Synopsis
This foundational introduction to modern dynamical systems covers traditional subjects, as well as modern topics such as fundamentals of dynamical systems theory and bifurcation theory. The volume emphasizes analyzing solutions rather than finding solution formulas, introduces numerical methods early in the book and provides case studies for each subject area. Many applications are accompanied with real data and are drawn from many disciplines including many from biological subjects. The volume addresses first order equations, linear first order equations, nonlinear first order equations, systems and higher order equations, homogeneous linear systems and higher order equations, nonhomogeneous linear systems, approximations and series solutions, nonlinear systems and Laplace transforms. For those needing an introduction to modern dynamical systems.