Sturm's name is most often associated with the simple version of Sturm-Liouville theory taught to undergraduates in a differential equations course. This is. Sturm-Liouville Theory. In the two preceding lectures I demonstrated the utility of Fourier series in solving PDE/BVPs. As we'll now see, Fourier series are just the. A basic introduction into Sturm-Liouville Theory. We mostly deal with the general 2nd- order ODE in self-adjoint form. There are a number of things covered.
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Further, they studied the discontinuous Sturm-Liouville problem with eigenparameter boundary conditions at two endpoints in [ 24 ] and extended the results of sturm liouville theory 18 ] to finite discontinuities case.
Sturm liouville theory papers [ 1922 sturm liouville theory, 2325 ], the authors obtained the estimations of eigenvalues and eigenfunctions of the discontinuous Sturm-Liouville problem with one inner point, containing an eigenparameter in the boundary condition.
Besides, the authors also discussed the completeness of the eigenfunctions of a regular discontinuous Sturm-Liouville problem in papers [ 1825 ].
The s that admit nontrivial solutions are called the eigenvalues and the corresponding nontrivial solutions are called eigenfunctions.
The constants and should not be both zero, same for and. Given the preceding, let us now solve the inhomogeneous problem: This sturm liouville theory Fourier series is troublesome because of its poor convergence properties.
It is not clear a priori whether the series converges pointwise.
Because of Fourier analysis, since the Fourier coefficients are "square-summable", the Fourier series converges in L2 sturm liouville theory is all we need for this particular theory to function.
Therefore, by using formula 4we obtain the solution: In this case, we could have found the answer using antidifferentiation.
To use the book, only a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory are assumed.