Advanced Differential Equations provides coverage of high-level topics in ordinary differential equations and dynamical systems. The book delivers difficult material in an accessible manner, utilizing easier, friendlier notations and multiple examples. Sections focus on standard topics such as existence and uniqueness for scalar and systems of differential equations, the dynamics of systems, including stability, with examples and an examination of the eigenvalues of an accompanying linear matrix, as well as coverage of existing literature. From the eigenvalues' approach, to coverage of the Lyapunov direct method, this book readily supports the study of stable and unstable manifolds and bifurcations.
Additional sections cover the study of delay differential equations, extending from ordinary differential equations through the extension of Lyapunov functions to Lyapunov functionals. In this final section, the text explores fixed point theory, neutral differential equations, and neutral Volterra integro-differential equations.
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Table of Contents
1. Preliminaries and Banach spaces2. 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
Authors
Youssef N. Raffoul Professor and Graduate Program Director, Department of Mathematics, University of Dayton, OH, USA. Youssef Raffoul holds the rank of Professor and is the Graduate Program Director in the Department of Mathematics at the University of Dayton. He joined the faculty in 1999. Dr. Raffoul 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. In 2018, Prof. Raffoul published Qualitative Theory of Volterra Difference Equations, a comprehensive study of the theory and applications of Volterra difference equations.
