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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

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Предметный указатель

Derivative, covariant      817
Derivative, Fourier transform of      450
Derivative, Laplace transform of      461
Derivative, normal      356
Derivative, ordinary, first, second and nth      43—44
Derivative, partial      see "Partial differentiation"
Derivative, total      157
Determinant form and $\epsilon_{ijk}$       791
Determinant form for curl      359
Determinants      264—268
Determinants and singular matrices      268
Determinants as product of eigenvalues      292
Determinants in terms of cofactors      264—265
Determinants of Hermitian conjugate matrices      267
Determinants of order three, in components      265
Determinants of transpose matrices      266
Determinants, adding rows or columns      267
Determinants, evaluation, using $\epsilon_{ijk}$       791
Determinants, evaluation, using Laplace expansion      264—265
Determinants, identical rows or columns      267
Determinants, interchanging two rows or two columns      267
Determinants, Jacobian representation      204 208 209
Determinants, notation      264
Determinants, product rule      267
Determinants, properties      266—268 827
Determinants, relationship with rank      272—273
Determinants, removing factors      267
Determinants, secular      285
Diagonal matrices      273
Diagonalisation of matrices      290—293
Diagonalisation of matrices, normal matrices      291—292
Diagonalisation of matrices, properties of eigenvalues      292—293
Diagonalisation of matrices, simultaneous      337—338
Diamond, unit cell      239
Die throwing      see "Probability"
Difference method for summation of series      122—123
Difference schemes for differential equations      1180—1183 1190—1192
Differentiable function of a complex variable      711—713
Differentiable function of a real variable      43
Differential equations      see "Ordinary differential equations" "Partial
Differential equations, particular, Bernoulli      483
Differential equations, particular, Bessel      541 564—568
Differential equations, particular, Chebyshev      541
Differential equations, particular, Clairaut      489
Differential equations, particular, diffusion      611 628—631 649 656—657 1192
Differential equations, particular, Euler      510
Differential equations, particular, Euler — Lagrange      835—836
Differential equations, particular, Helmholtz      671—676
Differential equations, particular, Hermite      541
Differential equations, particular, Lagrange      848
Differential equations, particular, Laguerre      541
Differential equations, particular, Laplace      612 623 650 651 1191
Differential equations, particular, Legendre      540 541 555—564
Differential equations, particular, Legendre linear      509—511
Differential equations, particular, Poisson      612 678—681
Differential equations, particular, Schroedinger      612 675 703 854
Differential equations, particular, simple harmonic oscillator      541
Differential equations, particular, Sturm — Liouville      849
Differential equations, particular, wave      609—610 622 626—628 647 671 849
Differential of vectors      344 350
Differential operators      see "Linear differential operator"
Differential, definition      44
Differential, exact and inexact      158—159
Differential, total      157
Differentiation      see also "Derivative"
Differentiation as gradient      43
Differentiation as rate of change      42
Differentiation from first principles      42—45
Differentiation of Fourier series      430
Differentiation of integrals      181—182
differentiation of power series      138
Differentiation, Chain rule      47—48
Differentiation, covariant      817—820
Differentiation, implicit      48—49
Differentiation, logarithmic      49
Differentiation, notation      44
Differentiation, product rule      45—47 49—51
Differentiation, quotient rule      48
Differentiation, theorems      56—58
Differentiation, using complex numbers      104
Diffraction      see "Fraunhofer diffraction"
Diffusion equation      611 621 628—631
Diffusion equation, combination of variables      629—631
Diffusion equation, integral transforms      681—683
Diffusion equation, numerical methods      1192
Diffusion Equation, Separation of Variables      649
Diffusion equation, simple solution      629
Diffusion equation, superposition      656—657
Diffusion of solute      611 629 681—683
Dihedral group      955 958
Dimension of irrep      930
Dimensionality of vector space      248
Dipole matrix elements      211 950 957
Dipole moments of molecules      919—920
Dirac $\delta$ -function      361 411 445—449
Dirac $\delta$ -function and convolution      453
Dirac $\delta$ -function and Green's functions      517 518
Dirac $\delta$ -function as limit of various distributions      449
Dirac $\delta$ -function as sum of harmonic waves      448
Dirac $\delta$ -function, definition      445
Dirac $\delta$ -function, Fourier transform of      449
Dirac $\delta$ -function, impulses      447
Dirac $\delta$ -function, point charges      447
Dirac $\delta$ -function, properties      445
Dirac $\delta$ -function, reality of      449
Dirac $\delta$ -function, relation to Fourier transforms      448 449
Dirac $\delta$ -function, relation to Heaviside (unit step) function      447
Dirac $\delta$ -function, three-dimensional      447 458
Direct product, of groups      914
Direct sum $\oplus$       928
Direction cosines      225
Dirichlet boundary conditions      635 745n
Dirichlet boundary conditions, Green's functions      688 690—699
Dirichlet boundary conditions, method of images      693—699
Dirichlet conditions, for Fourier series      421-—422
Disc, moment of inertia      211
Discontinuous functions and Fourier series      426—428
Discrete Fourier transforms      468
Disjoint events      see "Mutually exclusive events"
Displacement kernel      see "Kernel of integral equations displacement"
Distance from a line to a line      235—236
Distance from a line to a plane      236—237
Distance from a point to a line      233—234
Distance from a point to a plane      234—235
Distributive law for addition of matrix products      259
Distributive law for convolution      453 464
Distributive law for inner product      249
Distributive law for linear operators      254
Distributive law for multiplication by a scalar in a vector space of finite dimensionality      247
Distributive law for multiplication by a scalar in a vector space of infinite dimensionality      583
Distributive law for multiplication of a matrix by a scalar      256
Distributive law for multiplication of a vector by a complex scalar      226
Distributive law for multiplication of a vector by a scalar      218
Distributive law for scalar/dot product      224
Distributive law for vector/cross product      226
div      see "Divergence of vector fields"
Divergence of vector fields      358
Divergence of vector fields as integral      404 405
Divergence of vector fields in curvilinear coordinates      373
Divergence of vector fields in cylindrical polars      366
Divergence of vector fields in spherical polars      368
Divergence of vector fields, tensor form      821—822
Divergence theorem for tensors      803
Divergence theorem for vectors      407 408
Divergence theorem, physical applications      410—411
Divergence theorem, related theorems      409
Division axiom in a group      888
Division of complex numbers      94—95
Dot product      see "Scalar product"
Double integrals      see "Multiple integrals"

Drumskin      see "Membrane"
Dual tensors      798—799
Dummy variable      62
E, two-dimensional irrep      932 944 950
Eccentricity, of conic sections      16
Efficiency, of estimator      1074
Eigenequation for differential operators      581
Eigenequation for differential operators, more general form      582—583 601—602
Eigenfrequencies      325
Eigenfrequencies, estimation using Rayleigh — Ritz method      333—335
Eigenfunctions of integral equations      876
Eigenfunctions of Legendre equation      582
Eigenfunctions of simple harmonic oscillators      582
Eigenfunctions, completeness for an Hermitian operator      588
Eigenfunctions, construction of a real set for an Hermitian operator      590—591
Eigenfunctions, definition      582
Eigenfunctions, orthogonality for Hermitian operators      589—590
Eigenvalues      277—287
Eigenvalues of a general square matrix      283
Eigenvalues of a representative matrix      942
Eigenvalues of a unitary matrix      283
Eigenvalues of an Hermitian operator reality      588—589
Eigenvalues of anti-Hermitian matrices      see "Anti-Hermitian matrices"
Eigenvalues of Fredholm equations      867
Eigenvalues of Hermitian matrices      see "Hermitian matrices"
Eigenvalues of integral equations      867 875
Eigenvalues of linear differential operators, adjustment of parameters      854—855
Eigenvalues of linear differential operators, definition      582
Eigenvalues of linear differential operators, error in estimate of      852
Eigenvalues of linear differential operators, estimation      849—855
Eigenvalues of linear differential operators, higher eigenvalues      852 859
Eigenvalues of linear differential operators, Legendre equation      582
Eigenvalues of linear differential operators, simple harmonic oscillator      582
Eigenvalues of linear operators      277
Eigenvalues of normal matrices      278—281
Eigenvalues under similarity transformation      292—293
Eigenvalues, characteristic equation      285
Eigenvalues, definition      277
Eigenvalues, degenerate      287
Eigenvalues, determination      285—287
Eigenvalues, estimation for ODE      849
Eigenvalues, estimation using Rayleigh — Ritz method      333—335
Eigenvalues, notation      278
Eigenvectors      277—287
Eigenvectors of a general square matrix      283
Eigenvectors of a unitary matrix      283
Eigenvectors of anti-Hermitian matrices      see "Anti-Hermitian matrices"
Eigenvectors of commuting matrices      283
Eigenvectors of Hermitian matrices      see "Hermitian matrices"
Eigenvectors of linear operators      277
Eigenvectors of normal matrices      278—281
Eigenvectors, characteristic equation      285
Eigenvectors, definition      277
Eigenvectors, determination      285—287
Eigenvectors, normalisation condition      278
Eigenvectors, notation      278
Eigenvectors, stationary properties for quadratic/Hermitian forms      295—296
Einstein relation      442 642 703
Elastic deformations      802—803
Electromagnetic fields, flux      401
Electromagnetic fields, Maxwell's equations      379 414 828
Electrostatic fields and potentials from charge density      680 692
Electrostatic fields and potentials from complex potential      727
Electrostatic fields and potentials of line charges      696 726
Electrostatic fields and potentials, charged split sphere      668
Electrostatic fields and potentials, conducting cylinder in uniform field      730
Electrostatic fields and potentials, conducting sphere in uniform field      667
Electrostatic fields and potentials, infinite charged plate      694 736
Electrostatic fields and potentials, infinite wedge with line charge      738
Electrostatic fields and potentials, ininite charged wedge      736
Electrostatic fields and potentials, semi-infinite charged plate      736
Electrostatic fields and potentials, sphere with point charge      698
Ellipse as section of quadratic surface      297
Ellipse, area of      72 210 391
Ellipsoid, volume of      210
Elliptic PDE      620 623
Empty event $\emptyset$       963
End-points for variations, contributions from      841
End-points for variations, fixed      836
End-points for variations, variable      841—844
Energy levels of particle in a box      703
Energy levels of simple harmonic oscillator      604
Energy spectrum and Fourier transforms      456 457
Envelopes      176—178
Envelopes to a family of curves      176
Envelopes, equations of      177
Epimorphism      903
Equilateral triangle, symmetries of      889 894 923—924 952
Equivalence relations      906—908 910
Equivalence relations and classes      906
Equivalence relations, congruence      907—909
Equivalence relations, examples      912
Equivalence transformations      see "Similarity transformations"
Equivalent representations      926—928 941
Error function, erf      630 682 1204
Error terms in Fourier series      436—437
Error terms in Taylor series      142—143
Errors, first and second kind      1122
Essential singularity      724 750
Estimation of eigenvalues, linear differential operator      851—854
Estimation of eigenvalues, Rayleigh — Ritz method      333—335
Estimator, maximum-likelihood      1098
Estimators (statistics)      1072
Estimators (statistics), best unbiased      1075
Estimators (statistics), bias      1074
Estimators (statistics), central confidence interval      1080
Estimators (statistics), confidence interval      1079
Estimators (statistics), confidence limits      1079
Estimators (statistics), confidence region      1084
Estimators (statistics), consistency      1073
Estimators (statistics), efficiency      1074
Estimators (statistics), minimum-variance      1075
Estimators (statistics), standard error      1077
Euler equation, differential      510 528
Euler equation, trigonometric      96
Euler method, numerical      1181
Euler — Lagrange equation      835—836
Euler — Lagrange equation, special cases      836—840
Even functions      see "Symmetric functions"
Events      962
Events, complement of      963
Events, empty $\emptyset$       963
Events, intersection of $\cap$       962
Events, mutually exclusive      971
Events, statistically independent      971
Events, union of $\cup$       963
Exact differentials      158—159
exact equations      478 511—512
Exact equations, condition for      478
Exact equations, non-linear      525
expectation values      see "Probability distributions mean"
Exponential distribution      1032—1033
Exponential distribution from Poisson      1032
Exponential distribution, MGF      1033
Exponential function of a complex variable      95 719
Exponential function, Maclaurin series for      143
Exponential function, relation with hyperbolic functions      105
F-distribution (Fisher)      1132—1138
F-distribution (Fisher), critical points table      1137
F-distribution (Fisher), logarithmic form      1138
Fabry — Perot interferometer      149
Factorial function, general      1202
Factorisation, of a polynomial equation      7
Faithful representation      925 940
Fermat's principle      846 857
Fermi — Dirac statistics      980
Fibonacci series      531
Field lines and complex potentials      726
Fields, conservative      393—395
Fields, electrostatic      see "Electrostatic fields and potentials"

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