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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.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
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Издание: 2nd
Год издания: 1994
Количество страниц: 978
Добавлена в каталог: 30.08.2014
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Предметный указатель
MacDonald functions I 703
Maclaurin formula I 397
Maclaurin inequality II 649
Magnitude of vector I 168 I
Mainardi equations I 333
Maintenance strategy II 786
Majorant of function I 525
Majorant of series I 346 I II
Mapping II 344 see
Mapping, conformal II 289 ff
Mapping, continuous I 418
Mapping, contractive II 345
Mapping, definition I 46 II
Mapping, injective II 345
Mapping, into set, onto set I 46 II
Mapping, linear (systems of algebraic equations), composition of I 63
Mapping, linear (systems of algebraic equations), definition I 63
Mapping, linear (systems of algebraic equations), matrix notation for I 64
Mapping, one-to-one, between sets I 46
Mapping, one-to-one, between sets, substitution I 64
Mapping, regular I 418
Mapping, surjective II 344
Markov chain II 804
Markov chain, Chapman — Kolmogorov equations II 805
Markov chain, homogeneous II 804
Markov chain, Markov property II 804
Markov chain, transition, matrix II 804
Markov chain, transition, probability II 804
Markov inequality II 729
Markov process II 700
Markov process, failure intensity II 802
Markov process, Ghapman — Kolmogorov equation II 800
Markov process, homogeneous II 800
Markov process, initial and stationary distribution II 800
Markov process, Kolmogorov differential equations II 800 ff
Markov process, Markov property II 700
Markov process, transition, intensity II 801
Markov process, transition, probability II 709
Markov theorem II 732
Mass, integral calculus for, curves in space I 620
Mass, integral calculus for, plane curves I 618
Mass, integral calculus for, plane figures I 623
Mass, integral calculus for, solids I 626
Mass, integral calculus for, surfaces I 620
Mass, matrix II 465
Mathematical physics, problems of II 147 II II
Matrix, matrices, analysis II 110
Matrix, matrices, banded II 613
Matrix, Matrices, characteristic I 52
Matrix, Matrices, characteristic, polynomial of I 50
Matrix, Matrices, complex conjugate I 52
Matrix, Matrices, congruent I 64
Matrix, Matrices, conjunctive I 68
Matrix, Matrices, decomposed into diagonal blocks I 55 I
Matrix, Matrices, diagonal I 56
Matrix, matrices, diagonally dominant II 619
Matrix, Matrices, diagonals, principal and secondary I 26 I
Matrix, matrices, eigenvalues of I 59
Matrix, matrices, elementary divisors of I 58
Matrix, matrices, full II 626 II
Matrix, matrices, functions of II 110 II
Matrix, matrices, fundamental II 103 II
Matrix, matrices, Gram II 422 II
Matrix, Matrices, Hermitian I 53
Matrix, matrices, Hilbert II 611
Matrix, matrices, identity I 50 II
Matrix, matrices, ill-conditioned II 605
Matrix, matrices, in lower Hessenberg form II 638
Matrix, matrices, in upper Hessenberg form II 638
Matrix, matrices, indefinite I 67
Matrix, matrices, inverse I 50 II
Matrix, matrices, Jordan I 60 II
Matrix, matrices, Jordan, block I 60 II
Matrix, matrices, lambda- I 56
Matrix, matrices, lambda- , divisors I 57
Matrix, matrices, lambda- , elementary transformation I 56
Matrix, matrices, lambda- , equivalence I 56
Matrix, matrices, lambda- , invariant factors I 57
Matrix, matrices, lambda- , rational canonical form I 57
Matrix, matrices, lower triangular II 596
Matrix, matrices, mass II 465
Matrix, matrices, minor, of order I 28
Matrix, matrices, Moore — Penrose generalized inverse II 600
Matrix, matrices, multiplication of I 49
Matrix, Matrices, n-rowed square I 26
Matrix, matrices, negative definite I 67
Matrix, matrices, non-defective II 631
Matrix, Matrices, non-singular I 50
Matrix, matrices, of linear algebraic system I 33 II
Matrix, Matrices, operations on I 49 ff
Matrix, Matrices, orthogonal I 52 I
Matrix, Matrices, partitioned into blocks I 53
Matrix, matrices, plane rotation II 633
Matrix, matrices, positive definite I 67 II
Matrix, Matrices, product of I 49
Matrix, matrices, profile II 613
Matrix, matrices, pseudoinverse II 609
Matrix, matrices, rank, definition and theorems I 26 ff
Matrix, matrices, reflection II 641
Matrix, Matrices, regular I 50
Matrix, matrices, sequence of II 111
Matrix, matrices, series of II 111
Matrix, Matrices, signature of form I 67
Matrix, Matrices, similar I 59 II
Matrix, matrices, skew-symmetric I 51
Matrix, matrices, sparse II 611 II
Matrix, Matrices, square I 50
Matrix, matrices, stiffness II 423
Matrix, matrices, symmetric I 51
Matrix, matrices, Toeplitz II 611
Matrix, matrices, trace of I 53
Matrix, Matrices, transposed I 26
Matrix, Matrices, triangular I 55
Matrix, matrices, tridiagonal II 612
Matrix, Matrices, unitary I 53
Matrix, matrices, upper triangular I 55 II
Matrix, Matrices, upper triangular, eigenvalues of I 59
Matrix, matrices, Vandermonde II 611
Matrix, matrices, well-conditioned II 605
Maxima of functions I 392 ff I
Maximal solution of ordinary differential equation II 7
Maximum, likelihood, estimator II 749
Maximum, likelihood, estimator, for censored random samples II 790 ff
Maximum, likelihood, estimator, method II 749 ff
Maximum, principle, for harmonic functions II 177
Maximum, principle, for heat equation II 200
Mean(mean value) II 698
Mean(mean value) of linear transformation of random variables II 728
Mean(mean value) of stochastic process II 810 II
Mean(mean value), conditional II 706
Mean(mean value), curvature I 278
Mean(mean value), deviation II 701
Mean(mean value), sample II 736
Mean, curvature I 278
Mean, torsion I 279
Mean-value theorem(s) I 387 I
Mean-value theorem(s) for double integrals I 580
Mean-value theorem(s) for harmonic functions II 180 II
Mean-value theorem(s), generalization for several variables I 415
Mean-value theorem(s), generalized I 388
Measurable, functions I 561
Measurable, sets I 560
Median II 700
Median sample II 740
Mellin transform II 568
Meromorphic function II 267
Meromorphic function of several complex variables II 288
Mesh point II 546 II
Mesh point, boundary II 563
Mesh point, inner II 562
Mesh point, interior II 562
Method(s) of discretization in time II 215
Method(s) of finite differences II 546 ff
Method(s) of finite elements II 428 ff
Method(s) of parameters II 28 II
Method(s) of performing conformal mapping II 296 ff
Method(s) of Rothe II 215
Method(s) of Schwarz quotients II 87
Method(s) of separation of variables II 14 II
Method(s) of transfer and normalized transfer of boundary conditions II 519 ff
Method(s) of variation of parameters II 18 II II II
Method(s) Ritz II 422
Method(s) Runge — Kutta II 492 ff
Method(s), Fourier II 534 ff
Method(s), Galerkin II 427
Metric II 323
Metric axioms II 323
Metric invariant II 330
Metric spaces II 323 ff
Metric spaces, linear and other operators in II 344 ff
Metric tensor of space I 247
Meusnier theorem I 327
Milne device II 510
Milne formula II 511
Minima of functions I 392 I
Minimal angle condition II 448
Minimax, approximation II 669
Minimax, principle II 86
Minimum of functional of energy II 354 II II
Minkowski inequality I 9
Minor in determinant I 30
Mixed derivatives, interchangeability I 408
Mixed problems for partial differential equations II 150 II II II
Mixed process (ARMA) II 813 II
Mixed product of three vectors I 230
MODE II 700
Modulus of continuity II 071
Modulus of continuity, uniform II 671
Modulus of vector I 227
Moivre theorem I 11
Moivre — Laplace theorem II 733
Moment(s) II 698
Moment(s) of inertia, formulae for, plane figures I 95 ff
Moment(s) of inertia, formulae for, solids I 104 ff
Moment(s) of inertia, integral calculus for, curves in space I 620
Moment(s) of inertia, integral calculus for, plane curves I 619
Moment(s) of inertia, integral calculus for, plane figures I 624
Moment(s) of inertia, integral calculus for, solids I 628
Moment(s) of inertia, integral calculus for, surfaces I 631
Moment(s), central II 698
Moment(s), method of II 750 ff
Moment(s), mixed II 708
Moment(s), sample II 737
Monodromy theory II 277
Monogenic function II 246
Monotone operator II 372
Monotonic functions I 391
Monotonic sequences I 341
Montpellier conoid I 224
Moore — Penrose generalized inverse of matrix II 609
Movable (free) ends of admissible curves II 395
Moving, average (MA) II 812 II
Moving, polhode I 127
Moving, trihedron and Frenet formulae I 268 ff
Multigrid method II 625
Multiindex II 339
Multiple, angle formulae of trigonometric functions I 74
Multiple, comparison II 782
Multiple, point of curve I 261
Multiplication of matrices I 49
Multiplication of tensors I 255
Multiplication of vectors I 228 ff
Multiplicity of eigenvalue I 84 I
Multipliers, Lagrange mehod I 442
Multishooting method II 518
Multivariate, analysis II 785 ff
Multivariate, distribution II 704 II
Multivariate, process II 797
n-component (complex) vector I 24
n-coordinate (complex) vector I 24
N-dimensional sphere II 281
n-dimensional sphere in Euclidean space II 321
n-dimensional sphere in metric space II 326
n-dimensional torus II 280
n-dimensional vector space I 24
Nabla operator I 234
Napier rule I 84
Natural logarithms, base of I 341
Natural numbers I 2
Natural numbers, sums of powers of I 16
Navier — Stokes equations II 203
Negative half line I 174
Negative orientation I 229
Neighbourhood of point I 366 I II II
Neighbourhood of point in metric space II 326
Neil parabola I 126
Nephroid I 133
Nets (finite difference method) II 546 II
Neumann functions I 700
Neumann problem II 176 see
Neumann solution for Laplace and Poisson equations II 177 ff
Newton definite integral I 518
Newton formula, binomial theorem I 19
Newton interpolation formula II 680
Newton interpolation polynomial, general II 678
Newton method for attaining roots of algebraic equations II 658 II
Newton potential II 175
Newton problem II 176
Newton — Cotes quadrature formula I 556
Newton — Fourier method in conformal mapping II 312
Nicomedes conchoid I 152
Nodal parameters II 430
Node(s) of curves I 291
Node(s) of finite element II 430
Node(s) of interpolation II 675
Node(s) of quadrature formula I 555
Node(s), (differential equations) II 26
Non-developable sinface I 316
Non-zero function in I 664 II
Nonbasic variables II 837
Nonlinear elliptic boundary value problems II 210
Nonlinear partial diffeiential equations of first order II 160 ff
Nonlinear regression model I 779
Nonlinear systems, numerical solution II 662
Nonsingular conic sections I 189
Norm of element II 331
Norm of element, axioms of II 331
Norm of function I 663 I II
Norm of matrix II 604
Norm of matrix, spectral II 604
Norm of operator II 348
Norm of partition I 513 I
Norm of tangent vector I 266
Norm of vector I 227 II
Norm of vector, Euclidean II 603
Norm of vector, maximum II 604
Norm of vector, sum II 604
Norm of vector, uniform II 604
Normal acceleration I 276
Normal cycloid I 127
Normal distribution II 714
Normal epicycloid I 130
Normal equation of straight line I 177
Normal equations II 770
Normal form (of differential equation) II 68
Normal fundamental system II 55
Normal hypocycloid I 130
Normal plane I 271
Normal system of differential equations II 100
Normal vector to plane I 200
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