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Riley, Hobson — Mathematical Methods for Physics and Engineering

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Название: Mathematical Methods for Physics and Engineering

Авторы: Riley, Hobson

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-d edition

Количество страниц: 1253

Добавлена в каталог: 17.02.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Chi-squared ( $\chi^{2}$ ) distribution      1034
Chi-squared ( $\chi^{2}$ ) distribution and goodness of fit      1139
Chi-squared ( $\chi^{2}$ ) distribution and likelihood-ratio test      1125 1134
Chi-squared ( $\chi^{2}$ ) distribution and multiple estimators      1086
Chi-squared ( $\chi^{2}$ ) distribution, test for correlation      1143
Cholesky separation      318
Christoffel symbol $\Gamma^{k}_{ij}$       814—816
Christoffel symbol $\Gamma^{k}_{ij}$ from metric tensor      815 822
Circle of convergence      717—718
Circle, area of      72
Circuits, electrical, transients      491
Clairaut equation      489
Classes and equivalence relations      906
Closure of a group      885
Closure property of eigenfunctions of an Hermitian operator      601
Cofactor of a matrix element      264
Column matrix      255
Column vector      255
Combinations (probability)      975—981
Common ratio in geometric series      120
Commutation law for group elements      886
Commutative law for addition in a vector space of finite dimensionality      247
Commutative law for addition in a vector space of infinite dimensionality      583
Commutative law for addition of complex numbers      89
Commutative law for addition of matrices      256
Commutative law for addition of vectors      217
Commutative law for complex scalar/dot product      226
Commutative law for convolution      453 464
Commutative law for inner product      249
Commutative law for multiplication of a vector by a scalar      218
Commutative law for multiplication of complex numbers      91
Commutative law for scalar/dot product      224
Commutator, of two matrices      314
Comparison Test      128
Complement      963
Complement, probability for      967
Complementary equation      496
Complementary error function      1205
Complementary function (CF)      497
Complementary function (CF) for ODE      498
Complementary function (CF), partially known      512
Complementary function (CF), repeated roots of auxiliary equation      499
Completeness of basis vectors      248
Completeness of eigenfunctions of an Hermitian operator      588 601
Completeness of eigenvectors of a normal matrix      280
Completeness of eigenvectors of a normal matrix, spherical harmonics $Y^{m}_{\ell}(\theta,\phi)$       670
Completing the square as a means of integration      67—68
Completing the square for quadratic equations      35
Completing the square to evaluate Gaussian integral      442 684
Complex conjugate of a matrix      261—263
Complex conjugate of scalar/dot product      226
Complex conjugate z*, of complex number      92—94 715
Complex conjugate, properties of      93
Complex exponential function      95 719
Complex Fourier series      430—431
Complex Integrals      738—742 see "Contour
Complex integrals of $z^{-1}$       740
Complex integrals, Cauchy's      745—747
Complex integrals, Cauchy's theorem      742
Complex integrals, definition      739
Complex integrals, Jordan's lemma      761—762
Complex integrals, Morera's theorem      744
Complex integrals, principal value      760
Complex integrals, residue theorem      752—754
Complex logarithms      102—103 720
Complex logarithms, principal value of      103 720
complex numbers      86—117
Complex numbers $e^{i\theta}$       890
Complex numbers from roots of polynomial equations      86—87
Complex numbers, addition and subtraction of      88—89
Complex numbers, applications to differentiation and integration      104
Complex numbers, argument of      90
Complex numbers, associativity of addition and subtraction      89
Complex numbers, associativity of multiplication      91
Complex numbers, commutativity of addition and subtraction      89
Complex numbers, commutativity of multiplication      91
Complex numbers, complex conjugate of      see "Complex conjugate"
Complex numbers, components of      87
Complex numbers, de Moivre's theorem      see "de Moivre's theorem"
Complex numbers, division of      94—95 97—98
Complex numbers, division of, properties      95
Complex numbers, imaginary part of      86—87
Complex numbers, modulus of      90
Complex numbers, multiplication of      91—92 97—98
Complex numbers, multiplication of, as rotation in the Argand diagram      91—92
Complex numbers, notation      87
Complex numbers, polar representation of      95—98
Complex numbers, real part of      86—87
Complex numbers, trigonometric representation of      96
Complex potentials      725—730
Complex potentials and fluid flow      727—728
Complex potentials for circular and elliptic cylinders      728 730
Complex potentials for parallel cylinders      770
Complex potentials for plates      736—738 770
Complex potentials for strip      770
Complex potentials for wedges      737
Complex potentials under conformal transformations      730—738
Complex potentials, equipotentials and field lines      726
Complex power series      136
Complex powers      102—103
Complex variables      see "Functions of a complex variable" "Power "Complex
Components of a complex number      87
Components of a vector      221—222
Components of a vector in a non-orthogonal basis      238
Components of a vector, uniqueness      248
Conditional (constrained) variation      844—846
Conditional convergence      127
Conditional distributions      1040
Cone, surface area of      75—76
Cone, volume of      76
Confidence interval      1079
Confidence region      1084
Conformal transformations (mappings)      730—738
Conformal transformations (mappings), applications      735—738
Conformal transformations (mappings), examples      732—735
Conformal transformations (mappings), properties      730—732
Conformal transformations (mappings), Schwarz — Christoffel transformation      733—735
Congruence      907
Conic sections      15
Conic sections, eccentricity      16
Conic sections, parametric forms      17
Conic sections, standard forms      16
Conjugacy classes      910—912
Conjugacy classes in a class by itself      910
Conjugate roots of polynomial equations      102
Connectivity of regions      389
Conservative fields      393—395
Conservative fields, necessary and sufficient conditions      393—395
Conservative fields, potential (function)      395
Consistency, of estimator      1073
Constant coefficients in ODE      498—509
Constant coefficients in ODE, auxiliary equation      499
Constants of integration      63 474
Constrained variation      844—846
Constraints, stationary values under      see "Lagrange undetermined multiplers"
Continuity correction for discrete RY      1028
Continuity equation      410
Contour integration      758—768
Contour integration, infinite integrals      759—764
Contour integration, inverse Laplace transforms      765—768
Contour integration, residue theorem      752—754 758—768
Contour integration, sinusoidal functions      758—759
Contour integration, summing series      764—765
Contraction of tensors      788
Contradiction, proof by      32—34
Contravariant basis vectors      810
Contravariant basis vectors, derivative      814
Contravariant components of tensor      805—806
Contravariant components of tensor, definition      810
Control variates, in Monte Carlo methods      1173

Convergence of infinite series      717—718
Convergence of infinite series, absolute      127 717
Convergence of infinite series, complex power series      136
Convergence of infinite series, conditional      127
Convergence of infinite series, necessary condition      128
Convergence of infinite series, power series      135
Convergence of infinite series, power series, under various manipulations      see "Power series manipulation"
Convergence of infinite series, ratio test      718
Convergence of infinite series, rearrangement of terms      127
Convergence of infinite series, tests for convergence      128—134
Convergence of infinite series, tests for convergence, alternating series test      133
Convergence of infinite series, tests for convergence, comparison test      128
Convergence of infinite series, tests for convergence, grouping terms      132
Convergence of infinite series, tests for convergence, integral test      131
Convergence of infinite series, tests for convergence, quotient test      130
Convergence of infinite series, tests for convergence, ratio comparison test      130
Convergence of infinite series, tests for convergence, ratio test (D'Alembert)      129 135
Convergence of infinite series, tests for convergence, root test (Cauchy)      132 717
Convergence of numerical iteration schemes      1156—1158
Convolution theorem, Fourier transforms      454
Convolution theorem, Laplace transforms      463
Coordinate geometry      15—18
Coordinate geometry, straight line      15
Coordinate systems      see "Cartesian curvilinear cylindrical plane "Spherical
Coordinate transformations and integrals      see "Change of variables"
Coordinate transformations and matrices      see "Similarity transformations"
Coordinate transformations, general      809—814
Coordinate transformations, general, relative tensors      812
Coordinate transformations, general, tensor transformations      811
Coordinate transformations, general, weight      813
Coordinate transformations, orthogonal      781
Coplanar vectors      229
Correlation functions      455—457
Correlation functions, auto-correlation      456
Correlation functions, cross-correlation      455
Correlation functions, energy spectrum      456
Correlation functions, Parseval's theorem      457
Correlation functions, Wiener — Kinchin theorem      456
Correlation matrix, of sample      1072
Correlation of bivariate distributions      1042—1049
Correlation of sample data      1072
Correlation, chi-squared test      1143
Correspondence principle in quantum mechanics      1056
Cosets and congruence      907
cosh, hyperbolic cosine      105 720 see
Cosine in terms of exponential functions      105
Cosine, Maclaurin series for      143
Cosine, orthogonality relations      423
Counting irreps      see "Characters counting
Coupled pendulums      335 337
Covariance matrix, of linear least squares estimators      1116
Covariance matrix, of sample      1072
Covariance of bivariate distributions      1042—1049
Covariance of sample data      1072
Covariant basis vector      810
Covariant basis vector, derivative      814
Covariant components of tensor      805—806
Covariant components of tensor, definition      810
Covariant derivative      817
Covariant derivative of scalar      820
Covariant derivative, semi-colon notation      818
Covariant differentiation      817—820
CPF      see "Probability functions cumulative"
Cramer determinant      304—305
Cramer — Rao (Fisher's) inequality      1075 1076
Cramer's rule      304—305
Cross product      see "Vector product"
Cross-correlation functions      455
Crystal lattice      151
Crystal point groups      924
Cube roots of unity      101
Cube, rotational symmetries of      956
Curl of a vector field      359
Curl of a vector field as a determinant      359
Curl of a vector field as integral      404 406
Curl of a vector field in curvilinear coordinates      374
Curl of a vector field in cylindrical polars      366
Curl of a vector field in spherical polars      368
Curl of a vector field, curl curl      362
Curl of a vector field, Stake's theorem      412—415
Curl of a vector field, tensor form      823
Current-carrying wire, magnetic potential      662
Curvature      53—56
Curvature of a function      53
Curvature of space curves      348
Curvature, circle of      54
Curvature, radius of      54
CURVES      see "Plane curves and space curves"
Curvilinear coordinates      370—375
Curvilinear coordinates, basis vectors      370
Curvilinear coordinates, length and volume elements      371
Curvilinear coordinates, scale factors      370
Curvilinear coordinates, surfaces and curves      370
Curvilinear coordinates, tensors      804—826
Curvilinear coordinates, vector operators      373—375
Cut plane      762
Cycle notation for permutations      899
Cyclic groups      903 940
Cyclic relation for partial derivatives      160
Cycloid      376 844
Cylinders, conducting      see "Complex potentials for
Cylindrical polar coordinates      363—367
Cylindrical polar coordinates, area element      366
Cylindrical polar coordinates, basis vectors      364
Cylindrical polar coordinates, Laplace equation      661—664
Cylindrical polar coordinates, length element      366
Cylindrical polar coordinates, vector operators      363—367
Cylindrical polar coordinates, volume element      366
D'Alembert's ratio test      129 718
D'Alembert's ratio test in convergence of power series      135
D'Alembert's solution to wave equation      627
Damped harmonic oscillators      243
Damped harmonic oscillators and Parseval's theorem      457
Data modelling, maximum-likelihood      1097
De Broglie relation      442 642 703
De Moivre's theorem      98 758
De Moivre's theorem, applications      98—102
de Moivre's theorem, applications, finding the nth roots of unity      100—101
de Moivre's theorem, applications, solving polynomial equations      101—102
de Moivre's theorem, applications, trigonometric identities      98—100
Deconvolution      see "Fourier transforms deconvolution"
Defective matrices      283 316
Degeneracy of normal modes      952
Degeneracy, breaking of      953—955
Degenerate eigenvalues      280 287
Degenerate kernel      see "Kernel of integral equations separable"
Degree of ODE      474
Degree of polynomial equation      2
del $\nabla$       see "Gradient operator (grad)"
del squared $\nabla^{2}$ (Laplacian)      358 609
del squared $\nabla^{2}$ (Laplacian) as integral      406
del squared $\nabla^{2}$ (Laplacian) in curvilinear coordinates      374
del squared $\nabla^{2}$ (Laplacian) in cylindrical polar coordinates      366
del squared $\nabla^{2}$ (Laplacian) in polar coordinates      658
del squared $\nabla^{2}$ (Laplacian) in spherical polar coordinates      368 675
del squared $\nabla^{2}$ (Laplacian), tensor form      822
Delta function (Dirac)      see "Dirac $\delta$ -function"
Dependent random variables      1038—1047
Derivative      see also "Differentiation"
Derivative method for second series solution of ODE      551—554
Derivative of a function of a complex variable      711
Derivative of a vector      340
Derivative of basis vectors      342—343
Derivative of composite vector expressions      343—344
Derivative of function of a function      47 48
Derivative of hyperbolic functions      109—112
Derivative of products      45—47 49—51
Derivative of quotients      48
Derivative of simple functions      45
Derivative, absolute      824—826

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