| Teaching |
There
will be 2 hours lectures and 1 hour tutorials per week for 10 weeks
(including revision on week 10). Exercise sheets
will be posted on-line and given to students during the tutorials.
Solutions will be posted on-line later on.
My lectures will be mainly based on the notes of Dr G. Bowtell
who taught this course before. You can download an slighly updated version of those notes
here.
Students are expected to attend lectures and advised take their own notes. Beware
that having the lecture notes is no guarantee that you will understand the material if you
do not attend lectures.
The syllabus for this module can be found
here.
There are lots of books in the library that cover all or part of this module.
Most books with title
"Ordinary Differential Equations" or "Dynamical Systems" should cover much of what we will see.
Click
here
to find the list of books with these or similar titles in our library! Out of
these books, the one that I will use the most is "Dynamical systems : differential equations,
maps and chaotic behaviour", by D.K. Arrowsmith and C.M. Place. This is also available at our
library (see
here).
It may also be a good book to buy, specially if you want to continue studying Dynamical Systems
in your 3rd year.
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Assesment
|
The module will be assessed through a combination of coursework and exam.
There
will be 2 courseworks
(contributing 10% each towards the final mark) and an exam contributing 80%
to your final mark. A minimum of 40% must be obtained for both coursework and
exam in order to pass the module. The exam will take place in
April or May 2011 and
will consist of 5 questions.
You need to complete 3 questions out of 5 in order to get full marks.
The first coursework will be an in class, open book
and multiple choice test. It will take place on week 5 of term,
on the 10th
of February 2011, during the lecture. The second coursework will
be given out on week 8 of term (not counting reading week). Finally, there
will be an extra optional coursework, which will be given out on week 6. This will not count
towards your final mark, but any students that hand it in, will receive feedback on their work.
|
| Past
papers |
Solutions
to papers up to 2008 can be found here.
The 2010 & 2011 papers and solutions are available here.
|
Exercise
sheets
|
Sheet 1 and Solutions
Sheet 2 and Solutions
Sheet 3 and Solutions and
Phase diagrams question 2
Sheet 4 and Solutions
|
Handouts
|
Summary of solutions to type I, II, III and IV equations
Examples of phase diagrams of type I
Examples of phase diagrams of type II
Examples of phase diagrams of type III
Examples of phase diagrams of type IV
|
Coursework
|
In-class test solutions
Test 1 (green) and Solution
Test 2 (blue) and Solution
Test 3 (pink) and Solution
Test 4 (yellow) and Solution
Coursework 2
Coursework 2 is available here and the solutions can be found here
Please note that this coursework is optional and will not count towards your final mark
 Coursework 3
Coursework 3 is available here and the solutions can be downloaded from
here and the phase diagrams can be found here
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Software
|
The software that you will need to carry out the last exercise in exercise sheet 1 is available from
here.
It is an Excel file with a VBA subroutine (similar to the ones we saw in Programming last year!) which,
when run, produces a velocity diagram for a given system of differential equations.
In order to use the software, open the Excel file and go to the VBA editor.
You will see towards the beginning of the code that there are two lines
where you need to enter information about the equations you want to solve (the missing information is replaced by ...).
The lines "X_1=... and X_2=..." require you to enter the r.h.s.
of the equations. The line "Const Xmin = ..., Xmax = ..., Ymin = ..., Ymax = ..., N = ..." requires you to enter
the maximum and minimum values of the variables x and y in the
region where you want to do the plot. For the problem in exercise sheet 1, those values are 2 and -2 respectively.
Finally you need to
enter the value of N. This is a parameter that determines for how many points is the tangent line drawn.
N=25 is a reasonable value to take.
A detailed explanation of how the code works is available from Dr. G. Bowtell's
web page (see coursework 1).
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