Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 109
... reduces to the conventional ( ordinary or partial ) differential equation Similarly , the equation D ( r ) f ( r ) = g ( r ) reduces to a f ( r , t ) = f ( r , t ) Ət 2 · f ( r , t ) = D ( r ) f ( r , t ) It is clear , therefore , that ...
... reduces to the conventional ( ordinary or partial ) differential equation Similarly , the equation D ( r ) f ( r ) = g ( r ) reduces to a f ( r , t ) = f ( r , t ) Ət 2 · f ( r , t ) = D ( r ) f ( r , t ) It is clear , therefore , that ...
Página 139
... reduces to +00 or eireir cose = Σ infn , 1 +00 eir c ir cos è = Σi " J ( r ) eino n ( 10.40 ) n = -∞ By equating the real and imaginary parts of both sides of ( 10.40 ) it is found that cos ( r cos 0 ) = Jo ( r ) + 2 Σ i ^ J „ ( r ) ...
... reduces to +00 or eireir cose = Σ infn , 1 +00 eir c ir cos è = Σi " J ( r ) eino n ( 10.40 ) n = -∞ By equating the real and imaginary parts of both sides of ( 10.40 ) it is found that cos ( r cos 0 ) = Jo ( r ) + 2 Σ i ^ J „ ( r ) ...
Página 238
... reduces to ( 1/4 ) 220 . Hence 28 is the first approximation to the exact value 2. This result is astonishingly good considering the nature of the approximation and the amount of labor involved . For n = 3 , h = 1/3 , Eq . ( 18.4 ) reduces ...
... reduces to ( 1/4 ) 220 . Hence 28 is the first approximation to the exact value 2. This result is astonishingly good considering the nature of the approximation and the amount of labor involved . For n = 3 , h = 1/3 , Eq . ( 18.4 ) reduces ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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Términos y frases comunes
approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх