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

Gram — Schmidt orthogonalization      152 153
Graphical approach to the solution of a differential equation      22
Green’s functions      267
Green’s functions, for diffusion equation      243
Green’s functions, for Helmholtz equation      283 284
Green’s functions, for Laplace’s equation and wave equation      277
Green’s functions, for ordinary differential equation      39
Green’s functions, for vibrating drum      271
Green’s functions, for vibrating string      269
Gregory’s series      99 367
Group      424
Group, , $O^{+}(n)$       450
Group,       450
Group, abelian or commutative      425
Group, alternating      438
Group, characters of      433
Group, class      428
Group, coset      426
Group, infinite      449
Group, order      425
Group, physical applications of      440
Group, representation      430
Group, subgroup      426
Group, symmetric      425
Hamilton's variational principle      324
Hankel functions $H_n^{(1)}(z)$ , $H_n^{(2)}(z)$       185
Hankel functions $H_n^{(1)}(z)$ , $H_n^{(2)}(z)$ , spherical Hankel functions $h_{(1)}(x)$ , $h_{(2)}(x)$       229
Hankel transform      109 212
Heat conduction in a cube      234 245
Heat conduction in a cube, in a semi-infinite medium      240 245
Heat conduction in a cube, in a slab      235
Heat conduction in a cube, in an infinite medium      242
Heaviside step function      107
Helmholtz equation      227 232
Helmholtz equation, Green’s function      283 284
Helmholtz equation, in an equilateral triangle      237
Hermite differential equation      20
Hermite polynomial       21 196
Hermite polynomial , generating function of      211
Hermitian conjugate of a matrix      145
Hermitian kernel      306
Hermitian linear operator      263
Hermitian matrix      145
Hilbert space      162
Hilbert transform      109 316
Hill equation      200
Homogeneous differential equaiion, Ordinary      4 6 12
Homogeneous differential equaiion, partial      218
Homogeneous function      4
Homographic transformation      189
Homomorphic      430
Homomorphic relation of to $O^{+}(3)$       466
Horner’s method, for roots of polynomials      361
Hyperbolic partial differential equation      221
Hypergeomelric series or function      187
Hypergeomelric series or function, confluent hypergeometric function      195
Hypergeomelric series or function, convergence of      46
Hypergeomelric series or function, integral representation of      191
Hypergeometric differential equation      187
Hypergeometric differential equation, confluent hypergeometric differenital equation      194
Hypergeometric differential equation, second solution to      190
Idempotent matrix      145
Identity Theorem      482
Images, method of      245
Improper rotation      407
Indicia! equation      16
Infinitesimal rotation      455 464
Inhomogeneous differential equation      6
Inhomogeneous problems involving partial differential equations      267
Inner product      149
Integral equations      299
Integral equations, Fredhlom theorems for      301
Integral equations, in dispersion theory      316
Integral equations, in Volterra equations      300 311
Integral equations, Neumann and Fredholm series in      302
Integral equations, Schmidt — Hilbert theory for      305
Integral equations, variational approach to      340
Integral equations, Wiener — Hopf method for      312
Integral equations, with degenerate kernel      300
Integral representations      79
Integral representations, of       185
Integral representations, of       169 170
Integral representations, of $\delta(x)$       102
Integral representations, of $\delta(\textit{x})$       105
Integral representations, of ${}_1F_1(a, c; z)$       195
Integral representations, of ${}_2F_1(a, b; c; z)$       191
Integral transforms      96
Integral transforms, applied to integral equations      312
Integral transforms, applied to partial differential equations      239
Integral transforms, Fourier transforms      101
Integral transforms, Laplace transforms      107
Integral transforms, other transforms      109
Integral transforms, properties and applications      110
Integrals, evaluation      58
Integrals, evaluation, by contour integration      65
Integrals, evaluation, by differentiation or integration with respect to a parameter      60
Integrals, evaluation, by expansion in series      80
Integrals, evaluation, by saddle-point methods      82
Integrals, evaluation, by symmetry arguments      62
Integrals, evaluation, use of complex variables in      59
Integrating factor      3
Integration, numerical      349
Interpolation      345
Interpolation, error estimation      348
Interpolation, Lagrangian interpolation      347
Interval in Riemann geometry      416
Invariant subgroup      430
Inverse distance formula      170
Inverse, of a matrix      144
Inverse, of an operator      142
Irreducible representations      431
Irreducible representations, of $O^{+}(3)$       461
Irreducible representations, of       457
Irreducible representations, of       459
Irregular singular point of a differential equation      14
Isobaric differential equation      5 12
Isolated singularity      479
Isomorphism      430
Isomorphism, of Lie algebras of and       456 464
Isoperimetric problems      331
Iteration, applied to differential equations      25
Jacobi polynomials      194
Jacobian elliptic functions $sn\quad x$ , $cn\quad x$ , $dn\quad x$       204 209
Joint probability      374
Jordan’s lemma      67
Kernel of an integral equation      163 299
Kernel of an integral equation, degenerate      300
Kernel of an integral equation, displacement kernel      312
Kernel of an integral equation, symmetric, Hermitian      305 306
Kronecker delta $\delta_{ij}$ , $\delta_i^j$       100
Kronecker delta $\delta_{ij}$ , $\delta_i^j$ , as a Cartesian tensor      406
Kronecker delta $\delta_{ij}$ , $\delta_i^j$ , as a general tensor      4 2
Kummer function ${}_1F_1(a; c; z)$       195
Kummer’s transformation      197
Lagrange’s equations of motion      324
Lagrangian interpolation      347
Laguerre polynomial, $L_n^{\alpha}(z)$       196
Lang range multiplier      331
Laplace transforms      107
Laplace transforms, applied to a partial differential equation      240
Laplace transforms, applied to integral equation      312
Laplace transforms, convolution theorems      113
Laplace transforms, properties and applications      110
Laplace’s equation      218 232
Laplace’s equation, Green’s function      277
Laplace’s equation, two-dimensional      124
Laplace’s equation, variational approach to      333
Laplace’s integral representation of       170
Laurent expansion      479
Least-squares fit      391

Legendre elliptic integrals $F(\phi, k)$ , $E(\phi, k)$ , $\Pi(\phi, n, k)$ , $\textit{K}(k)$ , $\textit{E}(k)$ , $\textit{\Pi}(n, k)$       78 79
Legendre functions ,       167
Legendre functions , , associated functions ,       175 228
Legendre polynomials       16 169
Legendre’s differential equation      14 167
Legendre’s differential equation, associated equation      21 175 228
Legendre’s differential equation, second solution       174
Length of a vector      149
Levi — Civita antisymmetric symbol $e_{ijk\cdots}$ , as a Cartesian tensor      406
Levi — Civita antisymmetric symbol $e_{ijk\cdots}$ , as a general tensor      413
Levi — Civita antisymmetric symbol $e_{ijk\cdots}$ , as a tensor under       458
Levi — Civita antisymmetric symbol $e_{ijk\cdots}$ , as a tensor under       460
Lie algebra      456
Lie group      449
Lienard — Wiechert potential      282
Likelihood      387
Linear difference equation      355
Linear differential equation, with constant coefficients      6
Linear differential equation, with constant coefficients, first-order      3
Linear differential equation, with constant coefficients, series solution      13
Linear differential equation, with constant coefficients, with three regular singular points      187 190
Linear independence of vectors      140
Linear integral equation      299
Linear operators      141 163
Linear operators, Hermitian      263
Linear scalar function of a vector      148
Linear vector function of a vector      141
Linear vector space      139
Liouvilie's theorem      483
Loaded string      160
Lowering of tensor indices      416 458
Magnitude of a complex number      472
Mapping      472
Mathieu functions ,       200
Mathieu functions , , stability curves      201
Matrices      143
Matrices, diagonalization      158
Matrices, normal      160
Matrices, transformation matrix      147
Mean life of unstable particle      389
Mean value      381
Mellin transform      109
Meromorphic function      483
Metric      149
Metric tensor      416
Mittag — Lefler theorem      53
Mixed tensor      412
Modified Bessel functions ,       187
Molecular vibrations      154
Moments of a distribution      381
Multivalued function      473
Neumann boundary condition      219
Neumann series for integral equation      302
Newton’s method for roots of equations      360
Nonholonomic constraint      332
Nonsingular operator      142
Normal distribution      378
Normal form of one-dimensional wave equation      223
Normal frequencies, coordinates, modes      157
Normal frequencies, coordinates, modes, of circular drum      233
Normal frequencies, coordinates, modes, of equilateral triangle      239
Normal matrix      160
Normal subgroup      430
Normalization, of associated Legendre functions      175
Normalization, of Bessel functions      182
Normalization, of Legendre polynomials      173
Numerical methods, differentiation      349
Numerical methods, integration      349
Numerical methods, interpolation      345
Numerical methods, roots of equations      358
Numerical methods, solution of differential equations      353
Numerical methods, summing series      363
Operator, linear      141 163
Operator, linear, Hermitian      263
Order, of a group      425
Order, of a group element      427
Order, of differential equation      1
Ordinary point of a differential equation      14
Ordinary point of a differential equation, at infinity      19 20
Orthogonality, of associated Legendre functions      175
Orthogonality, of Bessel functions      181
Orthogonality, of eigenfunctions of Hermitian operator      263
Orthogonality, of eigenvectors of Hermitian matrix      152
Orthogonality, of group characters      435
Orthogonality, of group representations      432
Orthogonality, of Legendre polynomials      172
Orthogonality, of matrix      145
Orthogonality, of vectors      149
Orthonormal vectors      149
Oscillations, small      154
Osculating parameters      9
Outer product of vectors and tensors      405 406
Outgoing wave      230
Parabolic partial differential equation      221
Parameters of an infinite group      449
Parseval’s theorem      103
Partial differential equations      217
Partial differential equations, boundary conditions of      219 226
Partial differential equations, classification of      221
Partial differential equations, integral transform methods of      239
Partial differential equations, separation of variables in      226
Partial differential equations, Wiener — Hopf method of      245
Partial fraction representation of cotangent      52
Particular solution or integral      7
Pauli exclusion principle      442
Pauli spin matrices      465
Period of a group element      427
permutations      375
Perturbation theory      286
Perturbation theory, applied to circular drum      290 295
Perturbation theory, applied to Schr $\ddot{o}$ dinger equation      291
Perturbation theory, degenerate theory      293
Perturbation theory, rearranged series      292
Phase of a complex number      472
Pochhammer contours      192
Poisson distribution      379
Pole      480
Polyad, polyadic      408
Principal normal      409
Principal value integral      480
Probability theory      372
Probability theory, distributions      377 380
Projection operator      143
Proper rotation      407
Pseudo tensor      407
Quadrupole magnet      125
Quotient law      414
Raising of tensor indices      416
Random walk      396 397
Rank of a tensor      406
Ratio test for convergence of an infinite series      45
Rayleigh — Ritz method      337
Rearranged perturbation series      292
Reciprocity relation for Green’s functions      270
Recursion relations, for Bessel functions      179
Recursion relations, for coefficients in solution of differential equations      15 16 20
Recursion relations, for Legendre polynomials      171
Recursion relations, three-term, avoidance of      19 21
Recursion relations, three-term, occurrence for Mathieu functions      202
Reducible representation      431 435
Regula Falsi      360
Regular function      477
Regular representation of a group      437
Regular representation of a group, of a Lie algebra      469
Regular singular point of a differential equation      14
Regular singular point of a differential equation, at infinity      19 20
Relative likelihood      387
Relative tensor      413
Removable singularity      480
Representation of a Lie algebra      469

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