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



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Íàçâàíèå: Survey of Applicable Mathematics

Àâòîð: 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.
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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1969

Êîëè÷åñòâî ñòðàíèö: 1369

Äîáàâëåíà â êàòàëîã: 06.12.2013

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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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