Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 36
... Solve Eq . ( 1.13 ) . 5. Solve Eq . ( 1.14 ) . 6. Solve Eq . ( 1.15 ) . 7. Let SAS - 1 315 ( 3 ) " 1 M = 000 100 0 1 0 If f ( x ) has a convergent power series about x = O , show that f ( M ) = f ( 0 ) + Mƒ ' ( 0 ) + M2 2 ! -ƒ " ( 0 ) 8 ...
... Solve Eq . ( 1.13 ) . 5. Solve Eq . ( 1.14 ) . 6. Solve Eq . ( 1.15 ) . 7. Let SAS - 1 315 ( 3 ) " 1 M = 000 100 0 1 0 If f ( x ) has a convergent power series about x = O , show that f ( M ) = f ( 0 ) + Mƒ ' ( 0 ) + M2 2 ! -ƒ " ( 0 ) 8 ...
Página 48
... Solve the equations 4. Solve the equations 37 ( 19 ) " 3 x = ẞdx - B2y βδχ βγ y = 82x dẞy δβν ― x = ax + By + 1 j = Bx tay +1 x ( 0 ) = y ( 0 ) = 0 5. Solve by the Laplace transform method Eqs . ( 48 SYSTEMS WITH A FINITE NUMBER OF ...
... Solve the equations 4. Solve the equations 37 ( 19 ) " 3 x = ẞdx - B2y βδχ βγ y = 82x dẞy δβν ― x = ax + By + 1 j = Bx tay +1 x ( 0 ) = y ( 0 ) = 0 5. Solve by the Laplace transform method Eqs . ( 48 SYSTEMS WITH A FINITE NUMBER OF ...
Página 94
... Solve the problem of the temperature distribution in a slab of length L , given that the initial temperature is an arbitrary function of x , but that at all times after t O the two faces ( at x maintained at temperature T = 0 . = = 0 ...
... Solve the problem of the temperature distribution in a slab of length L , given that the initial temperature is an arbitrary function of x , but that at all times after t O the two faces ( at x maintained at temperature T = 0 . = = 0 ...
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