Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 94
... Exercises 1. Solve the problem of the temperature distribution in a slab of length L , given that the initial ... Exercise 1 approximately by considering a discrete system with three interior points . 4. Solve Exercise 2 approximately by ...
... Exercises 1. Solve the problem of the temperature distribution in a slab of length L , given that the initial ... Exercise 1 approximately by considering a discrete system with three interior points . 4. Solve Exercise 2 approximately by ...
Página 174
... Exercises 1. Verify by substitution the solution ( 12.14 ) of ( 12.10 ) . 2. Solve the differential equation ( 12.35 ) ... Exercise 3 , that 2 Σ n = 1 sin nπx sin nπx ' n2 = ( 1 - x ' ) x x < x ' -- = ( 1 − x ) x ' x > x ' and sin ( n + ...
... Exercises 1. Verify by substitution the solution ( 12.14 ) of ( 12.10 ) . 2. Solve the differential equation ( 12.35 ) ... Exercise 3 , that 2 Σ n = 1 sin nπx sin nπx ' n2 = ( 1 - x ' ) x x < x ' -- = ( 1 − x ) x ' x > x ' and sin ( n + ...
Página 223
... Exercises 1. Use the function e - c2 , where c is a constant , in the Rayleigh varia- tional principle to obtain an ... Exercise 1 of Chap . 14 . 2. Find a lower bound for the eigenvalue of Exercise VARIATIONAL ESTIMATES 223.
... Exercises 1. Use the function e - c2 , where c is a constant , in the Rayleigh varia- tional principle to obtain an ... Exercise 1 of Chap . 14 . 2. Find a lower bound for the eigenvalue of Exercise VARIATIONAL ESTIMATES 223.
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