method for boundary value problems 1058-61
Galerkin method of moments 1141-2
Gamma function 584
Gamma function, graph and table 586
Gauss - Markov theorem 1304 1315
Gauss - Ostrogradski theorem 642-3
Gauss - Seidel iteration method 1155-6
Gauss(ian), central difference interpolation formula 1231-2
Gauss(ian), curvature on a surface 368
Gauss(ian), function 588
Gauss(ian), fundamental equation for surfaces 371
Gauss(ian), hypergeometric equation 727 797 850
Gauss(ian), law of error 1316
Gauss(ian), theorem 665
Gauss(ian), theorem egregium 371
Gauss(ian), theorem in vector notation 278-9
General integral (differential equations) 735 737 818
Generating curve 165
generating function for Bessel functions 717
Generating function for Bessel functions, for Legendre polynomials 724
Generating lines, generators 259-60
Geodesic curvature 372-5
Geometric mean 47
Geometric rigidity 1241
Geometric sequence 54
Geometry and physics, application of integral calculus 645-63
Geometry, analytic 205-62
Geometry, differential 298-373
Geometry, signs and notation 29-30
Gradient curves on a surface 373
Gradient of a Scalar Field 270
Gradient of straight line 208
Graeffe method 1174-8
Gram determinant 461
graph paper 1187-9
Graph paper, rectangular, logarithmic, semilogarithmic, sine 1188
Graphical analysis 1213-9
Graphical analysis, differentiation 1213-4
Graphical analysis, integration 1214-7
Graphical representation of samples 1273
Graphical solution of differential equations 1217-9
Graphical solution of differential equations, isoclines method 1217-8
Graphical solution of differential equations, Kelvin method 1218-9
Gravitational field, equation for particle moving in 857
Greatest lower bound (g.l.b.) 43
Green's formula regarding self-adjoint problems 806
Green's function 811 892
Green's function, construction 812-4
Green's function, for special regions 893
Green's function, in conformal mapping 984
Green's identities 644
Green's resolvent 815
Green's theorem 634
Groups, definitions 85
Growth, curves 200-4
Growth, law of 200
Growth, Robertson's law of 202-3
Guldin's rules 662
H lder's condition 949
Hlder's condition, inequality 46 394
Half-angle formulae for trigonometric functions 112-3
Half-line directed, positive and negative 212
Hamilton nabla operator 272
Hankel functions 721
Harmonic analysis 714-6
Harmonic functions, properties of 890
Harmonic motion, simple 194
Harmonic oscillation curves 194
Harmonic series 382
Harmonic set of four points 229
Harmonics, spherical 725-7
Harnack theorems, first and second 890
Heat conduction equation 907-11
Heat conduction equation, Bessel functions applied to 1106
Heat conduction equation, first boundary value problem 1119-21
Heat conduction equation, infinite circular cylinder 1105-6
Heat conduction equation, rectangular regions 1103-4
Heat conduction equation, stationary 1102-3
Heat potentials 911
Heaviside operational calculus 1128
Heine's continuity definition 405
Helicoid 261 354
Helix axis 311
Helix, circular 311
Helix, cylindrical 335
Helix, slope of gradient 312
Hermite differential equation 729 798
Hermite polynomials 729
Hermitian forms 100-6
Hermitian forms, congruent 106
Hermitian matrices 106
Heron's formula 118 133
Higher degree hyperbolas 223-3
Higher degree parabolas 223-4
Hilbert - Schmidt theorem 928
Hilbert kernel 933
Hilbert space 1003-5
Hilbert space, operators in, bounded 1013-6
Hilbert space, operators in, unbounded 1016-9
histogram 1270
Holomorphic functions 941-2
Holomorphic functions, singular points 956-61
Homeomorphic image of a sphere 997
Homogeneous coordinates 225-6
Homogeneous functions, Euler's theorem 454-5
Homogeneous linear differential equations 743 776 782 867
Homographic mapping 973
Horner method for polynomials 60-61
Horner scheme applied to Everett formula 1235
Hyperbola 157-60 222-3
Hyperbola, as a conic section 227
Hyperbola, asymptotes of, and their directions 159
Hyperbola, branches 157
Hyperbola, conjugate 223
Hyperbola, conjugate diameter 159
Hyperbola, constructions 157-9
Hyperbola, eccentricity 157 222
Hyperbola, focal radius 157
Hyperbola, higher degree 163-5
Hyperbola, polar, equation for 230
Hyperbola, rectangular 223
Hyperbola, segment area 141
Hyperbola, standard equation for 222
Hyperbola, theorems 157-9
Hyperbolic equations 882 901-7
Hyperbolic equations, generalized solutions 901
Hyperbolic functions 128-30
Hyperbolic functions, inverse 130-2
Hyperbolic functions, relations between 129-30
Hyperbolic paraboloid 251
Hyperbolic point 364
Hyperbolic spiral 176
Hyperboloid(s), asymptotic cone of 2 252
Hyperboloid(s), of one and of 2 sheets 248-50
Hyperboloid(s), of one and of 2 sheets, canonical and transformed equations 254
Hyperboloid(s), of revolution 248-9
Hyperelliptic integrals 589
Hypergeometric distribution 1255
Hypergeometric distribution, functions 727
Hypergeometric distribution, Gauss equation 727 797 850
Hypocycloids 168-72
Hypocycloids, simple, astroid 172
Hypocycloids, Steiner's 171-2
Identity element of a group 85
Identity element of a group, matrix 88
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