Messages

The resit exam instructions have been posted in canvas. Notice that the first half of the exam will consist in giving a mini-lecture on a given topic.

The statistics is as follows:

• about half failed.
• among those who passed the grades are evenly spaced between A and E.

There will be a continuation exam at semesterstart. It will be oral and last around 40 minutes. One question will be to present a given part of the curriculum and another will to be solve an exercise given at the exam.

I have posted suggestions for solutions in Canvas.

I have posted pdfs with the exams of 2016 and 2019 (without solutions), and plan to go through them in the next lectures.

Questions that would not be natural this year are:

2016: Ex 2 (part of curriculum).

2019: Ex 1 (about mean value property). 

Solutions are now posted.

I have posted a scan with my notes on Galerkin methods.

I have posted solutions to many of the exercises, in Canvas.

I posted a scan with my notes on regularity.

I have updated the course notes with four sets of compulsory exercises and four exams. Enjoy :-)

I will post suggestions for solutions later on.

Note that the curriculum has changed slightly from year to year and that this can be reflected in the exercises.

For the rest of the semester we will cover the following topics:

- Regularity results (Evans 6.3).

- Maximum principles (Evans 6.4).

- Galerkin methods geared towards finite element methods.

On Thursday 11/4 the science library will open an exhibition celebrating the 200 years since Abel's breakthrough result concerning the solvability of general 5th order polynomial equations. The program is here:

Program

The lecture on Thursday is cancelled and everybody is strongly encouraged to attend the opening. This is a niece piece of cultural history.

I have included a definition of the norm on X in exercise 2 and a definition of C^1(\partial U) in exercise 4.

I updated the assignment with some minor modifications.

It's not really clear whether you are required to hand in the assignment in latex...

I have posted it in Canvas.

Since compact operators are no longer part of MAT3400 I will postpone the material on this topic to the end of the semester, time permitting.

After easter I will start with PDE theory corresponding to Chapter 6 in Evans.

I have posted 4 scans:

One scan on the Gagliardo Nirenberg Sobolev inequality.

Three scans on compactness:

- one scan on compact metric spaces with repetitions of MAT2400

- one scan on compact linear operators on Hilbert spaces

- one scan on how this applies to Sobolev spaces.

This lecture is cancelled. Feel free to work on the compulsory exercise :-)

I have posted a scan with last weeks lectures: traces and Poincar¨¦ inequality.

Today¡¯s lecture is cancelled due to illness.

Tomorrow I will speak about Sobolev spaces in dimension 1 (i.e. on an interval) based on the notes, which I have updated.

I posted a scan of todays lecture including a proof of Piola's identity.

I have posted scans with some notes and some solutions to exercises in Canvas.

On Monday 19/2 we will correct exercises from the notes.

distances: 1.4.3, 1.4.4, 1.4.5.

H?lder: 1.4.6 to 1.4.11.

Read all and do as many as you can... We will not have time to go through them all.

I have updated the notes with a section on measures and integration. On Feb 8th I will continue to lecture on that material. On Monday 12th we will do exercises. E.g. : 1.6.1, 1.6.3 and exercises on H?lder page 27 if we get that far.

I have updated the notes with a section on functional analysis. I will continue with that material tomorrow.