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Goertzel G. Ч Some Mathematical Methods of Physics
Goertzel G. Ч Some Mathematical Methods of Physics

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Ќазвание: Some Mathematical Methods of Physics

јвтор: Goertzel G.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1960

 оличество страниц: 312

ƒобавлена в каталог: 09.12.2012

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$RC$ line      73Ч78 85Ч92
Abstract vector spaces      50Ч66
Abstract vector spaces, Dirac notation for      67Ч72
Addition of matrices      10
Addition theorem, for Bessel functions      292Ч293
Addition theorem, for spherical harmonics      161
Adjoint of matrix, Hermitian      56 80 103Ч104
Adjoint operator      60 103
Aitken, A. C.      20
Amplitude, scattering      184
Analytic function      254
Analytic function, derivatives of      254Ч255
Analytic function, poles of      257
Analytic function, singularities of      256Ч257
Approximate methods, for determining eigenfunctions      215Ч223
Approximate methods, for determining eigenvalues      201Ч208 212Ч223
Approximation, Born      190Ч192
Associated Legendre functions      154
Asymptotic expansions      287Ч291
Asymptotic series, of Debye      281Ч292
Asymptotic series, of Hankel      291
Base vectors      52Ч54
Basis      52Ч54
Basis, change of      55Ч57 68 100Ч103
Basis, formation of      61Ч63
BauerТs formula      161
Bessel functions      135Ч142 280Ч281 283Ч287 290-293
Bessel functions, addition theorem for      292Ч293
Bessel functions, asymptotic behavior of      291
Bessel functions, generating function for      139
Bessel functions, integral representation of      280Ч281 283Ч284
Bessel functions, orthogonality of      140
Bessel functions, recurrence formulas for      135Ч136
Bessel functions, roots, table of      142
Bessel functions, series expansion for      286Ч287
Bessel functions, spherical      157
Bessel functions, spherical, recurrence formulas for      157
Bessel, equation of      134 280
Bethe, H.      154 159
Bi-orthonormality condition      54
Bierbach, L.      260
Biot, M. A.      20 232
Born approximation      190Ч192
Born, M.      190
boundary conditions      75 86Ч91
Bra      67
Bragg factor      194
Branch point      257
Byerly, W. E.      164
Campbell, G. A.      49 279
Carslaw, H. S.      49 127 279
Cauchy integral formula      38 257Ч 258
Cauchy integral theorem      255Ч256
Cauchy integral theorem, corollary of      256
Cauchy Ч Riemann equations      255
Change, of basis      55Ч57 68 100Ч103
Change, of variable      32Ч34
Characteristic equation      27
Characteristic function (eigenfunction)      104Ч105
Characteristic value      see Eigenvalue
Churchill, R. V.      49 279
Circular membrane      141Ч143
Collar, A. R.      20 232
Commutation rules      19 133 135 148 149
Commuting observables, complete set of      72 133 148
Commuting observables, matrices      30
Commuting observables, operators      133
Completeness      24Ч27 61Ч63
Complex variables, functions of      254Ч260
Condon, E. U.      154 159
Convolution theorem      47Ч48
Cooke, R. G.      66
Coordinate system      see Basis
Coordinate transformations      100Ч103 (see also Basis change
Copson, E. T.      260
Corson, E. M.      72
Cosine Fourier series      275
Cosine Fourier transform      269 275
Courant, R.      175 210 224 260
CramerТs Rule      248
Cross section, differential scattering      184
Cylindrical functions      134 280Ч294
Cylindrical functions, integral representation of      280Ч286
Cylindrical functions, recurrence formulas for      135Ч136
Cylindrical functions, theorems on      134Ч140 (see also Bessel functions)
Debye, P.      291 292
Degenerate matrix      26
Delta function      98Ч100
Delta, Kronecker      12
Determinant      14Ч15 24 251
Determinant, of matrix product      15 250Ч251
Diagonal matrix      7
Diagonalization of matrix      26Ч27 64
Difference equation      75
Difference equation, from variational principle      239Ч241
Difference operator      79Ч80
Difference operator, adjoint of      80
Differential operator      108Ч109
Differential scattering cross section      184
Diffraction, order of      196
Dirac delta function      98Ч100
Dirac notation      67Ч72
Dirac, P. A. M.      67 72 100 110
Doetsch, G.      49
Dual vector space      53
Duncan, W. J.      20 232
Dyad      51
Eigencolumns      22
Eigencolumns, complete set of      25
Eigenfunctions, of Legendrian      152Ч154
Eigenfunctions, orthogonality of      104Ч105
Eigenvalue problems, construction of      233Ч235
Eigenvalue, for matrix      22
Eigenvalue, for operator      60 70
Eigenvalue, of Hermitian operator      71 104
Eigenvalue, of Legendrian      149Ч151
Eigenvector      60 70
Emde, F.      142 145 294
Essential singularity      257
Expansion theorem      54
Expansions, asymptotic      287Ч291
Expansions, Fourier Ч Bessel      276Ч279
Expansions, multipole      179Ч180
Factorization of operators      132 155Ч156
Feshbach, H.      66 95 110 127 164 175 197 210 224 232
Formation of basis      61Ч63
Foster, R. M.      49 279
Fourier integral      268Ч272
Fourier series      272Ч275
Fourier series, cosine      275
Fourier transform      92 266Ч275
Fourier transform, cosine      269 275
Fourier Ч Bessel expansion      276Ч279
Fourier Ч Bessel integral      275Ч276
Fourier Ч Bessel transform      276
Frank, N. H.      95
Frazer, R. A.      20 232
Generating functions for Bessel functions      139
Gratings      192Ч196
Gray, A.      145 294
GreenТs function      165Ч175
GreenТs function, direct method of finding      168
GreenТs function, eigenfunction expansion for      166Ч 167
GreenТs Theorem      277
Grimshaw, M. E.      66
Halmos, P. R.      66
Hamburger, H. L.      66
Hankel function      284Ч286
Hankel function, asymptotic expansion of      291
Hankel function, integral representation of      285
Hankel function, spherical      157
Hankel transform      276
HankelТs asymptotic series      291
harmonic oscillator      4 45 46 50
Harmonics, spherical      153
Heat conduction, in infinite bar      113Ч114
Heat conduction, in infinite plate      128Ч134 140Ч141
Heat conduction, in infinite solid      163
Heaviside step function      99
Heaviside, O.      100
Heine, E.      164
Heitler, W.      154
Helmholtz equation      183
Hermitian adjoint of matrix      56 80 103Ч104
Hermitian matrix      64
Hermitian operator      70
Hermitian operator, eigenvalues of      71 104
Hermitian operator, eigenvectors for      105
Hermitian operator, theorems on      70Ч72
Hilbert, D.      175 210 224
Hildebrand, F. B.      232
Hobson, E. W.      164
Hull, T. E.      164
Hurwitz, A.      260
Identity matrix      11
Identity operator      60
Images, method of      123Ч126
Ince, E. L.      175
Infeld, L.      164
Integral formulas, Cauchy      38 257Ч258
Integral representation, for Bessel functions      280Ч281 283Ч284
Integral representation, for cylindrical functions      281Ч283
Integral representation, for Hankel functions      285
Integral theorem, Cauchy      255Ч256
Interference pattern      194
Inverse matrix      16
Inverse operator      165
Inversion formula, Laplace      44
Iteration procedures      225Ч232
Jaeger, J. C.      49 127
Jahnke, E.      142 145 294
Jeffreys, B. S.      20 256
Jeffreys, H.      20 256
K$\acute{a}$rm$\acute{a}$n, T. von      20 232
Kernel of operator      98
Ket      67
Kohn, W.      213
Kronecker delta      12
Laplace inversion formula      44
Laplace transform      44Ч45
Laplace transform, convolution theorem for      47
Laplacian      111 129 132 147
Laplacian, one-dimensional      111 127
Laplacian, one-dimensional, in circular domain      122Ч123
Laplacian, one-dimensional, in finite domain      119Ч122
Laplacian, one-dimensional, in infinite domain      112Ч116
Laplacian, one-dimensional, in semi-infinite domain      116Ч119
Laplacian, three-dimensional      146Ч163
Laplacian, two-dimensional      128Ч145
Legendre functions, associated      154
Legendre functions, RodrigueТs formula for      154
Legendre operator      see Legendrian
Legendrian      148
Legendrian, eigenfunctions of      152Ч154
Legendrian, eigenvalues of      149Ч151
Lense, J.      164
Linear equation      7
Linear independence      17
Linear operator      57
Linear operator, representation by matrix      57Ч60 69
Loaded string      78Ч79 241Ч242
MacDonald, J. K. L.      213
MacRobert, T. M.      145 164 294
Magnus, W.      145 294
Margenau, H.      20
Massey, H. S. W.      197
Mathews, G. B.      145 294
Matrices, addition of      10
Matrices, commuting      30
Matrices, diagonalization of      27Ч28
Matrices, equality of      10
Matrices, multiplication of      10Ч13
Matrix      7
Matrix, adjoint      56
Matrix, antisymmetric      8
Matrix, characteristic equation of      27
Matrix, conjugate transpose      56
Matrix, degenerate      26
Matrix, derivative of      10
Matrix, determinant of      see Determinant
Matrix, diagonal      7
Matrix, diagonalizable      26Ч27 64
Matrix, eigencolumns of      22
Matrix, eigenvalues of      22
Matrix, elements of      7
Matrix, function of      22Ч26 38Ч43
Matrix, hermitian      64
Matrix, Hermitian adjoint      56 80 103Ч104
Matrix, identity      11
Matrix, inverse of      16
Matrix, nondegenerate      27
Matrix, nonsingular      16
Matrix, normal      64
Matrix, notation      7Ч9
Matrix, null      11
Matrix, orthogonal      56
Matrix, positive definite      217
Matrix, rank of      18 249
Matrix, reciprocal of      see Inverse of above
Matrix, rectangular      7
Matrix, secular equation of      27
Matrix, singular      14
Matrix, skew-symmetric      8
Matrix, spectral representation of      26
Matrix, spectrum of      26
Matrix, square      7
Matrix, symmetric      8
Matrix, transpose of      15
Matrix, unit      11
Matrix, unitary      56 64
Matrix, zero      11
McLachlan, N. W.      49 145 294
Membrane, circular      141Ч143
Membrane, circular ring      143
Membrane, circular sector      143Ч144
Membrane, rectangular      130Ч131
Method, of images      123Ч126
Method, of partial waves      185Ч188
Method, of steepest descent      288
Method, pass      288
Methods, numerical      236Ч242
Monogenic function      254
Morse, P. M.      66 95 110 127 164 175 197 210 224 232
Mott, N. F.      197
Multiplication of matrices      10Ч13
Multipole expansion      179Ч180
Murphy, G. M.      20
Neumann function      285
Neumann function, asymptotic behavior of      290Ч291
Neumann function, spherical      157
Neumann, J. von      66
Nielsen, N.      145 293
Nondegenerate matrix      27
Nonsingular matrix      16
Normal coordinate      33
Normal matrix      64
Normal mode      33
Normal operator      61
Null matrix      11
Numerical methods      236Ч242
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