Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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Página 21
Gerald Goertzel, Nunzio Tralli. CHAPTER 2 Solution for Diagonalizable Matrices 2.1 Solution by Taylor Series A standard method for the solution of the differential equation ù ( t ) = Au ( t ) ( 2.1 ) yields the solution in the form of a ...
Gerald Goertzel, Nunzio Tralli. CHAPTER 2 Solution for Diagonalizable Matrices 2.1 Solution by Taylor Series A standard method for the solution of the differential equation ù ( t ) = Au ( t ) ( 2.1 ) yields the solution in the form of a ...
Página 34
... solution to ( 2.28 ) . Nevertheless , for certain ƒ a solution exists . To determine the restrictions on ƒ and the corresponding solutions , a simple procedure may be employed . The new variables v are introduced by Then or If λ1 = 0 ...
... solution to ( 2.28 ) . Nevertheless , for certain ƒ a solution exists . To determine the restrictions on ƒ and the corresponding solutions , a simple procedure may be employed . The new variables v are introduced by Then or If λ1 = 0 ...
Página 248
... solution if and only if the determinant of the coefficients | M | is unequal to zero . Thus we demonstrate the existence of a solution when | M | 0 by construction . Multiply the ith equation of ( 1A.8 ) by Mix , the cofactor of mix ...
... solution if and only if the determinant of the coefficients | M | is unequal to zero . Thus we demonstrate the existence of a solution when | M | 0 by construction . Multiply the ith equation of ( 1A.8 ) by Mix , the cofactor of mix ...
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