Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 130
... Membrane In the preceding section the operator V2 = d2 / dx2 + d2 / ǝy2 was studied in the infinite domain -∞ < x , y < + ∞o . The problem of the vibrating rectangular membrane whose equilibrium shape is a plane sheet furnishes one ...
... Membrane In the preceding section the operator V2 = d2 / dx2 + d2 / ǝy2 was studied in the infinite domain -∞ < x , y < + ∞o . The problem of the vibrating rectangular membrane whose equilibrium shape is a plane sheet furnishes one ...
Página 141
... Membrane 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 ...
... Membrane 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 ...
Página 300
... membrane , 143 Vibrating circular sector membrane , 143-144 Vibrating rectangular membrane , 130-131 Vibrating string , 93-94 , 121 , 206 , 213-215 , 221-223 , 236-239 Watson , G. N. , 145 , 294 Wave equation , one - dimensional , 115 ...
... membrane , 143 Vibrating circular sector membrane , 143-144 Vibrating rectangular membrane , 130-131 Vibrating string , 93-94 , 121 , 206 , 213-215 , 221-223 , 236-239 Watson , G. N. , 145 , 294 Wave equation , one - dimensional , 115 ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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Términos y frases comunes
approximate arbitrary ax² basis Bessel function boundary conditions chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined denoted determinant diagonal differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector eikr evaluate expansion finite number follows Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplace transform Laplacian linear operator linearly independent lowest eigenvalue matrix membrane method multiplication nonsingular normal obtained orthonormality conditions plane problem procedure relations representation result satisfies the boundary scattering sinh solve spherical spherical harmonics string Substitution theorem trial functions vanish variable vector space Verify wave write written y₁ yields York zero ηπχ πο ποχ ди ду дх