Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 5
... solving the equa- tions of motion suggests itself : What solutions exist in which the depend- ent variables do not ... solved for prescribed values of FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 5 Standardization of Notation.
... solving the equa- tions of motion suggests itself : What solutions exist in which the depend- ent variables do not ... solved for prescribed values of FORMULATION OF THE PROBLEM AND DEVELOPMENT OF NOTATION 5 Standardization of Notation.
Página 6
... solved is characterized by its form , as given in ( 1.11 ) , by the number of dependent variables n , and by the n2 numbers m1 ,, i , and jtaking on the n values 1 , 2 , . . . , n 1 , n independently . As can be seen from the examples ...
... solved is characterized by its form , as given in ( 1.11 ) , by the number of dependent variables n , and by the n2 numbers m1 ,, i , and jtaking on the n values 1 , 2 , . . . , n 1 , n independently . As can be seen from the examples ...
Página 87
... solving the latter ( discrete ) problem might be expected , in the limit as Ax → 0 , to lead to a procedure for solving ... solved is THE TRANSITION TO CONTINUOUS SYSTEMS 87 The RC Line-Transition to the Continuous Case Solution of the ...
... solving the latter ( discrete ) problem might be expected , in the limit as Ax → 0 , to lead to a procedure for solving ... solved is THE TRANSITION TO CONTINUOUS SYSTEMS 87 The RC Line-Transition to the Continuous Case Solution of the ...
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