Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 33
... normal coordinates . " A solution in which all v , but one are zero is called a normal mode . Thus , the jth normal mode is given by u ( t ) = S ̧ ̧v , ( t ) = S. , v , ( 0 ) e ^ st For the problem of Sec . 2.3 , as just considered , the ...
... normal coordinates . " A solution in which all v , but one are zero is called a normal mode . Thus , the jth normal mode is given by u ( t ) = S ̧ ̧v , ( t ) = S. , v , ( 0 ) e ^ st For the problem of Sec . 2.3 , as just considered , the ...
Página 64
... normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be considered as a special case of a Hermitian matrix . Any matrix U such that U + = U - 1 , or equivalently , U + U = UU + = 1 is ...
... normal matrices . Furthermore , any real symmetric matrix is a normal matrix , since such a matrix can be considered as a special case of a Hermitian matrix . Any matrix U such that U + = U - 1 , or equivalently , U + U = UU + = 1 is ...
Página 298
... Normal coordinate , 33 Normal matrix , 64 Normal mode , 33 Normal operator , 61 Null matrix , 11 Numerical methods , 236-242 Oberhettinger , F. , 145 , 294 Operator , adjoint , 60 , 103 in continuous systems , 96-110 , 132-135 a + , 132 ...
... Normal coordinate , 33 Normal matrix , 64 Normal mode , 33 Normal operator , 61 Null matrix , 11 Numerical methods , 236-242 Oberhettinger , F. , 145 , 294 Operator , adjoint , 60 , 103 in continuous systems , 96-110 , 132-135 a + , 132 ...
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