TMA4165 - Dynamical Systems Spring 2026
General Info
Messages
- The exam problems and solutions are now available under Previous exams.
- The grading is now complete, and your grade will be visible soon in Studentweb. Guidelines to examiners
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- Welcome to TMA4165 Dynamical Systems!
- 1st lecture: Monday 05.01, 08:15-10:00, KJL2
- 2nd lecture: Tuesday 06.01, 12:15-14:00, R23
- These pages will be updated regularly throughout the whole semester. As a consequence Blackboard will be used as little as possible, i.e., for important or urgent announcements or other information that does not need to be visible to the entire world.
- It is an advantage to have taken TMA4145 Linear Methods, but not a must.
- Office hours are now updated. And you can stop by my office to discuss the course, including the exercises.
- Tomorrow, 27.01, we will have a lecture (12:15-14:00) in G1. Starting from 03.02, we will have lectures (12:15-14:00) in KJL4.
- Next week (23.02–24.02) there will be no lectures.
- Since the lecturer is sick. There will be no lectures on Monday March 16 and Tuesday March 17. Relevant lecture notes will, however, be put on the webpage.
- Due to MTFYMA excursion, there are no lectures Monday March 23 and Tuesday March 24 (see Lecture plan).
What is this course about?
The main focus of this course is the study of systems of ordinary differential equations. While the solutions of some well-known families of equations and systems can be computed explicitly, this is not true in general. Instead one tries to understand how possible solutions will behave, without knowing an exact expression for the solutions. Questions that we will address are:
- Does a given system have at least one solution? If so, is there exactly one solution?
- Which influence has a slight change of a parameter or the initial data on the solution?
- If a system has a constant solutions, will solutions starting close by approach this constant solution in the long run or not?
- Is it possible to find out if a given system has at least one periodic solution? If so, what can be said about the period?
- Is it possible to sketch solutions without computing them explicitly?
- ….
For more details see the Course description.
Lecturer
- Office: 1152, Sentralbygg 2
- Office hours: Mondays 10:00-11:00, Tuesdays 14:00-14:30
Lectures
- Monday 08:15-10:00, KJL2
- Tuesday 12:15-14:00, KJL4 (week 2-4 R23, week 5 G1)
Exercises
- A problem set will be given every week.
- The problem sets are an essential part of the curriculum, but are not required to be handed in. Nevertheless it is recommend to not postpone solving the exercises.
- If you have questions about the exercises or the curriculum, you can either ask during the lecture hours, or during the office hours.
- On Tuesdays, 14:15-16:00, the room EL3 is reserved for us. You can use the room to collaborate on the exercises.
Books and reading material
- Main book:
- L. Perko: Differential Equations and Dynamical Systems.
- Note that you can get the PDF from Springerlink.
- Further reading:
- D.G. Schaeffer and J.W. Cain: Ordinary Differential Equations: Basics and Beyond, Springer Texts in Applied Mathematics Series, Springer, New York, 2016.
- H. Logemann and E.P. Ryan: Ordinary Differential Equations - Analysis, Qualitative Theory and Control, Springer Undergraduate Mathematics Series, Springer, London, 2014.
- I.R. Shafarevich and A.O. Remizov: Linear Algebra and Geometry, Springer-Verlag, Berlin Heidelberg, 2013. (Covers e.g. Jordan normal forms in detail.)
- G. Teschl: Ordinary Differential Equations and Dynamical Systems, Graduate Studies in Mathematics, Volume 140, Amer. Math. Soc., Providence, 2012. (Covers e.g. Hartman-Grobman in detail.)
Curriculum (tentative)
The curriculum consists of the material covered in the lectures and the exercises, supplemented with a few notes. See the lecture plan / topics page for details.
- Perko:
- Chapter 1: all
- Chapter 2: all except 2.11-2.13
- Chapter 3: all except 3.1, 3.5-3.6, 3.10-3.11
- Chapter 4: all except 4.3, 4.5-4.15
- Exercises
Exam
- (Digital) School Exam.
- Date and time: 26.05.2026, 15:00
- Support material code D: No printed or hand-written support material is allowed. A specific basic calculator is allowed.
- The exam will be given only in English. Students are free to answer in Norwegian or English.