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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
"Del" operator 272 442 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, 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
Ðåêëàìà
-neighbourhood of a point 
-neighbourhood of order r of a curve 
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