MATH 454 Differential Equations and Dynamical Systems

Driven by the needs of applications, this course provides an introduction to dynamical systems. The emphasis is on nonlinear systems; topics include linearization near equilibria, stability properties, limit cycles and bifurcations, Lorentz equations, and chaos. Both analytical and numerical techniques will be used. Students will learn how to use a software to implement numerical methods and visualize solutions. Examples of applications in mathematics, physics, chemistry, biology, biomedical engineering, mechanical engineering, neuroscience, and economics are included.