Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página ix
... Domain , - -∞0 < x < + ∞ 9.4 The Finite Domain , 0 ≤x≤L . 112 9.3 The Semi - infinite Domain , 0 ≤ x < + ∞ 116 119 9.5 The Circular Domain 9.6 The Method of Images 122 123 Chapter 10 The Laplacian ( V2 ) in Two Dimensions 10.1 ...
... Domain , - -∞0 < x < + ∞ 9.4 The Finite Domain , 0 ≤x≤L . 112 9.3 The Semi - infinite Domain , 0 ≤ x < + ∞ 116 119 9.5 The Circular Domain 9.6 The Method of Images 122 123 Chapter 10 The Laplacian ( V2 ) in Two Dimensions 10.1 ...
Página 112
... domain , 0 ≤ x ≤ L The boundary conditions on the functions f ( x , t ) in this domain are af дх дf = C1f ( 0 , t ) and = C2f ( L , t ) x = 0 дх x = L where C1 and C2 are constants . 4. The circular domain In this domain the boundary ...
... domain , 0 ≤ x ≤ L The boundary conditions on the functions f ( x , t ) in this domain are af дх дf = C1f ( 0 , t ) and = C2f ( L , t ) x = 0 дх x = L where C1 and C2 are constants . 4. The circular domain In this domain the boundary ...
Página 297
... domain , 122-123 in finite domain , 119-122 in infinite domain , 112-116 in semi - infinite domain , 116-119 three - dimensional , 146-163 two - dimensional , 128-145 Legendre functions , associated , 154 Rodrigue's formula for , 154 ...
... domain , 122-123 in finite domain , 119-122 in infinite domain , 112-116 in semi - infinite domain , 116-119 three - dimensional , 146-163 two - dimensional , 128-145 Legendre functions , associated , 154 Rodrigue's formula for , 154 ...
Contenido
Perturbation of Eigenvalues | 14 |
The Laplacian v2 in One Dimension | 18 |
Solution for Diagonalizable Matrices | 21 |
Derechos de autor | |
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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