Welcome to Nonlinear Systems (HT 2011)

Here is lots of relevant information for the HT 2011 iteration of the Nonlinear Systems course (Maths B8b).

Handwritten lecture notes from HT 2010 are available both here and at the site maintained by the Mathematical Institute. Typed versions of the lecture notes are available at the latter site. Note that I will sometimes say things in lectures that aren't in the other notes, so it is useful to come. (I have been known, for example, to hint at things that I think are good problems to ask.)

The mock exam (plus solutions) that I made in 2010 is posted. I suggest taking that as a practice exam when you're studying for the exam. There will ultimately be a revision session to go over those questions, so you'll want to take this under Examination conditions (though you don't need to wear sub fusc).

I have already posted the 4 problem sheets for the course.

Lecture times for HT 2011: M, W: 11:00 am - noon, MI, L1

The tutors are Mason Porter (2 classes), Konstantinos Zygalakis (2 classes), and Chong Luo (1 class). The TAs are Sofia Piltz (2 classes), Alhaji Cherif (2 classes), and Matt Webber (1 class).

There will be 5 classes:

1. Mason + Alhaji, even weeks (2,4,6,8); Thursday 10:30-12, DHSR2

2. Mason + Sofia, odd weeks (3,5,7,1); Thursday 10:30-12, DHSR2 (+ we'll see for TT 1)

3. Kostas + Alhaji, even (2,4,6,8); Fridays 10:30 - noon, DHSR3

4. Kostas + Sofia, odd (3,5,7,1); Fridays 10:30 - noon, DHSR3 in weeks 3 and 5, L3 in week 7 (+ we'll see for TT 1)

5. Chong + Matt, odd (3,5,7,1); Mondays 2 - 3:30 pm, DHSR1 in weeks 3 and 5, DHSR3 in week 7 (+ we'll see for TT 1)



There will also be a special classe (given by Kostas) to provide an introduction to Matlab. The timing for this still needs to be determined, but there will likely be two duplicate sessions in week 3. In the meantime, please download Matlab by following relevant links on the Mathematical Institute website.

Homework due times are as follows: Assignments for Thursday and Friday classes are due Mondays at 1pm, and assignments for the Monday class are due Thursdays at 1pm. Use the box for your section that has been placed in the basement of the Mathematical Institute.

Let me know if I missed anything.

Mock Exam and Solutions posted

You can find these on the sidebar. I will upload them to the MI website for B8b shortly.

Consultation Sessions: An Update

I have updated the consultation sessions. E.g., by student request, the Tuesday week 6 session to discuss the mock exam has been moved to Friday of week 5. Go to that blog entry for details.

B8b problem sheets from years past

One student asked me about these, as they were "posted" for a few minutes, so here is the answer that I wrote to this student:

Those are from prior years, and there was a need for a complete record of B8b, and that was
the easiest way for me to download them so that I had such a record (to do it without
bothering anybody else). They were thus "posted" for a few minutes.

I can post them again because I don't mind your having them, BUT I do not vouch for
anything in there being relevant for the current course---i.e., you are welcome to use them
if you want, but I make no promises whatsoever as to whether they will be helpful. They
were not posted there for revision, though also note that the practice exam will be ready
soon, and that is posted for revision.

Answer Sheet 4 posted

I have posted answer sheet 4. You can find relevant code for particular problems by googling or by going to the MI website for B8b. (Note that the code on the MI website is from prior years, but it should be fine.)

Corrected Solution Sheet 1 posted

I have corrected a couple of small points in problem 5c (thanks to eagle-eyed students for one of them!). I have also corrected a small point in problem 1c.

Consultation Sessions

Week 2: Thursday: 4 - 5 pm (Kostas; Gibson Building [OCCAM]; RI2.3; drop in)

Week 3: Monday: 10 am - 11 am, 11am - 12 noon (Me; DHSR1; drop in)
Thursday: 4 - 5 pm (Kostas; Gibson Building [OCCAM]; RI2.3; drop in)

Week 4: Monday: 10 am - 11 am, 11am - 12 noon (Me; DHSR3; drop in)
Thursday: 4 - 5 pm (Kostas; Gibson Building [OCCAM]; RI2.3; drop in)

Week 5: Thursday: 4 - 6 pm (Kostas; Gibson Building [OCCAM]; RI2.3; drop in)
Friday: 10 am - 12 noon (Me, DHSR3). [We will go over solutions to the "fake old exam".]

Week 6: Monday: 10 am - 12 noon (Me; L2). [We will again go over the solutions to a "fake old exam" in this session.]


Also, Kostas is planning to offer a Matlab session at some point as well as a set of consultation sessions. [My understanding is that this occurred during week 1.]


Update (5/2/10): I have noticed a couple of bugs in the MI's list of consultation sessions regarding what is being covered in which session. The correct information is here.

Update (5/10/10): The room has changed for the Monday consultation session in week 4. The Tuesday week 6 session to cover the mock exam has been moved to Friday of week 5.

Times and Places of Week 1 classes (covering problem sheet 4)

Tuesday: 13:30 - 15:00, 15:00 - 16:30 - both in DHSR3 (Tutor: Radek Erban)

Wednesday: 10:30 - 12:00 DHSR3 (Tutor: Mason Porter)

Friday: 10:00 - 11:30 DHSR1, 14:00 - 15:30 DHSR3 (Tutors: Kostas in the morning and Jara in the afternoon)

Solution Sheet 3 posted

I have posted solution sheet 3. I have also posted Matlab code to simulate the standard map.

Correction to Problem Sheet 3

There was a misplaced sign (relative to the parentheses) in problem 3. That has now been corrected.

Solution Sheet 2 posted

Solution sheet 2 is now posted. Let me know if you have any questions or if you've found any typos.

New Paper on Period Doubling Cascades and Chaos

The timing of this paper is excellent, as we've been discussing it in lecture. This new paper by Evelyn Sander and Jim Yorke is a (mostly) expository paper about the period doubling route to chaos. It includes some of the pictures that I mentioned but was unable to draw, and it also relates what we've seen in maps to what we have seen a bit (problem 5 on homework sheet 2) and what we will see more in flows. I don't recommend a cover-to-cover reading, but I think a perusal of relevant parts of the paper could be helpful.

Another Typo Correct in Homework Sheet 2

I have corrected equation (11) in homework sheet 2. The third term in the second equation of (11) should have (theta_3 - theta_2) as an argument for the sine instead of the (theta_2 - theta_3) that was there before. If you tried with the old version, you'll notice that the change of variables won't quite work.

This sheet was a bit buggy with typos. Sorry about that.

Solution Sheet 1 posted

I've posted the solutions for problem sheet 1.

Lecture Notes posted up through page 55

I have now posted the lecture notes through page 55. This finishes the notes except for the 'other topics', which have not been determined yet and won't be for a while. (Please let me know if there are any that particularly interest you.) I won't create those notes until the very end.

'Special Topics' at the end?

If you have any preferences for what special topics (the ones that could change from year to year in my version of this course) you would like to see covered at the end, please let me know. Nonlinear science is a very big field, and if anybody is particularly interested in covering something, I will endeavor to say something about relevant material.

Just let me know.

Typos Corrected in Homework 2

I have uploaded a revised version of homework sheet 2 in which minor typos have been corrected. There are two such typos:

(1) In problem 1, I changed the phrasing from "find" the phase portrait to "plot" the phase portrait to make it clearer.

(2) In problem 2c, I made the definition of q-twisted state more explicit, even though it was actually there anyway.

Neither of these typos should have caused any problems.

Update (2/01/10): There is an additional typo that might be a bit problematic. In problem 3, omega_1 = omega_3 starting in part (b). I inadvertently forgot to type that and hope that this has not caused any problems. I also found a minor typo in (3), which I have corrected (there is a factor of K missing in the denominator in the definition of rho).

Remaining Class Times (And then there were 5...)

Classes (5) and (7), as numbered in the blog entry below, have now been culled.
Class (1) is about to be culled, though it's still currently listed.

There exist only 5 classes

As you have seen from the MI websites, classes 5 and 7 have been culled. Class 1 is in the process of being culled, although it's still listed (with 3 students in it) as of this morning.

Thank you for your patience with this process.

Reversible Systems

I was e-mailed about reversible systems because of question (1) in homework sheet 1, and here is my answer (that I am posting here because it is relevant for everybody):

I checked the definition of reversible system after the lecture to check
whether I had a typo (given the question that came up). I don't remember
what I wrote on the board, but the one in the scanned lecture notes is
correct. Because of that, I didn't bring it up again in lecture the next
time.

In fact, it should be g(x,-y) = g(x,y), so it sounds like I put an extra
minus sign in the lectures.

You want invariance under (t,y) -> (-t,-y).

Lecture Notes posted up through page 43

Read the title.

Also, homework sheet 2 has been posted for a week or so, and homework sheet 3 will be posted shortly.

Problem Sheet 1 corrected

I forgot to put an equal sign in the statement of problem 7(a). This has now been corrected.