TATA71 · 6 credits · Basic level (G2F) · Matematik, Tillämpad matematik
Ordinary Differential Equations and Dynamical Systems
Active · next start HT 2026
67%
passed the latest ordinary exam
TEN1 · 15 Jan 2026 · 6 students
76%
passed the ordinary exams, all sittings over the last 5 years
TEN1 · 62 students
Part of 5 programmes
Exam
TEN1 Written examination
- 5
- 4
- 3
- U
Ordinary exams
76% passed · 62 students
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- 91%11
- 80%20
- 80%15
- 50%10
Re-exams
No sittings with at least 5 students.
- Get 4 or 5: 50% (62 students)
Show small sittings (8)
Sittings with fewer than 5 students, often credit transfers or special sittings. They are not part of any figure on this page.
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Other modules
Partial exams, hand-ins and labs. They are not part of the figures at the top.
Hand-in or lab
UPG1 Assignments
- G
Main rounds
100% passed · 32 students
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- 100%11
- 100%5
- 100%8
Later rounds
No sittings with at least 5 students.
Show small sittings (16)
Sittings with fewer than 5 students, often credit transfers or special sittings. They are not part of any figure on this page.
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About the course
Aim
To give deeper knowledge and improved skills in the subjects of ordinary differential equations (ODEs) and continuous-time dynamical systems. After completing the course, the student should be able to:
- Use some classical methods of finding exact solutions of ODEs.
- Qualitatively investigate dynamical systems (mainly in two dimensions): phase portrait, stability of equilibria.
- Formulate and analyze ODEs using simple models from physics, chemistry and biology.
Content
- Some exact solution methods for certain types of ODEs.
- Theorems about the existence and uniqueness of solutions.
- Time-continuous dynamical systems (systems of autonomous first-order ODEs).
- Linear dynamical systems: exact solution, phase portrait, classification, exponential function for matrices.
- Nonlinear dynamical systems: phase portrait, linearization around equilibrium points, stability, limit cycles.
- Various examples of applications.
- Linear ODEs with non-constant coefficients: fundamental matrix, reduction of order, variation of parameters.
- Orientation on numerical and symbolic solution of ODEs using computer.
- Orientation on bifurcations, Poincaré mapping, discrete-time dynamical systems and chaos theory.
- Examiner
- Hans Lundmark
- Scheduled hours
- 44 h
- Main field of study
- Matematik, Tillämpad matematik