MTH739U/P: Topics in
Scientific
Computing
Information
- Deadline for projects: April 1st (official) extended to April 15th
- Lecturer: Dr
Hugo Touchette
- Office: B53
Maths Building
- Module information/syllabus
- Lectures (2
hours/week): Thursday 9-11
- Tutorials (2
hours/week): Friday 11-13
- Office hours: Thursday
11-12, Friday 10-11
- Assessment: courseworks
50%; independent project 50%
- The School has a programming
seminar on wednesdays
Courseworks
- Weeks 1-3 coursework [pdf],
solutions [pdf]
CW due: Thurs
Feb 3, by 5pm
- Weeks 4-6 coursework [pdf],
solutions [pdf]
CW due: Thurs
Feb 24, by 5pm
- Weeks 7-8 coursework [pdf],
solutions [pdf] CW due: Mon
Mar 21, by 5pm
- Weeks 11-12 coursework
[pdf],
solutions [pdf] CW due: Fri
Apr 1,
by 5pm
Sources for lecture notes
- Chapter
1: Programming in Matlab/Octave
- Chapter 2: Numerical
solutions of ordinary differential equations
- Chapter 3: Random number
generation
- Chapter 4: Simulation of
stochastic processes
References
- R.L. Burden, J.D. Faires,
Numerical Analysis, Prindle, Weber & Schmidt, 1985.
(for PDEs, newer editions available at the library)
- F. J. Wright,
Computing with Maple,
Chapman/CRC Press, 2001. (for Maple and programming in general)
- F. Vivaldi,
Experimental Mathematics with
Maple, CRC Press, 2001. (for Maple)
- C. Moler, Numerical
Computing with MATLAB
- C. Moler, Experiments
with MATLAB
- S. Kay, Intuitive
Probability and Random Processes using Matlab, Springer, 2005.
(for stochastic processes)
- W. Krauth, Statistical
Mechanics: Algorithms and Computations, Oxford University Press, 2006.
(fo r random numbers)
- P. E. Kloeden, E. Platen, H.
Schurz, Numerical Solution of SDE Through Computer Experiments,
Springer, 1993. (for stochastic differential equations)
- W. H. Press, S. A.
Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes: The Art
of Scientific Computing, Cambridge University Press, 2007. (for ODEs,
random numbers and much more; see online
version)
Possible
projects
- Full implementation of
Runge-Kutta integration with applications
- Symplectic integrator (for
energy conserving, Hamiltonian dynamics)
- Double chaotic
pendulum
- Spherical pendulum
- Balancing stick dynamics
(delay differential equation)
- 2 and 3 body problems
- Comparison of different
orders of numerical integration
- Generation of stable
variates
- Generation of random vectors
- Random walks and diffusion
- Diffusion in 2 and 3
dimensions
- Random walk method for
finding minima of functions
- Levy random walks
- Fractals
- Iterated function systems
(dynamical maps)
- Bifurcations in dynamical
systems (examples)
- Delay differential equations
(e.g. Mackey-Glass equation)
- Fast Fourier
transform
- 3x+1 problem
- Black-Scholes model
- Strange attractors of
chaotic systems
- Feedback control systems
- Galton board (Binomial and
Gaussian distributions)
- Random matrices (2x2 and
3x3)
- Sampling estimation of Pi
- Partial differential
equations (applications to Burgers equation)
How to log on to
Windows XP
- Start the
computer
- Select the
'Standard Student Service'
environment
- Enter your login
name in the QM blue login
window
- Select the
'Windows Standard Service'
environment
- In the Novell
Client window, enter your
username and password
- That's it;
Windows XP should now start up
Starting Octave
- Select the
'Start'
(green) button
- Go to
'Programs/Dept/Octave/'
- Select 'Octave'
- In the Octave window, move
to your current directory by typing
cd 'G:/My Documents/'
- You can also move your
current directory to a USB stick
- Start your editor window by
typing
edit
Matlab/Octave resources
How to copy or save a graph
produced by Octave
- Method 1:
plot(...)
print figname.pdf -dpdf
- Method 2:
var=figure;
plot(...)
print(var,'-dpdf','figname.pdf')
- Method 3:
1. Right-click on the top blue bar of the graph
2. Select 'Options/Copy To Clipboard'
3. Paste the plot in a drawing software such as Gimp or IrfanView
(available in 'Programs/Public/14-Drawing')
4. Save you image in eps, gif, jpg or pdf in your document directory
- Note: On Mac computers, you
can save figures in pdf by choosing
'Save as' in the Aquaterm window
- Use the option '-deps' for
black and white encapsulated
postscript and '-depsc' for color encapsulated postscript
- See Help
on
print for more output formats
Network Octave bug on Windows
- For some reasons, Octave
doesn't see scripts (m-files) that are
newly created on network drives such as the 'G:' drive (your home
space) or USB sticks.
This is a known
issue apparently. The solution
is to type
path(path);
everytime you create a new function or script.
- This bug only affects
networked and mounted drives. You should
have no problem running Octave on your home PC or laptop.
Installing Octave
- On Windows: Download the
Octave Windows installer from the SourceForge
site and follow
the instructions of the installer
- On Mac: Download the Octave
app from the SourceForge
site and follow
the instructions of the installer
- Note for Mac users,
Mac OS v 10.5.8 and later (essentially
Snow Leopard): Octave won't work properly unless you fix a small bug.
Follow the instructions here
or here
Get Matlab
- Individual, student licenses
for Matlab cost about £60
- See Matlab
website for info
Other programming environments
- Maple (available on campus)
- Mathematica (available on campus)
- SciLab: Matlab-like, free
Copyright
©
HT 2010