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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
Finite difference method, nets, principal types 1112—1113 Finite difference method, nets, refinement 1113 First and second curvatures 315—319 First and second integral mean value theorems 554 First integrals (differential equations) 766 828 Fitting of curves to empirical data 1285—1301 Fitting of curves to empirical data, linear regression function 1288—1291 Fitting of curves to empirical data, linear regression function with several independent variables 1297—1299 Fitting of curves to empirical data, nonlinear regression functions 1299—1301 Fitting of curves to empirical data, principle of least squares 1285—1288 Fixed polhode 165 Floquet's theorem 774 Flow round an obstacle 980—981 Flux of a vector, physical meaning 278 Focal radius of a hyperbola 157 Focus of a parabola 223 Focus of an ellipse 221 Folium of Descartes 188—189 Forced oscillations, damped 199—200 Forced oscillations, undamped 195—196 Forward differences 1226—1227 Fourier coefficients 698 703 1005 Fourier integral 713 Fourier integral transform 1125 Fourier method, partial differential equations 1098—1108 Fourier series 702—720 Fourier series in 2 variables 712—713 Fourier series in complex form 711 Fourier series, differentiation and integration of 711—712 Fourier series, expansions of some important functions 707—711 Fourier series, generalized 698 Fourier series, harmonic analysis 714—716 Fourier series, pointwise convergence 702—703 Fourier series, trigonometric 702—720 Fourier transforms 1125 Fourier transforms, n-dimensional 1136 Fourier — Bessel expansion 720—721 Fredholm's alternative 920 1016 Fredholm's equation 917 Fredholm's integral equations 917 Fredholm's integral equations with symmetric kernels 928 Fredholm's integral equations, approximate determination of first eigenvalue 1142—1145 Fredholm's integral equations, approximate solutions by Galerkin's method of moments 1141—1142 Fredholm's integral equations, approximate solutions by reduction to linear algebraic equations system 1138—1141 Fredholm's integral equations, approximate solutions by replacement of kernel by degenerate kernel 1141 Fredholm's integral equations, approximate solutions by Ritz's method 1142—1145 Fredholm's integral equations, approximate solutions by successive approximations (iterations) 1137—1138 Free oscillations 194 196 Free vectors 264 Frenet formulae 308—309 frequencies 1266—1267 Frequencies, cumulated in probit scale 1272 Fresnel's integrals 582 589 Frobenius's theorem 71 Fuchsian, differential equations 793 Functional analysis 997—1019 Functional determinants 456—457 Functionals in metric spaces 1007 Functionals, maximum and minimum along a curve 1022 Functionals, quadratic, minimum of 1045 Functions of a complex variable 938—970 Functions of a Complex variable, analytic 941 Functions of a Complex variable, analytic, continuation of 968 Functions of a Complex variable, analytic, natural domain of 969 Functions of a Complex variable, Cauchy type of integrals 949—953 Functions of a complex variable, Cauchy — Riemann equations 941—942 Functions of a Complex variable, derivative 941—942 Functions of a Complex variable, fundamental concepts 938—943 Functions of a Complex variable, holomorphic (regular) 941—942 Functions of a Complex variable, integrals of 943—948 Functions of a Complex variable, limit and continuity 940 Functions of a Complex variable, Liouville's theorem 961 Functions of a Complex variable, Logarithmic 965—970 Functions of a Complex variable, Plemelj formulae 951 Functions of a Complex variable, regular 941—942 Functions of a Complex variable, residue theorem and its applications 962—965 Functions of a Complex variable, series 953—961 Functions of a Complex variable, series, Laurent's 958—961 Functions of a Complex variable, series, Taylor's 957—958 Functions of a Complex variable, univalent (simple) in a domain 943 Functions of bounded variation 408 Functions of two or more variables 440—485 Functions of two or more variables, extremes 476—484 Functions of two or more variables, important formulae 484—485 Functions of two or more variables, introduction of new variables 470—476 Functions of type B 603 605 Functions, algebraic 402 Functions, analytic 941 Functions, approximation 436—438 Functions, bounded 404 Functions, composite 399 441 Functions, composite, differentiation of 420 450—452 Functions, concave, convex 429 Functions, continuity of 404 442 Functions, continuously extensible 443 Functions, decomposition of 400 Functions, decreasing 428 Functions, dependence of 458—461 Functions, derivatives 415—422 Functions, domain of definition of 397—398 440 Functions, elementary 402 Functions, elementary and higher transcendental 403 Functions, equicontinuous 668 Functions, erf x, erfc x 589 Functions, even and odd 404 Functions, exponential 403 Functions, graphical representation 432 Functions, Green's 811 892 Functions, holomorphic 941 Functions, homogeneous, Euler's theorem 454—455 Functions, hyperbolic 128—130 Functions, implicit 461 468 Functions, important formulae 438—439 484—485 Functions, increasing 428 Functions, inverse 400 Functions, inverse, hyperbolic 130—132 Functions, investigation of 431—434 Functions, limits of 409—415 Functions, limits of, computation by l'Hospital's rule 426—428 Functions, linear combination of 460 Functions, linearly dependent, independent 460 Functions, local dependency of 460 Functions, mean-value theorem 452—454 Functions, meromorphic 960 Functions, monotonic 429 Functions, new variables, introduction and transformations 470—476 Functions, normed (normalized) 695 Functions, normed (normalized), with weight function 697 Functions, odd and even 404 Functions, piecewise smooth in a region 443 Functions, points of inflexion 429 Functions, rational 402 Functions, real 397 Functions, Regression 1288—1291 Functions, regular 941 Functions, relative (local) maximum and minimum 430 476 Functions, smooth 417 Functions, square integrable 691 Functions, stationary points 431 Functions, transcendental 402—404 Functions, type B in a region 605 Functions, uniformly bounded 666 Functions, vanishing at infinity 885 Fundamental sequence 999 Fundamental sequence, solutions of Laplace and heat conduction equations 892 908 Fundamental sequence, system 778 819 g.l.b. (greatest lower bound) 43 Galerkin method for boundary value problems 1058—1061 Galerkin method of moments 1141—1142 Gamma function 584 Gamma function, graph and table 586 Gauss — Markov theorem 1304 1315 Gauss — Ostrogradski theorem 642—643 Gauss — Seidel iteration method 1155—1156 Gauss(ian) central difference interpolation formula 1231—1232 Gauss(ian) curvature on a surface 368 Gauss(ian) function 588 Gauss(ian) fundamental equation for surfaces 371 Gauss(ian) hypergeometric equation 727 797 850 Gauss(ian) law of error 1316 Gauss(ian) theorem 665 Gauss(ian) theorem egregium 371 Gauss(ian) theorem in vector notation 278—279 General integral (differential equations) 735 737 818 Generating curve 165 generating function for Bessel functions 717 Generating function for Legendre polynomials 724 Generating lines, generators 259—260 Geodesic curvature 372—375 Geometric mean 47 Geometric rigidity 1241 Geometric sequence 54 Geometry and physics: application of integral calculus 645—663 Geometry, analytic 205—262 Geometry, differential 298—373 Geometry, signs and notation 29—30 Gradient of a Scalar Field 270 Gradient of straight line 208 Gradient, curves on a surface 373 Graeffe method 1174—1178 Gram determinant 461 graph paper 1187—1189 Graph paper, rectangular, logarithmic, semilogarithmic, sine 1188 Graphical analysis 1213—1219 Graphical analysis, differentiation 1213—1214 Graphical analysis, integration 1214—1217 Graphical representation of samples 1273 Graphical solution of differential equations 1217—1219 Graphical solution of differential equations, isoclines method 1217—1218 Graphical solution of differential equations, Kelvin method 1218 Gravitational field, equation for particle moving in 857 Greatest lower bound (g.l.b.) 43 Green's formula regarding self-adjoint problems 806 Green's function 811 892 Green's function for special regions 893 Green's function in conformal mapping 984 Green's function, construction 812—814 Green's identities 644 Green's resolvent 815 Green's theorem 634 Groups, definitions 85 Growth, curves 200—204 Growth, law of 200 Growth, Robertson's law of 202—203 Guldin's rules 662 Half-angle formulae for trigonometric functions 112—113 Half-line directed, positive and negative 212 Hamilton nabla operator 272 Hankel functions 721 Harmonic analysis 714—716 Harmonic functions, properties of 890 Harmonic motion, simple 194 Harmonic oscillation curves 194 Harmonic series 382 Harmonic set of four points 229 Harmonics, spherical 725—727 Harnack theorems, first and second 890 Heat conduction equation 907—911 Heat conduction equation, Bessel functions applied to 1106 Heat conduction equation, first boundary value problem 1119—1121 Heat conduction equation, infinite circular cylinder 1105—1106 Heat conduction equation, rectangular regions 1103—1104 Heat conduction equation, stationary 1102—1103 Heat potentials 911 Heaviside operational calculus 1128 Heine's continuity definition 405 Helicoid 261 354 Helix, axis 311 Helix, circular 311 Helix, cylindrical 335 Helix, slope of gradient 312 Hermite differential equation 729 798 Hermite polynomials 729 Hermitian forms 100—106 Hermitian forms, congruent 106 Hermitian matrices 106 Heron's formula 118 133 Higher degree, hyperbolas 223—223 Higher degree, parabolas 223—224 Hilbert kernel 933 Hilbert space 1003—1005 Hilbert space, operators in, bounded 1013—1016 Hilbert space, operators in, unbounded 1016—1019 Hilbert — Schmidt theorem 928 histogram 1270 Hoelder's condition 949 Hoelder's condition, inequality 46 394 Holomorphic functions 941—942 Holomorphic functions, singular points 956—961 Homeomorphic image of a sphere 997 Homogeneous coordinates 225—226 Homogeneous functions, Euler's theorem 454—455 Homogeneous linear differential equations 743 776 782 867 Homographic mapping 973 Horner method for polynomials 60—61 Horner scheme applied to Everett formula 1235 Hyperbola 157—160 222—223 Hyperbola, as a conic section 227 Hyperbola, asymptotes of, and their directions 159 Hyperbola, branches 157 Hyperbola, conjugate 223 Hyperbola, conjugate diameter 159 Hyperbola, constructions 157—159 Hyperbola, eccentricity 157 222 Hyperbola, focal radius 157 Hyperbola, higher degree 163—165 Hyperbola, polar, equation for 230 Hyperbola, rectangular 223 Hyperbola, segment area 141 Hyperbola, standard equation for 222 Hyperbola, theorems 157—159 Hyperbolic equations 882 901—907 Hyperbolic equations, generalized solutions 901 Hyperbolic functions 128—130 Hyperbolic functions, inverse 130—132 Hyperbolic functions, relations between 129—130 Hyperbolic paraboloid 251 Hyperbolic point 364 Hyperbolic spiral 176 Hyperboloid(s) of one and of two sheets 248—250 Hyperboloid(s) of one and of two sheets, canonical and transformed equations 254 Hyperboloid(s) of revolution 248—249 Hyperboloid(s), asymptotic cone of two 252 Hyperelliptic integrals 589 Hypergeometric distribution 1255 Hypergeometric distribution, functions 727 Hypergeometric distribution, Gauss equation 727 797 850 Hypocycloids 168—172 Hypocycloids, simple, astroid 172 Hypocycloids, Steiner's 171—172 Identity element of a group 85 Identity matrix 88 Imaginary and real axes 49 Imaginary lines, as forming a conic section 227 Imaginary part of a complex number 48 Implication 40 Implicit functions 461 468 Implicit functions, geometrical interpretations 462 Implicit functions, theorems on 461—470 Improper integrals 560—571
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