dc.contributor.advisor Henderson, Johnny dc.contributor.author Nguyen, Vy dc.contributor.other Baylor University. en_US dc.date.accessioned 2015-06-24T15:43:19Z dc.date.available 2015-06-24T15:43:19Z dc.date.copyright 2015-05-01 dc.identifier.uri http://hdl.handle.net/2104/9406 dc.description.abstract In this paper, we investigate special polynomial solutions of linear ordinary differential equations as functions of certain boundary conditions. We first look at solutions of y'' = 0 and y''' = 0, and observe the smooth dependence of the solutions on the boundary conditions by computing partial derivatives. Then, we characterize these partial derivatives according to their own respective boundary conditions. We also establish some relationships among these partial derivatives. In our generalization, we consider (n -􀀀 1)st degree polynomials as solutions of the boundary value problems of linear ordinary differential equations of nth derivative. We established these partial derivatives as (n -􀀀 1)st degree polynomials and satisfy their own respective boundary conditions. Finally, we discuss possible applications of the results of this paper through the modeling of hybrid phenomena with dynamic equations on time scales, and we mention extensions of the results to nonlinear differential equations. en_US dc.language.iso en_US en_US dc.rights Baylor University projects are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission. en_US dc.subject Applied Mathematics en_US dc.title Smoothness of Polynomials With Respect to Boundary Conditions As Solutions of Ordinary Differential Equations en_US dc.type Thesis en_US dc.rights.accessrights Worldwide access en_US dc.contributor.department Applied Mathematics. en_US dc.contributor.schools honors college en_US
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