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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

Fields, gravitational      see "Gravitational fields and potentials"
Fields, scalar      353
Fields, tensor      803
Fields, vector      353
Finite differences      1179—1180
Finite differences for differential equations      1180—1183
Finite differences from Taylor series      1179 1186
Finite differences, central      1179
Finite differences, forward and backward      1179
Finite differences, schemes for differential equations      1190—1192
Finite groups      885
First law of thermodynamics      179
First-order differential equations      see "Ordinary differential equations"
Fisher distribution      see "F-distribution (Fisher)"
Fisher's Inequality      1075 1076
Fluids, Archimedean up thrust      402 416
Fluids, complex velocity potential      727
Fluids, continuity equation      410
Fluids, cylinder in uniform flow      728
Fluids, flow      727—728
Fluids, flux      401 729
Fluids, irrotational flow      359
Fluids, sources and sinks      410—411 727
Fluids, stagnation points      727
Fluids, velocity potential      415 612
Fluids, vortex flow      414 728
Forward differences      1179
Fourier cosine transforms      452
Fourier series      421—438
Fourier series and separation of variables      652—655 657
Fourier series, coefficients      423—425 431
Fourier series, complex      430—431
Fourier series, differentiation      430
Fourier series, Dirichlet conditions      421—422
Fourier series, discontinuous functions      426 428
Fourier series, error term      436—437
Fourier series, examples, $x^{2}$       428—429
Fourier series, examples, $x^{3}$       430
Fourier series, examples, square-wave      424 425
Fourier series, examples, x      430 431
Fourier series, integration      430
Fourier series, non-periodic functions      428—430
Fourier series, orthogonality of terms      423
Fourier series, orthogonality of terms, complex case      431
Fourier series, Parseval's theorem      432—433
Fourier series, raison d'etre      421
Fourier series, standard form      423
Fourier series, summation of series      433
Fourier series, symmetry considerations      425 426
Fourier sine transforms      451
Fourier transforms      439—459
Fourier transforms as generalisation of Fourier series      439—441
Fourier transforms for integral equations      868—871
Fourier transforms for PDE      683—686
Fourier transforms in higher dimensions      457—459
Fourier transforms, convolution      452—455
Fourier transforms, convolution theorem      454
Fourier transforms, convolution, and the Dirac $\delta$ -function      453
Fourier transforms, convolution, associativity, commutativity, distributivity      453
Fourier transforms, convolution, definition      453
Fourier transforms, convolution, resolution function      452
Fourier transforms, correlation functions      455—457
Fourier transforms, cosine transforms      452
Fourier transforms, deconvolution      455
Fourier transforms, definition      441
Fourier transforms, discrete      468
Fourier transforms, evaluation using convolution theorem      454
Fourier transforms, examples, convolution      454
Fourier transforms, examples, damped harmonic oscillator      457
Fourier transforms, examples, Dirac $\delta$ -function      449
Fourier transforms, examples, exponential decay function      441
Fourier transforms, examples, Gaussian (normal) distribution      441
Fourier transforms, examples, rectangular distribution      448
Fourier transforms, examples, spherically symmetric functions      458
Fourier transforms, examples, two narrow slits      454
Fourier transforms, examples, two wide slits      444 454
Fourier transforms, Fourier-related (conjugate) variables      442
Fourier transforms, inverse, definition      441
Fourier transforms, odd and even functions      451
Fourier transforms, Parseval's theorem      456—457
Fourier transforms, properties: differentiation, exponential multiplication, integration, scaling, translation      450
Fourier transforms, relation to Dirac $\delta$ -function      448 449
Fourier transforms, sine transforms      451
Fourier's inversion theorem      441
Fraunhofer diffraction      443—445
Fraunhofer diffraction, diffraction grating      467
Fraunhofer diffraction, two narrow slits      454
Fraunhofer diffraction, two wide slits      444 454
Fredholm integral equations      864
Fredholm integral equations with separable kernel      866—867
Fredholm integral equations, eigenvalues      867
Fredholm integral equations, operator form      865
Fredholm theory      874—875
Frenet — Serret formulae      349
Frobenius series      545
Fuch's theorem      544
Function of a matrix      260
Functional      835
Functions of a complex variable      711—725 747—752
Functions of a complex variable, analyticity      712
Functions of a complex variable, behaviour at infinity      725
Functions of a complex variable, branch points      721
Functions of a complex variable, Cauchy — Riemann relations      713—716
Functions of a complex variable, Cauchy's integrals      745—747
Functions of a complex variable, conformal transformations      730—738
Functions of a Complex variable, derivative      711
Functions of a complex variable, differentiation      711—716
Functions of a complex variable, identity theorem      748
Functions of a complex variable, Laplace equation      715 725
Functions of a complex variable, Laurent expansion      749—752
Functions of a complex variable, multivalued and branch cuts      721—723 766
Functions of a complex variable, particular functions      718—721
Functions of a complex variable, poles      724
Functions of a complex variable, power series      716—718
Functions of a complex variable, real and imaginary parts      711 716
Functions of a complex variable, singularities      712 723—725
Functions of a complex variable, Taylor expansion      747—748
Functions of a complex variable, zeroes      725 754—758
Functions of one real variable, decomposition into even and odd functions      422
Functions of one real variable, differentiation of      42—51
Functions of one real variable, Fourier series      see "Fourier series"
Functions of one real variable, integration of      60—73
Functions of one real variable, limits      see "Limits"
Functions of one real variable, maxima and minima of      51—53
Functions of one real variable, stationary values of      51—53
Functions of one real variable, Taylor series      see "Taylor series"
Functions of several real variables, chain rule      160—161
Functions of several real variables, differentiation of      154—182
Functions of several real variables, integration of      see "Multiple integrals evaluation"
Functions of several real variables, maxima and minima      165—170
Functions of several real variables, points of inflection      165—170
Functions of several real variables, rates of change      156—158
Functions of several real variables, saddle points      165—170
Functions of several real variables, stationary values      165—170
Functions of several real variables, Taylor series      163—165
Fundamental solution      691—693
Fundamental theorem of algebra      86 88 770
Fundamental theorem of calculus      62—63
Fundamental theorem of complex numbers      see "de Moivre's theorem"
Gamma ,function definition and properties      1201
Gamma function as general factorial function      1202
Gauss — Seidel iteration      1160—1162
Gauss's theorem      700
Gaussian (normal) distribution $N(\mu,\sigma^{2})$       1021—1031
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ and Binomial distribution      1027
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ and central limit theorem      1037
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ and Poisson distribution      1029—1030
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , continuity correction      1028
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , CPF      1023
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , CPF, tabulation      1024

Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , cumulative probability function      1178
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , Fourier transform      441
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , integration with infinite limits      205 207
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , mean and variance      1022—1026
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , MGF      1027 1030
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , multiple      1030—1031
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , multivariate      1051
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , random number generation      1178
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , sigma limits      1025
Gaussian (normal) distribution $N(\mu,\sigma^{2})$ , standard variable      1022
Gaussian elimination with interchange      1159—1160
Gaussian integration      1168—1170
General Properties      see "Anti-Hermitian matrices"
General tensors, algebra      787—790
General tensors, contraction      788
General tensors, contravariant      810
General tensors, covariant      810
General tensors, dual      798—799
General tensors, metric      806—809
General tensors, physical applications      806—809 825—826
General tensors, pseudotensors      813
General tensors, tensor densities      813
Generalised likelihood ratio      1124
Generating functions, associated Legendre polynomials      594
Generating functions, Bessel functions      573 595
Generating functions, Chebyshev polynomials      597
Generating functions, Hermite polynomials      578 596
Generating functions, Laguerre polynomials      597
Generating functions, Legendre polynomials      562—564 594
Generating functions, probability      999—1009 see "Probability
Geodesies      825—826 831 856
Geometric distribution      1001
Geometric series      120
Gibbs' free energy      181
Gibbs' phenonmenon      427
Gradient of a function of one variable      43
Gradient of a function of several real variables      156—158
Gradient of scalar      354—358
Gradient of scalar, tensor form      821
Gradient of vector      785 818
Gradient operator (grad)      354
Gradient operator (grad) as integral      404
Gradient operator (grad) in curvilinear coordinates      373
Gradient operator (grad) in cylindrical polars      366
Gradient operator (grad) in spherical polars      368
Gradient operator (grad), tensor form      821
Gram — Schmidt orthogonalisation of eigenfunctions of Hermitian operators      589—590
Gram — Schmidt orthogonalisation of eigenvectors of Hermitian matrices      282
Gram — Schmidt orthogonalisation of eigenvectors of normal matrices      280
Gram — Schmidt orthogonalisation of functions in a Hilbert space      584—586
Gravitational fields and potentials, Laplace equation      612
Gravitational fields and potentials, Newton's law      345
Gravitational fields and potentials, Poisson equation      612 678
Gravitational fields and potentials, uniform disc      706
Gravitational fields and potentials, uniform ring      676
Green's functions      597—601 686—702
Green's functions and boundary conditions      518 520
Green's functions and Dirac $\delta$ -function      517
Green's functions and partial differential operators      687
Green's functions and Wronskian      533
Green's functions for ODE      188 517—522
Green's functions, diffusion equation      684
Green's functions, Dirichlet problems      690—699
Green's functions, Neumann problems      700—702
Green's functions, particular integrals from      520
Green's functions, Poisson's equation      689
Green's theorems in a plane      390—393 413
Green's theorems in three dimensions      408
Green's theorems, applications      639 689 743
Ground-state energy, harmonic oscillator      855
Ground-state energy, hydrogen atom      860
Group multiplication tables      892
Group multiplication tables, order five      904
Group multiplication tables, order four      892 894 903
Group multiplication tables, order six      897 903
Group multiplication tables, order three      904
Grouping terms as a test for convergence      132
Groups, Abelian      886
Groups, associative law      885
Groups, cancellation law      888
Groups, centre      911
Groups, closure      885
Groups, cyclic      903
Groups, definition      885—888
Groups, direct product      914
Groups, division axiom      888
Groups, elements      885
Groups, elements, order      889
Groups, examples, $\pm 1$ under multiplication      885
Groups, examples, alternating      958
Groups, examples, functions      897
Groups, examples, general linear      914
Groups, examples, integers under addition      885
Groups, examples, integers under multiplication (mod N)      891—893
Groups, examples, matrices      896
Groups, examples, permutations      898—900
Groups, examples, quaternion      915
Groups, examples, rotation matrices      890
Groups, examples, symmetries of an equilateral triangle      889
Groups, finite      885
Groups, identity element      885—888
Groups, inverse      885 888
Groups, isomorphic      893
Groups, mappings between      901—903
Groups, mappings between, homomorphic      901—903
Groups, mappings between, image      901
Groups, mappings between, isomorphic      901
Groups, nomenclature      944—945
Groups, non-Abelian      894—898
Groups, order      885 923 924 936 939 942
Groups, permutation law      889
Groups, subgroups      see "Subgroups"
Hamilton's principle      847
Hamiltonian      855
Hankel transforms      465
Harmonic oscillators, damped      243 457
Harmonic oscillators, ground-state energy      855
Harmonic oscillators, Schroedinger equation      855
Heat flow in bar      656—657 683 705
Heat flow in thin sheet      631
Heat flow, diffusion equation      611 629 656
Heaviside function      447
Heaviside function, relation to Dirac $\delta$ -function      447
Heisenberg's uncertainty principle      441—443
Helmholtz equation      671—676
Helmholtz equation, cylindrical polars      673
Helmholtz equation, plane polars      672—673
Helmholtz equation, spherical polars      674—676
Helmholtz potential      180
Hemisphere, centre of mass and centroid      198
Hermite equation      541 593 596
Hermite polynomials $H_{n}(x)$ , generating function      578 596
Hermite polynomials $H_{n}(x)$ , orthogonality      596
Hermite polynomials $H_{n}(x)$ , Rodrigues' formula      596
Hermitian conjugate      261—263
Hermitian conjugate and inner product      263
Hermitian conjugate, product rule      262
Hermitian forms      293—297
Hermitian forms, positive definite and semi-definite      295
Hermitian forms, stationary properties of eigenvectors      295—296
Hermitian kernel      see "Kernel of integral equations Hermitian"
Hermitian matrices      276
Hermitian matrices, eigenvalues      281—283
Hermitian matrices, eigenvalues, reality      281—282
Hermitian matrices, eigenvectors      281—283
Hermitian matrices, eigenvectors, orthogonality      282
Hermitian operators      587—591
Hermitian operators in Sturm — Liouville equations      591—592
Hermitian operators, boundary condition for simple harmonic oscillators      587—588
Hermitian operators, eigenfunctions, completeness      588

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