Advanced Differential Equations

Advanced Differential Equations
by: Youssef N. Raffoul (Author)
Publisher:
Edition: 1st
Publication Date: 2022/5/6
Language: English
Print Length: 364 pages
ISBN-10: 0323992803
ISBN-13: 9780323992800
Book 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.Includes content from a class-tested over multiple years with advanced undergraduate and graduate coursesPresents difficult material in an accessible manner by utilizing easier, friendlier notations, multiple examples and thoughtful exercises of increasing difficultyProvides 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 equationsRequires minimal background in real analysis and differential equationsOffers a partial solutions manual for student study
About the Author
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 coursesPresents difficult material in an accessible manner by utilizing easier, friendlier notations, multiple examples and thoughtful exercises of increasing difficultyProvides 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 equationsRequires minimal background in real analysis and differential equationsOffers a partial solutions manual for student study Read more