Advanced Differential Equations,
Edition 1
By Youssef N. Raffoul

Publication Date: 22 Apr 2022

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.

Key Features

  • 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
About the author
By Youssef N. Raffoul, Professor and Graduate Program Director, Department of Mathematics, University of Dayton, OH, USA
Table of Contents
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
Book details
ISBN: 9780323992800
Page Count: 364
Retail Price : £95.95
Kelley / Peterson, The Theory of Differential Equations: Classical and Qualitative, 2, Springer
Instructor Resources
Advanced students in undergraduate and graduate programs taking courses on Advanced Ordinary Differential Equations in Math, Science, and Engineering