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The exam and the lab reports are graded . The results will be sent to you by e-mail, but if you wish to see the graded exam, please come to my office Tuesday 29/3 at 10-12.
The exam on Thursday takes place in the V-building.
Please don't forget to fill in the course evaluation at GUL if you are a student at the University of Gothenburg, otherwise at Chalmer's course evaluation system .
Here are last year's exam questions: 2010-03-11 , 2010-06-04 , 2010-08-19 . But please do not hope that it is enough to solve the problems in those three exams to be sure to pass the exam this year. The course is defined by the course plan.
There is a small set of notes with some notions of topology, continuous functions etc. that you can read here
I hope that you find it more clear below how to sign up for the student presentations. I think that the web page works now ... please tell me (by e-mail) if there it does not work as it shoul.
You must sign up for the exam. Studets at the Univeristy of Gotheburg should look at the GU web page , and students at Chalmers must use the Chalmers student portal .
The list of theorems required for the exam, as well as the list of exercises refer to the Teschl's book as of Jan 10, 2011. If you have a differene version, please look at this local copy of the book.
Those of you who have not received a mail with a login for these web pages either did not give me your e-mail address today, or wrote in a way difficult to read. Please send me an e-mail in that case.
If you have not yet registered, please do so as soon as possible:
Chalmers students: you have to do this at the student portal no later then Jan. 24, 17.00h.
GU-students: you have to go to studera.nu . This is a web page in Swedish, but please ask a friend for help.

Teachers

Examiner and lecturer: Bernt Wennberg, wennbergchalmers.se, http://www.math.chalmers.se/~wennberg/

Exercises: Dawan Mustafa, dawanchalmers.se, homepage

Course literature

Gerald Teschl: Ordinary Differential Equations and Dynamical Systems ,
lecture notes avaliable from the author's web page,
but can soon also be purchased at The American Mathematical Society .
- Ch. 1: This is part of the course, but will only briefly be treated in the lectures; however, several exercises will be treated.
- Ch. 2: The basic existence and uniqueness results for the initial value problem are presented here, making this one of the most important chapters for the course.
- Ch. 3: Neither the Floquet-theory of ch. 3.6 nor the perturbation theory of ch. 3.7. are included. Most important is the theory of linear homogeneous systems.
- Ch. 4, 5: Not included.
- Ch. 6: Contains the basic defintions pertaining to dynamical systems. It is important for the course.
- Ch. 7,8 : Selected parts are included, in particular the Poincaré-Bendixon theorem. Examples are covered in exercise classes. The theory of Hamiltonian systems, the Kepler problem and the KAM-theory are not included.
- Ch. 9 : The local behaviour near fixed points; the Hartman Grobman theory.
- Ch. 10 - 13 : Some aspects of chaos and of discrete dynamical systems are covered in the computer exercise, but most of these chapters are not included in the course.
D.D. Arrowsmith and C.M.Place: An introduction to dynamical systems, Cambridge University Press.
available at Cremona; this is a very good book, which goes deaper into some parts of the course. It is not needed, however.
Some additional material (including some of my handwritten lecture notes) will be available in these web pages.
Instructions for the computer exercises, which will be made available from this web page.

Course structure

-- The course is decribed in the course syllabus, which states the learning goals of the course. From a practical point of view, the course consists of lectures, exercise classes and a compulsory computer assignment. In the exercise classes, some problems will be solved at the blackboard by a techer, but I expect students to participate actively. Every week some solustions will be presented by students rather than by teachers (see below about the assessment of the course). Of course ateacher will be present, to help out if it is needed, and to lead the discussion.
-- I will try to keep an up to date course diary , in which the progress of the course is recorded, together with for example comments on exercises.

Preliminary plan for lectures and classes

	Day	Topic, chapter	Comments, recommended exercises
V1
	18/1	An introduction to the course and practical matters A sweep through Ch. 1 of the book	All exercises from Ch. 1 are relevant
	18/1	Beginning of Ch. 2: the contraction mapping theorem.
	21/1	Exercises: P 1.1, (P1.2) , P1.6, P1.11, P1.20, P1.31	Tell me what is difficult and sign up for next week here

V2
	25/1	Basic ODE-theory; Picard-Lindelöf; Introduction to the computer exercise
	25/1	Exercises:
	28/1	Student's presentations Properties of solutions to odes Extension of solutions, differentility etc.	Tell me what is difficult and sign up for presentations on Feb 4 here

V3
	1/2	A little about numerical methods Linear systems
	1/2	Exercises: 2.20, 3.1, 3.2, 3.13. Please start working on your computer exercise, and ask if you need som help.
	4/2	Linear algebra: Matrix exponential invariant subspaces, Jordan forms	Tell me what is difficult and sign up for presentations on Feb 8 here

V4
	8/2	Linear systems; stable and unstable subspaces etc.
	8/2	Student's presentations Linear, non-autonomous systems
	11/2	Exercises:	Tell me what is difficult and sign up for presentations on Feb 18 here

V5
	15/2	Dynamical systems (Ch. 6).
	15/2	Exercises:
	18/2	Student's presentations Dynamical systems (Ch. 6)	Tell me what is difficult and sign up for presentations on Mars 4 here

V6
	22/2	Examples from Ch. 7
	22/2	The Poincaré Bendixon theorem
	25/2

V7
	1/3	Something about higher dimensional systems (from Ch. 8) Local behaviour near fixed points (Ch. 9)
	1/3
	4/3	Student's presentations Local behaviour near fixed points (Ch. 9)

V8
	8/3	Repetiton
	8/3	Repetition: an old exam
	10/3	NB. Check the offical schedule for exact date and time.

Computer assignment

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.

Assessment

To pass this course you should pass the written exam and complete the computer assignments.

Written examination
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, 2011).

During the exam the following aids are permitted: only pencil and eraser, no books, notes, calculators
Bring ID and students at Chalmers also should bring a receipt for the student union fee

You will be notified the result of your exam by email from LADOK (This is done automatically as soon as the exams have been marked an the results are registered)
The exams will then be kept at the students' office in the Mathematical Sciences building.
Check that the number of points and your grade given on the exam and registered in LADOK coincide.
Complaints of the marking should be written and handed in at the ...

Computer assignment
All hand-in shall be composed individually. (However, when working with the assignments, cooperation is encouraged.) The hand-ins should be delivered in the form a pdf-file sent to the examinor no later than the date of the written exam. The reports should be sufficiently complete to be read by someone who does not have axcess to the lab-instructions.

Active participation
Students are assumed to participate actively in the lectures and exercise classes. Starting from week 2, 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.

Course evaluation

In the beginning of the course, two student representatives for the course will be will be selected, who will meet with the lecturer for a halftime evaluation of course. A final evaluation will then take place in the end of the course. An evaluation form is available at . Please fill in your assesments in the web page..