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Advanced Differential Equations
Presents accessible coverage of difficult material on ODEs, stability and dynamical systems
Youssef N. Raffoul (Author)
9780323992800, Elsevier Science
Paperback / softback, published 22 April 2022
364 pages
23.5 x 19 x 2.3 cm, 0.75 kg
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.
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
Subject Areas: Differential calculus & equations [PBKJ]
