This course presents a broad introduction to the subject of dynamical systems, both continuous and discrete. We analyze the existence, uniqueness, stability, and control of linear and nonlinear systems and the topics of bifurcation, flows, limit cycles, chaos, and catastrophe theory. This course will serve students with bachelor¿s degrees in mathematics or closely related fields wishing to deepen their mathematics education, and technical professionals, high school teachers, and math instructors seeking professional development or qualifications for teaching community college courses.
Note: Graduate status required.
3 Graduate credits
Effective August 17, 2020 to present
- Students will be introduced to subject of dynamical systems, both continuous and discrete. Students will be able to solve linear systems explicitly.
- They will use the fundamental existence and uniqueness theory to analyze and evaluate nonlinear systems and their general insolvability with analytic techniques.
- They will be able to create models and use bifurcation theory to analyze stability of flows, find limit cycles, and identify the onset of chaos using the tools of linearization near fixed points, the Poincare-Bendixson Theorem, and Liapunov exponents in 1 and higher dimensions.