Ordinary Differential Equations II
Official Course Description
Ordinary differential equations are one of the most important mathematical tools within the natural sciences. They can be used to describe anything from population dynamics to quantum mechanics. We will begin by discussing some basic theorems about existence, uniqueness and approximation of solutions to initial value problems. After this, some concepts which are important for nonlinear systems, such as phase portraits and stability, will be studied. The last part of the course will focus on boundary value problems. In particular, we will discuss general eigenfunction expansions, which can be seen as generalised Fourier series and play an important role in quantum mechanics.