Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 38
... means of the Cauchy - integral formula from complex variable theory.1 f ( A ) = 1 f ( Z ) dz 2πi Jc Z A ( 3.1 ) This ... mean ZI – A where I and A are square matrices of the same order and Z is a scalar . This convention will be used in ...
... means of the Cauchy - integral formula from complex variable theory.1 f ( A ) = 1 f ( Z ) dz 2πi Jc Z A ( 3.1 ) This ... mean ZI – A where I and A are square matrices of the same order and Z is a scalar . This convention will be used in ...
Página 44
... means of ( 3.8 ) yields ( Z — A ) U ( Z ) = u ( 0 ) ( 3.11a ) U ( z ) = √ ܣ e4te - Ztu ( 0 ) dt = So e - Ztu ( t ) dt ( 3.12 ) The pair of relations u ( t ) U ( Z ) = = 1 § eztU ( Z ) dz 2πί e - Ztu ( t ) dt define an equivalence ...
... means of ( 3.8 ) yields ( Z — A ) U ( Z ) = u ( 0 ) ( 3.11a ) U ( z ) = √ ܣ e4te - Ztu ( 0 ) dt = So e - Ztu ( t ) dt ( 3.12 ) The pair of relations u ( t ) U ( Z ) = = 1 § eztU ( Z ) dz 2πί e - Ztu ( t ) dt define an equivalence ...
Página 97
... means other than the matrix L. Thus , in Chap . 6 it was found more convenient to define L by the relation g ( i ) = μ 82ƒ ( i ) = μ [ ƒ ( i + 1 ) − 2ƒ ( i ) + ƒ ( i − 1 ) ] with the boundary conditions1 f ( 0 ) = f ( n + 1 ) = 0 on ...
... means other than the matrix L. Thus , in Chap . 6 it was found more convenient to define L by the relation g ( i ) = μ 82ƒ ( i ) = μ [ ƒ ( i + 1 ) − 2ƒ ( i ) + ƒ ( i − 1 ) ] with the boundary conditions1 f ( 0 ) = f ( n + 1 ) = 0 on ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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Términos y frases comunes
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