Advanced Differential Equations

by Youssef N. Raffoul

Overview

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. - Includes content from a class-tested over multiple years with advanced undergraduate and graduate courses - Presents difficult material in an accessible manner by utilizing easier, friendlier notations, multiple examples and thoughtful exercises of increasing difficulty - Provides content that is appropriate for advanced classes up to, and including, a two-semester graduate course in exploring the theory and applications of ordinary differential equations - Requires minimal background in real analysis and differential equations - Offers a partial solutions manual for student study

Product Details

ISBN-13:	9780323992817
Publisher:	Elsevier Science & Technology Books
Publication date:	04/13/2022
Sold by:	Barnes & Noble
Format:	eBook
Pages:	364
File size:	25 MB
Note:	This product may take a few minutes to download.

About the Author

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.

Table of Contents

1. Preliminaries and Banach spaces2. Existence and uniqueness3. Systems of ordinary differential equations4. Stability of linear systems5. Qualitative analysis of linear systems6. Nonlinear systems7. Lyapunov functions8. Delay differential equations9. New variation of parameters

What People are Saying About This

From the Publisher

Presents accessible coverage of difficult material on ODEs, stability and dynamical systems

Editorial Reviews

"It is written by an author who is active exactly in the field of differential equations….

The book also has an application oriented part, as resulting from the presentation of several models taken from epidemics, electrical engineering, Lotka-Volterra population models. And last but not least, each chapter of the book is endowed with exercises; moreover, Student Resources are pointed out. Summarizing, a book worth to be studied." —zbMATH Open

From the Publisher