Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 94
... considering a discrete system with three interior points . 4. Solve Exercise 2 approximately by considering a discrete system with three interior points . 5. Consider the system shown below : XX Pin joint 94 SYSTEMS WITH AN INFINITE ...
... considering a discrete system with three interior points . 4. Solve Exercise 2 approximately by considering a discrete system with three interior points . 5. Consider the system shown below : XX Pin joint 94 SYSTEMS WITH AN INFINITE ...
Página 174
... Consider the differential equation d2 Lf ( x ) = = + = + = + f ( x ) = s ( x ) 0≤ x ≤1 dx2f ( x ) where s ( x ) is given . Then show by the direct method that ( a ) the Green's function for the operator and the associated boundary ...
... Consider the differential equation d2 Lf ( x ) = = + = + = + f ( x ) = s ( x ) 0≤ x ≤1 dx2f ( x ) where s ( x ) is given . Then show by the direct method that ( a ) the Green's function for the operator and the associated boundary ...
Página 213
... consider the approximate evaluation of the lowest eigenvalue ( 21 = 2 ) of the vibrating string problem d2 dx2 = y -λy y ( 0 ) = y ( 1 ) = 0 A simple function which satisfies the boundary conditions is the parabola y = x ( 1 − x ) ...
... consider the approximate evaluation of the lowest eigenvalue ( 21 = 2 ) of the vibrating string problem d2 dx2 = y -λy y ( 0 ) = y ( 1 ) = 0 A simple function which satisfies the boundary conditions is the parabola y = x ( 1 − x ) ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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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