Purchase textbook

Advanced Differential Equations,

Edition 1

Editors: By Youssef N. Raffoul

Publication Date: 22 Apr 2022

Educator resources

0 Reviews

Conformance

PDF/UA-1
The publication was certified on 20250728
For queries regarding accessibility information, contact [email protected]

Ways Of Reading

This e-publication is accessible to the full extent that the file format and types of content allow, on a specific reading device, by default, without necessarily including any additions such as textual descriptions of images or enhanced navigation.

Navigation

The contents of the PDF have been tagged to permit access by assistive technologies as per PDF-UA-1 standard.
Page breaks included from the original print source

Additional Accessibility Information

The language of the text has been specified (e.g., via the HTML or XML lang attribute) to optimise text-to-speech (and other alternative renderings), both at the whole document level and, where appropriate, for individual words, phrases or passages in a different language.

Note

This product relies on 3rd party tooling which may impact the accessibility features visible in inspection copies. All accessibility features mentioned would be present in the purchased version of the title.

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

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 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

ISBN: 9780323992800

Page Count: 364

Retail Price :

Kelley / Peterson, The Theory of Differential Equations: Classical and Qualitative, 2, Springer

Access to teacher/student resources is available to registered users with approved inspection copies or confirmed adoptions. To review this material, please request an inspection copy.

Advanced students in undergraduate and graduate programs taking courses on Advanced Ordinary Differential Equations in Math, Science, and Engineering