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Rektorys K. (ed.) — Survey of Applicable Mathematics
Rektorys K. (ed.) — Survey of Applicable Mathematics



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Íàçâàíèå: Survey of Applicable Mathematics

Àâòîð: 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.
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.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1969

Êîëè÷åñòâî ñòðàíèö: 1369

Äîáàâëåíà â êàòàëîã: 06.12.2013

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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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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