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Riley, Hobson — Mathematical Methods for Physics and Engineering
Riley, Hobson — Mathematical Methods for Physics and Engineering

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Название: Mathematical Methods for Physics and Engineering

Авторы: Riley, Hobson

Язык: en

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
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Предметный указатель
$e^{x}$      see "Exponential function"
$h_{n}(X)$      see "Hermite polynomials"
$j_{\ell}(z)$      see "Spherical Bessel functions"
$J_{\nu}(z)$      see "Bessel functions"
$n_{\ell}(z)$      see "Spherical Bessel functions"
$P^{m}_{\ell}(x)$      see "Associated Legendre functions"
$P_{\ell}(x)$      see "Legendre polynomials"
$tan^{—1} x$, Maclaurin series for      143
$Y^{m}_{\ell}(\theta,\phi)$      see "Spherical harmonics"
$Y_{\nu}(z)$, Bessel functions of second kind      568
$\delta$-function (Dirac)      see "Dirac $\delta$-function"
$\epsilon_{ijk}$, Levi-Civita symbol, tensor      790—795
$\epsilon_{ijk}$, Levi-Civita symbol, tensor, and determinant      791
$\epsilon_{ijk}$, Levi-Civita symbol, tensor, identities      792—793
$\epsilon_{ijk}$, Levi-Civita symbol, tensor, isotropic      794
$\epsilon_{ijk}$, Levi-Civita symbol, tensor, vector products      791
$\epsilon_{ijk}$, Levi-Civita symbol, tensor, weight      813
A, B, one-dimensional irreps      932 944 951
Abelian groups      886
Absolute convergence of series      127 717
Absolute derivative      824—826
Acceleration vector      341
Adams method      1184
Adams — Moulton — Bashforth, predictor-corrector scheme      1194
Addition rule for probabilities      967 972
Adjoint      see "Hermitian conjugate"
Adjoint operators      587—591
Adjustment of parameters      854—855
Algebra of complex numbers      88—89
Algebra of functions in a vector space      583
Algebra of matrices      256—257
Algebra of power series      137
Algebra of series      134
Algebra of tensors      787—790
Algebra of vectors      217—218
Algebra of vectors in a vector space      247
Algebra of vectors in component form      222
Algebraic equations, numerical methods for      see "Numerical methods for algebraic equations"
Alternating group      958
Alternating Series Test      133
Ammonia molecule, symmetries of      884
Ampere's rule (law)      387 414
Amplitude modulation of radio waves      450
Analytic (regular) functions      712
Angle between two vectors      225
Angular frequency      626n
Angular frequency in Fourier series      425
Angular momentum and irreps      935
Angular momentum of particle system      799—801
Angular momentum of particles      344
Angular momentum of solid body      402 800
Angular momentum, vector representation      241
Angular velocity, vector representation      227 241 359
Anti-Hermitian matrices      276
Anti-Hermitian matrices, eigenvalues      281—283
Anti-Hermitian matrices, eigenvalues, imaginary nature      282—283
Anti-Hermitian matrices, eigenvectors      281—283
Anti-Hermitian matrices, eigenvectors, orthogonality      282—283
Anticommutativity of vector/cross product      226
Antisymmetric functions      422
Antisymmetric functions and Fourier series      425 426
Antisymmetric functions and Fourier transforms      451
Antisymmetric matrices      275
Antisymmetric tensors      787 790
Antithetic variates, in Monte Carlo methods      1174
Aperture function      443
Approximately equal $\approx$, definition      135
Arbitrary parameters for ODE      475
Arc length of plane curves      74—75
Arc length of space curves      347
arccosech, arccosh, arccoth, arcsech, arcsinh, arctanh      see "Hyperbolic functions inverses"
Archimedean up thrust      402 416
Area element in Cartesian coordinates      191
Area element in plane polars      205
Area of circle      72
Area of ellipse      72 210
Area of parallelogram      227
Area of region, using multiple integrals      194—196
Area of surfaces      352
Area of surfaces, as vector      399—401 414
Area, maximal enclosure      838
arg, argument of a complex number      90
Argand diagram      87 711
Argument, principle of the      755
Arithmetic series      120
Arithmetico-geometric series      121
Arrays      see "Matrices"
Associated Legendre equation      594—595 666 670 703
Associated Legendre functions $P^{m}_{\ell}(x)$      666 703
Associated Legendre functions $P^{m}_{\ell}(x)$, generating function      594
Associated Legendre functions $P^{m}_{\ell}(x)$, orthogonality      594
Associated Legendre functions $P^{m}_{\ell}(x)$, Rodrigues' formula      594
Associative law for addition in a vector space of finite dimensionality      247
Associative law for addition in a vector space of infinite dimensionality      583
Associative law for addition of complex numbers      89
Associative law for addition of matrices      256
Associative law for addition of vectors      217
Associative law for convolution      453 464
Associative law for group operations      885
Associative law for linear operators      254
Associative law for multiplication by a scalar in a vector space of finite dimensionality      247
Associative law for multiplication by a scalar in a vector space of infinite dimensionality      583
Associative law for multiplication of a matrix by a scalar      256
Associative law for multiplication of a vector by a scalar      218
Associative law for multiplication of complex numbers      91
Associative law for multiplication of matrices      258
Atomic orbitals      957
Atomic orbitals, d-states      948 950 956
Atomic orbitals, p-states      948
Atomic orbitals, s-states      986
Auto-correlation functions      456
Automorphism      903
Auxiliary equation      499
Auxiliary equation, repeated roots      499
Average value      see "Mean value"
Axial vectors      798
Backward differences      1179
Basis functions for linear least squares estimation      1115
Basis functions in a vector space of infinite dimensionality      583—584
Basis functions of a representation      920
Basis functions of a representation, change in      926—927 929 934
Basis vectors      221—222 248—249 778 920
Basis vectors for particular irrep      948—950 958
Basis vectors, derivatives      814—816
Basis vectors, derivatives, Christoffel symbol $\Gamma^{k}_{ij}$      814
Basis vectors, linear dependence and independence      221
Basis vectors, non-orthogonal      250
Basis vectors, orthonormal      249—250
Basis vectors, required properties      221
Bayes' theorem      974—975
Bernoulli equation      483
Bessel correction to variance estimate      1090
Bessel equation      541 564—568 595 674
Bessel functions $J_{\nu}(z)$      662 672
Bessel functions $J_{\nu}(z)$, generating function      573 595
Bessel functions $J_{\nu}(z)$, integral relationships      572
Bessel functions $J_{\nu}(z)$, integral representation      574—575
Bessel functions $J_{\nu}(z)$, orthogonality      570—573
Bessel functions $J_{\nu}(z)$, recurrence relations      569—570
Bessel functions $J_{\nu}(z)$, second kind, $Y_{\nu}(z)$      568
Bessel functions $J_{\nu}(z)$, series      565 566 595
Bessel functions $J_{\nu}(z)$, series, $\nu = 0$      567
Bessel functions $J_{\nu}(z)$, series, $\nu = \pm 1/2$      566
Bessel functions $J_{\nu}(z)$, spherical      675
Bessel functions $J_{\nu}(z)$, zeroes of      662 673
Bessel inequality      251 586
Best unbiased estimator      1075
beta function      1203
Bias, of estimator      1074
Bilinear transformation, general      113
Binary chopping      1154
Binomial coefficient $^{n}C_{k}$      27—30 977—979
Binomial coefficient $^{n}C_{k}$ in Leibniz' theorem      50
Binomial coefficient $^{n}C_{k}$, elementary properties      26
Binomial coefficient $^{n}C_{k}$, identities      27
Binomial coefficient $^{n}C_{k}$, negative n      29
Binomial coefficient $^{n}C_{k}$, non-integral n      29
Binomial distribution Bin(n,p)      1010—1013
Binomial distribution Bin(n,p) and Gaussian distribution      1027
Binomial distribution Bin(n,p) and Poisson distribution      1016 1019
Binomial distribution Bin(n,p), mean and variance      1013
Binomial distribution Bin(n,p), MGF      1012
Binomial distribution Bin(n,p), recurrence formula      1011
Binomial expansion      143
Binormal to space curves      348
Birthdays, different      976
Bivariate distributions      1038—1049
Bivariate distributions, conditional      1040
Bivariate distributions, continuous      1039
Bivariate distributions, correlation      1042—1049
Bivariate distributions, correlation and independence      1042
Bivariate distributions, correlation, matrix      1045—1049
Bivariate distributions, correlation, positive/negative      1042
Bivariate distributions, covariance      1042—1049
Bivariate distributions, covariance, matrix      1045
Bivariate distributions, expectation (mean)      1041
Bivariate distributions, independent (uncorrelated)      1039
Bivariate distributions, marginal      1040
Bivariate distributions, variance      1042
Boltzmann distribution from constraints on total energy      174—176
Bonding in molecules      945 947—950
Born approximation      152 606
Bose — Einstein statistics      980
Boundary conditions and characteristics      633
Boundary conditions and Laplace equation      699 701
Boundary conditions for Green's functions      518 520—522
Boundary conditions for Green's functions, inhomogeneous      521
Boundary conditions for ODE      474 476 507
Boundary conditions for PDE      614 618—620
Boundary conditions for Sturm — Liouville equations      592
Boundary conditions, homogeneous and inhomogeneous      618 656 686 688
Boundary conditions, superposition solutions      651—657
Boundary conditions, types      635—638
Brachistochrone problem      843
Bragg formula      241
Branch cut      722
Branch points      721
Bromwich integral      765
bulk modulus      829
Calculus of residues      see "Zeroes of a function of a complex variable" "Contour
Calculus of variations, constrained variation      844—846
Calculus of variations, estimation of ODE eigenvalues      849
Calculus of variations, Euler — Lagrange equation      835—836
Calculus of variations, Fermat's principle      846
Calculus of variations, Hamilton's principle      847
Calculus of variations, higher-order derivatives      841
Calculus of variations, several dependent variables      841
Calculus of variations, several independent variables      841
Calculus of variations, soap films      839—840
Calculus of variations, variable end-points      841—844
Calculus, elementary      42—77
Cancellation law in a group      888
Canonical form, for second-order ODE      522
Card drawing      see "Probability"
Carrier frequency of radio waves      451
Cartesian coordinates      221—222
Cartesian tensors      779—804
Cartesian tensors, algebra      787—790
Cartesian tensors, contraction      788
Cartesian tensors, definition      784
Cartesian tensors, first-order      781—784
Cartesian tensors, first-order, from scalar      783
Cartesian tensors, general order      784—803
Cartesian tensors, integral theorems      803—804
Cartesian tensors, isotropic      793—795
Cartesian tensors, particular, conductivity      801
Cartesian tensors, particular, inertia      800
Cartesian tensors, particular, strain      802
Cartesian tensors, particular, stress      802
Cartesian tensors, particular, susceptibility      801
Cartesian tensors, physical applications      783 788—790 799—803
Cartesian tensors, second-order      784—803 817
Cartesian tensors, symmetry and antisymmetry      787
Cartesian tensors, tensor fields      803
Cartesian tensors, zero-order      781—784
Cartesian tensors, zero-order, from vector      784
Catenary      840 846
Cauchy boundary conditions      635
Cauchy distribution      994
Cauchy inequality      747
Cauchy integrals      745—747
Cauchy product      134
Cauchy root test      132 717
Cauchy theorem      742
Cauchy — Riemann relations      713—716 727 729 743
Cauchy — Riemann relations in terms of z and z*      715
Central differences      1179
Central limit theorem      1036—1038 1178
Central moments      see "Moments central"
Centre of a group      911
Centre of mass      198
Centre of mass of hemisphere      198
Centre of mass of semicircular lamina      200
Centroid      198
Centroid of plane area      198
Centroid of plane curve      200
Centroid of triangle      220—221
CF      see "Complementary function"
Chain rule for functions of one real variable      47—48
Chain rule for functions of several real variables      160—161
Change of basis      see "Similarity transformations"
Change of variables and coordinate systems      161—163
Change of variables in multiple integrals      202—210
Change of variables in multiple integrals, evaluation of Gaussian integral      205—207
Change of variables in multiple integrals, general properties      209—210
Change of variables in RVD      992—999
Character tables      935
Character tables, $\underline{S}_{4}$ or 432 or O      956 957
Character tables, 3m or 32 or $C_{3\nu}$ or $S_{3}$      935 939 950 952 958 959
Character tables, 43m or $T_{d}$      957
Character tables, 4mm or $C_{4\nu}$      944 948 950
Character tables, construction of      942—944
Characteristic equation      285
Characteristic equation of recurrence relation      505
Characteristic equation, normal mode form      325
Characteristic function      see "Moment generating functions (MGF)"
Characteristics and boundary curves      633
Characteristics and boundary curves, multiple intersections      633 638
Characteristics and the existence of solutions      632—638
Characteristics, first-order equations      632—633
Characteristics, second-order equations      636
Characteristics, second-order equations, and equation type      636
Characters      934—938 942—944
Characters and conjugacy classes      934 937
Characters of product representation      946—947
Characters, character tables, $A_{4}$      958
Characters, character tables, $D_{5}$      958
Characters, character tables, 4mm or $C_{4\nu}$ or $D_{4}$      955
Characters, character tables, quaternion      955
Characters, counting irreps      937—938
Characters, definition      934
Characters, orthogonality properties      936 944
Characters, summation rules      939
Charge (point), Dirac $\delta$-function respresentation      447
Charged particle in electromagnetic fields      376
Chebyshev equation      541 597
Chebyshev equation, polynomial solutions      578
Chebyshev polynomials $T_{n}(x)$, generating function      597
Chebyshev polynomials $T_{n}(x)$, orthogonality      597
Chebyshev polynomials $T_{n}(x)$, Rodrigues' formula      597
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