This course is replaced by MAT3440 – Dynamical systems.


Published June 2, 2017 7:05 PM

I have posted proposed solutions of the exam problems.

Hope you enjoyed the exam!!

Have a nice summer!



Published May 19, 2017 10:45 AM

We didn't get time to do the last section in the notes of TS. So from those the curriculum is

from the beginning of the second part "Calculus of variation" that starts on page 18 until the section called "Weierstrass' sufficency condition" on page 34. 

Published May 19, 2017 10:42 AM

Next weak I'll give short recapitulation of the course and do some exercises.


Here some exercises I can do:

Exam 2015 No 2, 3 and 5.

Exam 2010 No 1 and 2.

MAT 2310:

Exam 2006 No1

Exam 2009 No 1


Published May 9, 2017 8:49 AM

I plan to start on the exercises about calculus of variation tomorrow, but

one wanted me to do 2013 No 2b, so I'll do that.



Published May 8, 2017 11:02 AM

From the note by TS:

Exercise 1, 3, 5, 7, 8 and 9.



Published May 4, 2017 8:38 AM

A slight change in the curriculum. Theorem 4.7 about Lyaponov functions is included.



Published May 2, 2017 12:44 PM

I'll do the following exam problems in plenum:

2011 No. 1a and No 2.

2012 No. 2

2013 No. 1 and No. 2 a,b

2014 No. 1 and No.


We start in the second hour on this wednesday.



Published Apr. 19, 2017 10:58 AM

During the morning I have gotten ill - nauseous and dizzy - and I can not lecture to day. So the lecture is canceled.



Published Apr. 3, 2017 9:22 AM

There will be no lecture this Wednesday (that is, Wed Mar 5).



Published Mar. 15, 2017 2:22 PM

Since several of you have mid-term exams next week, we drop the lecture on Monday.

On Wednesday I'll give a short revue of what we have done so far, and do exercises (No 22 from exercises4, and start on exercises5).


Mon Mar 20: No lecture

Wed Mar 22: Revue + exercises

Good luck with mid-term exams!



Published Mar. 13, 2017 10:57 AM

Here are some exams problems that are relevant  (later in the course orthers will be as well).

June 2015 No 1,2 and 3

June 2014 No 1

June 2013 No 1

June 2012 No 1


Published Mar. 13, 2017 10:48 AM

One of the student representatives is Andrei Faitas 

Published Mar. 8, 2017 2:21 PM

You will get the problems for the mandatory assignment on Mon 20. March.


They must be delivered before Thu 20. April



Published Mar. 8, 2017 2:18 PM

To day I did the two examples on page 91.

During the exercise section I did problem 17 on page 70.


Next monday I 'll speek about theorem 3.11 (without proof)

and continue with chapter 3.

I'll tone down the proves, and concentrate on the content of the results and examples.

Next wednesday we continue with exercises from "exercises 4".

New exercises from chapter 3 will come soon.


Published Mar. 6, 2017 12:07 PM

This week we shall prove theorem 3.10 on page 86, the Picard Lindelöf existence and uniqueness theorem. Every thing is in the book on pages 72 - 87. I'll only do the first proof.

We start with background stuff:

I'll the def of the Picard iteration, then recall the def of the Lipschitz condition.

Speak about the sup-norm anduniform convergence and the function spaces C(J,R^n). A little about metric spaces

Cauchy sequences, convergence and completeness.

Then the Fix point theorem for contracting maps (theorem 3.4).

Then, finally, we'll prove th 3.10






Published Feb. 15, 2017 3:06 PM

Today, Wed Feb 15, I finished 2.6 (the example on page 53) and recalled briefly  the "phase portraits" in 2.2. On Mon Feb 20 I'll do 2.7.



Published Feb. 8, 2017 8:46 AM

Dagens forelesning er avlyst pga sykdom.



Published Feb. 1, 2017 2:32 PM

To day I almost finished 2.5.

On Mon Feb 6 I say a few words more about 2.5 and do  2.6.

May be we have time to start on 1.7.



Published Jan. 25, 2017 2:44 PM

To day I did section 2.3

On Mon Jan 30 I ll continue with 2.4, 2.5 and probably 2.6


And exercises  1 and 7 from the book. We continue with the exercises next wednesday.



Published Jan. 23, 2017 4:14 PM

To day Mon Jan 23 I did 2.1 and 2.1

On Wed Jan 25 we start on 2.3 and will probably have time to do 2.4 as well.


I ll do exercises in the second hour.



Published Jan. 23, 2017 9:22 AM

On Wed Jan 18 I basically finished chap 1, but I ll probably come back to some of the examples, like  the paragraph "Mechanincal systems". We started on chap 2.


Today on Mon Jan 23  I'll continue with chap 2.2, 2.3 and may be 2.4.

On Wed Jan 25 I'll continue with chap 2; ie 2.4 and probably 2.5



Published Jan. 16, 2017 4:21 PM

We decided to use the second hour every Wed for exercises, starting on Wed Jan 25.



Published Jan. 16, 2017 4:19 PM

To day  I basically  I did 1.1, 1.2, 1.3 and the part of 1.4  about population dynamics.

Then I started on 1.5.


On Wed Jan 19  I ll redo what I started on in 1.5 and do the rest of 1.5

I ll go back to 1.4 and do the paragraph called "Mechanical systems" and may be a few words about the two last paragraphs "Oscillating circuits" and "fluid mixing".

The paragraphs 1.6 and 1.7 are not in curriculum.

Then if time permits, I'll start on chapter 2.



Published Jan. 3, 2017 2:53 PM

We are going to use a new book for this course:

Differential Dynamical Systems by James D. Meiss

SIAM 2007

ISBN 978-0-898716-35-1