Applied Nonlinear Dynamics and Chaos
UBC Math 345, Jan-April 2012, Announcements
- 04.04
- Regarding the final exam:
- Time and location: April 13, 3:30-6pm, in MATH 204.
- Extra office hours before it: Wed and Thu 2-3pm (April 11 and 12).
- One page of 2-sided notes, and a non-programmable, non-graphing calculator are
allowed.
- It will cover up to and include section 10.4. Materials after that will not be
covered since we did not spend enough time on them.
- The content of the exam will be evenly distributed. The weight of each topic
will be roughly proportional to its lecture hours. See
Lecture summary page.
- The format of the exam consists of around 6 computation problems and one
multiple-choice problem with several sub-questions.
- 04.03
- TA comments on Homework 9 and Lab 5
-
Most people got perfect on the lab as long as
they recognized the existence of choatic behaviour, sensitivisty to
initial conditions in the first two cases and the lack thereof in the last
case.
- 03.28
- TA comments on Homework 8
-
I did not mark 8.2.9.
- For 8.3.1, many (if not, all) students made trapping regions that appeared
to be satisfactory visually, but they did not provide well defined boundaries in terms of
equations. I decided that I would accept a picture of a trapping region as long as it appeared
to be sound.
- 03.23
- TA comments on Homework 7
- Overall the assignments were well
done, but there is something that I think may need some clarification.
- The Poincare bendixson theorem requires that one can find a CLOSED
trapping region where the vector field points into the trapping region
(or at least is locally tangent to the boundary?) As long as students
gave a closed region where the vector field pointed in, or was tangent
to the boundary, I gave them full credit.
- TA comments on Lab 4
- I took some marks off the lab papers of some
students where it is obvious that figures were copied (i.e: one student
made the figures and shared them with others). My reasoning was that
learning how to use xppaut is a key component of the course and showing
proficiency and ability to use it is important.
- 03.16
- TA comments on Homework 6
- I think
students for the most part did very well.
- In question 6.8.7, many students did not state the key point for why
no periodic orbit exists near (1,3): That there is a trajectory along
the unstable manifold of the saddle point at (2,0) that approaches
(1,3).
Some students may have a grievance about lost marks here, which may
be valid as sometimes I was debating about whether their explanations
were good enough.
- 03.07
-
Final exam is scheduled on April 13, 3:30-6pm, in MATH 204
(our classroom is MATH 203).
- TA comments on Homework 5
- Overall: The assignment was well done. Marks
were deducted mainly
due to incompleteness of the questions (i.e. In 6.5.11, very few
students filled in the basin of attraction).
- 03.01
- The due date for Lab 3 is further postponed to Wednesday March 7.
- TA comments on Homework 4
- Overall:
- Very well done. Answers were well explained.
-
6.3.4:
- The vector field plots could be greatly improved by doing some
localized analysis about the fixed points (i.e: what are the eigenvectors
and eigenvalues of the linearized system? How do trajectories
approach/diverge from fixed points?)
- TA comments on Lab 2
- Students did pretty well in general, but often did not plot full
bifurcation curves with AUTO. (i.e: They did not plot a curve of stable
solutions). I took off a mark when that happened.
02.29
- The average of the midterm exam is 33.25 out of 50, or 66.5%.
I have decided to add 5 marks to everyone to raise the average.
- Lab 3 was due Friday March 2. You can hand it in on Monday March 5
since I posted lab 3 late. Homework 5 is still due Friday March 2.
- Due to a seminar at a nonusual time, I need to move the office hour
4-4:50pm on Thursday March 1 to 2:00pm - 3:30pm. This is a one-time only
change.
- 02.10
- Midterm exam on Feb 10 will cover up to and include section 6.5. It
will have 3 problems similar to those in the homework
assignments. One page of 2-sided cheat sheet is allowed.
- Final exam is scheduled on April 13, 3:30-6pm.
- TA comments on Homework 3
- I did not mark 3.6.3 for time and because the question was not
sufficiently structured to make for an easy marking job.
- I do not have any significant comments about this assignment.
02.03
- TA comments on Homework 2
- Overall:
- Kudos to many of you for catching the error in the solutions about the
subcritical pitchfork bifurcation in Question 3.4.11c). Those who noticed said
bifurcation have been given a bonus mark. Those who did not catch it will not be
penalized for missing it.
- Students should be careful to read the problem carefully as many marks are
lost for things like forgetting to state the stability of a fixed point,
etc. Please label axes and points of interest in your plots more clearly. I am
also going to be very picky about clear and explicit answers in the next
assignment. Ambiguity will be looked upon negatively and marks will be docked.
- Question: 3.4.11b)
- I decided that full credit could not be given for only drawing the curve of rx
- sin(x) to show that there was only one fixed point. A more analytical
explanation was called for. See solutions for an example.
- TA comments on Lab 1
-
Overall:
Well done! I can see that most students have a good grasp of xppaut and made
very lovely plots. Please do not feel restricted to the predefined plot window
with when making your figures. Try to choose plot windows that best capture the
behaviour of interest in a given question (i.e: the oscillatory behaviour in
question 2).
01.30
-
As announced in class last Friday, I would like to change my office
hours
to Wed 2pm-4pm and Thu 4-4:50pm. As before, you can make appointment with
me
in other times. You can expect to see me in my office in the above times
without making appointment.
- Due to the low attendance to the Lab, our TA will no longer appear in
the Lab. Instead, if you have any question about the lab assignments, you
can email him at [address removed].
If you have any question regarding the marking, please communicate with
me, not him, so as not to increase his work load.
01.23
- TA comments on Homework 1
- Overall:
- Good understanding of linear stability analysis and finding
stability by plotting one dimensional flow.
- Sketches were generally well done.
- Students should take greater care to make their final answers
explicit (i.e: Showing a plot of f(x) and the flow lines is
insufficient when asked to find fixed points and state their
stability).
- 2.3.3:
Note that N = 0 is not in the domain of -aN*ln(bN), and cannot be a
fixed point since N' is undefined there.
- 2.3.4:
Very few students stated the conditions on a,b,r needed for an
intermediate value of N for the relative growth rate to be maximized
at an intermediate value of N. Also, the stability of the fixed
points is dependent on the values of a,b, and r.
- 2.5.1:
c is not necessarily an integer. The question states that c is real
and constant only.
01.11
- Bonus points will given to the first person who informs me a mathematical error in the textbook or my solutions.
01.06 & 01.09
- Lab: LSK 121, Wednesdays from 01.11 to 04.11, 3pm-5pm.
Our TA will be there on the first 3 labs (01.11,
01.18 and 01.25) between 3-4pm to help you get familiar with the software.
- Office hours: M, W, Th 11-11:50am.
- Assignments are due Fridays.
01.04
- Welcome to Math 345!
Check this page frequently regarding any
announcements for the course.
- If you have registration issues, please visit this math department Registration
Issues webpage. The Math Department Undergraduate Chair, Professor Rajiv Gupta, will help you during the
Registration Assistance Sessions. Note that Math Instructors Do Not Have
the Authority to Sign You Into Their Section.
- I will send a test email to everyone this afternoon. Make sure you can
receive it.