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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,
Course litterature
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.

Week Chapter
An overview of the course with a view towards dynamical systems
Chapter 2
Existence and uniqueness of solutions to ODE's: Picard-Lindelöf Theory
Chapter 2
Existence and uniqueness of solutions to ODE's: Dependence on initial conditions
Exercise session

Chapter 3
Linear systems: Matrix exponentials and Jordan's Canonical Form
Chapter 3
Linear systems: Stability
Chapter 3
Floquet Theory
Exercise session

Chapter 3 + 6 Presentation of exercises + An overview of well-studied dynamical systems
Chapter 6 Stability: Liapunov's Method
Chapter 7 Planar systems: Poincaré-Bendixson's Theorem
Exercise session
Chapter 9 Presentation of exercises + Linearization: Stable and unstable manifolds
Chapter 9 Linearization: Hartman-Grobman's Theorem
Exercise session







Recommended exercises
Week Excersises

Computer labs

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 hand-ins (written reports) will be graded, and they will contribute to the final marks.

The lab instructions are written in a pdf-document . Please check that you are using an up to date version of the document.

Reference literature:
Tobin A. Driscoll, Learning MATLAB, ISBN: 978-0-898716-83-2 (The book is published by SIAM)
Course requirements
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 pdf-document, 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.
Active participation
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: 2011-03-10 , 2011-06-09 , 2011-08-27 , 2012-03-08 , 2012-06-05 .

During the exam the following aids are permitted: only pencil and eraser, no books, notes, calculators

Examination procedures
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 re-examination:
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.
Old exams