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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

Hermitian operators, eigenfunctions, orthogonality      589—590
Hermitian operators, eigenvalues, reality      588—589
Hermitian operators, Green's functions      597—601
Hermitian operators, importance of      583 588
Hermitian operators, properties      588—591
Hermitian operators, superposition methods      597—601
Higher-order differential equations      see "Ordinary differential equations"
Hilbert spaces      584—586
Hit or miss, in Monte Carlo methods      1174
Homogeneous boundary conditions      see "Boundary conditions homogeneous
homogeneous differential equations      496
Homogeneous simultaneous linear equations      298
Homogeneous, dimensionally      481 527—528
Homomorphism      901—903
Homomorphism, kernel of      902
Homomorphism, representation as      925
Hooke's law      802
Hydrogen atom      604
Hydrogen atom, electron wavefunction      211
Hydrogen atom, ground-state energy      860
Hydrogen atom, s-states      986
Hydrogen molecule, symmetries of      883
Hyperbola, as section of quadratic surface      297
Hyperbolic functions      105—112 720
Hyperbolic functions in equations      108
Hyperbolic functions, calculus of      109—112
Hyperbolic functions, definitions      105 720
Hyperbolic functions, graphs      105
Hyperbolic functions, identities      107
Hyperbolic functions, inverses      108—109
Hyperbolic functions, inverses, graphs      109
Hyperbolic functions, trigonometric analogies      105—107
Hyperbolic PDE      620 623
Hypergeometric distribution      1015—1016
Hypergeometric distribution, mean and variance      1015
Hypergeometric equation      603
Hypothesis testing      1119—1140
Hypothesis testing, errors, first and second kind      1122
Hypothesis testing, generalised likelihood ratio      1124
Hypothesis testing, generalised likelihood ratio test      1123
Hypothesis testing, goodness of fit      1138
Hypothesis testing, Neyman — Pearson test      1122
Hypothesis testing, null      1120
Hypothesis testing, power      1122
Hypothesis testing, rejection region      1121
Hypothesis testing, simple or composite      1120
Hypothesis testing, statistical tests      1120
Hypothesis testing, test statistic      1120
i, j, k (unit vectors)      223
i, square root of —1      87
Identity element of a group      885—888
Identity element of a group, uniqueness      885 887
Identity matrices      259 260
Identity operator      254
Imaginary part/term of a complex number      86—87
Importance sampling, in Monte Carlo methods      1172
Improper integrals      71
Improper rotations      795—797
Impulses, $\delta$ -function respresentation      447
Independent random variables      998 1042
Index of a subgroup      908
Indices, of regular singular points      546
Indicial equation      545
Indicial equation, distinct roots with non-integral difference      546—547
Indicial equation, repeated roots      547 551 553
Indicial equation, roots differ by integer      548—549 552
Induction, proof by      31—32
Inequalities, amongst integrals      73
Inequalities, Bessel      251 586
Inequalities, Schwarz      251 586
Inequalities, triangle      251 586
Inertia      see also "Moments of inertia"
Inertia, moments and products      800
Inertia, tensor      800
Inexact differentials      158—159
Inexact equation      479
Infinite integrals      71
Infinite integrals, contour integration      759—764
Infinite series      see "Series"
Inflection, general points of      53
Inflection, stationary points of      51—53
Inhomogeneous boundary conditions      see "Boundary conditions homogeneous
inhomogeneous differential equations      496
Inhomogeneous simultaneous linear equations      298
Inner product in a vector space      see also "Scalar product"
Inner product in a vector space of finite dimensionality      249—250
Inner product in a vector space of finite dimensionality and Hermitian conjugate      263
Inner product in a vector space of finite dimensionality, commutativity      249
Inner product in a vector space of finite dimensionality, distributivity over addition      249
Inner product in a vector space of infinite dimensionality      584
Integral equations from differential equations      862—863
Integral equations, eigenfunctions      876
Integral equations, eigenvalues      867 875
Integral equations, Fredholm      864
Integral equations, homogeneous      864
Integral equations, linear      863
Integral equations, linear, first kind      864
Integral equations, linear, second kind      864
Integral equations, methods for differentiation      871
Integral equations, methods for Fredholm theory      874—875
Integral equations, methods for integral transforms      868—871
Integral equations, methods for integral transforms, Fourier      868—871
Integral equations, methods for integral transforms, Laplace      869
Integral equations, methods for Neumann series      872—874
Integral equations, methods for Schmidt — Hilbert theory      875—878
Integral equations, methods for separable (degenerate) kernels      866—867
Integral equations, nomenclature      863
Integral equations, singular      864
Integral equations, Volterra      864
Integral test for convergence of series      131
Integral transforms      see also "Fourier transforms" "Laplace
Integral transforms, general form      465
Integral transforms, Hankel transforms      465
Integral transforms, Mellin transforms      465
Integrals      see also "Integration"
Integrals of vectors      see "Vectors calculus integration"
Integrals, definite      60
Integrals, double      see "Multiple integrals"
Integrals, Fourier transform of      450
Integrals, improper      71
Integrals, indefinite      63
Integrals, inequalities      73 586
Integrals, infinite      71
Integrals, Laplace transform of      462
Integrals, limits, containing variables      191
Integrals, limits, fixed      60
Integrals, limits, variable      62
Integrals, non-zero      946—947
Integrals, properties      61
Integrals, triple      see "Multiple integrals"
Integrals, undefined      60
integrand      60
Integrating factor (IF)      512
Integrating factor (IF), first-order ODE      479—481
Integration      see also "Integrals"
Integration as area under a curve      60
Integration as the inverse of differentiation      62—63
Integration constant      63
Integration from first principles      60—61
Integration in plane polar coordinates      71—72
Integration of Fourier series      430
Integration of functions of several real variables      see "Multiple integrals"
Integration of hyperbolic functions      109—112
integration of power series      138
Integration of simple functions      63—64
Integration of singular functions      71
Integration of sinusoidal functions      64—65
integration, applications      73—77
Integration, applications, finding the length of a curve      74—75
Integration, applications, mean value of a function      73—74

Integration, applications, surfaces of revolution      75—76
Integration, applications, volumes of revolution      76—77
Integration, formal definition      60
Integration, logarithmic      65
Integration, methods for, by inspection      63—64
Integration, methods for, by parts      68—70
Integration, methods for, by substitution      66—68
Integration, methods for, by substitution, completing the square      68
Integration, methods for, by substitution, ing the square      67
Integration, methods for, by substitution, t substitution      66—67
Integration, methods for, change of variables      see "Change of variables"
Integration, methods for, contour      see "Contour integration"
Integration, methods for, Gaussian      1168—1170
Integration, methods for, numerical      1164—1170
Integration, methods for, partial fractions      65—66
Integration, methods for, reduction formulae      70
Integration, methods for, trigonometrical expansions      64—65
Integration, methods for, using complex numbers      104
Integration, multiple      see "Multiple integrals"
Integration, multivalued functions      762—764 766
Intersection $\cap$ , probability for      see "Probability for
Intrinsic derivative      see "Absolute derivative"
Invariant tensors      see "Isotropic tensors"
Inverse hyperbolic functions      108—109
Inverse integral transforms, Fourier      441
Inverse integral transforms, Laplace      460 765—768
Inverse integral transforms, Laplace, uniqueness      460
Inverse matrices      268—271
Inverse matrices in solution of simultaneous linear equations      300—301
Inverse matrices, elements      269
Inverse matrices, product rule      271
Inverse matrices, properties      270—271
Inverse of a linear operator      254
Inverse of a product in a group      888
Inverse of element in a group uniqueness      885 888
Inversion theorem, Fourier's      441
Inversions as improper rotations      795
Inversions as symmetry operations      883—884
irregular singular points      540
Irreps      929
Irreps, counting      937—938
Irreps, dimension $n_{\lambda}$       939
Irreps, direct sum $\oplus$       928
Irreps, identity $A_{1}$       942 946
Irreps, n-dimensional      930 931 944
Irreps, number in a representation      929 937
Irreps, one-dimensional      930 931 935 941 944
Irreps, orthogonality theorem      932—934
Irreps, projection operators for      949
Irreps, reduction to      938
Irreps, summation rules for      939—941
Irrotational vectors      359
Isobaric ODE      482
Isobaric ODE, non-linear      527—528
Isoclines, method of      1188 1196
Isomorphic groups      893—898 900 901
Isomorphism (mapping)      902
Isotope decay      490 531
Isotropic (invariant) tensors      793—795 802
Iteration schemes for algebraic equations      1150—1158
Iteration schemes for differential equations      1185
Iteration schemes for integral equations      872—875
Iteration schemes, convergence of      1156—1158
Iteration schemes, Gauss — Seidel      1160—1162
Iteration schemes, order of convergence      1157
j, square root of —1      87
Jacobians and change of variables      209—210
Jacobians in terms of a determinant      204 208 209
Jacobians, analogy with derivatives      210
Jacobians, definition in three dimensions      208
Jacobians, definition in two dimensions      204
Jacobians, general properties      209—210
Joint distributions      see "Bivariate distributions" "Multivariate
Jordan's lemma      761—762
Kernel of a homomorphism      902 905
Kernel of an integral transform      465
Kernel of integral equations of form exp(—ixz)      869—871
Kernel of integral equations of linear integral equations      863
Kernel of integral equations, displacement      868
Kernel of integral equations, Hermitian      875
Kernel of integral equations, resolvent      873 874
Kernel of integral equations, separable (degenerate)      866—867
Kinetic energy of oscillating system      322
Klein — Gordon equation      643
Kronecker delta $\delta_{ij}$ and orthogonality      249
Kronecker delta, $\delta_{ij}$ ( $\delta^{j}_{i}$ ), tensor      111 790—795 805 811
Kronecker delta, $\delta_{ij}$ ( $\delta^{j}_{i}$ ), tensor, identities      792—793
Kronecker delta, $\delta_{ij}$ ( $\delta^{j}_{i}$ ), tensor, isotropic      794
Kronecker delta, $\delta_{ij}$ ( $\delta^{j}_{i}$ ), tensor, vector products      791
l'Hopital's rule      145—147
Lagrange equations      848
Lagrange equations and energy conservation      856
Lagrange undetermined multipliers      170—176
Lagrange undetermined multipliers and ODE eigenvalue estimation      851
Lagrange undetermined multipliers for functions of more than two variables      172—176
Lagrange undetermined multipliers in deriving the Boltzmann distribution      174—176
Lagrange undetermined multipliers with several constraints      172—176
Lagrange undetermined multipliers, application to stationary properties of the eigenvectors of quadratic/Hermitian forms      295
Lagrange undetermined multipliers, integral constraints      844
Lagrange's identity      230
Lagrange's theorem      907—908
Lagrange's theorem and the order of a subgroup      904
Lagrange's theorem and the order of an element      904
Lagrangian      848 856
Laguerre equation      541 596—597
Laguerre polynomials $L_{n}(x)$ , generating function      597
Laguerre polynomials $L_{n}(x)$ , orthogonality      596
Laguerre polynomials $L_{n}(x)$ , Rodrigues' formula      577 596
Lame constants      802
Lamina: mass, centre of mass and centroid      196—198
Laplace equation      612
Laplace equation in three dimensions, cylindrical polars      661—664
Laplace equation in three dimensions, spherical polars      664—671
Laplace equation in two dimensions      621 623 650 651
Laplace equation in two dimensions and analytic functions      715
Laplace equation in two dimensions and conformal transformations      735—738
Laplace equation in two dimensions, numerical method for      1191 1197
Laplace equation in two dimensions, plane polars      658—660
Laplace equation in two dimensions, separated variables      650
Laplace equation with specified boundary values      699 701
Laplace equation, expansion methods      676—678
Laplace equation, uniqueness of solution      676
Laplace expansion      264—265
Laplace transforms      459—465 765
Laplace transforms for ODE with constant coefficients      507—509
Laplace transforms for PDE      681—683
Laplace transforms, convolution theorem      463
Laplace transforms, convolution, associativity, commutativity, distributivity      464
Laplace transforms, convolution, definition      463
Laplace transforms, definition      459
Laplace transforms, examples, constant      459
Laplace transforms, examples, derivatives      461
Laplace transforms, examples, exponential function      459
Laplace transforms, examples, integrals      462
Laplace transforms, examples, polynomial      459
Laplace transforms, inverse      460 765—768
Laplace transforms, inverse, uniqueness      460
Laplace transforms, properties: translation, exponential multiplication, etc.      462
Laplace transforms, table for common functions      461
Laplacian      see "del squared $\nabla^{2}$ (Laplacian)"
Laurent expansion      749—752
Laurent expansion, analytic and principal parts      749
Laurent expansion, region of convergence      749
Least squares, method of      1113—1119
Least squares, method of, basis functions      1115
Least squares, method of, linear      1114
Least squares, method of, non-linear      1118
Least squares, method of, response matrix      1115
Legendre equation      540 541 555—564 582 593—594
Legendre equation as an example of a Sturm — Liouville equation      591

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