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Rektorys K. (ed.) — Survey of Applicable Mathematics
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Название: Survey of Applicable MathematicsАвтор: Rektorys K. (ed.) Аннотация: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1969Количество страниц: 1369Добавлена в каталог: 06.12.2013Операции: Положить на полку |
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Strophoid 189 Student's t-test 1273 Sturm — Liouville problem 806 Sturm's theorem 772 1171 Subnormal 162 339 Subsequences 377 Subset 83 Substantially singular point 347 Subtangent 162 339 Success, in Bernoulli experiment 1246—1247 Successive approximations, solving differential equations 1067—1069 Successive approximations, solving integral equations 1137 Summabilities of series 674 Supercritical damping 197 Superosculating circle 325 Superosculating curve 322 Supremum (l.u.b.) 43 Surface(s) of revolution 257 Surface(s), conical 262 Surface(s), contravariant and covariant vector, on 290 Surface(s), cuspidal edge 354 Surface(s), definition 247 Surface(s), differential calculus, applications to 657—661 Surface(s), discriminant 362 Surface(s), edge of regression 354 Surface(s), element of area 362 Surface(s), elliptic point of 363 Surface(s), envelope of 1-parameter family 356 Surface(s), equipotential 271 Surface(s), explicit equation of 344 Surface(s), finite piecewise smooth 343—344 Surface(s), first fundamental form 291 360—362 Surface(s), fundamental coefficients 362 Surface(s), Gaussian curvature 368 Surface(s), generator of 355 358 Surface(s), hyperbolic point of 363 Surface(s), integrals 638—645 Surface(s), integrals of first and second kinds 639—640 Surface(s), interior diameter 638 Surface(s), lines of curvature 369 Surface(s), mean curvature 368 Surface(s), non-developable 354 Surface(s), normal curvature 366 Surface(s), normal section radius of curvature 366 Surface(s), oriented 638 Surface(s), orthogonal conjugate net on 369 Surface(s), parabolic point of 363 Surface(s), parameters and parametric equations 344 Surface(s), regular points on 247 Surface(s), ruled 259 Surface(s), scalar on 290 Surface(s), scroll (skew surface) 354 Surface(s), second fundamental form 363—364 Surface(s), second order 247—257 Surface(s), shape with respect to tangent plane 363—364 Surface(s), simple finite piecewise smooth 604—605 Surface(s), singular points on 247 Surface(s), tensor on 287—292 Sylvester's law of inertia 105 Symbols O(g(x)), o(g(x)) 414 Symmetric kernels of integral equations 816 Symmetric matrices 89 Symmetric operators 1018 1045 Symmetric problems 805 Systematic errors 1316 Tabular inaccuracy 1228 1243 Tabulation of 2-variable functions 1239—1242 Tangent and cotangent, integrals, containing 539—541 Tangent(s) to a conic 229—232 Tangent(s), developable (surface) 354 Tangent(s), direction, angle and length, in polar coordinates 338—339 Tangent(s), drawn to a curve from an arbitrary point 341 Tangent(s), length, in polar coordinates 339 Tangent(s), plane of a surface 349 Tangent(s), plane to a curve 310 Tangent(s), surface 354 Tangent(s), theorem 117 Tangent(s), vector field 287 Tangent(s), vector of a curve 270 304 Tangential vector of a surface 349 Taylor's formula 434 Taylor's formula for polynomial 61 Taylor's series 681—682 957—958 Taylor's theorem 434 439 Taylor's theorem, generalization for several variables 452—454 Temperature distribution, example using Laplace transform 1129—1130 Tensor(s) in space 284—287 Tensor(s) on a surface 287—292 Tensor(s), alternating 294 Tensor(s), calculus 280—296 Tensor(s), characteristic numbers of 296 Tensor(s), conjugate directions 295 Tensor(s), contravariant and covariant 285 Tensor(s), contravariant and covariant on a surface 287 Tensor(s), deformation 287 294 Tensor(s), first fundamental of a surface 290 Tensor(s), indicatrix of a point 295 Tensor(s), indices, lowering and raising of 293 Tensor(s), metric of a space 285 Tensor(s), metric of a surface 290 Tensor(s), quadratic 285 Tensor(s), second fundamental, of a surface 291 Tensor(s), symmetric and skew-symmetric 293—294 Tensor(s), symmetric quadratic 292—297 Term-by-term differentiation 669 673 955 Term-by-term integration 668 672 955 Theoretical regression function and curve 1287 Tillot inequality 1169 Total differential 447—450 Tractrix 185 Trajectories to solutions of differential equations 761—762 Transcendent curve 301 Transcendental branch point of logarithmic function 967 Transcendental equations, numerical solution of 1168—1182 Transcendental functions 402 488 541—548 Transcendental real numbers 43 Transformation matrix of coordinate systems 281 Transformations of differential expressions into polar, cylindrical and spherical coordinates 472—476 Transformations, affine 227—229 Transformations, congruent, of cartesian coordinates in a plane 224—225 Transformations, mapping 84 455—458 Transformations, projective in a plane 228—229 transforms see "Integral transforms" Transient oscillations 200 Translation, cartesian coordinate system 236 Transparency used in nomography 1210—1213 Transparency used in nomography, positional contacts 1210 Transparency used in nomography, symbolic key (structural formula) 1211 Transparency used in nomography, transformation formulae 1212 Transversality conditions of variational problem 1039 Transverse vibrations of a rod, differential equations 853—854 Trapezoidal rule for definite integrals 593 Trefftz method for boundary value problems 1056—1058 Triangle(s), area of 207 Triangle(s), centroid of 238 Triangle(s), formulae for geometrical elements of 133—134 Triangle(s), general (scalene) 116 Triangle(s), general (scalene), formulae for determining 117—120 Triangle(s), general (scalene), fundamental and further relations 117—118 Triangle(s), general (scalene), solution 118—120 Triangle(s), geometrical formulae 133—134 Triangle(s), inequality 46 48 Triangle(s), spherical 120 Trigonometric equations 115—116 Trigonometric Fourier series 702—720 Trigonometric functions of same angle, relations among 109—113 Trigonometric functions, addition formulae 112—113 Trigonometric functions, behaviour of 109 Trigonometric functions, definitions of 108—109 Trigonometric functions, difference of 114 Trigonometric functions, expansions into series 684—685 Trigonometric functions, half-angle formulae 112—113 Trigonometric functions, higher powers of 114 Trigonometric functions, inverse 124—128 Trigonometric functions, multiple-angle formulae 112—113 Trigonometric functions, powers of 114 Trigonometric functions, product of 114 Trigonometric functions, relations between 130 Trigonometric functions, signs in individual quadrants 110 Trigonometric functions, sum of 114—115 Trigonometric functions, values for some special angles 111 Trigonometry, plane 116—120 Trigonometry, spherical 120—124 Triple integrals 618—622 Triple integrals, improper 623—628 Triple integrals, method of substitution for 621 Triple scalar product of three vectors 268 Trochoid 165 Tube, volume and moment of inertia 146 Twisted curve 301 Ultrahyperbolic equation 883 Umbilic, umbilical point 368—369 Undamped forced vibrations, differential equations 843 Undamped oscillations, forced, curves of 195—196 Undamped oscillations, free, curves of 194—195 Undetermined coefficients, Lagrange's method of 480—481 Uniform convergence, sequences with variable terms 666 954 Uniform convergence, series with variable terms 671 954 Uniformly bounded sequence 667—668 Uniformly convergent integral 574—575 Union of sets 83 Uniqueness of solution of problems in ordinary differential equations 731—738 Uniqueness of solution of problems in partial differential equations 887 904 906 910 Unit (tangent) vector of a curve 270 304 Univalent (simple) function in a region O 943 Unsubstantially singular point of a curve, or surface 299 347 Upper integral of Darboux sums 550 Van der Pol's equation 1097 Variables, Functions of 2 or more 440—485 Variables, separation for solving differential equation 739—741 Variance 1279 Variation coefficient 1266 Variation coefficient of parameters 780 Variational (direct) methods 1045—1064 Variational (direct) methods for eigenvalue problems in ordinary differential equations 1090—1093 Variational (direct) methods in conformal mapping 986—989 Vector(s) in 3-dimensional space 263 Vector(s) in algebra 62—63 Vector(s) of acceleration, components of 314 Vector(s) on a surface 289—292 Vector(s), 2- and 3-dimensional 206 Vector(s), absolute value 265 Vector(s), algebra 62—63 263—269 Vector(s), analysis 269—279 Vector(s), circulation along closed curve 276 Vector(s), collinear (parallel) and coplanar 265 Vector(s), complex 62 Vector(s), components, coordinates of 62 263 Vector(s), conformably collinear (parallel) 265—266 Vector(s), contravariant and covariant 280—285 Vector(s), cross product 267 Vector(s), curvilinear and surface integrals 276—279 Vector(s), derivative 269 Vector(s), direction angles, direction cosines 266 Vector(s), dot product of 266 Vector(s), equation of a straight line 243 Vector(s), field 269 Vector(s), field, divergence and curl 272—276 Vector(s), field, irrotational 273 Vector(s), field, solenoidal (sourceless) 272 Vector(s), flux of 278 Vector(s), inner product 266 Vector(s), laws 62 264 Vector(s), length or magnitude 206 265 Vector(s), linearly dependent or independent 62—63 Vector(s), magnitude, norm, modulus 265 Vector(s), mixed product 268 Vector(s), n-component (n-coordinate) 62 Vector(s), non-coplanar in space 281 Vector(s), notation for Stokes, Gauss and Green theorems 277—279 Vector(s), outer product 267 Vector(s), principal normal (unit) 270 Vector(s), product 264 267 Vector(s), rank of a system of 63 Vector(s), real 62 Vector(s), scalar product of 266 Vector(s), signs and notation 30—31 Vector(s), space 1001—1003 Vector(s), space, n-dimensional 62 Vector(s), triple product 268 Vector(s), vector product 267 Vector(s), zero or null 62 263 Vibrating string equation 1098—1102 Virtual cone 254 Virtual quadric 256 Virtual sphere 247 Void set 83 Volterra integral equations 934—936 Volumes, formulae 142—149 653—657 Wallis's product 381 396 Wave equation 901—907 Weakly nonlinear oscillator 1095—1097 Weierstrass, M-test 671—672 954 Weierstrass, theorem 408 954—955 Weight function 697 Weighted average, weighted variance 1267 Weingarten, fundamental equation for surfaces 371 Well posed problems 866 Work done by force moving along a given curve 661 Wronskian determinant 776—777 Z-nomogram 1201 Zero, divisors 86 Zero, vector 63 263 Zeta function 672
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