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Rektorys K. — Survey of Applicable Mathematics.Volume 2.
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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2nd

Год издания: 1994

Количество страниц: 978

Добавлена в каталог: 30.08.2014

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Предметный указатель
Regular functions      II 247
Regular hypersurfaces in $E_{n}$      II 392
Regular mapping      I 417
Regular nets      II 549
Regular part of Laurent series      II 266
Regular point of curve      I 261
Regular point of f(z)      II 264
Regular point of surface      I 309
Regular polygon      I 98
Regular singularity      II 69
Regular system of decompositions      II 447
Regular value of operator      II 355
Rein hard t domain      II 280
Relative complement of sets      I 45
Relative maximum and minimum      I 392 I
Relatively compact space      II 329
Reliability, censoring      II 789 ff
Reliability, estimation      II 789 ff
Reliability, function      II 786
Reliability, hazard rate (failure rate, force and mortality)      II 787 II
Reliability, probability of failure and survival      II 786
Reliability, redundancy      II 789
Reliability, redundancy, active (parallel) and standby      II 789
Reliability, system      II 786
Reliability, theory      II 786
Remainder(s) of finite difference approximation      II 547
Remainder(s) of interpolation formula      II 676
Remainder(s) of quadrature formula      I 555
Remainder(s) of Taylor formula      I 397 I
Remes algorithm      II 672
Removable singular point on curve or surface      I 261 I
Removable singularity, theorem of      II 181 II
Renewal theory      II 786
Repeated integrals      I 581
Representing functions      II 412 II
Residual of linear algebraic system      II 605 II II
Residual sum of squares      II 770 II
Residue theorem      II 270
Resolvent      II 97 II II
Resonance curve      I 158 I
Response variable      II 767
Revolution, surfaces of      I 219
Rhombus, formulae for geometrical elements      I 97
Ricatti differential equation      II 21
Richardson extrapolation      II 512
Riemann and Lebesgue integration, distinction between      I 562
Riemann integration      I 512
Riemann sphere      II 243
Riemann surface      II 273
Riemann theorem (conformal mapping)      II 293
Riemann zeta function      I 643
Riemann — Schwarz reflection principle      II 301
Riesz — Fischer theorem      II 352
Right conoid      I 316
Right helicoid      I 273
Right parallelepiped, moment of inertia      I 105
Right parallelepiped, volume and surface area of      I 105
Rings, associative, commutative, division      I 47
Rings, solid, volume, surface area and moment of inertia of      I 111
Risk, consumer's and producer's      II 792
Ritz method      II 305 II II
Ritz method in conformal mapping      II 305
Ritz method, convergence of      II 424
Ritz — Galerkin method      II 427
Robertson law of growth      I 164
Rolle theorem      I 387
Romberg quadrature formula      I 557
Root-mean-square      I 9
Roots of algebraic equations (polynomials)      I 21 II
Roots of algebraic equations (polynomials), Budan — Fourier theorem      II 651
Roots of algebraic equations (polynomials), connection with eigenvalues of matrices      II 652
Roots of algebraic equations (polynomials), Descartes theorem      II 650
Roots of algebraic equations (polynomials), estimates for      II 649 ff
Roots of algebraic equations (polynomials), Lagrange, Maclaurin, Tillot inequalities      II 649
Roots of algebraic equations (polynomials), Sturm theorem      II 651
Rotation, cartesian coordinate system      I 198
Rothe function      II 217
Rothe method      II 215 II
Ruled surfaces      I 221 I I
Ruled surfaces, undevelopable      I 316
Ruling lines      I 221
Runge — Kutta methods (formulae)      II 492 ff
Runge — Kutta methods (formulae), Bieberbach error estimate      II 495
Runge — Kutta methods (formulae), Fehlberg      II 493
Runge — Kutta methods (formulae), Heun      II 493
Runge — Kutta methods (formulae), modified Euler      II 492
Runge — Kutta methods (formulae), standard      II 493
Rytz costruction of axes of ellipse      I 118
Saddle point      II 27
Sample(s)      II 735
Sample(s) from normal distribution      II 738 ff
Sample(s), censored      II 789
Sample(s), characteristics      II 736
Sample(s), coefficient, correlation      II 737
Sample(s), coefficient, correlation, of skewness and kurtosis      II 737
Sample(s), coefficient, correlation, of variation      II 737
Sample(s), correlation and covariance matrix      II 738
Sample(s), covariance      II 738
Sample(s), function of stochastic process      II 797
Sample(s), mean      II 736
Sample(s), median      II 740
Sample(s), moment      II 737
Sample(s), moment, central      II 737
Sample(s), ordered      II 739
Sample(s), quantile      II 741
Sample(s), random      II 735
Sample(s), range      II 740
Sample(s), size of      II 736
Sample(s), space      II 736
Sample(s), standard deviation      II 737
Sample(s), variance      II 736
Sampling inspections (sampling plans)      II 792
Sarrus rule      I 31
Scalar (inner) product      II 221 II II
Scalar (inner) product in Hilbert space      II 333
Scalar (inner) product in Hilbert space, axioms of      II 333
Scalar (inner) product in space $L_{2}$      I 663 II II
Scalar (inner) product of functions      I 663
Scalar (inner) product of functions, axioms of      II 333
Scalar (inner) product of vectors      I 228
Scalar (inner) product on a surface      I 252
Scalar (inner) product, energetic      II 361
Scalar field, gradient of      I 232
Scalar on surface      I 252
Scalar potential      I 233
Scheffe method      II 782 II
Schmidt orthogonalization process      I 677
Schwarz constants and quotients      II 87 II
Schwarz inequality      I 356 I II II II
Schwarz — Cauchy inequality      I 356
Schwarz — Christoffel theorem      II 302
Screw surface      I 316
SCROLL      I 316 I
Second curvature      I 278
Second mean value theorem      I 516
Second, order derivatives      I 379 I
Sector of annulus, geometrical formulae      I 101
Sector of circle, geometrical formulae      I 99
Segment of circle, geometrical formulae      I 99
Self-adjoint, differential equation      II 66 II
Self-adjoint, operator      II 79 II II II
Self-adjoint, space      II 350
Self-tangency, point of      I 291
Semi-axis, polar coordinates      I 178
Semi-closed interval      I 359
Semi-open interval      I 359
Semiconvergent series      I 660
Semicubical parabola      I 126
Semidiscrete methods      II 215 II
Seminorm      II 449
Sentences      I 1
Separable space      II 328
Separation of variables      II 14 II
Sequence(s) in metric space      II 325
Sequence(s) of constant terms      I 336
Sequence(s) of equicontinuous functions      I 639
Sequence(s) of functions of complex variable      II 260
Sequence(s) of matrices      II 111
Sequence(s) of partial sums      I 641 II II
Sequence(s) of uniformly bounded functions      I 638
Sequence(s) with variable terms, integration and differentiation of      I 639—641
Sequence(s) with variable terms, uniformly convergent      I 637
Sequence(s), bounded above or below      I 339
Sequence(s), Cauchy      II 327
Sequence(s), convergent      I 337 I II
Sequence(s), decreasing      I 341
Sequence(s), fundamental      II 327
Sequence(s), important formulae and limits      I 342
Sequence(s), increasing      I 341
Sequence(s), monotonic      I 341
Sequence(s), oscillating      I 344
Sequence(s), subsequences of      I 339
Sequential acceptance sampling      II 795 ff
Sequential analysis      II 795
Series in two or more variables      I 651
Series of functions of complex variables for functions sin z, cos z, $e^{z}$      II 263
Series of functions of complex variables, convergent      II 260
Series of functions of complex variables, convergent, uniformly      II 261
Series of functions of complex variables, domain of convergence      II 261
Series of functions of complex variables, Laurent      II 265
Series of functions of complex variables, power      II 262
Series of functions of complex variables, Taylor      II 264
Series with variable terms, condition of convergence      I 642
Series with variable terms, differentiation      I 644
Series with variable terms, integration      I 643
Series with variable terms, survey of important formulae      I 654 I
Series with variable terms, uniformly convergent      I 642
Series, application of      I 658
Series, convergent and divergent      I 344 I
Series, divergent, application of      I 659
Series, expansion into      I 650 I
Series, harmonic      I 344
Series, power      I 645 ff
Series, power, radius of convergence      I 646
Series, tables      I 355 ff
Series, Taylor      I 652
Serret — Frenet formulae      I 270
Set(s), bounded      II 322
Set(s), closed      II 321 II
Set(s), compact      II 329
Set(s), concepts of      I 44
Set(s), connected      II 320
Set(s), convex      II 321
Set(s), countable      II 323
Set(s), countable, at most      II 323
Set(s), dense      II 326
Set(s), harmonic of four points      I 191
Set(s), linear      II 330
Set(s), mapping of, definitions      I 46
Set(s), measurable      I 560
Set(s), open      II 320 II II
Set(s), point of accumulation (cluster point, limit point)      II 319
Set(s), regions      II 320
Several variables, functions of      I 402 ff
Several variables, functions of, composite functions, limit, continuity      I 403 ff
Several variables, functions of, extremes      I 438
Several variables, functions of, introduction of new variables      I 432
Several variables, functions of, partial derivatives of      I 407
Several variables, functions of, survey of important formulae      I 446 ff
Several variables, functions of, transformations      I 432 ff
Sheaf of planes      I 203
Shells, problems in theory of      II 203
Shepard correction      II 744
Shooting method      II 515 ff
Sigma $(\sigma)$, algebra      II 691
Sigma $(\sigma)$, limits      II 716
Significance, level of test      II 756
Significance, test of, in normal regression model      II 773 ff
Similar matrices      I 59 II
Simple abstract function      II 366
Simple epicycloid      I 125
Simple function      II 248
simple harmonic motion      I 156
Simple hypocycloid      I 125
Simple operator (mapping)      II 345
Simple pole      II 267
Simplex method      II 848
Simply connected region      II 321 II
Simpson quadrature formula      I 557
Simpson rule      I 557
Sine and cosine, integrals containing      I 491 ff
Sine curves      I 155
Sine integral      I 450 I
Sine Theorem      I 79
Single layer potential      II 1S4 II
Singular conic sections      I 189
Singular integral (solution)      II 11 II
Singular integral equations      II 238
Singular points of curve      I 261 I
Singular points of differential equations      II 26 II
Singular points of holomorphic functions      II 267
Singular points of surface      I 306
Singular value of matrix      II 607
Singular value, decomposition of matrix      II 607
Skew, curve      I 263
Skew, field      I 48
Skew, lines, distance between      I 207
Skew, surface      I 316 I
Skew, symmetric, matrices      I 51
Skew, symmetric, tensors      I 256
Slack variables      II 828
Slope of straight line      I 170
Small numbers, computation with      I 398 ff
Smooth, curve      I 261 I I
Smooth, function      I 379
Smooth, surface      I 306
Sobolev space      see "Space(s)"
Sobotka rectification of circular arc      I 114
Solenoidal (sourceless) vector field      I 234
Solid analytic geometry, coordinate systems      I 195 ff
Solid analytic geometry, coordinate systems, cylindrical (semi-polar)      I 196
Solid analytic geometry, coordinate systems, rectangular      I 195
Solid analytic geometry, coordinate systems, spherical (polar)      I 196
Solid analytic geometry, linear concepts      I 199 ff
Solid analytic geometry, quadrics      I 209 ff
Solid analytic geometry, surfaces of revolution, ruled surfaces      I 219 ff
Solids of type A      I 575
Solids, integral calculus, application of      I 624
Solids, volumes, surfaces, centroids and moments of inertia      I 104 ff
Solution of inequalities      I 7
Solution of integral equations      see "Integral equations"
Solution of ordinary differential equations      see "Differential equations ordinary"
Solution of partial differential equations      see "Differential equations partial"
SOR method      II 619
Space(s) of distributions      II 342
Space(s) of elementary events      II 689
Space(s), $E_{n}$      II 321
Space(s), $H_{A}$      II 361
Space(s), $L_{2}(a, b)$, $L_{2}(\Omega)$      II 323 II II
Space(s), $L_{p}(a, b)$, $L_{p}(\Omega)$      II 324 II
Space(s), $\mathbb{C}^{n}$, $\mathbb{R}^{2n}$      II 278
Space(s), adjoint      II 350
Space(s), Banach      II 331
Space(s), C([a, b]), $C(\overline{\Omega})$      II 325
Space(s), compact      II 329
Space(s), complementary subspace      II 335
Space(s), complete      II 327
Space(s), complex $C_{n}$      II 322
Space(s), curve, definition      I 263
Space(s), dual      II 349
1 2 3 4 5 6 7 8 9 10 11 12 13 14
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