Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 31
... whence Step 4 u ( t ) = Σ§ ̧¡e111x ; e ( 1-9 ) 1 -9 ) 1/2 ( c 2 ( cd ) 1⁄2 ( c d ) + α ) + ( 12 ) ore- = ( ) ea + mysle + This is the result found in Sec . 2.3 . Alternately , steps 3a and 4a may be carried out . Step 3a whence Similarly ...
... whence Step 4 u ( t ) = Σ§ ̧¡e111x ; e ( 1-9 ) 1 -9 ) 1/2 ( c 2 ( cd ) 1⁄2 ( c d ) + α ) + ( 12 ) ore- = ( ) ea + mysle + This is the result found in Sec . 2.3 . Alternately , steps 3a and 4a may be carried out . Step 3a whence Similarly ...
Página 91
Gerald Goertzel, Nunzio Tralli. whence ποχ S. ( x ) = NL sin L - ωσ -lim 2 1 - cos [ To Ax / ( L + Ax ) ] ( 4x ) 2 Δ - 0 77202 L2 ( 3a ) Suppose e ( x , 0 ) = ΣA , S , ( x ) . Then whence [ ′′ e ( x , 0 ) 5 , ( x ) dx = Σ d.‚A . = A ...
Gerald Goertzel, Nunzio Tralli. whence ποχ S. ( x ) = NL sin L - ωσ -lim 2 1 - cos [ To Ax / ( L + Ax ) ] ( 4x ) 2 Δ - 0 77202 L2 ( 3a ) Suppose e ( x , 0 ) = ΣA , S , ( x ) . Then whence [ ′′ e ( x , 0 ) 5 , ( x ) dx = Σ d.‚A . = A ...
Página 92
... whence the Fourier transform of f ( d2 / dx2 ) g ( x ) is given by1ƒ ( —σ22 / L2 ) G .. 1 This result may also be obtained from ( 7.16 ) , if ƒ is expressible as a polynomial or series in d2 / dx2 , by integration by parts a suitable ...
... whence the Fourier transform of f ( d2 / dx2 ) g ( x ) is given by1ƒ ( —σ22 / L2 ) G .. 1 This result may also be obtained from ( 7.16 ) , if ƒ is expressible as a polynomial or series in d2 / dx2 , by integration by parts a suitable ...
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