Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página ix
... Infinite Insulated Plate . Cartesian Coordinates • 128 10.3 The Vibrating Rectangular Membrane . 130 10.4 Conduction of Heat in an Infinite Insulated Plate ; Plane Polar Coordinates 131 10.5 Theorems on Cylindrical Functions ( of ...
... Infinite Insulated Plate . Cartesian Coordinates • 128 10.3 The Vibrating Rectangular Membrane . 130 10.4 Conduction of Heat in an Infinite Insulated Plate ; Plane Polar Coordinates 131 10.5 Theorems on Cylindrical Functions ( of ...
Página 122
... infinite , approach those of Sec . 9.3 for & becoming infinite . In particular , ( 9.36 ) may be written as ( with w1 == nπ / L ) d ( x − x ' ) - Σ - 2 n = 1 L 200 = - sin wax sin wax ' Σ ( n + 1 π n = 1 which becomes , for infinite L ...
... infinite , approach those of Sec . 9.3 for & becoming infinite . In particular , ( 9.36 ) may be written as ( with w1 == nπ / L ) d ( x − x ' ) - Σ - 2 n = 1 L 200 = - sin wax sin wax ' Σ ( n + 1 π n = 1 which becomes , for infinite L ...
Página 297
... infinite bar , 113-114 in infinite plate , 128-134 , 140-141 in infinite solid , 163 Heaviside , O. , 100 Heaviside step function , 99 Heine , E. , 164 Heitler , W. , 154 Helmholtz equation , 183 Hermitian adjoint of matrix , 56 , 80 ...
... infinite bar , 113-114 in infinite plate , 128-134 , 140-141 in infinite solid , 163 Heaviside , O. , 100 Heaviside step function , 99 Heine , E. , 164 Heitler , W. , 154 Helmholtz equation , 183 Hermitian adjoint of matrix , 56 , 80 ...
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