TMA014/MMA421, Ordinary Differential Equations and Dynamical systems, 2017/18

Latest news

Welcome to the course! The schedule for the course can be on TimeEdit.


Docent Michael Björklund,

Course literature

During the course I will write - and continually update - lecture notes, which to a large extent are based on the exposition in Gerald Teschl's book "Ordinary Differential Equations and Dynamical systems", which is freely accessible on the author's homepage:

Other alternative/complementary sources will be posted shortly.

Lecture notes

Course outline

The course splits into lectures (Mondays + Fridays) and exercise classes (Wednesdays).

During the lectures, important results and their technical details will be discussed,
while the exercise classes are devoted to examples, tricks and counterexamples.
Starting from the 2nd week, I will post recommended exercises from Teschl's book.


Room Topic Comments
Jan 15, 13.15-15.00 MVL14
Motivation through examples - Special flows

Jan 19, 08.00-10.00
Picard-Lindelöf I - Banach's Fixed Point Theorem

Jan 22, 13.15-15.00
MVL14 Picard-Lindelöf II - Dependence on initial values

Jan 26, 08.00-10.00
Picard-Lindelöf III - The Variation Principle

Jan 29, 13.15-15.00
Linear ODEs and their fundamental solutions

Feb 2, 08.00-10.00 MVL15 Exponential map
Feb 5, 13.15-15.00 MVL14 Hamiltonian ODEs and their (global) flows I
Feb 9, 08.00-10.00 MVL14 Hamiltonian ODEs and their (global) flows II
Feb 12, 13.15-15.00 MVL14 Lyapunov stability at fixed points
Feb ??, ??? ??? Periodic orbits and and a bit of Floquet Theory
Feb 19, 13.15-15.00 MVL14 Structural stability and Hartman-Grobman I
Feb 23, 08.00-10.00 MVL15 Structural stability and Hartman-Grobman II
Feb 26, 13.15-15.00 MVL14 Planar systems: Poincare-Bendixon
Mar 2, 08.00-10.00 MVL15 Summary + Loose ends
Mar 5, 13.15-15.00 MVL14 An old exam

Exercise classes

Exercise class Room
Topic Comments
Jan 17, 10.00-11.45
Toy problems + Old tricks
Jan 24, 10.00-11.45
Some counterexamples
Jan 31, 10.00-11.45
Explicit calculations
Feb 7,  10.00-11.45

Feb 14, 10.00-11.45

Feb 21, 10.00-11.45 MVL14

Feb 28, 10.00-11.45 MVL14

Mar 7,  10.00-11.45 MVL14

Mandatory computer lab

The course includes a mandatory (computer assisted) home assignment; details will be posted here shortly. You will have to hand in a (not hand-written) report, which will be graded, and the grade contributes to the final grade of the course. Although you are encouraged to cooperate, the reports must be composed individually.

Lab instructions

Reference literature for Matlab:

Learning MATLAB, Tobin A. Driscoll ISBN: 978-0-898716-83-2 (The book is published by SIAM).

Course requirements

The learning goals of the course can be found in the course plan.


More details will be posted shortly.

Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

Old exams

Since the lecturer/examiner is new, the exam might be slightly different from earlier years. A "Model Exam" will be posted shortly, as well as exams from earlier years.