Some Mathematical Methods of PhysicsMcGraw-Hill, 1960 - 300 páginas |
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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
Solution for Diagonalizable Matrices | 21 |
12 | 37 |
Vector Spaces and Linear Operators | 50 |
Derechos de autor | |
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analytic approximate arbitrary asymptotic ax² Bessel function boundary conditions chap coefficients consider constant contour coordinates corresponding cylindrical functions d₁ d²/dx² defined denotes determinant diagonal differential equation Dirac notation ei(p eigen eigencolumn eigenfunctions eigenvalue equation eigenvalue problem eigenvector eikr element evaluate expansion finite number follows Fourier integral theorem function f(x given Green's function Hence Hermitian Hermitian matrix Hermitian operator infinite integral representation integrand inverse Laplacian linear lowest eigenvalue matrix method multiplication notation obtained operator orthonormality conditions perturbation plane relations result Ritz method row or column saddle point saddle-point method satisfy the orthonormality scattering sinh solution solve spherical spherical harmonics substitution transformation functions trial functions vanish variable vector vector space verified wave written yields zero ηπχ πρ ди ду дх