Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 29
... procedure will be applied to two examples . Step 1 Find the eigenvalues of A. That is , find the roots λ1 , λ2 , . characteristic equation Step 2 | 24 | = 0 An of the Find the eigencolumns of A. That is , solve the n sets of equations ...
... procedure will be applied to two examples . Step 1 Find the eigenvalues of A. That is , find the roots λ1 , λ2 , . characteristic equation Step 2 | 24 | = 0 An of the Find the eigencolumns of A. That is , solve the n sets of equations ...
Página 40
... procedure : a . Find q ( Z ) = ( Z - A ) -1 by solving the matrix equation 1 ( Z — A ) q ( Z ) = 1 b . Find f1 , ( A ) ... procedure is illustrated by the following three examples : Example 1 1- ( 9 ) A = According to step a in the ...
... procedure : a . Find q ( Z ) = ( Z - A ) -1 by solving the matrix equation 1 ( Z — A ) q ( Z ) = 1 b . Find f1 , ( A ) ... procedure is illustrated by the following three examples : Example 1 1- ( 9 ) A = According to step a in the ...
Página 141
... procedure 1 . 10.7 The Circular 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 ...
... procedure 1 . 10.7 The Circular 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 ...
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