Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 121
... string , take the string as lying along the x axis from x = 0 to x = L and denote by y ( x , t ) the displacement at right angles to the axis at any point x at any time t . The equation of motion is 22 a12 y ( x , t ) = c2 22 ax2 y ( x ...
... string , take the string as lying along the x axis from x = 0 to x = L and denote by y ( x , t ) the displacement at right angles to the axis at any point x at any time t . The equation of motion is 22 a12 y ( x , t ) = c2 22 ax2 y ( x ...
Página 206
... String As an application of the procedure described above , consider the variation in frequency and shape of a string whose mass per unit length is varied from its original condition of uniformity . The string is taken as extending ...
... String As an application of the procedure described above , consider the variation in frequency and shape of a string whose mass per unit length is varied from its original condition of uniformity . The string is taken as extending ...
Página 237
... string lie along the x axis in the region 0 ≤ x ≤ a , and let the density distribution be denoted by p ( x ) . Then , the actual string might be approximated by a weightless string loaded with n masses m , at the points Xi = ih h i ...
... string lie along the x axis in the region 0 ≤ x ≤ a , and let the density distribution be denoted by p ( x ) . Then , the actual string might be approximated by a weightless string loaded with n masses m , at the points Xi = ih h i ...
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