Introduction to differential equations and dynamical systems (1-2 ov)
February 15-24, 2000, Department of Mathematics
Teacher: Professor Heinz Junek from the University of Potsdam, Germany
Teaching language: English/Finnish
(Updated March 16, 2000)

Heinz is the Prey, Lenni the Predator

Other photos:
Heinz, Pekka and Matti are assisting the Computer Lab session
Pekka and Heinz
Snowy forest in Koli
Visitors at Koli peak

A Short Video Clips from the Computer Lab work
Course Material (to be updated gradually) in
http://www.joensuu.fi/sciences/mathematics/DidMat/Junek/StudyMaterial.html


Examination in Joensuu:Friday 25.2.2000, 12-14 in M17
Exam is designed by Heinz and Jussi, and Jussi is responsible for the rest.

You may use all the course material (or as Heinz said: "Anything")
in the exam.

Everyone MUST fill in the course evaluation form in the Web,
designed by Lasse Eronen et. al. (not ready yet).
Its URL address will be sent to you next week and it will also appear here:


The course starts on Tuesday morning in the lecture room M20, 2nd floor,
in the Psychology Wing of the M building (also Y6).
All lectures are kept there, see the more detailed program below.

The students are asked to note the following:

LECTURES: 1. Please note that you are expected to have papers, pencils and calculators of your own.
Brief lecture notes will be delivered during the first sessions.
2. The lectures are delivered by video conferencing to Jyväskylä.
This means that no extra noises and non-relevant disturbing should occur during the two hour lectures.
Of course mathematical questions are wellcomed.
3. The final program will be negotiated at latest on Wednesday afternoon.

COMPUTER ACTIVITIES: Everyone should have a User Name and Password for the University computer system (either cc, cs or joyx). Those who have not yet, please contact the Computer Centre (ATK-keskus) in M-building, 2nd floor.

There are 16 registered participants + some teachers & assistants in the Joensuu group..

Professor Junek gives 5 two-hour lectures, 4 two-hour computer labs and 4 two-hour exercise sessions
on the topics described below. Possibly there are a couple of meetings in Finnish.
The mathematical software Maple V will be used extensively,
but participants are not expected to be used to Maple V programming.
There will be Finnish speaking tutoring assistants during the Maple activities.

The volume of the course can be 1 or 2 credit (Finnish ov) .
Active participation to all sessions is enough for 1 ov,
and another 1 ov can be achieved by attending the course examination.

The course can be accepted into "Mathematics laudatur" 181300 or included in mathematics subject studies or "cum laude".
The members of faculty and the graduate students acting as assistants or tutors during the course can have it as a 1 credit
"Special course on didactical mathematics" 180702.

We can accept at most 25 participants, and they will be chosen in the order of registration.
Therefore all must registrate through email to Martti Pesonen, or by signing up the list on the Mathematics Department
bulletin board in the third floor of the M-building.

The course is related to the MODEM teacher exchange between the Universities of Joensuu, Jyväskylä and Potsdam.
The lectures will be transmitted to Jyväskylä through video-conferencing.

Contents and aims
Mathematical models of real systems of the physical, biological, chemical or busines world are mostly formulated as differential equations and as dynamical systems. In this course we will introduce into theoretical and practical aspects of this topic.
The course will emphasis the following subjects:
- How to modellize practical problems (growth models, spreading of epidemic diseases, dynamics of finance)
- What are the typical models and their long term behaviour?
- How to solve the equations explicitely, numerically or by use of computer based methods?
- How to attack the problems with the new computer era tools as Computer Algebra Systems (CAS)?
- How to use Maple V as an example of an CAS?
The activity of the students will be supported by a tuned system of lectures, exercises and practical computer activities.

Course schedule (print the table version in Landscape mode: Time-Table)

Lectures: In Auditorium M20
Tuesday   15.2.2000   8-10
Wednesday 16.2.2000   8-10
Thursday  17.2.2000  16-18
Tuesday   22.2.2000  16-18
Wednesday 23.2.2000   8-10

Exercises:
Wednesday 16.2.2000  16-18 M19
Thursday  17.2.2000  10-12 M19
Friday    18.2.2000  12-14 M19
Thursday  24.2.2000  10-12 M5

Computer Labs:
Wednesday 16.2.2000  14-16 M17
Thursday  17.2.2000  12-14 M17
Tuesday   22.2.2000  10-12 M17
Wednesday 23.2.2000  12-14 M17

Examination: Friday 25.2.2000 12-14 M17

Course Program

1. Growth and decay: Some dynamical systems
Malthus and Verhulst model, discrete and continuous difference and differential equations

2. Differential equations
Initial value problems, separable variables, linear differential equations

3. Existence, uniqueness and stability of the solutions
Direction fields, existence and uniqueness hypothesis, numerical methods

4. Linear systems and linear equations of second order
The flow x(t) = exp(At) x0, phase diagrams

5. Critical points and stability
Classification of critical points, stability, Ljapunov method


More info:

Dr. Martti E. Pesonen
Martti.Pesonen@Joensuu.Fi
http://www.joensuu.fi/matemluonto/matematiikka/

Prof. Heinz Junek
junek@rz.uni-potsdam.de

Dr. Lenni Haapasalo
Lenni.Haapasalo@joensuu.fi
http://www.joensuu.fi/lenni

Other links:
University of Potsdam
http://www.uni-potsdam.de
MODEM teacher exchange
http://www.joensuu.fi/lenni/erasmus.html