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.
Summabilities of seriesI 645 Summation convention (tensors)I 243 Supercritical dampingI 159 Superosculating circleI 284 Supremum (l.u.b.)I 5 Surface(s) of revolutionI 219 Surface(s), conicalI 224 Surface(s), contravariant and covariant vector onI 252 Surface(s), cuspidal edgeI 316 Surface(s), definitionI 209I Surface(s), differential calculus, application toI 628 Surface(s), discriminantI 324 Surface(s), edge of regrassionI 316 Surface(s), element of areaI 324 Surface(s), elliptic point ofI 325 Surface(s), envelope of one-parameter familyI 318 Surface(s), equipotentialI 233 Surface(s), explicit equation ofI 306 Surface(s), finite piecewise smoothI 305 Surface(s), first fundamental formI 253I Surface(s), fundamental coefficientsI 324 Surface(s), Gaussian curvatureI 330 Surface(s), generator ofI 317I Surface(s), hyperbolic point ofI 325 Surface(s), integralsI 009 ff Surface(s), integrals, of first and second kindsI 610—611 Surface(s), interior diameterI 609 Surface(s), lines of curvatureI 331 Surface(s), mean curvatureI 330 Surface(s), non-developableI 316 Surface(s), normal curvatureI 328 Surface(s), normal section radius of curvatureI 328 Surface(s), orientedI 609 Surface(s), orthogonal conjugate net onI 331 Surface(s), parabolic point ofI 325 Surface(s), parameters and parametric equationsI 306 Surface(s), regular points onI 209I Surface(s), ruledI 221 Surface(s), scalar onI 252 Surface(s), scroll (skew surface)I 316 Surface(s), second fundamental formI 325 Surface(s), second orderI 209 ff Surface(s), shape with respect to tangent planeI 325 Surface(s), simple finite piecewise smoothI 575 Surface(s), singular point onI 209I Surface(s), tensor onI 251 Surjective operator (mapping)II 344 Sylvester law of inertiaI 67 Symbols O(g(x)), o(g(x))I 376 Symmetric eigenvalue problemII 82 Symmetric kernels of integral equationsII 231 Symmetric matricesI 51 Symmetric operatorsII 359 Symmetric problemsII 82 System(s), closed in Hilbert spaceII 337 System(s), closed in Hilbert space, in space I 675 System(s), complete in Hilbert spaceII 337 System(s), complete in Hilbert space, in space I 675 System(s), of decompositionsII 447 System(s), of decompositions, regularII 447 System(s), of ordinary differential equationsII 2IIII System(s), of partial differential equationsII 149II System(s), orthogonal in Hilbert spaceII 336 System(s), orthogonal in Hilbert space, in space I 670 System(s), orthonormal in Hilbert spaceII 336 System(s), orthonormal in Hilbert space, in space I 670 T-schemeI 557II t-testII 757 ff Table of analysis of varianceII 782 Table of Bessel functions , , , I 695I Table of boundary value problemsII 411 Table of Fourier transformsII 582II Table of integralsI 470—511I Table of Laplace transformsII 578II Table of Legend re polynomialsI 707 Table of solved differential equationsII 120 ff Table of zeros of , and their derivativesI 695 Table, contingencyII 763 Table, correlationII 741 Table, frequencyII 741 Tabular pointsII 675 Tangent and cotangent, integrals containing themI 501 ff Tangent(s) to conicI 191 ff Tangent(s), developable (surface)I 316 Tangent(s), direction, angle and length, in polar coordinatesI 300 Tangent(s), drawn to curve from arbitrary pointI 303 Tangent(s), length, in polar coordinatesI 301 Tangent(s), plane of surfaceI 311 Tangent(s), plane to curveI 272 Tangent(s), surfaceI 316 Tangent(s), theoremI 79 Tangent(s), vector fieldI 249 Tangent(s), vector to curveI 232I Tangential vector to surfaceI 311 Taylor expansion for functions of one complex variableII 264 Taylor expansion for functions of several complex variablesII 285 Taylor expansion methodII 491 Taylor formulaI 396 Taylor formula for polynomialsI 23 Taylor seriesI 652II Taylor theoremI 396I Taylor theorem for several variablesI 414 Temperature distribution, examples using, finite difference methodII 559 Temperature distribution, examples using, Fourier methodII 539 ff Temperature distribution, examples using, Laplace transformII 571II Tensor(s), alternatingI 256 Tensor(s), calculusI 242 ff Tensor(s), characteristic numbers ofI 258 Tensor(s), conjugate directionsI 257 Tensor(s), contravariant and covariantI 247 Tensor(s), contravariant and covariant, on surfaceI 249 Tensor(s), deformationI 249I Tensor(s), first fundamental of surfaceI 252 Tensor(s), in spaceI 246 ff Tensor(s), indicatrix of pointI 257 Tensor(s), indices, lowering and raising ofI 255 Tensor(s), metric, of spaceI 247 Tensor(s), metric, of surfaceI 252 Tensor(s), metric, on surfaceI 251 Tensor(s), quadraticI 247 Tensor(s), second fundamental of surfaceI 253 Tensor(s), symmetric and skew-symmetricI 255 Tensor(s), symmetric quadraticI 254 Term-by-term, differentiationI 644II Term-by-term, integrationI 643IIII Termination criterion for iterative methodsII 616 Test(s) of linearityII 775 Test(s) of significance in normal linear regression modelII 773 ff Test(s) of size II 756 Test(s), chi-squareII 761 Test(s), Fisher, of periodicityII 819 Test(s), functionII 82 Test(s), goodness of fitII 760 Test(s), hypothesisII 755 Test(s), Kolmogorov — SmirnovII 763 Test(s), one-sampleII 757 Test(s), one-sided and two-sidedII 756 Test(s), pairedII 759 ff Test(s), parametric and non-parametricII 755 Test(s), tII 757 ff Test(s), two-sampleII 757 ff Test(s), uniformly most powerfullII 756 Theorem(s) on continuous extension of functional and operatorII 340 Theorem(s) on convergence, of finite difference methodII 565II Theorem(s) on convergence, of finite element methodII 447 Theorem(s) on eigenvalues, of differential equationsII 84 Theorem(s) on eigenvalues, of operatorsII 355IIII Theorem(s) on existence and uniqueness of solution of problems, in ordinary differential equationsII 5IIII Theorem(s) on existence and uniqueness of solution of problems, in partial differential equationsII 177IIIIIIIIII Theorem(s) on Fredholm integral equationsII 225
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