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

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Ќазвание: Survey of Applicable Mathematics

јвтор: Rektorys K. (ed.)


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.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1969

 оличество страниц: 1369

ƒобавлена в каталог: 06.12.2013

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ѕредметный указатель
"Del" operator      272
$\delta$-neighbourhood of a point      442
2 or more variables, functions of      440Ч485
2 or more variables, functions of, extremes      476Ч484
2 or more variables, functions of, introduction of new variables, transformations      470Ч476
2 or more variables, functions of, survey of important formulae      484Ч485
Abel's identity      777
Abel's integral equation      937
Abel's summability of a series      674
Abel's tests for convergence of a series      388
Abel's theorem of power series      676 956
Abelian groups      85
Absolute accuracy, absolute error, of a scale      1186Ч1187
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      1076Ч1080
Adams method of solving differential equations by interpolation      1080Ч1082
Addition of tensors      292
Addition of trigonometric functions, formulae      112Ч113
Addition of vectors      263Ч264
Addition theorem for expectations      1259
Addition theorem for variances      1261
Adjoined equations      802 914
Adjoined system of coordinates      234
Adjustment of data by method of least squares      1317Ч1320
Admissible parameter      302
Affine ratio and transformations      227Ч229
Airy's function in problems of elasticity      943
Airy's function, biharmonic equation for      912Ч913
Algebra, fundamental theorem of      59
Algebra, signs and notations      27Ч29
Algebraic branch point      967
Algebraic curves      187Ч194 301 327
Algebraic equations of higher degree      75Ч77
Algebraic equations, Numerical solution of      1168Ч1182
Algebraic equations, Quadratic, cubic, biquadratic      77Ч79
Algebraic real numbers      43
Alignment nomograms      1195Ч1210
Alignment nomograms, anamorphosis, conditions of      1196
Alignment nomograms, binary field      1207Ч1208
Alignment nomograms, grouped      1207
Alignment nomograms, skeleton      1204Ч1206
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      205Ч232
Analytic geometry, solid      233Ч262
Anamorphosis of collinear nomogram      1196
Anchor ring, equation of      258
Angle(s) between a line and a plane      246
Angle(s) between two curves      342
Angle(s) between two planes      240
Angle(s) between two straight lines      212Ч215 246
Angle(s) of contingence      316
Angle(s), bisectors of      216
Angle(s), circular measure and degrees      107Ч108
Angle(s), trigonometric functions of      109Ч111
Angular frequency      194
Annuloid, volume, surface area, moment of inertia      149
Aperiodic motions      197
Applications of integral calculus in geometry and physics      645Ч665
Approximate expressions      436Ч438
Approximate numbers, arithmetic operations with      1242Ч1244
Approximate tests of significance      1276
Approximation(s) of a function by a polynomial      408
Approximation(s), approximate methods in boundary value problems      1045Ч1064 1083Ч1090 1109Ч1124
Approximation(s), curve constructions      203Ч204
Approximation(s), eigenvalue problems      1090Ч1095 1054 1059
Approximation(s), first and higher, to various functions      437Ч438
Approximation(s), Fredholm's integral equations      1137Ч1145
Approximation(s), periodic solutions      1095Ч1097
Approximation(s), successive, method of, for integral equations      1137Ч1138
Approximation(s), successive, method of, for ordinary differential equations      1067
Archimedes's spiral      173
Archimedes's spiral, constructions and theorems      174Ч175
Archimedes's spiral, equation in polar coordinates      174
Arcsin, arccos, arctan, arccot functions      124Ч128
Areas of plane figures, formulae for      133Ч142
Areas of plane figures, integral calculus      651Ч652
Argand diagram      48
Argument(s) of a complex number      49
Argument(s) of a function      397
Argument(s), calculation by 'regula falsi' method      1179 1237
Argument(s), calculation by interpolation      1237
Argument(s), equidistant (equal)      1225
Arithmetic and Algebra      39Ч106
Arithmetic mean      1265
Arithmetic operations with approximate numbers      1242Ч1244
Arithmetic sequences      54
Arsinh, arcosh, artanh, arcoth functions      130Ч132
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      326Ч330
Asymptotes of plane curves, in polar coordinates      340Ч341
Asymptotic behaviour of integrals of differential equations      771
Asymptotic cone of two hyperboloids      252
Asymptotic curve (or line) on a surface      370
Asymptotic directions on a surface      364
Asymptotic expansions of series      688Ч690
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      1226Ч1227
Banach fixed-point theorem      1008
Banach space      1003Ч1004
Banachiewicz's method      1151
Basic argument      1225
Basic uniform (regular) scale      1184
Bernoulli and Whittaker method      1172Ч1173
Bernoulli coefficients      549
Bernoulli differential equation      746Ч747
Bernoulli experiment      1246
Bernoulli lemniscate      189Ч190
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      716Ч721
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      1233Ч1234
beta function      587
Biharmonic equation for Airy's function      912Ч913
Binary field in nomogram      1207Ч1208
Binomial distribution      1255Ч1256
Binomial equations      80Ч81
Binomial integrals, reduction formulae for      528
Binomial series      682Ч683
Binomial theorem and coefficients      57Ч58
Binormal (unit vector) to a curve      307Ч308
Biquadratic equations, solution, algebraic      80
Biquadratic equations, solution, by factorization      79
Bisectors of angles between 2 straight lines      215Ч216
Bisectors of angles of triangle      118
Bolzano Ч Cauchy condition      375 383 410
Bolzano Ч Cauchy condition of uniform convergence      666 671
Bolzano Ч Cauchy condition, improper integrals      560 567
Bolzano Ч Weierstrass theorem      378
Boundary point of a set      995
Boundary properties in conformal mapping      985Ч986
Boundary value problems of ordinary differential equations      1083Ч1090
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      1086Ч1087
Boundary value problems of ordinary differential equations, approximate solution by finite difference method      1084Ч1086
Boundary value problems of ordinary differential equations, approximate solution by least squares method      1086Ч1087
Boundary value problems of ordinary differential equations, approximate solution by perturbation method      1088Ч1089
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      1083Ч1084
Boundary value problems of partial differential equations      860
Boundary value problems of partial differential equations, approximate solution, direct methods      1045Ч1064
Boundary value problems of partial differential equations, approximate solution, finite difference method      1113Ч1123
Boundary value problems of partial differential equations, approximate solution, Galerkin, Kantorovitch, Ritz and Trefftz methods      1052Ч1061
Boundary value problems of partial differential equations, approximate solution, least squares method      1086Ч1088
Boundary value problems of partial differential equations, approximate solution, product method      1098Ч1108
Boundary value problems of partial differential equations, approximate solution, transformation to finding the minimum of a quadratic functional      1045Ч1046
Boundary value problems of partial differential equations, approximate solution, variational methods      1045Ч1064
Boundary-correspondence principle      981
Bounded diameter      151
Bounded operator      1013
Bounded sequence      377
Bounded variation, functions of      408Ч409
Bounds of real numbers      43
Brachistochrone problem      1027Ч1029
Branch points of infinite and finite order      967
Branches of a hyperbola      157
Budan Ч Fourier theorem      1171
Bundle of planes      242
C-region      988Ч989
Calculus of variations      1020Ч1044
Calculus of variations, $\varepsilon$-neighbourhood of order r of a curve      1021
Calculus of variations, brachistochrone problem      1027Ч1029
Calculus of variations, categories of problems, "movable (free) ends of admissible curves"      1037Ч1040
Calculus of variations, categories of problems, elementary      1020Ч1029
Calculus of variations, categories of problems, functionals depending on a function of n variables      1034Ч1037
Calculus of variations, categories of problems, simplest case of izoperimetric problem      1040Ч1044
Calculus of variations, curves of the r-th class      1020Ч1021
Calculus of variations, distance of order r between two curves      1020
Calculus of variations, Euler equation and special cases      1026
Calculus of variations, Euler Ч Poisson equation      1033
Calculus of variations, formulation of individual problems      1021 1029Ч1030 1032 1036Ч1037 1037Ч1038 1041
Calculus of variations, isoperimetric problem      1041
Calculus of variations, necessary conditions for extrema in problems of calculus of variations      1025Ч1026 1030Ч1031 1032Ч1034 1036 1038Ч1041 1041Ч1044
Calculus, differential      397Ч485
Calculus, integral      486Ч665
Calculus, operational      1025Ч1036
Calculus, tensor      280Ч296
Calculus, vector      263Ч279
Cardioid      170Ч171
Cartesian coordinates in plane geometry      205
Cartesian coordinates in plane geometry, congruent transformations      224Ч225
Cartesian coordinates in plane geometry, relations with polar coordinates      217Ч218
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      236Ч237
Cartesian product of sets      83
Cask volume formulae      149
Cassinian ovals      189
Catenaries (chainettes)      183Ч186
Catenaries (chainettes), constant strength      185Ч186
Catenaries (chainettes), general      183Ч185
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      1197Ч1198
Cauchy continuity definition      404Ч405
Cauchy form of Taylor's theorem      435
Cauchy inequality      46 571
Cauchy integral formula and theorem      946Ч948
Cauchy integrals, type of      949Ч953
Cauchy method      875
Cauchy principal value of integral      562 582
Cauchy problem      860Ч861
Cauchy problem in hyperbolic and parabolic equations      901 907
Cauchy problem, generalized      863
Cauchy problem, special      860Ч861
Cauchy problem, uniqueness and well-posed nature, in hyperbolic and parabolic equations      904 909
Cauchy problem, using complete integral      873Ч874
Cauchy product of series      392
Cauchy root tests for convergence of series      385
Cauchy sequence      999
Cauchy theorem      387 952
Cauchy Ч Dirichlet formula      762
Cauchy Ч Riemann equations      941Ч942
Cauchy Ч Riemann integrals      551
Cauchy Ч Schwarz inequality      571
Central dispersions theory      774
Central-difference interpolation formulae      1230Ч1236
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      133Ч142
Centroids, solids      142Ч149
Cesaro 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      98Ч100
Characteristic matrix of a square matrix      97
Characteristic polynomial of a matrix, eigenvalues or characteristic zeros or numbers      97Ч100
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      594Ч595
Chebyshev inequality      1252
Chebyshev polynomials      728 848
Choleski's method      1151
circle      151Ч152 219Ч220
Circle of curvature      323Ч324
Circle, circumscribed on triangle      118
Circle, conchoid of a      191
Circle, constructions of      150Ч151
Circle, diameter, bounded and conjugate      151
Circle, equation of      219
Circle, equation of, in polar coordinates      220
Circle, formulae for geometrical elements of      137Ч139
Circle, inscribed in triangle      118
Circle, involute of      172Ч173
Circle, Involute of, curtate and prolate      173
Circle, parametric equations of      219Ч220
Circle, rectification of, Kochanski's and Sobotka's      151Ч152
Circle, superosculating      325
Circle, Thalet's      151
Circular cask, volume formula      149
Circular frequency      194
Circumferences, formulae for plane figures      133Ч142
Cissoid of Diocles      187Ч188
Clairaut, differential equation      758
Clairaut, generalized equation      873
Clark's canonical form      1197
Clark's canonical form, transformation of nomographic order      1197
Classifying of data      1268
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