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Sommerfeld A. — Partial Differential Equations in Physics
Sommerfeld A. — Partial Differential Equations in Physics

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Название: Partial Differential Equations in Physics

Автор: Sommerfeld A.

Аннотация:

From the table of contents: Fourier Series and Integrals; About partial differential equations; Boundary Value Problems in Heat Conduction; Cylinder and Sphere Problems; Eigen-functions and Eigen-values; Problems of wireless telegraphy.


Язык: en

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1949

Количество страниц: 335

Добавлена в каталог: 28.03.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abraham, M.      223 244 256
Absorption condition      190
Addition theorem, of Bessel and Hankel functions      107 234
Addition theorem, of spherical harmonios      133
Addition theorem, of the preceding and the standing wave      146
Adjoint, differential form      44
Airy integrals      118 123 149
Alkali atoms      206
Anharmonic analysis      27
Anharmonic analysis, normalization condition of      293
Antenna      239
Antenna, frame      245 267
Antenna, horizontal      243
Antenna, magnetic      see "Frame"
Antenna, vertical      242
Approximation at a point of discontinuity      12
Approximation at a point of discontinuity, oscillating      17 26
Approximation at a point of discontinuity, osculating      17 26
Associated spherical harmonics      126
Associated spherical harmonics, normalization of      132
Associated spherical harmonics, recursion formula for      132
Associated spherical harmonics, with negative index m      128
Asymptotic representation, of Hankel functions      100 119
Asymptotic representation, of Hankel functions, of spherical harmonics      146
Balmer term      200 204
Bauer, G.      235
Baule, B.      37
Bending of beams      303
Bessel functions      84
Bessel functions, generating function      107
Bessel functions, integral representation of      86
Bessel functions, integral representation of functions in terms of      109
Bessel functions, summation over the roots of      295
Bessel functions, with fractional indices      111
Bipole      151
Bohr, N.      201
Boundary condition, adiabatic      63
Boundary condition, adiabatic, homogeneous, inhomogeneous      82 177
Boundary condition, adiabatic, isothermal      63
Boundary condition, adiabatic, of exterior heat conduction      64
Boundary value problems, general, in acoustics and heat conduction      177 180
Boundary value problems, general, in acoustics and heat conduction, exterior, of the wave equation      214
Boundary value problems, general, in acoustics and heat conduction, in the potential equation      181
Boundary value problems, general, in acoustics and heat conduction, of the first and second kind      53
Bush and Caldwell      4
Caratheodory, C.      320
Characteristics, theory of      36
Charge cloud      205
Christoffbl, E.B.      159
Circuit relations for $H^{1}_{n}$ and $H^{2}_{n}$      293
Circuit relations for $H^{1}_{n}$ and $H^{2}_{n}$, semi      251 253
Completeness relation      5
Confluent hypergeometric function      154
Couette flow      292
Courant — Hilbert      172 179
Cylinder function, general      86
Cylinder problems of heat conduction      101
Cylindrical wave      100 108
D'Alembert's solution of the wave equation      41
Darwin, C.G.      129
de Broglie, L.      207
de l'Hospital's rule      93
Debye, P., asymptotic representation of the Hankel functions      119
Debye, saddel point method of      116 118
Delta function      3 27 58 72
Diffusion      33
Diffusion, coefficient      34
Diffusion, Fick's law      34
Dipole, Hertz      151 236
Dipole, Hertz, magentic      268
Dirac, P.A.M.      27 183
Direction characteristic of the horizontal antenna      261
Dirichlet, discontinuous factor      290 299
Dirichlet, discontinuous factor, problem of potential theory      130 186
Dispersion by colloidal particles      224
Drop lines      99
Earth absorption in radio      271
Earth's temperature      68
Eigen value spectrum, continuous and discontinuous      188
Eigen Values      466
Eigen values, continuous spectrum      188 193
Eigen values, degenerate case      167
Eigen values, in wave mechanics      200
Eigen values, of the hydrogen atom      204 225
Eigen-differentials      211
Eigenfunctions      166
Eigenfunctions, conjugate complex      186
Eigenfunctions, improper and proper      221
Eigenfunctions, of the hydrogen atom      204 225
Eigenfunctions, regular and singular      221
Elastic rod      33 291
Electrodynamics of variable fields, differential equation of      32
Elliptic differential equations      38 42
Epstein, P.      255
Error, mean square      2 22
Euler's constant      94
Faber, G.      99
Fluid friction      33
Fourier analysis, anharmonic      27 77
Fourier analysis, anharmonic, analysis of crystals      20
Fourier analysis, anharmonic, integral      19 59
Fourier analysis, anharmonic, representation of coefficients      3
Fourier analysis, anharmonic, transformation      21
Fourier series      1
Fourier series, convergence of      14
Fourier, J.B.      1 92 101
Frank-mises      80 192 236
Fredholm — Hilbert theory of integral equations      169
Freedom, degrees of, infinite number for oscillating systems      169
Frequency $\omega$      20 84
Function space      180
Fundamental state of the H atom      205
Fundamental theorem of the theory of oscillating systems with an infinite number of degrees of freedom      178
Gauss, C.F.      1 94 153 171
Gauss, law of error      59
Gauss, law of error, series      153
Gauss, theorem of the arithmetic mean in potential theory      181 295
Gegenbauer polynomials      227 229
Generating function, of the Bessel functions of integral index      107
Generating function, of the Bessel functions of integral index, of spherical harmonics      123
Gibbs' phenomenon      12
Gibbs, W.      12
Gordon, W.      200
Gratiatos, J.      289
Green's function for self-adjoint differential equations      49 61 198
Green's function for self-adjoint differential equations, as the solution of an integral equation      183
Green's function for self-adjoint differential equations, for a continuous spectrum      193
Green's function for self-adjoint differential equations, for the wave equation      182
Green's function for self-adjoint differential equations, for the wave equation in the exterior of a sphere      198
Green's function for self-adjoint differential equations, in many-dimensional space      232
Green's function for self-adjoint differential equations, of the sphere in potential theory      134
Green's function for self-adjoint differential equations, one dimensional      291
Green's function for self-adjoint differential equations, reciprocity of the      50 217
Green's theorem      45
Green's theorem, for linear heat conduction      55
Green's theorem, the second form of      291
Hankel functions, integral representation of      88
Hankel functions, integral representation of, asymptotic representation      98 294
Hankel functions, integral representation of, logarithmic singularity of $H_{0}$      294
Hankel functions, integral representation of, with fractional index      113
Hankel, symbol      117
Harmonic analyzer      4
Heat conduction, linear      35
Heat conductivity      34
Heat conductivity, ratio of outer and inner      293
Heat conductivity, ratio with electric conductivity      293
Heat equation      34
Heisenberg, W.      201
Hermite polynomials      27 302
Hertz, concave mirror experiment      162
Hertz, concave mirror experiment, dipole      236 237
Hertz, concave mirror experiment, force line diagrams for the oscillating dipole      244
Hertz, concave mirror experiment, vector      238
Hertz, H.      236 244 276
Hilbert space      179 184
Hilbert, D.      166
Hobson, E.W.      129
Hydrogen eigenfunctions      204 225
Hydrogen radius      205
Hyperbolic differential equation      38 41
Hypergeometric function, differential equation of the      152
Hypergeometric function, differential equation of the, confluent      154
Image, electric      135
Integral equations, Hilbert's theory of      169 184
Integral equations, Hilbert's theory of, orthogonality theorem      188
Integral sine      11
Integration, complex      290
inversion      136
Inversion, center of      139
Inversion, sphere of      139
Ionosphere (Kenelly — Heaviside layer)      236
Jacobi, C.G.J.      72
Kepler problem for the H atom      201
Kernel, resolving      50
Kernel, resolving, symmetric      184
Laguerre, differential equation      204
Laguerre, differential equation, polynomials      27 205 302
Lame wave function      224
Lame, G.      81
Laplace operator      32
Laplace, P.S.      131
Laurent series      109
Legendre polynomials      129
Leibniz series      12
Liouville theorem on conformal mapping      140
Lyman series      204
Magnus — Oberhettinger      235
Many dimensional space, spherical wave and Green's, function in      232
Mapping, con formal through reciprocal radii      139
Marconi, G.      262
Mathieu equation      168
Maxwell, J.C.      130 135 152 247
Meander line      7
Measurement, general electrodynamic system of      237
Membrane, vibrating      166
Method of least squares      22
Mie, G., dispersion by colloidal particles      224
Misdirection and correct direction in range finding      267
Monge, theory of characteristics      37
Mott and Massey      209
Multipole, electric      149 see "Bipole" "Quadrupole" "Octupole"
Murray, F.H.      257
Navier — Stokes equation      34 292
Neumann function      90
Neumann, C. and F.      158
Newtonian potential      49 123
Nicholson, J.W.      122
Niessen, K.F.      257
Nodal lines of the vibrating membrane      170 174
Non-uniform convergence of the approximation process      12
Normal coordinates      169
Normalization of the eigenfunction in the infinite domain      210
Normalizing condition      3
Numerical distance      256
Octupole      151
Ohm G.S.      179
Ohm — Rayleigh principle      179
Ohm's law      34
Orthogonality condition      2 22 124
Oscillating membrane      33 166
Oscillating membrane, string      33
Oscillations, Free and forced      182
Ott, H.      256
Parabolic coordinates in the wave mechanical scattering problem      225
Parabolic differential equations      38 43
Partial differential equation of the second order, most general form of a linear      36
pass method      99
Perturbation theory in wave mechanics      170 188
Pipe, open and covered      291
Plane wave      84
Plate, flow, laminar, of an incompressible viscous fluid      291
Poincare, fundamental theorem of the theory of eigenfunctions      168
Poincare, fundamental theorem of the theory of eigenfunctions, domain of validity of asymptotic series      117
Poissons's equation      182
Poissons's equation, integral      138
Potential equation, in hydrodynamics      32
Potential theory, Dirichlet problem      130 186
Potential theory, Dirichlet problem Green's function for a sphere      134
Potential theory, Dirichlet problem one dimensional      291
Probability concept in wave mechanics      201 205
Quadrupole      151
Quantum number, azimuthal, radial, principal, nagnetic      202 203
Radiation condition      189
Radiation energy      270
Radio on a plane and spherical earth      236
Rainbow      224
Rainbow, Airy's theory      123
Rare gases as eight-shells      206
Rayleigh, theory of sound      179
Reciprocal radii      135
Reciprocity law      50 184
Reflection of the plane wave on the sphere      224
Relativity, special theory of, its differential equation      32
Rellich, F.      192
Renner, F.      275 277
Resonance catastrophe      187
Riemann's two-sheeted space      80
Riemann's two-sheeted space, integration of the hyperbolic differential equation      52
Riemann's two-sheeted space, problem of sound waves      164
Riemann, B.      109
Ring problem in heat conduction      71
Rutherford's model of the H atom      200 210
Rutherford's model of the H atom, formula of nuclear physics      206
Rydberg constant      201 204
s-term      206
Saddle point method      98
Saddle point method, according to Debye      116 118
Sauter, F.      192 215
Scattering, wave mechanical      206
Schlaefli      88
Schmidt, E.      184
Schoenflies, A.      81
Schroedinger, E.      166
Schroedinoer, equation      35 200
Self-adjointness, condition of      45
Semi-convergent      116
Series expansions in linear differential equations      92
Sommerfeld, A.      57 80 88 221 235
Sommerfeld, A., and Renner, F.      277
Spherical geometry      140
Spherical harmonics      123
Spherical harmonics, addition theorem of      133 146
Spherical harmonics, as special case of the hypergeometric differential equation      153
Spherical harmonics, asymptotic representation of      146
Spherical harmonics, development by      21
Spherical harmonics, difference equation      124
Spherical harmonics, differential equation of      123
Spherical harmonics, generating function of      123
Spherical harmonics, integral representation of      130
Spherical harmonics, Laplace integral of      131
Spherical harmonics, of non-integral index      155
Spherical harmonics, of the second kind      157
Spherical harmonics, of the second kind, generating function      158
Spherical harmonics, of the second kind, integral representation      158
Spherical harmonics, of the second kind, their singularity      157
Spherical harmonics, orthogonality and normalization con-dition      124
Spherical harmonics, zonal      127 131
Spherical wave      109 143
Stefan — Boltzmann law      64
Surface spherical harmonics      130
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