Course Language:

English

Course Objectives:

Main goals are to provide the properties of the systems of linear and nonlinear equations, the development of their general solutions, the linearization of nonlinear systems, adjoint equations, Green’s functions and Sturm-Liouville equations.

Course Content:

Self-adjoint second order equations, general theorems. Green's function. Spectral theory. Sturm-Liouville systems, Liouville normal forms. Orthogonal functions and their completeness. Stability of first order systems of equations. Autonomous systems, matrix exponential functions and general solutions of systems of equations with constant coefficients Autonomous,gradient and Hamiltonian systems, Lyapunov functions.. Linearization. Periodic solutions, Poincare-Bendixon theorem.

Course Methodology:

1: Lecture, 2: Problem Solving

Course Evaluation Methods:

A: Written examination, B: Homework