Advanced Differential Equations
Published on 22. April 2022
Book
Paperback/Softback
364 pages
978-0-323-99280-0 (ISBN)
Description
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.
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.
Reviews / Votes
"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
More details
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Elsevier Science & Technology
Target group
College/higher education
Product notice
Paperback (trade)
Dimensions
Height: 235 mm
Width: 191 mm
Thickness: 19 mm
Weight
627 gr
ISBN-13
978-0-323-99280-0 (9780323992800)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Youssef N. Raffoul
Advanced Differential Equations
E-Book
04/2022
Academic Press
€86.99
Available for download
Person
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.
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.
Content
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
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