Rektorys K. — Survey of Applicable Mathematics.Volume 2.
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Название: Survey of Applicable Mathematics.Volume 2.
Автор: Rektorys K.
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.
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.
Fourier seriesI 673I Fourier series in 2 variablesI 688 Fourier series in complex formI 687 Fourier series, differentiation and integration ofI 687 Fourier series, expansions of some important functionsI 682 ff Fourier series, generalizedI 673IIII Fourier series, generalized, in Hilbert spaceII 336 Fourier series, harmonic analysisI 691 Fourier series, pointwise convergenceI 678 Fourier series, trigonometricI 678 Fourier transformII 568 Fourier transform, fastI 691II Fourier transform, n-dimensionalII 584 Fraction defectiveII 792 Frame of bidiscII 279 Frazer diagramII 681 Frechet derivativeII 373 Frechet differentialII 373 Fredholm, alternativeII 225II Fredholm, equationsII 223 Fredholm, integral equationsII 223 ff Fredholm, integral equations, approximate, determination of first eigenvalueII 591 Fredholm, integral equations, approximate, solution, by Galerkin methodII 589 Fredholm, integral equations, approximate, solution, by replacement of kernel by degenerate oneII 589 Fredholm, integral equations, approximate, solution, by Ritz methodII 589 Fredholm, integral equations, approximate, solution, by successive approximationsII 585 Fredholm, integral equations, approximate, solution, using quadrature formulaeII 586 Fredholm, integral equations, with symmetric kernelsII 231 Fredholm, theoremsII 225 Free oscillationsI 156I Free vectorsI 226 Frenel integralsI 544I Frenet formulaeI 270 Frequency of eventII 690 Frequency of observationII 741 Frequency of observation, cumulative and relativeII 741 Frequency, classII 742 Frequency, empirical and theoreticalII 761 Frequency, marginalII 764 Frequency, StabilityII 690 Frequency, tableII 741 Frobenius theoremI 33 Function(s) of bounded variationI 370 Function(s) of class II 375II Function(s) of one complex variableII 243 ff Function(s) of one complex variable, analyticII 276II Function(s) of one complex variable, analytic, continuation ofII 275II Function(s) of one complex variable, analytic, natural domain ofII 276 Function(s) of one complex variable, Cauchy — Riemann equationsII 246 Function(s) of one complex variable, Cauchy, integral formulaII 253 Function(s) of one complex variable, Cauchy, theoremsII 252IIII Function(s) of one complex variable, Cauchy, type of integralsII 255 Function(s) of one complex variable, derivativeII 246II Function(s) of one complex variable, domain of definitionII 244 Function(s) of one complex variable, fundamental conceptsII 243 ff Function(s) of one complex variable, holomorphicII 247 Function(s) of one complex variable, integral ofII 249 ff Function(s) of one complex variable, limit and continuityII 245II Function(s) of one complex variable, Liouville theoremII 269 Function(s) of one complex variable, logarithmicII 272 ff Function(s) of one complex variable, meromorphicII 267 Function(s) of one complex variable, Plemelj formulaeII 257 Function(s) of one complex variable, poleII 267 Function(s) of one complex variable, regularII 247 Function(s) of one complex variable, residue theoremII 270 Function(s) of one complex variable, seriesII 249 ff Function(s) of one complex variable, series, LaurentII 265 Function(s) of one complex variable, series, TaylorII 264 Function(s) of one complex variable, simpleII 248 Function(s) of one complex variable, univalent in domainII 248 Function(s) of several complex variablesII 277 ff Function(s) of several complex variables, "edge of the wedge" theoremII 286 Function(s) of several complex variables, "Kugelsatz"II 286 Function(s) of several complex variables, analytic continuation ofII 286 Function(s) of several complex variables, ballII 278 Function(s) of several complex variables, bidiscII 279 Function(s) of several complex variables, biholomorphic mappingII 288 Function(s) of several complex variables, Cauchy integral formulaII 285 Function(s) of several complex variables, Cauchy — Riemann equationsII 283 Function(s) of several complex variables, completeII 280 Function(s) of several complex variables, complex, derivativeII 282 Function(s) of several complex variables, complex, differentiable functionII 282 Function(s) of several complex variables, complex, differentialII 282 Function(s) of several complex variables, complexified light coneII 280 Function(s) of several complex variables, distinguished boundaryII 279 Function(s) of several complex variables, domain of holomorphyII 287 Function(s) of several complex variables, frameII 279 Function(s) of several complex variables, holomorphicII 283 Function(s) of several complex variables, holomorphic, mappingII 288 Function(s) of several complex variables, holomorphic, relativistic fieldII 280II Function(s) of several complex variables, identity theoremII 285 Function(s) of several complex variables, light coneII 280 Function(s) of several complex variables, light cone, backwardII 281 Function(s) of several complex variables, light cone, forwardII 281 Function(s) of several complex variables, meromorphicII 288 Function(s) of several complex variables, pluriharmonicII 284 Function(s) of several complex variables, point of indeterminationII 288 Function(s) of several complex variables, polycylinderII 278 Function(s) of several complex variables, polydiscII 278 Function(s) of several complex variables, polydisc, with vectorial radiusII 279 Function(s) of several complex variables, Reinhardt domainII 280 Function(s) of several complex variables, Taylor expansionII 285 Function(s) of several complex variables, tube domainII 280 Function(s) of several complex variables, uniqueness theoremII 285 Function(s) of two or more variablesI 402 ff Function(s) of two or more variables, extremesI 438 ff Function(s) of two or more variables, important formulaeI 446 ff Function(s) of two or more variables, introduction of new variablesI 432 ff Function(s) of type BI 574I Function(s) with compact supportII 339 Function(s), abstractII 364see Function(s), algebraicI 364 Function(s), analyticII 276II Function(s), approximationI 398 Function(s), bei x, ber xI 704 Function(s), boundedI 366 Function(s), compositeI 361I Function(s), composite, differentiation ofI 382I Function(s), concaveI 391 Function(s), continuity ofI 366I Function(s), continuous, on curveI 576 Function(s), continuous, on surfaceI 576 Function(s), continuously extensibleI 405 Function(s), convexI 391 Function(s), decomposition ofI 362 Function(s), decreasingI 390 Function(s), dependence ofI 420 ff Function(s), derivatives ofI 377 ff Function(s), differentiableI 378I Function(s), domain of definition ofI 359I Function(s), elementaryI 364 Function(s), equal almost everywhereI 560II Function(s), equicontinuousI 639 Function(s), equivalentI 664 Function(s), erf x, erfc xI 551 Function(s), evenI 366 Function(s), exponentialI 365 Function(s), graphical representation ofI 394 Function(s), GreenII 93II Function(s), harmonicII 175 Function(s), higher transcendentalI 365 Function(s), holomorficII 247 Function(s), homogeneousI 416 Function(s), homogeneous, Euler theoremI 416 Function(s), hyperbolicI 90 ff Function(s), implicitI 423I Function(s), important formulaeI 400 ffI Function(s), increasingI 390 Function(s), inverseI 362 Function(s), inverse, hyperbolicI 92 ff