Dynamics and Computation

COURSE OBJECTIVE
In this course you will be given an overview of the theory of discrete and continuous dynamical systems (first period), as well as a foundation in the most commonly applied numerical algorithms used to solve algebraic and dynamic problems (second period) found in concrete applications.

At the end of the course, the student is able to

• analyse one and two-dimensional difference and differential equations systems
• solve systems of non-linear ODEs numerically
• linearise a non-linear system, compute corresponding eigenvalues (by hand and numerically), and draw conclusions on the stability of fixed points
• use several numerical algorithms in concrete applications
• make programs in Matlab

COURSE CONTENT
Dynamical Systems part:
1. Discrete-time dynamical systems
2. Ordinary Differential Equations in 1 and 2 dimensions: graphical methods, linearisation, phase plane analysis
3. General theory of linear ODEs, solving initial value problems.
4. If there is enough time: dependence of solutions on parameters.

Numerical part:
1. Finding roots of nonlinear equations
2. Least Squares, curve fitting
3. Eigenvalue Problems, Pagerank
4. Fast Fourier Transforms, analysing signals
5. Numerical methods for ODEs

TEACHING METHODS
Lectures, tutorials, computer labs

TYPE OF ASSESSMENT
Written exam (part 1) and computer programming exercises (part 2)