Publication Date


Date of Final Oral Examination (Defense)


Type of Culminating Activity


Degree Title

Master of Science in Mathematics



Major Advisor

Barbara Zubik-Kowal, Ph.D.


Mary Jarratt Smith, Ph.D.


Uwe Kaiser, Ph.D.


Although valuable understanding of real-world phenomena can be gained experimentally, it is often the case that experimental investigations can be found to be limited by financial, ethical or other constraints making such an approach impractical or, in some cases, even impossible. To nevertheless understand and make predictions of the natural world around us, countless processes encountered in the physical and biological sciences, engineering, economics and medicine can be efficiently described by means of mathematical models written in terms of ordinary or/and partial differential equations or their systems. Fundamental questions that arise in the modeling process need care that relies on the use of mathematical analysis. It is also the case that more realistic models directly relevant to the specific area of application are often nonlinear, calling for a robust treatment of general classes of differential equations. This thesis is devoted to developing a range of proof techniques for the mathematical analysis of general classes of both linear and nonlinear and both ordinary and partial differential equations that help in gaining an understanding of the fundamental properties of their solutions.