MA-310 Nonlinear Differential Equations and Dynamic Systems
- ECTS Credits:
- 10
- Responsible department:
- Faculty of Engineering and Science
- Course Leader:
- Yuriy Rogovchenko
- Lecture Semester:
- Autumn
- Teaching language:
- English
- Duration:
- 1 term
The course is connected to the following study programs
- Industrial Mathematics, Bachelor's Programme
Teaching language
EnglishRecommended prerequisites
60 sp in mathematics including MA-226
Course contents
This course introduces basic analytic and qualitative methods for analysing differential equations and dynamical systems. It covers local theory (existence and uniquenessl, equilibria, linearization, stabile manifold theorem) and gobal theory (limits, periodic paths, the Poincare map, homoclinic and heteroclinic orbits). Basic techniques for phase-analysis and stability theory will be discussed. Other subjects can encompass bifurcations, perturbation methods, discrete dynamical systems, chaos and applications.
Learning outcomes
Upon successful completion of the course, the student will be able to
-
Have knowledge about basic priciples and techniques in the theory of differential equations and dynamical systems
-
Know the basic properties of linear systems
-
Have knowledge about techniques for analysing phase-spaces
-
Identify relevant analytic and geometric methods and use these for qualitative analysis of non-linear systems (equilibria, limit cycles, stability and bifurcations).
-
Apply theoretical knowledge for investigating real world problems
Examination requirements
Mandatory hand-ins must be approved. See Canvas for details.
Teaching methods
Lectures, group work, and mandatory hand-ins. Estimated workload of the course is 267 hours.
Evaluation
The person responsible for the course decides, in cooperation with student representative, the form of student evaluation and whether the course is to have a midway or end of course evaluation in accordance with the quality system for education, chapter 4.1.
Admission for external candidates
No
Offered as Single Standing Module
Yes. Subject to availability or capacity.
Assessment methods and criteria
Individual, oral exam. Graded grade.
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-434 – Nonlinear Differential Equations and Dynamic Systems | 7.5 |