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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
"Del" operator      272
$\delta$-neighbourhood of a point      442
2 or more variables, functions of      440—485
2 or more variables, functions of, extremes      476—484
2 or more variables, functions of, introduction of new variables, transformations      470—476
2 or more variables, functions of, survey of important formulae      484—485
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      1186—1187
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      1076—1080
Adams method of solving differential equations by interpolation      1080—1082
Addition of tensors      292
Addition of trigonometric functions, formulae      112—113
Addition of vectors      263—264
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      1317—1320
Admissible parameter      302
Affine ratio and transformations      227—229
Airy's function in problems of elasticity      943
Airy's function, biharmonic equation for      912—913
Algebra, fundamental theorem of      59
Algebra, signs and notations      27—29
Algebraic branch point      967
Algebraic curves      187—194 301 327
Algebraic equations of higher degree      75—77
Algebraic equations, Numerical solution of      1168—1182
Algebraic equations, Quadratic, cubic, biquadratic      77—79
Algebraic real numbers      43
Alignment nomograms      1195—1210
Alignment nomograms, anamorphosis, conditions of      1196
Alignment nomograms, binary field      1207—1208
Alignment nomograms, grouped      1207
Alignment nomograms, skeleton      1204—1206
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      205—232
Analytic geometry, solid      233—262
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      212—215 246
Angle(s) of contingence      316
Angle(s), bisectors of      216
Angle(s), circular measure and degrees      107—108
Angle(s), trigonometric functions of      109—111
Angular frequency      194
Annuloid, volume, surface area, moment of inertia      149
Aperiodic motions      197
Applications of integral calculus in geometry and physics      645—665
Approximate expressions      436—438
Approximate numbers, arithmetic operations with      1242—1244
Approximate tests of significance      1276
Approximation(s) of a function by a polynomial      408
Approximation(s), approximate methods in boundary value problems      1045—1064 1083—1090 1109—1124
Approximation(s), curve constructions      203—204
Approximation(s), eigenvalue problems      1090—1095 1054 1059
Approximation(s), first and higher, to various functions      437—438
Approximation(s), Fredholm's integral equations      1137—1145
Approximation(s), periodic solutions      1095—1097
Approximation(s), successive, method of, for integral equations      1137—1138
Approximation(s), successive, method of, for ordinary differential equations      1067
Archimedes's spiral      173
Archimedes's spiral, constructions and theorems      174—175
Archimedes's spiral, equation in polar coordinates      174
Arcsin, arccos, arctan, arccot functions      124—128
Areas of plane figures, formulae for      133—142
Areas of plane figures, integral calculus      651—652
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      39—106
Arithmetic mean      1265
Arithmetic operations with approximate numbers      1242—1244
Arithmetic sequences      54
Arsinh, arcosh, artanh, arcoth functions      130—132
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      326—330
Asymptotes of plane curves, in polar coordinates      340—341
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      688—690
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      1226—1227
Banach fixed-point theorem      1008
Banach space      1003—1004
Banachiewicz's method      1151
Basic argument      1225
Basic uniform (regular) scale      1184
Bernoulli and Whittaker method      1172—1173
Bernoulli coefficients      549
Bernoulli differential equation      746—747
Bernoulli experiment      1246
Bernoulli lemniscate      189—190
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      716—721
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      1233—1234
beta function      587
Biharmonic equation for Airy's function      912—913
Binary field in nomogram      1207—1208
Binomial distribution      1255—1256
Binomial equations      80—81
Binomial integrals, reduction formulae for      528
Binomial series      682—683
Binomial theorem and coefficients      57—58
Binormal (unit vector) to a curve      307—308
Biquadratic equations, solution, algebraic      80
Biquadratic equations, solution, by factorization      79
Bisectors of angles between 2 straight lines      215—216
Bisectors of angles of triangle      118
Bolzano — Cauchy condition      375 383 410
Bolzano — Cauchy condition of uniform convergence      666 671
Bolzano — Cauchy condition, improper integrals      560 567
Bolzano — Weierstrass theorem      378
Boundary point of a set      995
Boundary properties in conformal mapping      985—986
Boundary value problems of ordinary differential equations      1083—1090
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      1086—1087
Boundary value problems of ordinary differential equations, approximate solution by finite difference method      1084—1086
Boundary value problems of ordinary differential equations, approximate solution by least squares method      1086—1087
Boundary value problems of ordinary differential equations, approximate solution by perturbation method      1088—1089
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      1083—1084
Boundary value problems of partial differential equations      860
Boundary value problems of partial differential equations, approximate solution, direct methods      1045—1064
Boundary value problems of partial differential equations, approximate solution, finite difference method      1113—1123
Boundary value problems of partial differential equations, approximate solution, Galerkin, Kantorovitch, Ritz and Trefftz methods      1052—1061
Boundary value problems of partial differential equations, approximate solution, least squares method      1086—1088
Boundary value problems of partial differential equations, approximate solution, product method      1098—1108
Boundary value problems of partial differential equations, approximate solution, transformation to finding the minimum of a quadratic functional      1045—1046
Boundary value problems of partial differential equations, approximate solution, variational methods      1045—1064
Boundary-correspondence principle      981
Bounded diameter      151
Bounded operator      1013
Bounded sequence      377
Bounded variation, functions of      408—409
Bounds of real numbers      43
Brachistochrone problem      1027—1029
Branch points of infinite and finite order      967
Branches of a hyperbola      157
Budan — Fourier theorem      1171
Bundle of planes      242
C-region      988—989
Calculus of variations      1020—1044
Calculus of variations, $\varepsilon$-neighbourhood of order r of a curve      1021
Calculus of variations, brachistochrone problem      1027—1029
Calculus of variations, categories of problems, "movable (free) ends of admissible curves"      1037—1040
Calculus of variations, categories of problems, elementary      1020—1029
Calculus of variations, categories of problems, functionals depending on a function of n variables      1034—1037
Calculus of variations, categories of problems, simplest case of izoperimetric problem      1040—1044
Calculus of variations, curves of the r-th class      1020—1021
Calculus of variations, distance of order r between two curves      1020
Calculus of variations, Euler equation and special cases      1026
Calculus of variations, Euler — Poisson equation      1033
Calculus of variations, formulation of individual problems      1021 1029—1030 1032 1036—1037 1037—1038 1041
Calculus of variations, isoperimetric problem      1041
Calculus of variations, necessary conditions for extrema in problems of calculus of variations      1025—1026 1030—1031 1032—1034 1036 1038—1041 1041—1044
Calculus, differential      397—485
Calculus, integral      486—665
Calculus, operational      1025—1036
Calculus, tensor      280—296
Calculus, vector      263—279
Cardioid      170—171
Cartesian coordinates in plane geometry      205
Cartesian coordinates in plane geometry, congruent transformations      224—225
Cartesian coordinates in plane geometry, relations with polar coordinates      217—218
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      236—237
Cartesian product of sets      83
Cask volume formulae      149
Cassinian ovals      189
Catenaries (chainettes)      183—186
Catenaries (chainettes), constant strength      185—186
Catenaries (chainettes), general      183—185
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      1197—1198
Cauchy continuity definition      404—405
Cauchy form of Taylor's theorem      435
Cauchy inequality      46 571
Cauchy integral formula and theorem      946—948
Cauchy integrals, type of      949—953
Cauchy method      875
Cauchy principal value of integral      562 582
Cauchy problem      860—861
Cauchy problem in hyperbolic and parabolic equations      901 907
Cauchy problem, generalized      863
Cauchy problem, special      860—861
Cauchy problem, uniqueness and well-posed nature, in hyperbolic and parabolic equations      904 909
Cauchy problem, using complete integral      873—874
Cauchy product of series      392
Cauchy root tests for convergence of series      385
Cauchy sequence      999
Cauchy theorem      387 952
Cauchy — Dirichlet formula      762
Cauchy — Riemann equations      941—942
Cauchy — Riemann integrals      551
Cauchy — Schwarz inequality      571
Central dispersions theory      774
Central-difference interpolation formulae      1230—1236
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      133—142
Centroids, solids      142—149
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      98—100
Characteristic matrix of a square matrix      97
Characteristic polynomial of a matrix, eigenvalues or characteristic zeros or numbers      97—100
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      594—595
Chebyshev inequality      1252
Chebyshev polynomials      728 848
Choleski's method      1151
circle      151—152 219—220
Circle of curvature      323—324
Circle, circumscribed on triangle      118
Circle, conchoid of a      191
Circle, constructions of      150—151
Circle, diameter, bounded and conjugate      151
Circle, equation of      219
Circle, equation of, in polar coordinates      220
Circle, formulae for geometrical elements of      137—139
Circle, inscribed in triangle      118
Circle, involute of      172—173
Circle, Involute of, curtate and prolate      173
Circle, parametric equations of      219—220
Circle, rectification of, Kochanski's and Sobotka's      151—152
Circle, superosculating      325
Circle, Thalet's      151
Circular cask, volume formula      149
Circular frequency      194
Circumferences, formulae for plane figures      133—142
Cissoid of Diocles      187—188
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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