Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 29
... Step 3 Express the given u ( 0 ) as a linear combination of the eigencolumns of A. That is , find x such that u ( 0 ) = SX = M i = 0 Step 4 Write down the answer : u ( t ) = eu ( 0 ) = e11sx = serey x = A slightly different form for steps ...
... Step 3 Express the given u ( 0 ) as a linear combination of the eigencolumns of A. That is , find x such that u ( 0 ) = SX = M i = 0 Step 4 Write down the answer : u ( t ) = eu ( 0 ) = e11sx = serey x = A slightly different form for steps ...
Página 30
... step 3a , in place of sr = 1 , one finds the matrix d1r such that sd d - 1r = 1 . The answer , as given in step 4a , becomes sded - 1r . But e ^ is a diagonal matrix and all diagonal matrices commute with each other ( two matrices p and ...
... step 3a , in place of sr = 1 , one finds the matrix d1r such that sd d - 1r = 1 . The answer , as given in step 4a , becomes sded - 1r . But e ^ is a diagonal matrix and all diagonal matrices commute with each other ( two matrices p and ...
Página 31
Gerald Goertzel, Nunzio Tralli. Step 3 whence Step 4 SX = 1 u ( t ) = Σ § ̧¡e1 ‚ ¢ ( ^ ) ( ^ ) x = 1/2 = = u ( 0 ) · $ ( c + d ) - = ( 2 ) = 11 / 2 ( c + d ) + This is the result found in Sec . 2.3 . Alternately , steps 3a and 4a may be ...
Gerald Goertzel, Nunzio Tralli. Step 3 whence Step 4 SX = 1 u ( t ) = Σ § ̧¡e1 ‚ ¢ ( ^ ) ( ^ ) x = 1/2 = = u ( 0 ) · $ ( c + d ) - = ( 2 ) = 11 / 2 ( c + d ) + This is the result found in Sec . 2.3 . Alternately , steps 3a and 4a may be ...
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