Physical Sciences and Mathematics Commons^™

Transformations Of Differential Equations And Applications, Despina Andrea Stavri

Masters Theses

The Sturm-Liouville problems introduced by Jacques Charles Francois Sturm and Joseph Liouville in the 19^thcentury are very important in applied mathematics. Singular Sturm-Liouville problems and two physical problems are discussed. The two physical problems are solved using two methods: Exact and asymptotic solutions. Also, the Sturm-Liouville problem's are classified using the Weyl-Kodaira Theorem. A general transformation of a third order differential equation is introduced. Oscillation and non-oscillation theorems on an infinite interval for a third order differential equation are stated. New versions of these theorems are introduced for the special cases and examples are given to illustrate them. …

Application Of The Green’S Function For Solutions Of Third Order Nonlinear Boundary Value Problems, Shannon Mathis Morrison

Masters Theses

Green’s functions are used to prove a collection of existence and uniqueness theorems for third order nonlinear boundary value problems. Several examples of Green’s functions for both second and third order boundary value problems are given. Various applications of the existence theorems are presented in detail.

A Study Of The Homology Of Subset Spaces And Their Connection To The K-Sat Problem In Computer Science, Oliver J. Thistlethwaite

Masters Theses

It is the purpose of this thesis to introduce an idea for studying questions of computer science via topology. We begin by describing the homology of a certain space constructed from a given subset of the power set of any finite set. We then discuss how this relates to the k-SAT problem in computer science.

We shall use computers as a tool to calculate the homology groups as well as the Euler characteristic of some of these spaces. Due to the sheer number of calcu- lations needed, doing the necessary computations by hand is both impractical and impossible.

In addition, …