Difference Equations and Applications

Difference Equations and Applications provides unique coverage of high-level topics in the application of difference equations and dynamical systems. The book begins with extensive coverage of the calculus of difference equations, including contemporary topics on l_p stability, exponential stability, and parameters that can be used to qualitatively study solutions to non-linear difference equations, including variations of parameters and equations with constant coefficients, before moving on to the Z-Transform and its various functions, scalings, and applications. It covers systems, Lyapunov functions, and stability, a subject rarely covered in competitor titles, before concluding with a comprehensive section on new variations of parameters.

Exercises are provided after each section, ranging from an easy to medium level of difficulty. When finished, students are set up to conduct meaningful research in discrete dynamical systems. In summary, this book is a comprehensive resource that delves into the mathematical theory of difference equations while highlighting their practical applications in various dynamic systems. It is highly likely to be of interest to students, researchers, and professionals in fields where discrete modeling and analysis are essential.

• Provides a class-tested resource used over multiple years with advanced undergraduate and graduate courses
• Presents difficult material in an accessible manner by utilizing easy, friendly notations, multiple examples, and thoughtful exercises of increasing difficulty 
• Requires minimal background in real analysis and differential equations 
• Covers new and evolving topic areas, such as stability, and offers a partial solutions manual for in book exercises 

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.