Messages

• The previous message indicated that the 2013 exam would be given priority. The only feedback I've got indicates that this is a good idea.
  However, I have also learned that phase planes is a topic some of you struggle with. I'll say a few words if time permits.
• An error discovered in the solution to the 2014 exam; new version will be uploaded by tonight.

So nobody shows up ... well most of you do have exams. 

• If you want 2012 covered the upcoming Tuesday - or intend to show up at all - please leave me a note. 
• By now, seminars have covered full "recent" exams 2017, 2015 (in pieces), 2014 and 2009, and parts of several others. 
• So I suggest that you use 2012 (mentioned above) and 2013 for "mock exams". I'll leave 2013 for the 29th.
• Q: Do you need another "mock exam" (i.e. an "unseen" full set)?

Other than that, I suggest that you do the remaining parts of 2016 and 2011. 

Nobody showed up this Tuesday. Next Tuesday, 1220 is occupied. I (Nils) will be in my office 1243, but should a larger room be required - something I doubt - we'll find one. 

Page 2 should say "satisfies Arrow's sufficiency condition, so we know
we have the optimal solution."

So I'm here Wednesday after all, but I'll keep the Tuesday up as well.

I will not be available Wednesday. I am however available Tuesday from 1330-ish (about the same time, 1220 will be available as well, it seems). 

My apologies for the inconvenience. (That said: Median attendance has been 1 person.)

• Eric's notes from today are uploaded. 
• Nils' consultation hours the remaining part of the semester:  
  • tomorrow (1220)
  • Wednesday in a week (1220)
  • None May 2nd. Then switch to Tuesday 1015-12 (i.e., lecture time):
  • Tue 8th (1220)
  • only if requested on the 15th: room 1220 is not vacant, but we'll find a room if you are interested in the middle of your other exams
  • Tue 22nd (1220)
  • Tue 29th (1220).
• The Leibniz rule: as mentioned in class, the exam will not assume it was known. (But, if you want to have a look: the note for Math2 is here.) 

Added afterwards: and the seminar problem sets are as "DRAFT"ed.

The note for tomorrow, Optimal control theory #3, had an unsolvable question (due to a detail I didn't spot). The correct one has on the handwritten part of page 2: "Question: where could we / can we not end up at T?"

If your copy doesn't ask that, please reload.

• Note for tomorrow (handwritten, largely).
• Revised note for today (only a sign fixed). 
• Curriculum note on optimal control. This was replaced shortly thereafter by a corrected version; if the line just below the title doesn't read Things you need to know (and a few things you need not care about)", then please reload. 

[message supersedes one from earlier today.]

While you wait for my lecture note for tomorrow (to be uploaded later this afternoon), check that curriculum note.

Edit: if your version does not say "Things you need to know (and a few things you need not care about)." just below the title, please reload.

• Uploaded: Note for tomorrow, and Eric's notes from Friday's seminar.
• Next seminar: Eric is unavailable this week.
  I propose: to postpone it to Tuesday in a week (lecture time & place). If so:
  • A lecture on Friday, covering proof by induction and your requested review topics?
  • Difference eq's and dynamic programming: Wed-Tue-Wed rather than Tue-Wed-Tue.
• Also need to discuss: review closer to the exam (which is June 1st).
  I propose, to be discussed in one of this week's lectures:
  • To allocate some "consultation hour sessions" without agenda - or with requests.
  • But: would like to know when your other exams make it infeasible. (Besides I have a couple of calendar issues too.)
• Finally, Ida pointed out to me that although the Leibniz rule is now Mathematics 2 (not 3) curriculum, some of you have taken an earlier version of Ma...

... and bugfix for today. 

In the typeset note on diff.eq.'s, an "eigenvalue" in last line of p1 should be "eigenvector"; corrected version uploaded, and thanks for notifying me. - Nils

So by rushing Bernoulli's differential equation, we got done with diff.eq.'s today. Tomorrow, we'll cover double and multiple integrals. 

• Lecture schedule updated with book references.
• Brief preview note uploaded
• Also, upon request: a note on linear diff.eq. (systems) and stability.

The update in the lecture schedule might cause changes to the problems drafted, but I will be hesitant to add much (if anything) for the upcoming seminar.

• Note for tomorrow uploaded.
• The lecture schedule is (retro-) updated with correction mentioned earlier today.
• Also, draft schedule for the rest of the semester - with draft problem assignments - are posted.
  I can still put up a review lecture/problem seminar close to the exam though.

So last Wednesday was FMEA 6.4-6.6 (MA2 2.6-2.8). Tomorrow is FMEA 6.6-6.9 though only local stability (MA2 2.8-2.11). 

Some old, which use overbar for vectors/matrices.

If you want to see plots on how linear homogeneous (constant-coefficient) 2x2 systems look, then there is a lot out there on the 'net; e.g., these slides. (Beware, no special font is used to indicate vector/matrix.)

Short draft note is a bit old/new/borrowed/blue again. 

Then the schedule. Upon popular request, an experiment: turn my consultation hours into a "Mathematics 2 workshop" thing. See http://www.uio.no/studier/emner/sv/oekonomi/ECON4140/v18/timeplan/index.html#SEM-F . (None the first Wednesday after Easter.)

A solution note covering this and the previous seminar is uploaded.

Problems for next week will in part require Tuesday's lecture; there will be some diff.eq.'s and some drill on trigonometric functions. Expect at least the following to be included now or assigned later:

• 4-03 and 4-04 (the Leibniz rule is now Math 2 curriculum, but sin/cos are not ...)
• 5-05 (may not be given priority)
• 6-08
• 6-10. It is not curriculum to solve this equation from scratch, but given the hint it is curriculum to be able to construct the general solution of the homogeneous. For (b) ... make an educated guess!
• 6-12 (a) and first question in (b). Terminology: equilibrium value = constant solution.
  The rest will be assigned for later.
• 6-02. In (b), try the hint and fit coefficients!

You should also be able to do 6-01.

So 3-05 (c) reassigned due to a mistake of mine, one Math2 review problem introduced, and the last problem relegated to "optional".

• Seminar problems will be updated later today. You can consider the last "awkward"-tagged quasiconcavity drill purely optional, but another problem will be added.
• I have uploaded draft notes for tomorrow - a mix of old and new, so a bit of redundant stuff on pages 3 and 7. (And for some strange reason, it refused to add margins to the right - so they are to the left.)
• Tomorrow may either be first trigonometrics and then diff.eq.'s; or, diff.eq's and then introduce sin/cos when we need them. 
• I also updated today's note with the missing "b".

"DRAFT". I will probably add a problem after Tuesday's lecture. You can start working from the top in any case, and for now consider the last (quasiconcavity) problem optional.

I will post solutions to today.

So the max/min #3 and #4 are for the two upcoming lectures.

Both are "drafts".