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| Rektorys K. — Survey of applicable mathematics |
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| Предметный указатель |
Differential equations, Ordinary, central dispersions theory 774
Differential equations, Ordinary, directional elements and fields 732
Differential equations, Ordinary, elementary methods of integration 738-48
Differential equations, Ordinary, Euler's equation 784-5
Differential equations, Ordinary, exact 748-52
Differential equations, Ordinary, existence and uniqueness of solution, theorems 733-8
Differential equations, Ordinary, first integral of 766 828
Differential equations, Ordinary, general integral of system 818
Differential equations, Ordinary, geometrical interpretation 732
Differential equations, Ordinary, homogeneous (in different senses) 741 743
Differential equations, Ordinary, homogeneous (in different senses), with constant coefficients 782-790
Differential equations, Ordinary, integrals of 731-2 737
Differential equations, Ordinary, integrating factor 750-1
Differential equations, Ordinary, integration, elementary methods 738-48
Differential equations, ordinary, linear homogeneous 776
Differential equations, Ordinary, linear homogeneous, discontinuous solutions 798-801
Differential equations, Ordinary, linear homogeneous, periodic solutions 774-5
Differential equations, Ordinary, linear non-homogeneous, constant coefficients, special right-hand side 786-90
Differential equations, Ordinary, linear non-homogeneous, variation of parameters method 780-2
Differential equations, Ordinary, linear of order  775
Differential equations, Ordinary, linear of second order with variable coefficients 790
Differential equations, Ordinary, Lipschitz condition 734-5
Differential equations, Ordinary, normal system 818
Differential equations, Ordinary, not solved with respect to derivative 753-61
Differential equations, Ordinary, oscillatory solutions 771
Differential equations, Ordinary, periodic solutions 774 1095
Differential equations, Ordinary, periodic solutions, perturbation method for weakly nonlinear oscillator 1095-7
Differential equations, Ordinary, separation of variables 739-41
Differential equations, ordinary, singular points 751-2
Differential equations, Ordinary, singular points, node and saddle point 752
Differential equations, Ordinary, singular solution (integral) 758-9
Differential equations, Ordinary, solution 731-2 737
Differential equations, Ordinary, solution, approximate 1065-82
Differential equations, Ordinary, solution, by parameter method 763-6
Differential equations, Ordinary, solution, by separation of variables 739-41
Differential equations, Ordinary, solution, by variation of parameter 744-5
Differential equations, Ordinary, solution, dependence on parameters and initial conditions 770
Differential equations, Ordinary, solution, stability of 827
Differential equations, ordinary, systems of 817
Differential equations, Ordinary, systems of, canonical form 817-8
Differential equations, Ordinary, systems of, dependence and stability of solutions 826-8
Differential equations, Ordinary, systems of, first integrals of 828-32
Differential equations, Ordinary, systems of, homogeneous, fundamental, non-homogeneous 819-24
Differential equations, Ordinary, systems of, vector (matrix) form 818-9
Differential equations, Ordinary, table of solved 832-57
Differential equations, Ordinary, with regular singularity 793
Differential equations, oscillatory solution 772
Differential equations, partial 858-916
Differential equations, Partial, basic concepts 858-67
Differential equations, Partial, characteristic strip (characteristic of first order) 876
Differential equations, Partial, complete integral 875
Differential equations, Partial, distinguished from "ordinary" 730
Differential equations, Partial, elliptic 884-901
Differential equations, Partial, first order 867-81
Differential equations, Partial, first order, general integral 871
Differential equations, Partial, generalised solutions 900 904
Differential equations, Partial, Harnack and Liouville theorems 890-1
Differential equations, Partial, Heat conduction equation 907-11
Differential equations, Partial, hyperbolic and ultrahyperbolic 882-3 901-7
Differential equations, Partial, integrability, conditions of 859
Differential equations, Partial, integral strip, integral elements 876
Differential equations, Partial, linear homogeneous of the first order 867
Differential equations, Partial, linear nonhomogeneous of the first order 869
Differential equations, Partial, linear of second order, classification 882-4
Differential equations, Partial, methods of solution, Finite difference 1109-24
Differential equations, Partial, methods of solution, functional analytic 900
Differential equations, Partial, methods of solution, infinite series (Fourier, product method) 1098-1108
Differential equations, Partial, methods of solution, operational 1125-36
Differential equations, Partial, methods of solution, operational, variation of a parameter 871
Differential equations, Partial, methods of solution, variational (direct) 1045-64
Differential equations, Partial, nonlinear of the first order 871
Differential equations, Partial, order of 859
Differential equations, Partial, parabolic 882-3 907-11
Differential equations, Partial, potential of 884
Differential equations, Partial, problems 860; see Cauchy
Differential equations, Partial, problems, boundary value 860
Differential equations, Partial, problems, Dirichlet and Neumann 865 886-901; Neumann
Differential equations, Partial, problems, mixed 860
Differential equations, Partial, problems, of mathematical physics 866
Differential equations, Partial, problems, some other 911-6
Differential equations, Partial, problems, well-posed 866
Differential equations, Partial, quasilinear of the first order 864
Differential equations, Partial, second order linear, classification 882-4
Differential equations, Partial, self-adjoint 914
Differential equations, Partial, systems of 911
Differential equations, Partial, ultrahyperbolic 883
Differential equations, Partial, wave 901-7
Differential equations, systems of 730 817
Differential equations, trajectories 761-2
Differential equations, uniqueness of solution 734-7
Differential geometry, Curves 298-343
Differential geometry, surfaces 343-373
Differential, partial 450
Differential, total 447
Differentiation, change of order 446
Differentiation, composite functions 420 450-2
Differentiation, of Fourier series 711
Differentiation, of series with variable terms 673 955
Dihedral angle, volume and centroid of 144
Dimensional finite 1136
Diocles's cissoid 187-8
Directed distance 205
Directed half-line and line segment 212
Directed segments (vectors) 264
Directed straight line, theorems and examples 212-5
Direction cosines 212
Direction cosines, of normal to a surface 351-2
Direction cosines, of tangent to coordinate curves 347
Direction vector of a line 244
Directional element and field (differential equations) 732
Directrix curve 259-60
Dirichlet and Neumann problems 886-901
Dirichlet and Neumann problems, existence of solution 887-90
Dirichlet and Neumann problems, for Laplace (or Poisson) equation 886
Dirichlet and Neumann problems, interior and exterior 886
Dirichlet and Neumann problems, uniqueness of solution 887
Dirichlet formula 762
Dirichlet formula, regarding self-adjoint problems 806
Dirichlet problem for Laplace's equation 886
Dirichlet problem in partial differential equations 865
Dirichlet test for convergence of series 388
Discontinuity, points of 406
Discontinuity, removable 407
Discontinuity, types of 406-7
Discontinuous solution of a differential equation 798
Discriminant curve of differential equation 759
Discriminant of an equation of the third order 78
Discriminants of conic sections 226
Discriminating cubic of a quadric 256
Distance between 2 parallel planes 241
Distance between 2 points in plane 206
Distance between 2 skew straight lines 245
Distance of point from a straight line 216 245
Distance of point from plane 240
Distance, directed 205
Distribution function 1249
Distributions, integral valued 1255
Distributive laws of vectors 264
Divergence of a vector 272
Divergent integrals, sequences, series 375 382 560 566 623
Divergent series, application of 688-9
Divided differences 1221-2
Division on a scale 1185
Division rings 86
Domain of convergence of a series 954
Domain of definition of a function 397-8 440
Double integral 605
Double integral, evaluation by repeated integration 610-4
Double integral, geometric meaning 607
Double integral, improper 623-8
| Double integral, method of substitution 615-8
Double linear interpolation 1240-2
Double linear interpolation, point of a curve 299 328
Double series 389
Du Bois - Reymond form of variation 1025
Dupin's indicatrix 368
Edge of regression of a surface 354
Eigenfunction 804 915 920 1015
Eigenfunction, orthogonality 810
Eigenvalue problems, approximate solution of ordinary differential equations 1090-7
Eigenvalue problems, approximate solution of ordinary differential equations, by a finite difference method 1094-5
Eigenvalue problems, approximate solution of ordinary differential equations, by variational (direct) methods 1090-3
Eigenvalue problems, comparison function of 804 915
Eigenvalue problems, for matrices 97 1161
Eigenvalue problems, in ordinary differential equations 801 1090
Eigenvalue problems, in partial differential equations 913-5
Eigenvalue problems, positive definite 805
Eigenvalue problems, regular 807
Eigenvalue problems, self-adjoint 805 816 915
Eigenvalue problems, symmetric 805
Eigenvalues,  -fold or simple 807
Eigenvalues, calculation by iterative method, matrices 1162
Eigenvalues, definition of 97 804 1015
Eigenvalues, numerical calculation 1054 1059 1090-1095 1161
Eigenvalues, numerical calculation, by iterative and by direct methods 1160-7
Eigenvalues, of matrices, connection with roots of algebraic equations 1171-2
Elasticity, plane problems of 912
Elasticity, problem in theory of 943
Electric current, differential equation 833 1128
Elementary symmetric functions 76
Elements of a set 82
Elimination method for solving linear algebraic equations 1146-60
ellipse 152-6 221
Ellipse, as a conic section 227
Ellipse, as a conic section, equation for polar 230
Ellipse, centres of curvature at vertices 156
Ellipse, centroid of 140
Ellipse, circumference, approximate calculation 139-40
Ellipse, circumference, table 140
Ellipse, constructions 153-6
Ellipse, definition 221
Ellipse, eccentricity 139 153 221
Ellipse, foci and focal radius 152 221
Ellipse, major and minor axes and vertices 152-3
Ellipse, Rytz construction 156
Ellipse, sector, area of 140
Ellipse, standard equation of 221
Ellipse, tangent or normal to 154
Ellipse, theorems 152-4
Ellipse, vertex circles 153
Ellipsoid, canonical and transformed equations 254
Ellipsoid, moment of inertia 148
Ellipsoid, oblate and prolate 148
Ellipsoid, real and virtual 254
Ellipsoid, volume and surface area 148
Ellipsoid, volume determined by repeated integration 612
Elliptic equations 884-901
Elliptic integral 589
Elliptic integral, complementary 590-1
Elliptic integral, complete of first and second kind 590-1
Elliptic paraboloid, equation 250
Elliptic point 364
Elliptic sector, area of 140
Elliptic sector, formula for area of 140
Empirical data, Fitting of curves to 1285-1301
Empirical regression curve 1287
Empty set 83
End point of vector 264
Entire transcendental function 961
Envelope of 1-parameter family of plane, curves 330-4
Envelope of 1-parameter family of plane, of surfaces 355
Epicycloid 168-72
Equality of tensors 292
Equations, algebraic, linear, solution by numerical methods 1146-60
Equations, algebraic, non-linear and transcendental, numerical solution 1168-1182
Equations, algebraic, of higher degrees 75-77
Equations, algebraic, solution by interpolation 1237-9
Equations, binomial 80-81
Equations, Biquadratic (or quartic) 79-80
Equations, cubic 77-79
Equations, differential 730-857 858-916
Equations, Euler 917-36; see below Equations Integral
Equations, Linear systems 70-75
Equations, non-linear systems, numerical solution 1180-2
Equations, quadratic 77
Equations, reciprocal 81-82
Equations, straight line 208-12 243
Equiangular spiral 177
Equicontinuous functions 668
Equidistant arguments, interpolation formulae 1225
Equidistant curves 334-5
Equipotential surfaces 270-1
Equitangential curve 343
EQUIVALENCE 39-40
Equivalence, of systems 70
Error(s), function 589
Error(s), law of 1315-7
Error(s), law of, Gaussian 1316
Error(s), mean square 1318
Error(s), propagation, law of 1320-1
Error(s), sum of squares 1287 1307
Error(s), systematic and random 1316
Estimation, confidence interval 1274 1277
Estimation, errors, absolute and relative 1242-4
Estimation, method of maximum likelihood 1277-9
Estimation, point and interval 1277
Estimation, theory of 1277-9
Estimation, unbiassed 1277
Euclidean algorithm 59
Euclidean space 996
Euler - Ostrogradski equation 1037
Euler - Poisson equation 1033
Euler coefficients 549
Euler constant 381 579 585
Euler equation, for an extremal in variational problem 1030-1
Euler equation, linear differential 784-5
Euler equation, special cases in calculus of variations 1026-9
Euler integral (function) of first kind 587
Euler integral (function) of second kind 584
Euler relation 957
Euler summability of series 674
Euler theorem on homogeneous functions 454-5
Euler theorem regarding curvature 367
Euler triangle 120-1
Euler triangle, formulae for 123-4
Events and probabilities 1245-8
Everet interpolation formula 1234-6
Everet interpolation formula, written in Horner form 1235
Evolutes of curves 335
exact differential equations 748-52
Existence and uniqueness theorems for solution in ordinary differential equations 731-8
Existence and uniqueness theorems for solution in partial differential equations 887 904 906 910
Explicit equation of a curve on a surface 348
Explicit equation of a plane curve 302
Explicit equation of a surface 344
Exponent of the power of a number 50
Exponential curve 181-3
Exponential equations 53
Exponential function 403
Extremal -dimensional variety 1037
Extremal hypersurface 1037
Extremal of a variational problem 1030 1033 1037
Extremes of functions 430 476
Extremum, constrained 479
Extremum, of a functional 1022
Factorial symbol 55
Field of force of a unit charge at origin of coordinate system 272
Finite difference method 1084 1094 1109-24
Finite difference method, applied to solving Differential equations, partial 1109-24
Finite difference method, basic concepts 1109-24
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