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 2 e , ( 1 ) = 2 sin πίσ πισ Σ sin ex ( 0 ) n + 1. = 1 n + 1 n + 1 πο μ + a sin ( s ) ds n + λ = −μ ( 2 — : πα - 2 cos n + ( 6.21 ) 6.4 The Loaded String If one has a string of ...
... formal solution of ( 6.4 ) as given in ( 6.7 ) one has 2 e , ( 1 ) = 2 sin πίσ πισ Σ sin ex ( 0 ) n + 1. = 1 n + 1 n + 1 πο μ + a sin ( s ) ds n + λ = −μ ( 2 — : πα - 2 cos n + ( 6.21 ) 6.4 The Loaded String If one has a string of ...
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 -w 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 -w and f ( x , y ) ...
Página 140
... formal solution to the heat - conduction equation ( 10.17 ) is T ( r , 0 , t ) = eav31T ( 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 ) = eav31T ( 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
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