Advanced Differential Equations

Youssef N. Raffoul holds the rank of Professor and is Graduate Program Director in the Department of Mathematics at the University of Dayton, US. Prof. Raffoul joined the faculty in 1999. He obtained a B.S. and M.S. from the University of Dayton in mathematics in 1987 and 1989. After receiving his Ph.D. in mathematics from Southern Illinois University at Carbondale in 1996, he joined the faculty of the Mathematics Department at Tougaloo College in Mississippi, where he became the department chair for two years until he came to Dayton. Prof. Raffoul has published extensively in the area of functional differential and difference equations and has won several awards for his research, most recently the Career in Science Award from the Lebanese Government. Prof. Raffoul published four books: Qualitative Theory of Volterra Difference Equations; with Professor Murat Adivar, Stability, Periodicity, and Boundedness in Functional Dynamical Systems on Time Scales; Advanced Differential Equations (Academic Press, 2022); and his fourth book, Applied Mathematics for Scientists and Engineers.

1. Preliminaries and Banach spaces
2. Existence and uniqueness
3. Systems of ordinary differential equations
4. Stability of linear systems
5. Qualitative analysis of linear systems
6. Nonlinear systems
7. Lyapunov functions
8. Delay differential equations
9. New variation of parameters