TMA4165 - Dynamical Systems Spring 2025

General Info

Messages

  • Re-sit exam:
    • The exam and a solution can be found on the previous exams page.
  • Exam:
    • If you never had a digital exam before, where you write on paper: Info about school exam with handdrawings
    • All exercises will have the same code.
    • Do not write with a pencil or use red ink.
    • Write with a black or blue pen.
  • Reference group:
    • If you have any remarks, request, complaints etc. regarding this course, contact the lecturer or the reference group.
  • Welcome to TMA4165 Dynamical Systems!
  • 1st lecture: Monday 6.1, 15:00-17:00, F3
  • 1st exercise class: Friday 17.1, 12:00-14:00, R93
  • 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.
    • If not: On the lecture plan page you find a column called assumed knowledge, which states for every lecture which definitions and results from TMA4145 we will use / apply. Look those up before attending the lecture.

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

  • Katrin Grunert
  • Office: 1150, Sentralbygg 2
  • Office hours: Wednesday 15:00-16:00 and by appointment, i.e., send me an email

Lectures

  • Monday 15:00-17:00, F3
  • Tuesday 12:00-14:00, F3

Exercise assistant

Exercises

  • Friday 12:00-14:00, R93
  • A problem set will be given every week.
  • The problems sets will be supervised and discussed in the exercise class. They 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.
  • In general the exercise class is the right place to
    • get help with the problem sets
    • discuss and ask questions about the material covered in the course

Books and reading material

  • Main book:
    • L. Perko: Differential Equations and Dynamical Systems.
    • Note that you can get the PDF from Springerlink.

Curriculum

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
  • The notes, which can be found on the lecture plan / topics page.
    • Dependence on parameters and initial data
    • Hartman-Grobman theorem
    • Stability of limit cycles
  • Exercises

Reference group

Name Email add @

Exam

  • School exam.
  • Date and time: 26.05.2025, 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.
2025-08-14, Katrin Grunert