Messages - Page 3

On Friday I proved theorem 3.3.4 in Tom's (theorem 14.4.4 in the red book, for those who read that). In to day's lecture I'll start on 3.4 which is about an application of Banach' fixed point theorem to differential equations. If time permits, I'll start on 3.5

Geir

Ark4 with exercises for week 8 is posted:

Thursday 23/2: 3, 4, 8, 10, 11, 12.

Friday 24/2: The rest on Ark4.

G

I have made a sheet with solutions to the friday exercises on Ark1. They are sketchy, some times only extended hints, but anyhow, I hope they will be useful for you.

I also posted a small note about Perron's theorem, which I talked about a little more than a week ago. It is not part of the curriculum, but made for those of you who are interested.

Geir

Yesterday - monday 6/2 - I started on chap. 3. We did 3.1 and most of 3.2, but due to a fire alarm, we had no time to the proof of prop 3.2.4. Will do that on friday. I will also do exercises 7 and 8 in 3.2 in the lecture. Then we go on with 3.3, and may be if the time permits, start on 3.4.

Geir

Exercises on fridays has been moved from room B71 to room 534. Time and place is updated.

Exercises for week 7:

Thursday 16/2: From Ark3: 3, 4, 5, 6, 9, 10, 12; From Ark2: No 27, 28

Friday 17/2: From Ark3: No: 1,2, 7, 8, 11, 13

G

Exercises for week 6:

Thursday 9/2: From Ark2: No 2, 7, 8, 16, 17, 19, 20.

Friday 10/2: From Ark2: No 1, 5, 6, 9, 11, 12, 15, 23, 24.

G

In the lecture yesterday (Monday 23. Jan) I did what was left about open/closed sets and did continuous functions --- that is, we have done sections 2.2 and 2.3 in Tom's notes. I also include a little about the closure of a set, basically problem 7 on page 33 in Tom's.

On friday I'll do section 2.4 on complete metric spaces and Banach's fixed point theorem.

Next week we will do 2.5 and parts of 2.6 about compact spaces. The entire section 2.5 will be done, but from 2.6 only def 2.6.1, prop 2.6.2 and the statement of theorem 2.6.6 (i.e not the proof) will be included.

That week I am in USA, so Inger Christin Borge will give the lectures.

To day I did open and closed sets until prop. 2.3.6 in Tom's notes. I also did continuous functions, def 2.2.4 and prop 2.2.5.

On monday I ll do prop 2.2.6 and def 2.2.7 and, finish 2.3, and may be start on 2.4, complete spaces.

Ha en god helg!

Geir

There is also a misprint in problem 7: f(x)=0 in stead of f(0)=0. Corrected version of Ark1 is on the web.

Geir

Exercise No 6 on Ark1 was not very clearly formulated. I have changed it, and hopefully it is better now!

Geir

Yesterday I did 12.1 from the book and started on 12.2. This corresponds basically to 2.1 and 2.2 from Tom's notes. On Friday I'll speak more about closed and open sets, interior, exterior points, etc, corresponding to 12.3 in the book and 2.3 in Tom's notes.

Then: continuous functions, complete spaces (with Banach's Fix Point Theorem) , compact spaces,....

In the future I will follow Tom's notes more than the book - they are better and much easier to read than book - so, if you have not bought the book yet, you do not need to, you will do very well with Tom's. If I give exercises from the book, I'll copy them on the sheets!

Geir

Just one thing: I have no idea why our only group is called group 5. May be by same reason catch 22 is called catch 22!

G

Exercises for group 5:

Friday 27/1 : From Ark1 No 1, 2, 3, 6, 8, 10, 11

Friday 3/2 : From Ark1 No 13, 14, 15, 16, 19, 23.

Computing exercises:

Thursday 19/1 : From Analysedrypp. Ch 1: No 4, 5, 6, 7. Ch 2: 1, 2, 4, 6. Ch 3: 1, 2, 3, 4.

You will find Analysedryppe under the heading Forkurs.

Thursday 26/1 : From Ark1: No 4, 5, 7, 9, 12.

Thursday 2/2 : From Ark1: No 17, 18, 20 , 21, 22, 24.

Geir

I have posted a sheet with exercises called Ark1 . It covers next week and the week after.

Geir

Important: Tom Lindstr?m has now made new version of his very good notes from last semester, and we will to a great extent rely on those as an addition to the book.

Chapter 1 of the notes sums up some of the preliminaries, so what is covered in the course starts at chapter 2.

You find a link to them under the heading Undervisningsmateriale .

Geir

Wellcome to MAT2400!

I have posted plans for the first three weeks, further plans will come when I see how things are proceeding.

Geir

Tidspunkt for forkurs er kl. 09.15-16.00, 12.-13. januar (i Lille aud. ?st (?157) i Fysikkbygningen). Velkommen! Du kan hente papirkopi av undervisningsmateriale i ekspedisjonen i 7. etasje i Niels Henrik Abels hus.

Det vil holdes forkurs 12. og 13. januar - se under undervisningstilbud til venstre.