Welcome to the course.
The schedule for the course can be found via the link to webTimeEdit top of the page.
Course coordinator and examiner: Michael
Björklund,
micbjochalmers.se
Gerald Teschl:
Ordinary Differential
Equations and Dynamical Systems , which can be purchased
at
The American Mathematical Society .
However, a version of the book is also available for download from
the
author's web page.
Some additional material will be available in these web pages.
Lectures
Week 
Chapter

Contents

20/1

All

An overview
of the course with a view towards dynamical systems

22/1

Chapter 2

Existence and uniqueness
of solutions to ODE's: PicardLindelöf Theory

24/1

Chapter 2

Existence and uniqueness
of solutions to ODE's: Dependence on initial conditions

27/1

Exercise session


29/1

Chapter 3

Linear systems: Matrix
exponentials and Jordan's Canonical Form

31/1

Chapter 3

Linear systems: Stability

3/2

Chapter 3

Floquet Theory

5/2

Exercise session


7/2

Chapter 3 + 6 
Presentation of exercises +
An overview of wellstudied dynamical systems

10/2

Chapter 6 
Stability: Liapunov's Method 
12/2

Chapter 7 
Planar systems: PoincaréBendixson's
Theorem 
14/2

Exercise session 

17/2

Chapter 9 
Presentation of exercises +
Linearization: Stable and unstable manifolds 
19/2

Chapter 9 
Linearization: HartmanGrobman's Theorem 
21/2

Exercise session


24/2



26/2



28/2



3/3



5/3



7/3



Recommended exercises
The
purpose of the computer assignments is to
1) give a deeper understanding of the theory that is presented in
the lectures.
2) give a training in the use of mathematical software.
The assignments are compulsory, and the handins (written reports)
will be graded, and they will contribute to the final marks.
The lab instructions are written in a
pdfdocument . Please check that you are using an up to
date version of the document.
Reference literature:
Tobin A. Driscoll, Learning MATLAB, ISBN:
9780898716832 (The book is published by SIAM)
To pass this course you should pass the written
exam and complete the computer assignments, and participate
acively as stated below.
The written report on the computer assignment should be composed
individually. However, it is allowed, and encouraged, to work
together in pairs. In the report, each student should then state
with whom she/he has worked. The report should be delivered to the
examinor in electronic form, preferrably as a pdfdocument,
no later than the date of the written exam. The reports
should be sufficiently complete to be read by somebody who does
not have axcess to the lab instructions.
The final grade of the course is based on the marks of the written
exam, which accounts for about 70% of the final grade, and the
grade on the lab report, which accounts for about 30% of the final
grade. The participation problem solving at the black board is
required for passing the course, but other than that does not
influence the final grade.
Students are assumed to participate actively in
the lectures and exercise classes. Starting from week 3, students
will present the solution to some of the exercises at the black
board. In the beginning of the week, there will be a list of
problems presented on the web page, and a form to sign up for the
problems. Signing up for a problem means that the student agrees
to present the solution in front of the class in the next lecture.
The teacher will then choose, more or less randomly, among those
students who have signed up.
To pass the course, a student must sign up for at least 30% of
the total number of proposed problems, and if selected to
present a solution, to show that he/she is well prepared to do
so.
The purpose of this to improve the student's ability of
communicating mathematical ideas orally.
The written exam consists of problems to be
solved and of theory questions.
Some more inforamation about the written exam, and a list of
important theory questions are given in the
exam information sheet (check that you have the version
from January 11, 2013).
Here are some old examp papers to look at:
20110310 ,
20110609 ,
20110827 ,
20120308 ,
20120605 .
During the exam the following aids are permitted: only pencil and
eraser, no books, notes, calculators
In
Chalmers Student Portal you can read about when exams are
given and what rules apply on exams at Chalmers.
At the link
Scedule
you can find when exams are given for courses at University of
Gothenburg.
At the exam, you should be able to show valid identification.
Before the exam, it is important that you report that you want to
take the examination. If you study at Chalmers, you will do this
by the
Chalmers Student Portal, and if you study at University of
Gothenburg, so sign up via
GU's
Student Portal.
You can see your results in Ladok by logging on to the Student
portal.
At the annual examination:
When it is practical a separate review is arranged. The date of
the review will be announced here on the course website. Anyone
who can not participate in the review may thereafter retrieve and
review their exam on Mathematical sciences study expedition,
Monday through Friday, from 9:00 to 13:00. 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 reexamination:
Exams are reviewed and picked up at the Mathematical sciences
study expedition, Monday through Friday, from 9:00 to 13:00. Any
complaints about the marking must be submitted in writing at the
office, where there is a form to fill out.