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Thesis: The Sturm-Liouville Problem

Koning, D.E. (2017) Thesis: The Sturm-Liouville Problem. Master's Thesis / Essay, Mathematics.

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Abstract

This thesis treats the Sturm-Liouville problem, a typical case of some differential equation subject to certain boundary conditions. After a short introduction this problem is explored using the separation of variables method to solve a differential equation associated with the Sturm-Liouville theory. Then some basic properties of vector spaces and inner product spaces will be given and the L^2 space will be discussed, which is one of the most common examples of a Hilbert space. This enables us to describe the convergence, completeness and orthogonality of functions in the L^2 space. Using this, differential operators which are self-adjoint will be explored since this concept applies to the operator associated with the Sturm-Liouville problem treated in this thesis. Thereafter the Sturm-Liouville problem itself shall be discussed and some spectral properties concerning the eigenvalues and eigenfunctions will be proven. Finally the theory discussed thus far will be illustrated by working out an example and some applications of this subject will be given.

Item Type: Thesis (Master's Thesis / Essay)
Degree programme: Mathematics
Thesis type: Master's Thesis / Essay
Language: English
Date Deposited: 15 Feb 2018 08:29
Last Modified: 15 Feb 2018 08:29
URI: http://fse.studenttheses.ub.rug.nl/id/eprint/15431

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