Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 78
... formal solution of ( 6.4 ) as given in ( 6.7 ) one has e , ( t ) = 2 n + 1 = 1 n Σ sin πίσ n e n + 1 + at Σ sin Lk = 1 n + 1 πκσ ex ( 0 ) πα + μ sin ́e ̄ * o * E ( S ) ds n + 1 0 πο = - 2 cos n + 1 . ( 6.21 ) 6.4 The Loaded String If ...
... formal solution of ( 6.4 ) as given in ( 6.7 ) one has e , ( t ) = 2 n + 1 = 1 n Σ sin πίσ n e n + 1 + at Σ sin Lk = 1 n + 1 πκσ ex ( 0 ) πα + μ sin ́e ̄ * o * E ( S ) ds n + 1 0 πο = - 2 cos n + 1 . ( 6.21 ) 6.4 The Loaded String If ...
Página 129
... formal solution of ( 10.1 ) is T ( x , y , t ) = eav11T ( x , y , 0 ) ( 10.2 ) To write the solution explicitly one must determine the eigenvalues and eigenfunctions belonging to the operator V2 . Denote these by -2 and f ( x , y ) ...
... formal solution of ( 10.1 ) is T ( x , y , t ) = eav11T ( x , y , 0 ) ( 10.2 ) To write the solution explicitly one must determine the eigenvalues and eigenfunctions belonging to the operator V2 . Denote these by -2 and f ( x , y ) ...
Página 140
... formal solution to the heat - conduction equation ( 10.17 ) is T ( r , 0 , t ) = eav2tT ( r , 0,0 ) ( 10.51 ) Since the eigenfunctions of the operator V2 in the domain 0 ≤r < ∞ , 002 and their inverses are now known [ expressions ...
... formal solution to the heat - conduction equation ( 10.17 ) is T ( r , 0 , t ) = eav2tT ( r , 0,0 ) ( 10.51 ) Since the eigenfunctions of the operator V2 in the domain 0 ≤r < ∞ , 002 and their inverses are now known [ expressions ...
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