Course - Dynamical Systems - TMA4165
TMA4165 - Dynamical Systems
About
Examination arrangement
Examination arrangement: School exam
Grade: Letter grades
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| School exam | 100/100 | 4 hours | D |
Course content
The course gives an introduction to dynamical systems with an emphasis on analytical and qualitative methods for linear and nonlinear ordinary differential equations. Topics covered: Linear and nonlinear systems, existence and uniqueness, continuous dependence, phase plane analysis, equilibria, limit cycles, stability, Lyapunov's direct method, index theory, the Poincaré-Bendixson theorem, and examples of applications. Additional topics that may change from year to year may include bifurcations, discrete dynamical systems and chaos, topics from calculus of variations and classical mechanics.
Learning outcome
1. Knowledge. The student knows basic concepts and methods from the theory of dynamical systems, including analytical and geometrical techniques for the study of qualitative properties of solutions. In particular, the student is familiar with linear and nonlinear systems, existence and uniqueness, continuous dependence, phase plane analysis, equilibria, limit cycles, stability, Lyapunov's direct method, index theory, the Poincaré-Bendixson theorem, the additional topics and examples of applications.
2. Skills. The student is able to apply his or her knowledge to the study of concrete examples. The student masters central techniques of proof and is able to apply these to related problems.
Learning methods and activities
Lectures and exercises.
Further on evaluation
Retake of examination may be given as an oral examination. The retake exam is in August. Students are free to choose Norwegian or English for written assessments.
Recommended previous knowledge
Courses TMA4100/05/10/15/20 Calculus 1/2/3/4K and TMA4145 Linear Methods or equivalent.
Course materials
Will be announced at the start of the course.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| SIF5025 | 7.5 |
Version: 1
Credits:
7.5 SP
Study level: Third-year courses, level III
Term no.: 1
Teaching semester: SPRING 2025
Language of instruction: English
Location: Trondheim
- Mathematics
- Technological subjects
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: School exam
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Spring ORD School exam 100/100 D INSPERA
-
Room Building Number of candidates - Summer UTS School exam 100/100 D INSPERA
-
Room Building Number of candidates
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"