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 ...
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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