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Bitsadze A.V. — Equations of Mathematical Physics
Bitsadze A.V. — Equations of Mathematical Physics



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Íàçâàíèå: Equations of Mathematical Physics

Àâòîð: Bitsadze A.V.

ßçûê: en

Ðóáðèêà: Ôèçèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 1980

Êîëè÷åñòâî ñòðàíèö: 318

Äîáàâëåíà â êàòàëîã: 25.06.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
Abel, N. H.      45 227
Abel’s integral equation      45 227
Adjoint equation      177 193
Adjoint operator      86 193
Admitted functions      303
Analytic continuation      146
Analytic function      100
Analytic function of one complex variable      98ff
Analytic function of several complex variables      165
Analytic function, of real variables      170
Angle-preserving property      106 173
Antiderivative      124
Area mass density      41
Asymptotic expansion      291
Bessel, W. F.      256 261 270 271
Bessel’s equation      259
Bessel’s equation of the first kind      259
Bessel’s equation of the second kind (or Neumann’s functions)      271
Bessel’s equation of the third kind (or Hankel’s functions)      270
Bessel’s equation, (cylindrical) functions      261
Bessel’s equation, inequality      256
Boundary condition      44
Boundary-value problem first (or Dirichlet’s)      34
Boundary-value problem first (or Dirichlet’s) with oblique derivative boundary condition      91
Boundary-value problem first (or Dirichlet’s), Poincar$\acute{e}$’s      91
Boundary-value problem first (or Dirichlet’s), second (or Neumann’s)      83 91
Boundary-value problem first (or Dirichlet’s), third (mixed)      91
Branch of a many-valued function      113
Branch point      114
Bubnov — Galerkin method      310
Bubnov, I. G.      310
Cauchy — Dirichlet problem      204ff
Cauchy — Hadamard formula      103
Cauchy — Riemann partial differential equations for two independent variables      40 97
Cauchy — Riemann partial differential equations for two independent variables for several independent variables      165
Cauchy, A. L.      40 97 103 118 150 165 168
Cauchy-type integral      124
Cauchy’s for Laplace’s equation      192
Cauchy’s, general      188ff
Cauchy’s, integral formula      121 168
Cauchy’s, principal value of a singular integral      150ff
Cauchy’s, problem (or initial-value problem)      34
Cauchy’s, theorem      118ff
Characteristic curve      21
Characteristic determinant      19
Characteristic direction      21
Characteristic form      15
Characteristic value (number)      217
Chebyshev, P. L.      261
Chebyshev’s equation      261
Chebyshev’s equation, functions      261
Chebyshev’s equation, polynomials      262
Circle of convergence      103
Circulation      38
Closed contour negatively oriented      116
Closed contour negatively oriented, positively oriented      116
Coefficient of thermal conductivity      43
Coiiformal mapping      108
Coiiformal mapping of a circle onto a circle      111
Coiiformal mapping of a half-plane onto a circle      111
Coiiformal mapping of a half-plane onto a half¬plane      110
Coiiformal mapping, angle-preserving property of      106 173
Coiiformal mapping, Gauss      173
Coiiformal mapping, in Euclidean space      172ff
Complex integration      116ff
Complex integration, of a power function      119ff
Complex vector space      163
Composite function      108
Composition formula for singular integrals      240
Condition for solvability of Neumann problem      83
conformal      87
Conjugate harmonic functions      126
Continuity principle for analytic functions      147
Convolution (or German faltung)      281
Derivative(s) of analytic function of one variable      101
Derivative(s) of analytic function of one variable of a volume potential      67ff
Derivative(s) of analytic function of one variable of analytic function of several variables      166
Derivative(s) of analytic function of one variable, normal, of a double layer potential      80
Derivative(s) of analytic function of one variable, normal, of a single-layer potential      82
Derivative(s) of analytic function of one variable, tangential, of a single-layer potential      151
Derivative(s) of analytic function of one variable, total, of an analytic function of several variables      165
Differential of an analytic function of one variable      101
Dipole      75
Dipole, axis of      75
Dipole, polarization (or dipole moment) of      75
Dirac, P. A. M.      284
Dirac’s delta function      284ff
Dirac’s delta function, principle      305
Dirac’s delta function, problem (or first boundary-value problem)      34 91
Dirichlet, P. G. L.      34 42 91 303
Dirichlet’s integral      142 303
Domain of dependence      181
Domain of dependence of influence      182
Domain of dependence of propagation of solution of wave equation      182
D’Alembert, J.      180
D’Alembert’s formula      180
Eigenfunction      218 248
Eigenvalue      248
Eigenvalue problem      305ff
Eigenvalue problem, transcendental      141
Elliptic partial differential equations      16 18 47ff
Entire function      141
Equation of oscillation of a membrane      251
Equation of oscillation of a membrane of a string      180 246
Equation of oscillation of a membrane, ff      264
Equations of mathematical physics      37
Essential singular point of an analytic function      138
Euler, L.      41 50 303
Euler’s equation      41 303
Euler’s equation, gamma function      50 272
Exponential function      114
Extended complex plane      98
Extremum principle for elliptic partial differential equations      92
Extremum principle for harmonic functions      53
Extremum principle for heat conduction equation      200
Field intensity      38
Finite-difference approximation of a differential equation      286ff
Flux through a contour      38
Force function of a field      39
Fourier, J. B. J.      43 273
Fourier’s coefficients      255
Fourier’s coefficients, inverse      273
Fourier’s coefficients, inverse transformation      273
Fourier’s coefficients, law of heat conduction      43
Fourier’s coefficients, method (or method of separation of variables)      246ff
Fourier’s coefficients, transform of a function      273
Fourier’s coefficients, transformation      273
Fredholm, E. I.      36 210 217 218 219 221
Fredholm’s of the first kind      36
Fredholm’s of the second kind      36 210
Fredholm’s of the third kind      36
Fredholm’s, alternative      221
Fredholm’s, first theorem      217
Fredholm’s, integral equation      36
Fredholm’s, second theorem      218
Fredholm’s, third theorem      219
Function(s) analytic      100
Function(s) of a complex variable      98
Function(s) of a complex variable, continuous      99
Function(s) of a complex variable, monogenic      99
Function(s), conjugate      126
Function(s), exponential      114
Function(s), Hankel’s (or Bessel’s, of the third kind)      270
Function(s), harmonic      26 47
Function(s), infinite-sheeted      115
Function(s), infinite-valued      115
Function(s), inverse      105 113
Function(s), limit of      99
Function(s), logarithmic      113
Function(s), many-sheeted      113
Function(s), many-valued      113
Function(s), meromorphic      141
Function(s), metaharmonic      259
Function(s), monogenic      99
Function(s), Neumann’s (or Bessel’s, of the second kind)      271
Function(s), one-valued      98
Function(s), power      111
Function(s), special      261
Function(s), univalent (or one-sheeted)      104
Fundamental (or elementary) solution      14
Fundamental (or elementary) solution of heat conduction equation      33
Fundamental (or elementary) solution) of Laplace’s equation      27
Fundamental (or elementary) solution), principal      94
Galerkin, B. G.      310
Gauss — Ostrogradsky formula      31
Gauss, K. F.      31 73 173
Gauss’ formula      73
Generalized potential function for a double layer      96
Generalized potential function for surface distribution of mass      95
Generalized potential function for volume distribution of mass      89
Goursat problem      192
Goursat, E.      192
Green, G.      55 87 234
Green’s function      55ff 234
Green’s function, symmetry of      55
Green’s Theorem      87
Grid-point      286
Grid-size      286
H$\ddot{o}$lder, O.      150
Hadamard, J. S.      103 192
Hamilton, R. W.      26 41
Hamiltonian operator (or nabla or del)      26
Hamilton’s principle      41
Hankel, H.      270
Hankel’s function (or Bessel’s function of the third kind)      270
Harmonic function(s)      26 47
Harmonic function(s), conjugate      126
Harmonic function(s), regular at infinity      48
Harmonic polynomial      28
Harnack, A.      64
Harnack’s theorem      64
Hartogs, F.      166
Hartogs’ theorem      166
Heat conduction equation      32 200ff
Heat conduction equation, non-homogeneous      208
Helmholtz equation      94 252
Helmholtz, H. L. F.      94 252
Hilbert, D.      240
Hilbert’s integral equation      240
Hilbert’s integral equation, inverse transformation      241
Hilbert’s integral equation, on a finite interval      243
Hilbert’s integral equation, transformation      241
Holder’s condition for a function of one variable      150
Holder’s condition for a function of one variable for a function of several variables      236
Huygens, C.      178
Huygens’ principle      178
Hyperbolic partial differential equation      16 18 176ff
Image of a point (under a mapping)      105
Image, (or transform) of a function under an integral transformation      272
Improperly posed (or not well- posed) problem      33 192
Indefinite integral      123
Infinite-sheeted function      115
Infinite-valued function      115
Initial conditions      44
Integral equation      35ff 210ff
Integral equation with kernel having logarithmic singularity      244
Integral equation, Abel’s      45 227
Integral equation, Fredholm’s      36
Integral equation, Fredholm’s, of the first kind      36
Integral equation, Fredholm’s, of the second kind      36 210
Integral equation, Fredholm’s, of the third kind      36
Integral equation, Fredholm’s, with degenerate kernel      215ff
Integral equation, Hilbert’s      240
Integral equation, linear      35
Integral equation, linear, homogeneous      35
Integral equation, linear, non-homogeneous      35
Integral equation, singular      236
Integral equation, singular, of the theory of the wing of an airplane      242
Integral equation, singular, with logarithmic singularity      244
Integral equation, Volterra’s      37
Integral equation, Volterra’s, of the first kind      226
Integral equation, Volterra’s, of the second kind      37 211
Integral equation, Volterra’s, with multiple integral      225
Integral operator      35
Integral representation of a harmonic function      50
Inverse function      105 113
inversion      84 175
Isolated singular point      138
Isolated singular point, at infinity      140
Iterative method (or method of successive approximations)      210ff
Jordan curve      76
Jordan, C.      76
Kernel of an integral equation      35
Kernel of an integral equation, Cauchy’s      240
Kernel of an integral equation, degenerate      215
Kernel of an integral equation, Hilbert’s      240
Kernel of an integral equation, iterated      219
Kernel of an integral equation, resolvent      219
Kernel of an integral equation, symmetric      224
Kirchhoff’s formula      177
Kirehhoff, G.      177
Lagrange adjoint operator      267
Lagrange, J. L.      267
Laguerre, E. N.      262
Laguerre’s equation      262
Laplace, P. S.      26 263 272
Laplace’s equation      26
Laplace’s equation, inverse      272
Laplace’s equation, nverse transform (or inverse image or the original)      272
Laplace’s equation, operator      26
Laplace’s equation, surface (spherical) harmonics      263
Laplace’s equation, transform (or image) of a function      272
Laplace’s equation, transformation      272
Laurent, P. M. H.      135
Laurent’s expansion (series)      136
Laurent’s expansion (series), principal (or singular) part of      137
Laurent’s expansion (series), regular part of      137
Laurent’s expansion (series), theorem      135
Lebesgue, H.      49
Lebesgue’s integral      49
Legendre, A. M.      264
Legendre’s equation      264
Legendre’s equation, associated      264
Legendre’s equation, functions      264
Leibniz, G. W.      124
Limiting values of Cauchy-type integral      154ff
Linear partial differential equation      14
Linear-fractional function      102
Liouville, J.      63 134 247
Liouville’s theorem for analytic functions      134
Liouville’s theorem for analytic functions for harmonic functions      63
Lyapunov curve      158
Lyapunov, A. M.      158
Maximum Modulus Principle      127
Mean-square deviation      255
Mean-value formula for a ball      53
Mean-value formula for a ball for a sphere      53
Mellin, R. H.      274
Mellin’s, inverse      275
Mellin’s, transform of a function      275
Mellin’s, transformation      274
Meromorphic function      141
Metaharmonic equation      259
Metaharmonic function      259
Method(s) of separation of variables (or Fourier’s method)      246ff
Method(s), finite-difference      286ff
Method(s), of integral transformations      266ff
Method(s), saddle-point      301
Method(s), variational      303
Minimizing sequence      307
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