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Handwritten note uploaded here. Should be correct, after I fixed a detail on what is required. I bet some of you submitted a much nicer phase plane sketch than mine.

And, Kolmogorov decided to award the lottery prize to G?ril. Congratulations. 

- Nils.

• First, concerning the exam: I assume everybody knows that the exam is open-book, and that by now you have gotten used to the new location.
  The problem set is English only, but - see the first link - you can write your papers in Norwegian, Swedish, Danish or English.
• The solution note for 2016 had the sign of the beta in 4(b) wrong. I hacked the PDF and uploaded, but you do not need it if you just change the sign "by hand".
• Availability before the exam: Tuesday (the day before the exam), I (Nils) have a Mathematics 2 review 1015-12 and possibly extended as long as they need it, but after that I will be available. Thu+Fri+Mon: drop by, or send e-mail to be sure. ...

You requested a review lecture then. 1015 appears to be fine with you. I have one minor reservation for the time, but let us schedule that. 

Usually I cover the most recent exam. It is now uploaded together with a note from the grading committee; no formal guideline was written then.

- Nils

(English from now on.)
Concerning the 5150 problem, I had to update the text again. Stability of 2nd-order equations will require Monday's lecture, and maybe we should not focus on the case that is stable but not asymptotically so. 
As pointed out in the now-deleted message in Norwegian: You shall not deduce the equation nor worry where it emerges from (though, take note that 0<p<1), and you shall not deduce K; just take it to be a constant. Also, for a particular solution when p=1/2: see the hint.

- Nils

Jeg har ordin?rt treffetid fra 1415. Om det skulle v?re behov: send meg en mail.

The evaluation form is up, as announced in class. In order to reach those who attend seminars only, the administration may send a mail to everyone. 

I routinely put up a review session at the end, covering, inter alia, the last ordinary exam which I will publish in the folder fairly soon; that review will be after the last ordinary teaching, if it can be fit to schedule. Yikai or possibly Eric may discuss time with you. 

Eric got a request for a little bit of teaching on software. Just like the complex numbers, I think that is something that should not take "ordinary" teaching time. Then the review lecture is also "bonus" in addition to what is allocated. So here is my suggestion:

• If we can fit a review lecture, then Eric can spend a bit of time on a seminar introducing you to ... Matlab, likely. 
• That could mean more leftovers from the seminar - that can be covered in the revi...

Tomorrow: 

• Proof by induction. 
• Whatever else - please e-mail me requests by tonight, and I will catch them by tomorrow morning. I have one: MA2 ch 4 (concave and quasiconcave functions) - practical problems and problem types.

Also, the control theory note is updated; on two occasions it said p(0) when it should have been initial time t₀ and I caught a few typos and changed wording a bit.

... with examples. We will be done with that on Monday.

Also, Eric's notes for seminar 7.

Please let me know if this is overload.

This message supersedes the one from yesterday.  

I was made aware that the subsections stated in the diff.eq. part of the lecture schedule, is not precisely what we have been doing. A note is uploaded. 

Jeg foresl?r ? ta det p? onsdag klokka 1415, har reservert auditorium 4.
Komplekse tall er ikke direkte eksamensrelevant, men det kan f? en del ting til ? falle p? plass.

Diskuterer det i morgen.

Next week there is lecture on Monday, but nothing on Tuesday. We'll discuss on Monday which of the below problems that should be assigned for the seminar Tuesday 28th.

Problems: 

• Here is a screendump of a couple of problems assigned for last year. The first of these is a "puzzle"-ish problems you should not spend too much time on, but you should definitely have a look at the last, shorter one.
• 1-05, 1-04, 1-07 and 1-08; 1-08 might be hard - if so, try 1-01 first. In 1-07, you need to know that "mutually orthogonal" means that the dot product of any two of these, is zero.

Also, Eric's notes for the two first seminar are uploaded.

I have had a look at the schedule, and there is some lecture "lost" to some arrangement.  In order to be able to assign problems for these weeks where there are few seminars, I switch order. The schedule will be updated in a few minutes, but Monday will be the following:

Eigenvectors and eigenvalues

Given a square matrix A. Question: for what vectors x does there exist a number ¦Ë such that Ax =¦Ëx? These (eigen-)vectors and numbers (eigenvalues) have applications for topics we have already covered, and for topics to follow later.

Read: FMEA 1.5, 1.7 (1.6, 1.8 in 1.ed) / LA 10.3, 10.5 

Not so many, since I conjecture there may be some of the "previously" posted that could still be requested - please let me know by Monday.

• By late tonight, please send me suggestions for whatever of the problems to cover tomorrow. I'll look into it. So short in advance, I will certainly have to just make an executive decision.
• The end of the problem:
  • We found a threshold value, which I denote as t, which was 288/23. It had the following properties: if (and only if!) k>t, then positive definite; if k<t, then indefinite. We know that the form is not negative semidefinite, so for k=t there are only two possibilities: indefinite, or positive semidefinite. 
    The following shows positive semidefiniteness at the threshold level k=t:
  • k is a parameter in the function, and Q depends continuously on k. 
  • For any k>t, it is so that Q(x,y,z)>0 for every non-null (x,y,z); that is positive definiteness (which we have proven!)
  • Fix (x,y,z). Then Q(x,y,z)=q(k) depends on k only. For k>t, q(k)>0. Let k->t from above. Then q...

The contact student is G?ril Louise Andreassen, username gorillan (I said it would be easy to remember, and I forgot the "n") - and then @student.sv.uio.no , written this way for the sake of spamshielding. 

There is no seminar next week. Nevertheless, do the posted problems to next Monday - and le'ts then discuss the need to spend a bit of Tuesday's lecture to cover anything.

Messages stay in English for the time being, in case someone who are less fluent in Norwegian needs to follow the course from the distance - but I'd appreciate a notification as to whether there are any who need it.

The course web page now links to a live document of problem assignments, which I will update weekly. The problems for the first seminar are assigned.

It may be a bit too much for two weeks, since I added a couple of problems (and the optional ones). It would be helpful if on Monday you have some idea on what to give priority to.

Old exam problem sets, and the compendium, are found in the left margin link "Problems for seminars etc.". Please start doing a little bit of each of the following topics, and then on Tuesday we will discuss briefly what the first seminar should focus on: 

• Let f(x) = g(||x||). What is the gradient of f, in matrix form?
• General differentiation/integration drill for trig. functions: 
  • Differentiate f(t) = tan t = sin t / cos t, and write the answer in two ways: one which has only "cos" (no sin nor tan) and one which has only "tan" (no sin nor cos).
  • From the previous point, you should be able to show that the derivative of arctan t is 1/(1+t^2).
  • Here is a one which you should not spend too much time on, but which shows the method of substitution in a way that might be a bit less familiar: 
    F...

As mentioned today, I will put in a little bit of this. Suggested reading in advance: https://en.wikipedia.org/wiki/Radian - and find the "Rad" button on your calculators.

The content of the course is by and large the same as previous semesters. You will either need the English or the Norwegian syllabus. Problems will largely be the same as well; last year's problems can be found at http://www.uio.no/studier/emner/sv/oekonomi/ECON4140/v16/seminarproblems.html 

The order of topics will be slightly modified, with elements form integration first. As of now, only the first week is entered into the schedule, but when that is done, we will start on convexity (which most of you should know from ECON4200).

- Nils