To familiarize students with basic ideas and fundamental techniques to solve ordinary differential equations.

To illustrate the breadth of applications of ODEs and fundamental importance of related concepts.    

After completing the module students should be: 

- familiar with elementary techniques for the solution of ODE''s, and the idea of reducing a complex ODE to a simpler one;

- familiar with basic properties of ODE, including main features of initial value problems and boundary value problems, such as existence and uniqueness of solutions;

- well versed in the solution of linear ODE systems (homogeneous and non-homogeneous) with constant coefficients matrix;

- aware of a range of applications of ODE.

Introduction, Important ODEs and their analytic solutions.

Initial value problem. Fundamental properties of ODE.  Picard theorem. 

Second order linear ODE with constant and non-constant coefficients.

Solution of second order linear ODE in series.          

Boundary value problem. Fredholm theorem.

Matrix methods for solving homogeneous and non-homogeneous linear systems with constant coefficients. Eigensystem.

PDEs solved by separation of variables and ODEs.