Mathews J., Walker R.L. — Mathematical methods of physics :: Электронная библиотека попечительского совета мехмата МГУ

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Mathews J., Walker R.L. — Mathematical methods of physics

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Название: Mathematical methods of physics

Авторы: Mathews J., Walker R.L.

Аннотация:

This well-known text treats a variety of essential topics, ranging in difficulty from simple differential equations to group theory. Physical intuition, rather than rigor, is used to develop mathematical facility, and the authors have kept the text at a level consistent with the needs and abilities of upper-division students. This book covers subjects which are often ignored in traditional texts; for example, statistics and the fitting of experimental data, dispersion relations and super-convergence relations and the group SU(3).

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1971

Количество страниц: 515

Добавлена в каталог: 24.11.2013

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Предметный указатель

, beta function      76
$ber_n\quad x$ , $bei_n\quad x$       187
, Mathieu function      200
$Ci\quad x$ , cosine integral function      61 77
$cn\quad x$ , elliptic function      209
$dn\quad x$ , elliptic function      209
$D_{m', m}^l$ , rotation matrix      462
$E(\phi, k)$ . elliptic integrals      79
$F(\phi, k)$ , elliptic integral      78
, Hermite polynomials      21 196
$H_n^{(1)}(z)$ , $H_n^{(2)}(z)$ , Hankel functions      185
$h_{(1)}(x)$ , $h_{(2)}(x)$ , spherical Hankel functions      229
, Bessel function      179
elliptic integral      79
$L_n^{\alpha}(z)$ , Laguerre polynomial      196
, $O^{+}(n)$ groups      450
, $O^{+}(n)$ groups, irreducible representations of $O^{+}(3)$       461
symbol, Riemann      189
, Legendre polynomial      16 169
, associated Legendre function      175
Legendre function of the second kind      174
, Mathieu function      200
$sn\quad x$ , elliptic function      204
group      450
group, irreducible representations of       457
group, irreducible representations of       459
-distribution of Student      398
$W_{k,m}$ , Whittaker functions      197
, second solution of Bessel’s equation      180
$Y_{im}(\Omega)$ , spherical harmonics      175 178
$\textit{WKB}$ method      27
$\textit{WKB}$ method, applied to Schr $\ddot{o}$ dinger equation, gives Bohr — Sommerfeld quantization condition      37
$\textit{WKB}$ method, connection formulas      28 34 36 116
${}_1F_1(a; c; x)$ , confluent hypergeometric function      195
${}_2F_1(a; b; c; x)$ , hypergeometric series      187
A posteriori probability      373
a priori probability      373
Abelian group      425
Absolute convergence      44
Absolute tensor      414 418
Absorptive part of scattering amplitude      316
Addition theorem for spherical harmonics      176
Adjoint representation      469
Airy integral      117
Algebra of a group      425
Alternating gradient synchrotron      125
Alternating group       438
Analytic continuation      482
Analytic function      477
Anticommutator      470
Antilinearity      149
Antisymmetric matrix      145
Antisymmetric symbol of Levi-Civita $e_{ijk\cdots}$ , as a general tensor      413
Antisymmetric symbol of Levi-Civita $e_{ijk\cdots}$ , as a tensor under       458
Antisymmetric symbol of Levi-Civita $e_{ijk\cdots}$ , as a tensor under       460
Antisymmetric symbol of Levi-Civita $e_{ijk\cdots}$ , as Cartesian tensor      406
Argument of a complex number      472
Associated Legendre equation      21 175 228
Associated Legendre function       22 175 228
Asymptotic series, definition of      81
Asymptotic series, for       82
Asymptotic series, for erf x      81
Asymptotic series, for gamma function      84 89
Autocorrelation function      386
Bashforth — Adams — Milne method      354
Basis, of vector space      141
Basis, of vector space, orthonormal      149
Bayes’ Theorem      375
Bernoulii differential equation      4
Bernoulli numbers      48 49
Bessel functions, $ber_n\quad x$ , $bei_n\quad x$       187
Bessel functions,       179
Bessel functions, , recursive calculations      356
Bessel functions, , zeros      233
Bessel functions,       180
Bessel functions, generating function      183
Bessel functions, Hankel functions $H_n^{(1)} (x)$ , $H_n^{(2)} (x)$       185
Bessel functions, integral representations      184 185
Bessel functions, modified Bessel functions ,       187
Bessel functions, orthogonality and normalization integrals      181 182
Bessel functions, recursion relations      179
Bessel functions, spherical Bessel functions ,       187 229
Bessel's integral      184
Bessel’s equation      12 16 178
Bessel’s equation, second solution      17 180
Bessel’s inequality      166
Beta function       76
Binomial coefficient      376
Binomial distribution      378
Binormal      409
Block matrices      146
Block wave functions      200
Bohr — Sommerfeld quantization condition      37
Born approximation      303
Boundary conditions for partial differential equations      219 226
Boundary-valve problems      229 266
Bounded variation      97
Brachistrochrone      325
Branch line, cut, and point      474
Branch of a function      474
Calculus of variations      322
Calculus of variations, applied to eigenvalue problems      333
Calculus of variations, applied to integral equations      340
Calculus of variations, isoperimetric problems of      331
Calculus of variations, variable endpoints      329
Cartesian tensors      406
Cauchy boundary condition      2 9
Cauchy principal value integral      480
Cauchy — Riemann differential equations      124 477
Cauchy — Schwarz inequality      165
Cauchy’s integral formula      478
Cauchy’s integral formula, applied to dispersion relations      129
Cauchy’s integral formula, used to derive integral representations      169 184
Cauchy’s Theorem      478
Causality and dispersion relations      130
Central limit theorem      383
Characteristic function of a distribution      382
Characteristics      221
Characters of a group      433
Characters of a group, orthogonality      435
Charged conducting strip      127
Chi-square distribution      395
Chi-square test      394
Christoffel symbol, of first kind      417
Christoffel symbol, of second kind      418
Circle of convergence      479
Clairaut equation      5
Classes in a group      428
Closure      266
Cofactor      144
Cogredient      147
Combinations and permutations      375
Commutative group      425
Commuting operators      142
Complementary function      6
Completeness      141 266
Completeness, of eigenfunctions of Sturm — Liouville differential equations      338
Complex conjugate      472
Complex number      471
Components, of a linear operator      141
Components, of a linear scalar function      148
Components, of a vector      141
Conditional probability      374
Confluent hypergeometric equation and function      194
Conformal transformations      123
Conformal transformations, Schwartz transformation      137
Congruent transformation      156
Conjugate linearity      149
Conjugate representations of       461
Conjugate vector or tensor      458

Connection formulas for $\textbf{WKB}$ method      28 34 36 116
Continued fraction      203
Contour integration      65
Contour integration, applied to Green’s function      279
Contra variant vector      411
Contraction of tensor indices, in       458
Contraction of tensor indices, in       460
Contraction of tensor indices, in general coordinates      412
Contraction of tensor indices, in three-space      407
Contragredient      147
Contravariant tensor      412
Convergence, absolute      44
Convergence, criteria for infinite series      44
Convergence, of hypergeometric series      46
Convergence, of series solution of Legendre equation      47
Convergence, “ in the mean”      340
Convolution theorems      113
Coordinate system for a vector space      14
Coordinate transformations      146
Coordinate transformations, congruent transformation      156
Coordinate transformations, similarity transformation      148
Coordinate transformations, unitary transformation      150
Coset of a group      426
Cosine transform      103
Cosine-integral fuction $Ci\quad x$       61 77
Covariant differentiation      418
Covariant tensor      412
Covariant vector      411
Curvature of a curve      409
Curvature tensor of Riemann      419
Cycle notation for symmetric group      426
Cycloid      327
Decomposable representation      431
Degenerate eigenvalue      152 233 265 440
Degenerate kernel of integral equation      300
Degenerate perturbation theory      293
Degenerate perturbation theory, as an application of group theory      443
Degree of differential equation      1
Delta function, Dirac      102
Delta function, in three dimensions      106
Delta, Kronecker      100
Density function      265
Diagonalization of matrices      153 158
Difference equation, linear      355
Differential equations, numerical solution      353
Differential equations, ordinary      1
Differential equations, ordinary, $\textit{WKB}$ method of      27
Differential equations, Ordinary, exact      2
Differential equations, ordinary, graphical discussion of      22
Differential equations, ordinary, homogeneous      4 6 12
Differential equations, ordinary, isobaric      5 12
Differential equations, ordinary, linear      3 6
Differential equations, ordinary, separable      2
Differential equations, ordinary, series solutions of      13
Differential equations, partial      217
Differential equations, partial, integral transform methods      239
Differential equations, partial, separation of variables      226
Differential equations, partial, Wiener — Hopf method      245
Differential geometry      402
Differential geometry, Frenet formulas      410
Differentiation, Numerical      349
Diffusion equation      218 234 235 240 242 276
Dimensionality of a vector space      140
Dirac delta function      102
Dirac delta function, in three dimensions      106
Dirichlet boundary condition      219
Dispersion relations      129
Dispersion relations, as integral equations      316
Dispersion relations, subtracted      135
Displacement kernel      312
Double factorial       172
Double periodicity of elliptic functions      206
Dual space      149
Dyad, dyadic      408
Eigenfunctions, of a Hermitian operator      263
Eigenfunctions, of Schr\ddot{o}dinger equation      21
Eigenvalues, group-theoretic approach to      443
Eigenvalues, of a Hermitian matrix      152
Eigenvalues, of a Hermitian operator      263
Eigenvalues, of a matrix      151 260
Eigenvalues, of an infinite-dimensional matrix      163
Eigenvalues, of integral equation      299 301
Eigenvalues, of Schr\ddot{o}dinger equation      21 25
Eigenvalues, variational approach to      333
Eigenvalues,degenerate      152 233 265 440
Eigenvectors, of a linear operator      150
Eigenvectors, of a matrix      261
Eigenvectors, orthogonality properties of      152 263
Elastic waves, differential equation for      255
Elements of a matrix      143
Elliptic functions $sn\quad x$ , $cn\quad x$ , $dn\quad x$       204 209
Elliptic integrals $F(\phi, k)$ , $E(\phi, k)$ , $\Pi(\phi, n, k)$ , $\textit{K}(k)$ , $\textit{E}(k)$ , $\textit{\Pi}(n, k)$       78 79
Elliptic partial differential equations      221
Entire function      483
Envelope of solutions of a differential equation      6
Equilateral triangle, normal modes of      237
Equivalence, of group elements      428
Equivalence, of group representations      431
Error estimates in interpolation      348
Error estimates in interpolation, for Bashforth — Adams — Milne method      354
Error function $erf\quad x$       77
Error function $erf\quad x$ ,asymptotic expansion of      81
Error matrix      393
Essential singularity      480
Euler angles      404
Euler numbers      48 57
Euler — Lagrange equation      324
Euler — Maclaurin formula      365
Euler’s transformation      54
Exact differential equation      2
expectation value      381
Exponential iniegral       77
Exponential iniegral , asymptotic expansion of      82
Faithful representation      430
Floquet’s theorem      198 199
Fourier series      96
Fourier series, complex form      100
Fourier series, for $\cos\quad kx$       52
Fourier series, Gibbs’ phenomenon      98 120
Fourier transforms      101
Fourier transforms, applied to a partial differential equation      242
Fourier transforms, applied to integral equation      312
Fourier transforms, convolution theorem for      1 3
Fourier transforms, in complex plane      246
Fourier transforms, in three dimensions      105
Fourier transforms, properties and applications      110
Fourier transforms, sine and cosine transforms      103
Fourier — Bessel transform      109
Fredholm integral equation      300
Fredholm solution of integral equation      303 320
Frenet formulas      410
Fresnel integrals ,       77
Fully reducible representation      431
Functional      323
Functional derivative      324
Fundamental solution      274
Fundamental tensor      415
Gamma function $\Gamma(x)$       59 75
Gamma function $\Gamma(x)$ , asymptotic expansion of      84 89
Gaussian distribution      378 381 384
Gaussian function      106
Gaussian integration      351
Gaussian random process      386
Generating function, for Bessel functions      183
Generating function, for Hermite polynomials      21
Generating function, for Legendre polynomials      170
Generating function, for moments of a probability distribution      382
Generators of a group      450
Geodesic      420
Gibbs’ phenomenon      98 120

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