Nonlinear Differential Equations and Dynamic Systems
Included in Study
Mathematics, Master's Programme
Bachelor in mathematics.
On successful completion of the course, the student
has the knowledge of fundamental concepts and techniques from the theory of differential equations and dynamical systems
is familiar with basic properties of linear systems
knows techniques of phase space analysis
can identify appropriate analytical and geometric methods and use them for the qualitative analysis of nonlinear systems (equilibria, limit cycles, stability, bifurcations)
can apply theoretical knowledge to examine real world problems
The course introduces fundamental analytical and qualitative methods for the analysis of differential equations and dynamical systems. It covers both local theory (existence and uniqueness, equilibria, linearization, stable manifold theorem) and global theory (global existence, limit sets, periodic orbits, Poincaré map, homoclinic and heteroclinic orbits). Basic techniques of phase analysis and stability theory are discussed. Additional topics may include bifurcations, perturbation methods, discrete dynamical systems, chaos, applications in natural sciences and engineering problems.
Lectures and work in small groups. The course has an expected workload of around 200 hours
As part of course work, students should write a short essay on selected topic and present it orally.
Assessment methods and criteria
Oral individual examination. Graded assessment.
The study programme manager, in consultation with the student representative, decides the method of evaluation and whether the courses will have a midterm- or end of term evaluation, see also the Quality System, section 4.1. Information about evaluation method for the course will be posted on Canvas.