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 |
The Laplacian V² in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
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approximate arbitrary asymptotic ax² base vectors basis Bessel functions boundary conditions Chap coefficients consider constant continuous systems contour corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation eigen eigencolumns eigenfunctions eigenvalue problem eigenvectors elements evaluate expansion finite number follows formula given Green's function Hence Hermitian matrix Hermitian operator infinite integral representation integral theorem inverse Laplace transform linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company method multiplication nonsingular normal matrix obtained orthonormality conditions perturbation procedure relations result Ritz method satisfies scattering sinh solution solve spherical substitution transformation functions trial functions vanish variable vector space Verify wave whence write written x₁ y₁ yields York zero ηπχ παχ ди ду дх