# Student Project

## General Information

• The project is optional and to take it you must register—see below for instructions.
• It counts for 30 % of the final grade in the course whether you take it or not.
• The project is published on Monday November 7 at 10:00.
• Deadline: Monday November 21 at 16:00.
• Expected amount of work per student is $2 \times 12 \times 45 \text{ minutes} = 18 \text{ hours}$, provided that the student is up-to-date on theory and has completed the problem sets.

## Project description

##### Evaluation

The project counts 30 points out of 100 of the final grade. The evaluation will be based on how much you have done, how you have done it, and how you present the results in the report (see the "How to write the report"). Of the 30 points, 20 will be given to Part 1 of the project, 10 to Part 2. The presentation will count for roughly 1/3 (of the 30 points).

## FAQ and other information given during the project

Information of joint interest will be given here, so please take a look once in a while.

• 17.11: Part II, the DAE problem, the assignment in the second last paragraph on page 8.
With "Show the similar result for the error estimator" I mean: Show that $le_{n+1}=V_4-V_3 = Q [Y_4^T-Y_3^T,Z_4^T-Z_3^T]^T$ where $Y_i$ is what you get when applying the method to (12a), and $Z_i = G(t_n+c_ih,Y_i)$. And it should work for all index 1 problems as defined in the text, not only the test example.
• 17.11: About the differentiator circuit: Also the currents $I_Q$ and $I_a$ are unknown variables.
Your DAE-solver should be able to solve the circuit equation (middle of page 9) directly.
The output of interest is the voltage $u_3$.
• 15.11: One additional advise about how to write the report, and what to include and what to leave out. Imagine that you are writing to a friend who took the course last year, who know the curriculum, but do not know the project and has not seen the project description. How will you explain what you have done, how you did it and the results. How would you like to get it explained?
And: the report does not have to be 12 pages long, shorter can be as good (but longer is not allowed).
• 13.11: Some typos in the circuit equation on p.9 has been corrected.
• 13.11: The woodpecker: "impact from the sleeve" means when going from eq.(II) to eq.(I), not the other way.
• 13.11: Some typo's in the woodpecker problem: Table 1 has been updated. In (8), $m_s$ has been corrected to $m_2$, and there was a missing + in the formula below "Impact of the sleeve at the top".
• 11.11: We are not going to give any support during the weekends.
• 10.11: Matlab has apparently the possibility to do symbolic manipulation. Your are free to use this in the theory part.
But there should be NO symbolic manipulations in the implementation of onestep and RKs.
• 10.11: Some errors in the example on page 8 has been corrected (there were some missing 4s).
• 10.11: NB! You are supposed to modify your code from Part I to solve the problems of Part II.
• 10.11: Point [8]. There should be 6 graphs, but you may have more than one graph in each figure.
• 9.11: NB! The function call in point [9] should be: function [t, y, iflag, nfun, njac] = RKs(f, jac, t0, tend, y0, Tol, h0) where jac is the function Jac(t,y) used in onestep().
• 9.11: The last formula on page 9 has been corrected to $V(t)=0.01 \cdot \sin$$(2\pi \times 10^8 t)$ $[V]$
• 8.11: There is now a document on how to write the report (see above). Moreover, the $\LaTeX$ template (see below) has been updated accordingly, and we have uploaded some figures from the project description for convenience.
• 8.11: Supervision tomorrow, 12:15-14:00 will be given in Anne's office (SBII, 1348).
• 8.11: There was a typo in the second equation in the Robertson reaction (7): it should be $y_2'=0.04$$y_1$$-10^4y_2y_3 - 3\times 10^7y_2^2$.
The pdf-file of the project description is corrected.
• 7.11: Supervision is given during the supervision sessions—these amount to 24.5 hours in total; see below. We will not answer questions regarding the solutions of the exercises by email.
• 7.11: Someone noticed a typo in eq. (33) in the NODE note. This is corrected now. The correct expression is $R(z)=1+zb^\top(I-zA)^{-1}\mathbb{1}$.

## Registration

• Students can form groups of up to 2 members, but you will possibly be 3 in total. Those of you who want to be in a group, but have not found a partner, may be placed in an existing group of 2 members.
• Please read the instructions and sign up with following form as soon as you can.

Registration closes on Friday November 4 at 16:00.

## What and How to Hand In

Your work should contain:

1. A written report of maximum 12 pages as an electronic PDF (shorter is of course allowed).
• You can write in English or Norwegian.
• The document should preferably be written in $\LaTeX$, but you are allowed to use Word etc. if this is a big issue.
• If you prefer $\LaTeX$, we recommend that you use the following document template for convenience:
• Download the files
• Place them in the same folder, and start typesetting your answers in project.tex.
2. A compressed (ZIP) file containing all your relevant script files in MATLAB or Python.

Please name your PDF and compressed file as

• tma4215_*_*_*.pdf and
• tma4215_*_*_*.zip (or whatever format you use),

respectively, where the stars are placeholders for your last names.

Send both files by email to anne [dot] kvarno [at] math [dot] ntnu [dot] no with "TMA4215 Project" in your subject heading.

## Academic Honesty and Anti-Plagiarism Guidelines

• You are free to discuss problems between groups, but you must write your reports independently.
• If you use material or information from the literature, make sure you provide proper citation and references.

## Help Sessions

Please view this page if you need help to find Nullrommet (380A).
Anne's office (1348) is in the 13th floor of central building II.

### Week 45 (Nov 7–Nov 11)

Day Time Room Person
Monday
Tuesday 10:15-12:00 K5 Anne
Wednesday 12:15-14:00 1348, SBII Anne
Thursday 13:15-15:00 1348, SBII Anne
Friday 12:15-14:00 Nullrommet (380A) Fredrik
Friday 14:15-16:00 1348, SBII Anne

### Week 46 (Nov 14–Nov 18)

Day Time Room Person
Monday 16:00-18:00 Nullrommet (380A) Anne
Tuesday 10:15-12:00 Nullrommet (380A) Fredrik/Anne
Wednesday 12:15-14:00 1348, SBII Anne
Wednesday 14:15-16:00 Nullrommet (380A) Fredrik
Thursday 12:15-14:00 Nullrommet (380A) Fredrik
Thursday 14:15-16:00 1348, SBII Anne
Friday 12:15-14:00 Nullrommet (380A) Fredrik
Friday 14:15-16:00 1348, SBII Anne

### Week 47 (Nov 21)

Day Time Room Person
Monday 12:15-14:00 Nullrommet (380A) Fredrik

Deadline: Monday November 21 at 16:00.

## Technical Tips for Effective Group Work

• Use some file-sharing service à la Dropbox.
• ShareLaTeX is a popular collaborative $\LaTeX$ editor that "allows muliple users to edit the same document simultaneously and see each other's changes in real time. The program supports almost all $\LaTeX$ features, including inserting images, bibliographies, equations, and much more." NTNU also has a licence which makes it possible to synchronize to Dropbox. Please see NTNU's page on ShareLaTeX for more info.