Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 109
... differential operator of the form D ( r ) = αV2 + ß where a and ẞ are constants and V2 is the Laplacian operator 2 ... equation Lf ( r ) = g ( r ) reduces to the conventional ( ordinary or partial ) differential equation Similarly , the ...
... differential operator of the form D ( r ) = αV2 + ß where a and ẞ are constants and V2 is the Laplacian operator 2 ... equation Lf ( r ) = g ( r ) reduces to the conventional ( ordinary or partial ) differential equation Similarly , the ...
Página 141
... differential equation for the circular membrane is the same as for the rectangular one , but the boundary condition is different : the trans- verse displacement y is always zero on a circle of radius p about the origin . To solve the ...
... differential equation for the circular membrane is the same as for the rectangular one , but the boundary condition is different : the trans- verse displacement y is always zero on a circle of radius p about the origin . To solve the ...
Página 174
... differential equation ( 12.35 ) and verify that the solution is identical with ( 12.37 ) and ( 12.38 ) . 3. Consider the differential equation ď2 dx2 Lf ( x ) = === f ( x ) = s ( x ) 0 ≤ x ≤1 where s ( x ) is given . Then show by the ...
... differential equation ( 12.35 ) and verify that the solution is identical with ( 12.37 ) and ( 12.38 ) . 3. Consider the differential equation ď2 dx2 Lf ( x ) = === f ( x ) = s ( x ) 0 ≤ x ≤1 where s ( x ) is given . Then show by the ...
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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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