Course Objectives: The course covers ordinary differential equations and dynamical systems. We start with the basic elements of the ODE theory (existence, uniqueness, and smooth dependence, linear systems), proceed with properties of dynamical systems (stability theory, invariant manifolds, hyperbolic and center points) and finish with periodic and homoclinic orbits (Floquet multipliers, Poincare maps, Melnikov functions). Since this is the first graduate course in applied mathematics, the material does not include special and advanced topics, but focuses on general methods and theorems.
Syllabus: Ordinary differential equations: well-posed initial value problems (i.e. existence, uniqueness, continuation and continuous dependence), general non-autonomous linear systems, special linear systems (autonomous, periodic), classical stability theory, bifurcation and asymptotic methods.
Instructor: Dr. Dmitry Pelinovsky, HH-422, ext.23424, e-mail: firstname.lastname@example.org
Lectures: Monday, Thursday (9:30-11:00), HH-207
Office hours: Monday, Thursday (11:00-11:30)
"Ordinary Differential Equations: Qualitative Theory" by L. Barreira and C. Valls (AMS, 2012), ISBN 978-0-8218-8749-3
"Ordinary Differential equations with applications" by C. Chicone (Springer-Verlag, 2006), ISBN 0-387-30769-9
Assignments: Four home assignments will be distributed during the classes with specific deadlines. The texts for assignments and solutions will be posted on the course webpage.
Presentations: The course is completed by student presentations.
Presentation - 60%
Assignments - 40%