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Here is a link to solution suggestions for yesterday's exam. Thank you for taking the course and have a nice summer!
The curriculum is the following sections from Tveito and Winther’s book (will elaborate on important points next week):
1.1-1.4
2.1-2.4 (excluding 2.2.3)
3.1-3.8
4.1-4.5
5.1-5.3
6.1-6.4
7.1-7.5
8.1-8.5
9.1-9.5
10.1-10.2.
I've corrected the hand-ins of Oblig 2, and I'm happy to say that the performance was broadly very good. A solution suggestion to Oblig 2 is uploaded to the "file" directory in Canvas.
Particularly in question 3 a) it was perhaps not clear whether a simple reference to the theory or a mathematical argument for the sought maximum principle was requested. Let me therefore note that for full score on an exam, I expect a mathematical argument for why a property holds, unless otherwise is clearly stated.
I have uploaded my notes for the topics mentioned above in the folder "Some lecture notes". Among other things, the proof argument for Lemma 2 in Lecture 29 (see Proposition 9.3 in TW) is polished in the notes.
Oblig 2 can now be downloaded from here
There was a typo on the third last line (line -3) of page 3: |u^n_j - v^m_j| should have been |u^m_j - v^m_j|. Oblig 2 online is now corrected.
I made a bit of mess of the formal solution in exercise 5.3 a) in the lecture today. In particular the solution of T_0'' = - \lambda_0 T_0 for t >=0, when \lambda_0 =0. As we speculated, the general solution of this ODE is indeed T_0(t) = \bar{a}_0 + \bar{b}_0 t for some constants \bar{a}_0 and \bar{b}_0 that are to be determined from the initial conditions of the PDE. See the solution suggestions for one way of solving this problem.
Is uploaded to Canvas. See Files/oblig1Solution.pdf
Here are some notes explaining why u(x) = c_1 cos(beta*x) + c_2 sin(beta*x) is the general solution of the above ODE.
I will not upload lecture notes to the web page this year, but my lectures will not deviate so much from last year's lecture notes, that can be found?here, and solutions to some exercises can be found?here
Click this link for hints to homework exercises that are not covered during lectures. The document will be updated most weeks of the course.
The student representatives in this course are Zejing Wang (zejingw@math.uio.no) and Zhen Wei Luo (zhenwl@math.uio.no).
The first lecture will be on Thursday 18/1. The course will be based on the book Introduction to partial differential equations by Tveito and Winther. I will give an outline of the topics we will cover and the structure of lectures and exercise sessions in the first lecture.