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Welcome to the course! The schedule for the course can be on TimeEdit.
Examiner
Docent Michael Björklund, micbjo@chalmers.seCourse 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:
https://www.mat.univie.ac.at/~gerald/ftp/book-ode/ode.pdf
Other alternative/complementary sources will be posted shortly.
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.
Lectures
| Lecture |
Room | Topic | Comments |
|---|---|---|---|
| Jan 15, 13.15-15.00 | MVL14 |
Motivation
through examples - Special flows |
|
| Jan
19, 08.00-10.00 |
MVL15 |
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 |
MVL14 |
Picard-Lindelöf
III - The Variation Principle |
|
|
Jan 29, 13.15-15.00 |
MVL14 |
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 |
MVL14 |
Toy problems + Old tricks | |
| Jan
24, 10.00-11.45 |
MVL14 |
Some counterexamples | |
| Jan
31, 10.00-11.45 |
MVL14 |
Explicit calculations | |
| Feb
7, 10.00-11.45 |
MVL14 |
||
| Feb
14, 10.00-11.45 |
MVL14 |
||
| 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.
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.
Examination
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.