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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

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Издание: 2-d edition

Количество страниц: 1253

Добавлена в каталог: 17.02.2013

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Предметный указатель

Normal to a plane      232
Normal to coordinate surface      372
Normal to surface      352 356 396
Normalisation of eigenfunctions      589
Normalisation of eigenvectors      278
Normalisation of functions      585
Normalisation of vectors      223
Null (zero) matrix      259 260
Null (zero) operator      254
Null (zero) space, of a matrix      298
Null (zero) vector      218 247 583
Null operation, as identity element of group      886
Nullity, of a matrix      298
Numerical methods for algebraic equations      1149—1156
Numerical methods for algebraic equations, binary chopping      1154
Numerical methods for algebraic equations, convergence of iteration schemes      1156—1158
Numerical methods for algebraic equations, linear interpolation      1152—1153
Numerical methods for algebraic equations, Newton — Raphson      1154—1156
Numerical methods for algebraic equations, rearrangement methods      1151—1152
Numerical methods for integration      1164—1170
Numerical methods for integration, Gaussian integration      1168—1170
Numerical methods for integration, midpoint rule      1194
Numerical methods for integration, Monte Carlo      1170
Numerical methods for integration, nomenclature      1165
Numerical methods for integration, Simpson's rule      1167
Numerical methods for integration, trapezium rule      1166—1167
Numerical methods for ordinary differential equations      1180—1190
Numerical methods for ordinary differential equations, accuracy and convergence      1181
Numerical methods for ordinary differential equations, Adams method      1184
Numerical methods for ordinary differential equations, difference schemes      1181—1183
Numerical methods for ordinary differential equations, Euler method      1181
Numerical methods for ordinary differential equations, first-order equations      1181—1188
Numerical methods for ordinary differential equations, higher-order equations      1188—1190
Numerical methods for ordinary differential equations, isoclines      1188
Numerical methods for ordinary differential equations, Milne's method      1182
Numerical methods for ordinary differential equations, prediction and correction      1184—1186
Numerical methods for ordinary differential equations, reduction to matrix form      1190
Numerical methods for ordinary differential equations, Runge — Kutta methods      1186—1188
Numerical methods for ordinary differential equations, Taylor series methods      1183—1184
Numerical methods for partial differential equations      1190—1192
Numerical methods for partial differential equations, diffusion equation      1192
Numerical methods for partial differential equations, Laplace's equation      1191
Numerical methods for partial differential equations, minimising error      1192
Numerical methods for simultaneous linear equations      1158—1164
Numerical methods for simultaneous linear equations, Gauss — Seidel iteration      1160—1162
Numerical methods for simultaneous linear equations, Gaussian elimination with interchange      1159—1160
Numerical methods for simultaneous linear equations, matrix form      1158—1164
Numerical methods for simultaneous linear equations, tridiagonal matrices      1162—1164
O(x), order of      135
Observables in quantum mechanics      282 588
Odd functions      see "Antisymmetric functions"
ODE      see "Ordinary differential equations"
Operators, linear      see "Linear operators" "Linear "Linear
Order of approximation in Taylor series      140n
Order of convergence of iteration schemes      1157
Order of group      885
Order of group element      889
Order of ODE      474
Order of permutation      900
Order of subgroup      903
Order of subgroup and Lagrange's theorem      907
Order of tensor      779
Ordinary differential equations (ODE)      see also "Differential equations particular"
Ordinary differential equations (ODE), boundary conditions      474 476 507
Ordinary differential equations (ODE), complementary function      497
Ordinary differential equations (ODE), degree      474
Ordinary differential equations (ODE), dimensionally homogeneous      481
Ordinary differential equations (ODE), exact      478 511—512
Ordinary differential equations (ODE), first-order      474 490
Ordinary differential equations (ODE), first-order higher-degree      486—490
Ordinary differential equations (ODE), first-order higher-degree, soluble for p      486
Ordinary differential equations (ODE), first-order higher-degree, soluble for x      487
Ordinary differential equations (ODE), first-order higher-degree, soluble for y      488
Ordinary differential equations (ODE), general form of solution      474—476
Ordinary differential equations (ODE), higher-order      496—529
Ordinary differential equations (ODE), homogeneous      496
Ordinary differential equations (ODE), inexact      479
Ordinary differential equations (ODE), isobaric      482 527—528
Ordinary differential equations (ODE), linear      480 496—523
Ordinary differential equations (ODE), non-linear      524—529
Ordinary differential equations (ODE), non-linear, exact      525
Ordinary differential equations (ODE), non-linear, isobaric (homogeneous)      527—528
Ordinary differential equations (ODE), non-linear, x absent      524
Ordinary differential equations (ODE), non-linear, y absent      524
Ordinary differential equations (ODE), order      474
Ordinary differential equations (ODE), ordinary point      see "Ordinary points of ODE"
Ordinary differential equations (ODE), particular integral (solution)      475 498 500—501
Ordinary differential equations (ODE), singular point      see "Singular points of ODE"
Ordinary differential equations (ODE), singular solution      475 487 488 490
Ordinary differential equations, methods for canonical form for second-order equations      522
Ordinary differential equations, methods for canonical form for second-order equations, eigenfunctions      581—602
Ordinary differential equations, methods for canonical form for second-order equations, equations containing linear forms      484—486
Ordinary differential equations, methods for canonical form for second-order equations, equations with constant coefficients      498—509
Ordinary differential equations, methods for canonical form for second-order equations, Green's functions      517—522
Ordinary differential equations, methods for canonical form for second-order equations, integrating factors      479—481
Ordinary differential equations, methods for canonical form for second-order equations, Laplace transforms      507—509
Ordinary differential equations, methods for canonical form for second-order equations, numerical      1180—1190
Ordinary differential equations, methods for canonical form for second-order equations, partially known CF      512
Ordinary differential equations, methods for canonical form for second-order equations, separable variables      477
Ordinary differential equations, methods for canonical form for second-order equations, series solutions      537—558 564—568
Ordinary differential equations, methods for canonical form for second-order equations, undetermined coefficients      500
Ordinary differential equations, methods for canonical form for second-order equations, variation of parameters      514—516
Ordinary points of ODE      539 541—544
Ordinary points of ODE, indicial equation      549
Orthogonal lines, condition for      12
orthogonal matrices      275—276 778 779
Orthogonal matrices, general properties      see "Unitary matrices"
Orthogonal systems of coordinates      370
Orthogonal transformations      781
Orthogonalisation (Gram — Schmidt) of eigenfunctions of an Hermitian operator      589—590
Orthogonalisation (Gram — Schmidt) of eigenfunctions of an Hermitian operator, eigenvectors of a normal matrix      280
Orthogonalisation (Gram — Schmidt) of eigenfunctions of an Hermitian operator, functions in a Hilbert space      584—586
Orthogonality of eigenfunctions of an Hermitian operator      589—590
Orthogonality of eigenvectors of a normal matrix      280—281
Orthogonality of eigenvectors of an Hermitian matrix      282
Orthogonality of functions      584
Orthogonality of terms in Fourier series      423 431
Orthogonality of vectors      223 249
Orthogonality properties of characters      936 944
Orthogonality theorem for irreps      932—934
Orthonormal basis functions      584
Orthonormal basis vectors      249—250
Orthonormal basis vectors under unitary transformation      290
oscillations      see "Normal modes"
Outcome, of trial      961
Outer product of two vectors      785
Pappus' theorems      198—200
Parabolic PDE      620 623
Parallel axis theorem      242
Parallel vectors      227
Parallelepiped, volume of      229—230
Parallelogram equality      252
Parallelogram, area of      227 228
Parameter estimation (statistics)      1072—1097 1140
Parameter estimation (statistics), Bessel correction      1090
Parameter estimation (statistics), error in mean      1140
Parameter estimation (statistics), mean      1086
Parameter estimation (statistics), variance      1087—1090
Parameter estimation, maximum-likelihood      1097
Parameters, variation of      514—516
Parametric equations of cycloid      376 844
Parametric equations of space curves      346
Parametric equations of surfaces      351
Parity inversion      944
Parseval's theorem for Fourier series      432—433
Parseval's theorem for Fourier transforms      456—457
Parseval's theorem, conservation of energy      457
Partial derivative      see "Partial differentiation"
Partial differential equations (PDE)      608—640 646—702 see particular"
Partial differential equations (PDE), arbitrary functions      613—618

Partial differential equations (PDE), boundary conditions      614 632—640 656
Partial differential equations (PDE), characteristics      632—638
Partial differential equations (PDE), characteristics, and equation type      636
Partial differential equations (PDE), equation types      620 643
Partial differential equations (pde), first-order      614—620
Partial differential equations (PDE), general solution      614—625
Partial differential equations (PDE), homogeneous      618
Partial differential equations (PDE), inhomogeneous equation and problem      618—620 678—681 686—702
Partial differential equations (PDE), methods for, change of variables      624—625 629—631
Partial differential equations (PDE), methods for, constant coefficients      620
Partial differential equations (PDE), methods for, constant coefficients, general solution      622
Partial differential equations (PDE), methods for, integral transform methods      681—686
Partial differential equations (PDE), methods for, method of images      see "Method of images"
Partial differential equations (PDE), methods for, numerical      1190—1192
Partial differential equations (PDE), methods for, separation of variables      see "Separation of variables"
Partial differential equations (PDE), methods for, superposition methods      650—657
Partial differential equations (PDE), methods for, with no undifferentiated term      617—618
Partial differential equations (PDE), particular solutions (integrals)      618—625
Partial differential equations (PDE), second-order      620—631
Partial differentiation      154—182
Partial differentiation as gradient of a function of several real variables      154—155
Partial differentiation, chain rule      160—161
Partial differentiation, change of variables      161—163
Partial differentiation, definitions      154—156
Partial differentiation, properties      160
Partial differentiation, properties, cyclic relation      160
Partial differentiation, properties, reciprocity relation      160
Partial fractions      18—25
Partial fractions and degree of numerator      21
Partial fractions as a means of integration      65—66
Partial fractions in inverse Laplace transforms      460 508
Partial fractions, complex roots      22
Partial fractions, repeated roots      23
Partial sum      118
Particular integrals (PI)      475 see methods "Partial methods
Partition of a group      906
Partition of a set      907
Parts, integration by      68—70
Path integrals      see "Line integrals"
PDE      see "Partial differential equations"
PDF      see "Probability functions density
Penalty shoot-out      1056
Pendulums, coupled      335 337
Periodic function representation      see "Fourier series"
Permutation groups $S_{n}$       898—900
Permutation groups $S_{n}$ , cycle notation      899
Permutation law in a group      889
permutations      975—981
Permutations, degree      898
Permutations, distinguishable      977
Permutations, order of      900
Permutations, symbol $^{n}P_{k}$       975
Perpendicular axes theorem      212
Perpendicular vectors      223 249
pf      see "Probability functions"
pgf      see "Probability generating functions"
PI      see "Particular integrals"
Plane curves, length of      74—75
Plane curves, length of, in Cartesian coordinates      74
Plane curves, length of, in plane polar coordinates      75
Plane polar coordinates      71 342
Plane polar coordinates, arc length      75 367
Plane polar coordinates, area element      205 367
Plane polar coordinates, basis vectors      342
Plane polar coordinates, velocity and acceleration      343
Plane waves      628 649
Planes and simultaneous linear equations      305—306
Planes, vector equation of      231—232
Plates, conducting      see also "Complex potentials for
Plates, conducting, line charge near      696
Plates, conducting, point charge near      694
Point charges, $\delta$ -function respresentation      447
Point groups      924
Points of inflection of a function of one real variable      51—53
Points of inflection of a function of several real variables      165—170
Poisson distribution $Po(\lambda)$       1016—1021
Poisson distribution $Po(\lambda)$ and Gaussian distribution      1029—1030
Poisson distribution $Po(\lambda)$ as limit of Binomial distribution      1016 1019
Poisson distribution $Po(\lambda)$ , mean and variance      1018
Poisson distribution $Po(\lambda)$ , MGF      1019
Poisson distribution $Po(\lambda)$ , multiple      1020—1021
Poisson distribution $Po(\lambda)$ , recurrence formula      1018
Poisson equation      606 612 678—681
Poisson equation, fundamental solution      691—693
Poisson equation, Green's functions      688—702
Poisson equation, uniqueness      638—640
Poisson summation formula      467
Poisson's ratio      802
Polar coordinates      see "Plane polar" "Cylindrical "Spherical
Polar representation of complex numbers      95—98
Polar vectors      798
Pole, of a function of a complex variable, contours containing      758—768
Pole, of a function of a complex variable, order      724 750
Pole, of a function of a complex variable, residue      750—752
Polynomial equations      1—10
Polynomial equations, conjugate roots      102
Polynomial equations, factorisation      7
Polynomial equations, multiplicities of roots      4
Polynomial equations, number of roots      86 88 770
Polynomial equations, properties of roots      9
Polynomial equations, real roots      1
Polynomial equations, solution of using de Moivre's theorem      101—102
Polynomial solutions of ODE      544 554—555
Populations, sampling of      1065
Positive definite and semi-definite quadratic/Hermitian forms      295
Positive semi-definite norm      249
Potential energy of ion in a crystal lattice      151
Potential energy of magnetic dipoles, vector representation      224
Potential energy of oscillating system      323
Potential function and conservative fields      395
Potential function, complex      725—730
Potential function, electrostatic      see "Electrostatic fields and potentials"
Potential function, gravitational      see "Gravitational fields and potentials"
Potential function, vector      395
Power series and differential equations      see "Series solutions of differential equations"
Power series in a complex variable      136 716—718
Power series in a complex variable, analyticity      718
Power series in a complex variable, circle and radius of convergence      136 717—718
Power series in a complex variable, convergence tests      717 718
Power series in a complex variable, form      716
Power series, interval of convergence      135
Power series, Maclaurin      see "Maclaurin series"
Power series, manipulation: difference, differentiation, integration, product, substitution, sum      137—138
Power series, Taylor      see "Taylor series"
Power, in hypothesis testing      1122
Powers, complex      102—103 719
Prediction and correction methods      1184—1186 1194
Prime, non-existence of largest      34
Principal axes of Cartesian tensors      800—802
Principal axes of conductivity tensors      801
Principal axes of inertia tensors      800
Principal axes of quadratic surfaces      297
Principal axes of rotation symmetry      944
Principal normals of space curves      348
Principal value of complex integrals      760
Principal value of complex logarithms      103 720
Principle of the argument      755
probability      966—1053
Probability distributions      981 see
Probability distributions, bivariate      see "Bivariate distributions"
Probability distributions, change of variables      992—999
Probability distributions, generating functions      see "Moment generating functions" "Probability
Probability distributions, mean $\mu$       986—987
Probability distributions, mean of functions      987
Probability distributions, mode, median and quartiles      987
Probability distributions, moments      989—992
Probability distributions, multivariate      see "Multivariate distributions"
Probability distributions, standard deviation $\sigma$       988
Probability distributions, variance $\sigma^{2}$       988
Probability for intersection $\cap$       962

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