Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 13
... specified relative to the position of the specified index ( ¡ in this case ) . Using this notation , one has as the rule for forming the product of two matrices 1.6 Warnings ( mp ) ,; = m¡.P.3 ( 1.39 ) The use of the same notation for ...
... specified relative to the position of the specified index ( ¡ in this case ) . Using this notation , one has as the rule for forming the product of two matrices 1.6 Warnings ( mp ) ,; = m¡.P.3 ( 1.39 ) The use of the same notation for ...
Página 75
... specified if and only if , given arbitrary x , y = Mx is known . Either from ( 6.1 ) , ( 6.2 ) , and ( 6.3 ) or from ( 6.5 ) it is clear that Y1 = μ ( x ; −1 — 2x ; + xi + 1 ) Y1 = μ ( x - x1 ) — μsX1 Yn = μ ( xn − 1 - Xn ) — μ LX n i ...
... specified if and only if , given arbitrary x , y = Mx is known . Either from ( 6.1 ) , ( 6.2 ) , and ( 6.3 ) or from ( 6.5 ) it is clear that Y1 = μ ( x ; −1 — 2x ; + xi + 1 ) Y1 = μ ( x - x1 ) — μsX1 Yn = μ ( xn − 1 - Xn ) — μ LX n i ...
Página 236
... specified ) function of position along the string . If one adopts the viewpoint that the precise form of the density variation along the string is unimportant , he may replace the arbitrary given density distribution by a distribution ...
... specified ) function of position along the string . If one adopts the viewpoint that the precise form of the density variation along the string is unimportant , he may replace the arbitrary given density distribution by a distribution ...
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