Acknowledgments

This dissertation would not be possible without several contributions. First, I would like to thank my advisor, Professor Peter R. Wolenski, for his guidance, patience, and enthusiasm about mathematics. From the beginning, when I attended his course in Differential Equations, he was very supportive and available to discuss mathematics with me. I would also like to thank the members of my Advising Committee for their support and direction. In particular, Professor Neubrander was a great source of direction and encouragement as I made decisions along the way. In addition, special thanks are extended to Professor Oxley who provided guidance and support in the area of teaching and to Professor Shipman who was always available to discuss mathematics and share his experiences in the mathematical field. It is a pleasure to thank the staff in the mathematics department for providing me with a great working environment. I especially thank Mr. Anthony Picado and Mr. Jeff Sheldon. I would especially like to thank my family and friends for their support and encouragement throughout the past few years. I would not have been able to finis