MA-434 Nonlinear Differential Equations and Dynamic Systems
- ECTS Credits:
- 7.5
- Responsible department:
- Faculty of Engineering and Science
- Course Leader:
- Yuriy Rogovchenko
- Lecture Semester:
- Autumn
- Duration:
- 1 term
The course is connected to the following study programs
Prerequisites
Bachelor in mathematics.
Course contents
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.
Learning outcomes
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)
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can apply theoretical knowledge to examine real world problems
Examination requirements
Required assignments must be approved, see Canvas for more information.
Teaching methods
Lectures, work in small groups and compulsory assignements. The course has an expected workload of around 200 hours
Evaluation
The person responsible for the course, 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.
Offered as Single Standing Module
Yes.
Assessment methods and criteria
Oral individual examination. Graded assessment.
Reduction of Credits
This course’s contents overlap with the following courses. A reduction of credits will occur if one of these courses is taken in addition:
| Course | Reduction of Credits |
|---|---|
| MA-310 – Nonlinear Differential Equations and Dynamic Systems | 7.5 |