Phalafala, Rakgwahla, Jessica2018-07-092018-07-092017Phalafala, Rakgwahla Jessica (2018) Darboux transformations on Sturm-Liouville eigenvalue problems with eigenparameter dependant transmission conditions, University of the Witwatersrand, Johannesburg, https://hdl.handle.net/10539/24838https://hdl.handle.net/10539/24838A dissertation submitted in fulfillment of the requirements for the degree of Master of Science to the Faculty of Science, University of the Witwatersrand, Johannesburg, 2017Sturm-Liouville eigenvalue problems arise prominently in mathematical physics. An innumerous amount of complexities have been encountered in solving these problems and a myriad of techniques have been explored over the century. In this work, we investigate one such technique, namely the Darboux-Crum trans formation. This transformation transforms an existing problem into one that is readily solvable or displays properties that are better understood. In particular, we focus our attention on the e↵ect the Darboux-Crum transformation has on the eigenparameter dependence of the transmission condition of our Sturm-Liouville eigenvalue problem.Online resource (iv, 79 leaves)enSturm-Liouville equationEigenvaluesThesis