Advanced Differential Equations

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.