Instructor: Dr. Péter SIMON

Text:  C. Chicone, Ordinary Differential Equations with Applications or L. Perko, Differential Equations and Dynamical Systems
 

Prerequisite: Calculus; linear algebra (linear spaces, basis, matrix operations, eigenvalues, eigenvectors); multivariable calculus (differentiation of functions in several variables, implicit function theorem).

Course description: This course provides an introduction into ordinary differential equations. We show methods to solve certain equations, then the existence and uniqueness of solutions is dealt with. The second part of the course is devoted to the modern qualitative theory of dynamical systems.

Topics:

Existence and uniqueness theory (application of Banach’s fixed point theorem), Gronwall’s lemma, global solution.

Linear differential equations, the exponential of matrices.

Higher order linear differential equations, boundary value problems.

Autonomous differential equations, dynamical systems.

Stability theory, Liapunov’s direct method.

Attractors, limit sets, the Poincare-Bendixson theorem.

Periodic solutions, Floquet theory.

Topological classification of dynamical systems, elementary bifurcations.