Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página ix
... Domain , 0 ≤ x ≤ L. 9.5 The Circular Domain 9.6 The Method of Images 105 • 107 108 111 111 112 0 ≤ x < + ∞ 116 119 122 123 Chapter 10 The Laplacian ( v2 ) in Two Dimensions 128 • 10.1 Introduction 128 10.2 Conduction of Heat in an ...
... Domain , 0 ≤ x ≤ L. 9.5 The Circular Domain 9.6 The Method of Images 105 • 107 108 111 111 112 0 ≤ x < + ∞ 116 119 122 123 Chapter 10 The Laplacian ( v2 ) in Two Dimensions 128 • 10.1 Introduction 128 10.2 Conduction of Heat in an ...
Página 112
... domain , 0 ≤ x ≤ L The boundary conditions on the functions f ( x , t ) in this domain are af дх af = C1f ( 0,1 ) and = C2f ( L , t ) дх x = L x = 0 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 af = C1f ( 0,1 ) and = C2f ( L , t ) дх x = L x = 0 where C1 and C2 are constants . 4. The circular domain In this domain the boundary ...
Página 119
... domain contains , for 2 < 0 , the isolated point eigenvalue 2a as well as the continuous set -w2 , all w real and positive . 9.4 The Finite Domain , 0 ≤ x ≤ L Consider the Laplacian d2 / əx2 in the finite domain 0 ≤ x ≤ L for such ...
... domain contains , for 2 < 0 , the isolated point eigenvalue 2a as well as the continuous set -w2 , all w real and positive . 9.4 The Finite Domain , 0 ≤ x ≤ L Consider the Laplacian d2 / əx2 in the finite domain 0 ≤ x ≤ L for such ...
Contenido
34 | 12 |
Solution for Diagonalizable Matrices | 21 |
The Evaluation of a Function of a Matrix for an Arbitrary Matrix | 38 |
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approximation arbitrary ax² basis Bessel functions boundary conditions Chap coefficients column consider constant continuous systems contour coordinates corresponding cylindrical functions d²/dx² defined definition denoted determinant diagonal differential equation Dirac notation domain eigencolumns eigenfunctions eigenvectors elements evaluate expansion F₁ finite number follows formula Fourier given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral inverse Laplacian linear operator linearly independent lowest eigenvalue Mathematical matrix McGraw-Hill Book Company method multiplication nonsingular normal number of degrees obtained orthonormality conditions Physics problem relations representation result Ritz method scattering sinh solution solve spherical spherical harmonics string Substitution theorem transform trial functions vanish variable vector space Verify w₁ wave write written x₁ Y₁ yields York zero ηπχ ди ду дх