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

Representations of a group      430
Representations of a group, characters in      433
Representations of a group, orthogonality theorem of      432
Representations of a group, reducible, irreducible, decomposable      431
Representations of a group, regular      437
Representations of a group, Schur’s lemma      432
Residues, theorem      65 66 480
Resolvent kernel, of integral equation      303 309
Retarded potential      280
Riemann symbol      189
Riemann curvature tensor      419
Riemann geometry      416
Riemann sheet, surface      474
Riemann zeta function      45 53
Rodrigues' formula for Legendre polynomials      169
Roots of equations, Horner’s method      361
Roots of equations, Horner’s method, Newton’s method      360
Roots of equations, Horner’s method, regula falsi      360
Rotation matrix $D^l_{m'm}(R)$       462
Rotation matrix $D^l_{m'm}(R)$ , for       463
Rotation matrix $D^l_{m'm}(R)$ , for       465
Runge — Kutta method      353
Saddle-point methods      82
Saddle-point methods, applied to Airy integral to derive $\textit{WKB}$ connection formula      116
Scalar product      149
Scalar product, for infinite-dimensional vector space      162
Scalar, as a tensor of rank zero, Cartesian      406
Scalar, as a tensor of rank zero, Cartesian, general      411
Schl $\ddot{a}$ fli's integral representation of       169 170
Schl $\ddot{a}$ fli's integral representation of , of       184
Schmidt — Hilbert theory of integral equations      305
Schrodinger equation      218
Schrodinger equation, as example for perturbation theory      291
Schrodinger equation, Born approximation in scattering theory      303
Schrodinger equation, for harmonic oscillator      19
Schrodinger equation, graphical discussion of      24
Schrodinger equation, solution by $\textit{WKB}$ method      36
Schur's lemma      432
Schwartz reflection principle      482
Schwartz transformation      137
Second solution, of Bessel’s equation      17 18 180
Second solution, of confluent hypergeometric equation      196
Second solution, of hypergeometric equation      191
Second solution, of Legendre’s equation      167
Secular equation      146
Separable (ordinary) differential equation      2
Separation of variables      226 235
Series asymptotic      81
Series asymptotic, $\sum(1\n^2)=\mathcal{S}(2)$       52 363
Series asymptotic, convergence criteria of      44
Series asymptotic, familiar series      48
Series asymptotic, for $sec\quad x$       57
Series asymptotic, for $tan\quad x$ and $ctn\quad x$       50
Series asymptotic, infinite      44
Series asymptotic, miscellaneous devices for summing      50
Series solutions of differential equations      13
Series solutions of differential equations, associated Legendre equation      21
Series solutions of differential equations, Bessel’s equation      16
Series solutions of differential equations, Hermite equation      20
Series solutions of differential equations, indicial equation      16
Series solutions of differential equations, irregular singular point      14
Series solutions of differential equations, Legendre’s equation      14
Series solutions of differential equations, near a regular singular point      14 16
Series solutions of differential equations, near an ordinary point      14
Series solutions of differential equations, recursion relations for the coefficients      15 16 20
Series solutions of differential equations, singularities at infinity      19
Sheet, Riemann      474
Similarity transformation      148
Simpson’s rule      350
Sine transform      103
Sine-integral function $Si\quad x$       61 77
Singular points of a differential equation, at infinity      19
Singular points of a differential equation, regular and irregular      14
Singular solution of a differential equation      5
Small oscillations      154
Sommerfeld — Watson transformation      75
Special functions      167
Special functions, Bessel functions      17 178
Special functions, beta function      67
Special functions, confluent hypergeometric functions      194
Special functions, elliptic functions      204
Special functions, Gamma function      75
Special functions, Hermite polynomial      21 188
Special functions, hypergeomeiric functions      187
Special functions, Legendre functions      16 167
Special functions, Mathieu functions      198
Spherical Bessel functions       187 229
Spherical Bessel functions , , asymptotic behavior      230
Spherical harmonics $Y_{lm}(\Omega)$       175 178
Spherical harmonics $Y_{lm}(\Omega)$ , addition theorem      167
Spherical harmonics $Y_{lm}(\Omega)$ , as basis for representations of $O^{+}(3)$       462
Spinor, spinor representations of $O^{+}(3)$       466
Spur of a matrix      145
Stability, of numerical integration of a parabolic equation      226
Stability, of numerical integration of differential equations      354
Standard deviation      381
Standard error      388

Stationary phase, method of      90
Stationary random process      386
Statistical independence      374
Statistics      372
Steepest descent, method of      82
Step function (Heaviside)      107
Stirling’s formula      84 89
Stokes’ phenomenon      33
Stream function      127
Structure constants of a Lie group      456
Student /-distribution      398
Sturm — Liouville differential equation      264
Sturm — Liouville differential equation, completeness of eigenfunctions      338
Sturm — Liouville differential equation, variational approach      334
Subgroup      426
Subgroup, invariant or normal      430
Subtracted dispersion relation      135
Summing series numerically      363
Superconvergence relation      138
Symmetric group on objects, $S_{n}$       425
Symmetric kernel      305
Symmetric matrix      145
Symmetry arguments for evaluating integrals      62
Symmetry groups      426 441 443
Symmetry of Green’s functions      270
Synthetic division      361
Tabulated integrals      75
Tabulated integrals, beta function       76
Tabulated integrals, cosine-integral $Ci\quad x$       61 77
Tabulated integrals, elliptic integrals $F(\phi, k)$ , $E(\phi, k)$ , $\Pi(\phi, n, k)$ , $\textit{K}(k)$ , $\textit{E}(k)$ , $\textit{\Pi}(n, k)$       78 79
Tabulated integrals, error function erf x      77
Tabulated integrals, exponential integral       77
Tabulated integrals, gamma function $\Gamma(x)$       59 75
Tabulated integrals, sine-integral $Si\quad x$       61 77
Tabulated integrals, Taylor’s series      14 479
Tensor analysis, Cartesian tensors      403
Tensor analysis, general tensor analysis      410
Tensor density      414
Tensor, Cartesian      403 406
Tensor, general      412
Tensor, metric      416
Tensor, relative      413
Tensor, Riemann curvature      419
Tensor, symmetric, antisymmetric      414
Tensor, under       458
Tensor, under       460
Torsion      409
Trace of a matrix      145
Transfer matrix      166
Transformation group      450
Transformation matrix      147
Transformation matrix, congruent transformation      156
Transformation matrix, for rotations in three-space      404
Transformation matrix, similarity transformation      148
Transformation matrix, unitary transformation      150
Transpose of a matrix      145
Trapezoidal rule      350
Triad      408
Twisted cubic      422
Unbiased estimate      399
Uncertainty principle      105 107
Undetermined coefficients, method of      7
Unimodular unitary group       450
Unitarity condition on scattering amplitude      316 317
Unitary matrix      145
Unitary transformation      150
Variance      381
Variation of parameters      8
Variational derivative      324 327 328
Variations, calculus of      322
Variations, calculus of, applied to eigenvalue problems      333
Variations, calculus of, applied to integral equations      340
Variations, calculus of, isoperimetric problems in      331
Variations, calculus of, variable end points      329
Vector space, linear      139
Vector space, linear, basis      141
Vector space, linear, linear operators      141
Vectors      140
Vectors, Cartesian      404
Vectors, components      141
Vectors, contravariant and covariant      411
Vectors, linearly independent      140
Vectors, orthogonality      149
Vectors, under       457
Vectors, under       459
Vibrating drum      231 266 271
Vibrating drum, with perturbation      290 295
Vibrating string      262 269
Vibrations, small      154
Volterra integral equation      300 311
Wave equation      217 218 222 227 278
Wave equation, Green’s function      278
Whittaker equation and functions      197
Wiener — Hopf method, applied to integral equation      312
Wiener — Hopf method, applied to partial differential equation      245
wronskian      31 35
Zeta function, Riemann, $\zeta(s)$       45 53

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