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Rektorys K. (ed.) — Survey of Applicable Mathematics
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Íàçâàíèå: Survey of Applicable MathematicsÀâòîð: 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.
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1969Êîëè÷åñòâî ñòðàíèö: 1369Äîáàâëåíà â êàòàëîã: 06.12.2013Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
Ïðåäìåòíûé óêàçàòåëü
Differential equations: Ordinary, approximate solutions of eigenvalue problems 1090—1097 Differential equations: Ordinary, approximate solutions of initial value problems 1065—1083 Differential equations: Ordinary, asymptotic behaviour of integrals 771 Differential equations: Ordinary, central dispersions theory 774 Differential equations: Ordinary, directional elements and fields 732 Differential equations: Ordinary, elementary methods of integration 738—748 Differential equations: Ordinary, Euler's equation 784—785 Differential equations: Ordinary, exact 748—752 Differential equations: Ordinary, existence and uniqueness of solution: theorems 733—738 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 with constant coefficients 782—790 Differential equations: Ordinary, integrals of 731—732 737 Differential equations: Ordinary, integrating factor 750—751 Differential equations: Ordinary, integration, elementary methods 738—748 Differential equations: Ordinary, linear homogeneous 776 Differential equations: Ordinary, linear homogeneous, discontinuous solutions 798—801 Differential equations: Ordinary, linear homogeneous, periodic solutions 774—775 Differential equations: Ordinary, linear non-homogeneous, constant coefficients, special right-hand side 786—790 Differential equations: Ordinary, linear non-homogeneous, variation of parameters method 780—782 Differential equations: Ordinary, linear of order n 775 Differential equations: Ordinary, linear of second order with variable coefficients 790 Differential equations: Ordinary, Lipschitz condition 734—735 Differential equations: Ordinary, normal system 818 Differential equations: Ordinary, not solved with respect to derivative 753—761 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—1097 Differential equations: Ordinary, separation of variables 739—741 Differential equations: Ordinary, singular points 751—752 Differential equations: Ordinary, singular points, node and saddle point 752 Differential equations: Ordinary, singular solution (integral) 758—759 Differential equations: Ordinary, solution 731—732 737 Differential equations: Ordinary, solution by parameter method 763—766 Differential equations: Ordinary, solution by separation of variables 739—741 Differential equations: Ordinary, solution by variation of parameter 744—745 Differential equations: Ordinary, solution, approximate 1065—1082 Differential equations: Ordinary, solution, dependence on parameters and initial conditions 770 Differential equations: Ordinary, solution, stability of 827 Differential equations: Ordinary, table of solved 832—857 Differential equations: Ordinary, with regular singularity 793 Differential equations: Partial 858—916 Differential equations: Partial, basic concepts 858—867 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—881 Differential equations: Partial, first order, general integral 871 Differential equations: Partial, generalised solutions 900 904 Differential equations: Partial, Harnack and Liouville theorems 890—891 Differential equations: Partial, Heat conduction equation 907—911 Differential equations: Partial, hyperbolic and ultrahyperbolic 882—883 901—907 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—884 Differential equations: Partial, methods of solution, finite difference 1109—1124 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—1136 Differential equations: Partial, methods of solution, operational, variation of a parameter 871 Differential equations: Partial, methods of solution, variational (direct) 1045—1064 Differential equations: Partial, nonlinear of the first order 871 Differential equations: Partial, order of 859 Differential equations: Partial, parabolic 882—883 907—911 Differential equations: Partial, potential of 884 Differential equations: Partial, problems of mathematical physics 866 Differential equations: Partial, problems, boundary value 860 Differential equations: Partial, problems, Cauchy 860 Differential equations: Partial, problems, Dirichlet and Neumann 865 886—901 Differential equations: Partial, problems, mixed 860 Differential equations: Partial, problems, some other 911—916 Differential equations: Partial, problems, well-posed 866 Differential equations: Partial, quasilinear of the first order 864 Differential equations: Partial, second order linear, classification 882—884 Differential equations: Partial, self-adjoint 914 Differential equations: Partial, systems of 911 Differential equations: Partial, ultrahyperbolic 883 Differential equations: Partial, wave 901—907 Differential geometry, Curves 298—343 Differential geometry, surfaces 343—373 Differential, partial 450 Differential, total 447 Differentiation of Fourier series 711 Differentiation of series with variable terms 673 955 Differentiation, change of order 446 Differentiation, composite functions 420 450—452 Dihedral angle, volume and centroid of 144 Diocles's cissoid 187—188 Directed distance 205 Directed half-line and line segment 212 Directed segments (vectors) 264 Directed straight line, theorems and examples 212—215 Direction, cosines 212 Direction, cosines of normal to a surface 351—352 Direction, cosines of tangent to coordinate curves 347 Direction, vector of a line 244 Directional element and field (differential equations) 732 Directrix curve 259—260 Dirichlet and Neumann problems 886—901 Dirichlet and Neumann problems for Laplace (or Poisson) equation 886 Dirichlet and Neumann problems, existence of solution 887—890 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—407 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—689 Divided differences 1221—1222 Division on a scale 1185 Division, rings 86 Domain of convergence of a series 954 Domain of definition of a function 397—398 440 Double integral 605 Double integral, evaluation by repeated integration 610—614 Double integral, geometric meaning 607 Double integral, improper 623—628 Double integral, method of substitution 615—618 Double linear interpolation 1240—1242 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 for matrices 97 1161 Eigenvalue problems in ordinary differential equations 801 1090 Eigenvalue problems in partial differential equations 913—915 Eigenvalue problems, approximate solution of ordinary differential equations 1090—1097 Eigenvalue problems, approximate solution of ordinary differential equations by a finite difference method 1094—1095 Eigenvalue problems, approximate solution of ordinary differential equations by variational (direct) methods 1090—1093 Eigenvalue problems, comparison function of 804 915 Eigenvalue problems, positive definite 805 Eigenvalue problems, regular 807 Eigenvalue problems, self-adjoint 805 816 915 Eigenvalue problems, symmetric 805 Eigenvalues of matrices, connection with roots of algebraic equations 1171—1172 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—1167 Eigenvalues, p-fold or simple 807 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—1160 ellipse 152—156 221 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—140 Ellipse, circumference, table 140 Ellipse, constructions 153—156 Ellipse, definition 221 Ellipse, eccentricity 139 153 221 Ellipse, foci and focal radius 152 221 Ellipse, major and minor axes and vertices 152—153 Ellipse, Rytz construction 156 Ellipse, sector, area of 140 Ellipse, standard equation of 221 Ellipse, tangent or normal to 154 Ellipse, theorems 152—154 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—591 Elliptic integral, complete of first and second kind 590—591 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—334 Envelope of 1-parameter family of surfaces 355 Epicycloid 168—172 Equality of tensors 292 Equations, algebraic, linear, solution by numerical methods 1146—1160 Equations, algebraic, non-linear and transcendental, numerical solution 1168—1182 Equations, algebraic, of higher degrees 75—77 Equations, algebraic, solution by interpolation 1237—1239 Equations, binomial 80—81 Equations, Biquadratic (or quartic) 79—80 Equations, cubic 77—79 Equations, differential 730—857 858—916 Equations, integral 917—936 Equations, Linear systems 70—75 Equations, non-linear systems, numerical solution 1180—1182 Equations, quadratic 77 Equations, reciprocal 81—82 Equations, straight line 208—212 243 Equiangular spiral 177 Equicontinuous functions 668 Equidistant arguments, interpolation formulae 1225 Equidistant curves 334—335 Equipotential surfaces 270—271 Equitangential curve 343 EQUIVALENCE 39—40 Equivalence of systems 70 Error(s), function 589 Error(s), law of 1315—1317 Error(s), law of, Gaussian 1316 Error(s), mean square 1318 Error(s), propagation, law of 1320—1321 Error(s), sum of squares 1287 1307 Error(s), systematic and random 1316 Estimation, confidence interval 1274 1277 Estimation, errors, absolute and relative 1242—1244 Estimation, method of maximum likelihood 1277—1279 Estimation, point and interval 1277 Estimation, theory of 1277—1279 Estimation, unbiassed 1277 Euclidean algorithm 59 Euclidean space 996 Euler coefficients 549 Euler constant 381 579 585 Euler equation for an extremal in variational problem 1030—1031 Euler equation, linear differential 784—785 Euler equation, special cases in calculus of variations 1026—1029 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—455 Euler theorem regarding curvature 367 Euler triangle 120—121 Euler triangle, formulae for 123—124 Euler — Ostrogradski equation 1037 Euler — Poisson equation 1033 Events and probabilities 1245—1248 Everet interpolation formula 1234—1236 Everet interpolation formula, written in Horner form 1235 Evolutes of curves 335 exact differential equations 748—752 Existence and uniqueness theorems for solution of problems in ordinary differential equations 731—738 Existence and uniqueness theorems for solution of problems 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—183 Exponential equations 53 Exponential function 403 Extremal of a variational problem 1030 1033 1037 Extremal, hypersurface 1037 Extremal, n-dimensional variety 1037 Extremes of functions 430 476 Extremum of a functional 1022 Extremum, constrained 479 Factorial n symbol 55 Field of force of a unit charge at origin of coordinate system 272 Finite difference method 1084 1094 1109—1124 Finite difference method, applied to solving Differential equations, partial 1109—1124 Finite difference method, basic concepts 1109—1124 Finite difference method, basic theorems 1123—1124 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—1086 Finite difference method, Dirichlet problem 1119—1123 Finite difference method, eigenvalue problems for ordinary differential equations 1904—1905 Finite difference method, error estimates 1119 Finite difference method, formulae for differential operators 1113—1117
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