Course Objectives: The course covers the qualitative theory of ordinary differential equations and dynamical systems. After an introduction of main elements of the ODE theory (existence, uniqueness, and smooth dependence, linear systems), properties of dynamical systems (stability theory, invariant manifolds, hyperbolic and center points) are studied. The course finishes at the theory of periodic and homoclinic solutions (Floquet multipliers, Poincare indices, 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: email@example.com
Lectures: Monday, Wednesday (9:00-10:30), HH-312
Office hours: Monday, Wednesday (10:30-11:30)
"Ordinary Differential Equations: Qualitative Theory" by L. Barreira and C. Valls (AMS, 2012)
"Differential equations and dynamical systems" by L. Perko (Springer-Verlag, 2001), ISBN 0-387-95116-4
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%