Semester projects

There will be two semester projects in this class. Together they count 30% of the final mark.

OBS! This page will be updated with additional information during the project period.

The second project will count for 20% of the final grade.
Deadline: November 17, 23:59.

Project description

• 16.11: There has been some misunderstanding related to the degrees of freedom for natural cubic splines. Assume there is \(n+1\) interpolation points, and hence \(n\) intervals. In the first place there are \(4n\) unknown coefficients to be determined. However, due to continuity of the spline function and its first and second derivative, we subtract \(3(n-1)\) degrees of freedom. Furthermore, for natural cubic splines, the second derivative is set to zero at the two endpoints, so we also subtract these degrees of freedom. Summing up, there is a total of \(n+1\) degrees of freedom. I am sorry for the confusion I have given some of you. As the deadline for the project is already tomorrow, we will condone other interpretations.
• 11.11: The use of convergence rate in the problem description may be a little confusing as the lecture book uses this term differently. What we mean by convergence rate, is what the book refers to as convergence order (defined on page 22). That is, if the error goes as \(E \approx Cn^{-p}\). You may check this by plotting \(\log(E)\) against \(\log(n)\) and see if you get a straight line for large \(n\). If so, then the slope of the line is equal to \(p\). Furthermore, if the error goes as \(E \approx Ca^n\) for some constants \(C\) and \(a<1\) for large enough \(n\), then the convergence is said to be exponential. You can check if the error decays exponentially in \(n\) by plotting \(\log(E)\) against \(n\) and see if you get a straight line for large enough \(n\).
• 03.11: Regarding the self-contained MATLAB file: It is not possible to define functions in a script file. A possible work-around is to wrap your script inside a function with no input or output. Then all your subfunctions may be placed below this main function. I suggest you all to use multiple files when implementing and testing your routines. Finally, when you are done, simply copy/paste all necessary code into one single file. Remember to test that your code actually works as a stand-alone, i.e., copy your file to an empty directory and run it from there.
• 27.10: You can work in groups of up to 4 students. I will assume that you work in the same groups as in Project 1. If you need to make changes, send me a mail. For those of you that worked alone or in pairs, but now want to work in a larger group, send me a mail immediately and I will try to put you together with others.

• Table with Newton-Cotes quadrature weights: nc_weights.tab
• Tables with Gauss-Legendre quadrature points and weights: gl_points.tab, gl_weights.tab
• Help to write a short report
• Latex template
• Here are two short reports taken from the proceeding of the ECMI 2008 conference. Use them as examples on how short papers can be written. They are here for the format, not for their contents. Example 1, Example 2.

There will be no lectures in week 45 and 46. Instead, there will be supervision of the project. This is in addition to the exercise sessions on Thursdays. All supervision will take part in Nullrommet.

Please watch out for updated information here during the project.

The first project counts for 10% of the final mark.
Deadline: September 20, 23:59.

Project description

You may work in groups of up to 4 persons. Create the groups and send your student numbers to lars [dot] odsater [at] math [dot] ntnu [dot] no. If you are only one or two person(s), but want to work together with others, you may indicate so in the mail, and I will try to put you together with others in the same situation.

How to submit your first project
1- Make a folder and name it with your student numbers separated by '-' (e.g. "12345-23456-…")
2- Place all the relevant files into it
3- Zip the folder
4- Send to lars [dot] odsater [at] math [dot] ntnu [dot] no

Supervision of project 1 will take place at these times:

• Thursday September 3, 14:15-15:00 in Nullrommet (together with Exercise 2)
• Wednesday September 9, 14:15-15:00 in Nullrommet
• Thursday September 10, 14:15-15:00 in Nullrommet
• Monday September 14, 16:15-17:00 in Nullrommet
• Thursday September 17, 14:15-15:00 in Nullrommet (together with Exercise 3)