roject due date: May $15($Sharp$,$ no extension$)$

$$ Work in groups of $4$ maximum. No name will be added after

submission

$$ Only Octave $($or MATLAB$)$ is allowed.

$$ Submit the files $($programming files and the report $($using the

template$)$ converted to PDF$)$ electronically via Moodle all in one zipped file. Note that your programmes will be checked and executed.

$$ The name of the submitted file has to contain a name and ID of one of the group members

$$ Names of group members have to appear within the programming files and report

Project description

Objective: find dimensions of a door that fits inside the arcade $($touches the arcade at too points, as in the figure$)$ with the door covering a maximum surface.

$$

Contact Arcade$-$Door

Arcade

$(-1,0)$

$(0,0)$

$(1,0)$

$$

Assume that the floor is the x$-$axis and the y$-$axis is at the centre of the door $($see figure above$).$

The arcade is given by the polynomial function.

arc$()=08162432+0+1+2+3$ where the coefficients, $0,1,...$ are the digits of your student ID$.($exp:

ID$=153310,$ then $()=8563432+12)$ Required work:

$$ You need to find the coordinate of the contact Arcade$-$Door points, such that the door is the largest possible $($in term of surface, the maximum surface$).$ Note that the problem is symmetric, you need to find only one contact point $($between $0$ and $1)$ and to other one is simply the negative value.

$$ You need to consider $4$ cases: $2$ rectangle doors and two square shaped doors.

$$ For each case you change the arcade equation by considering the ID digits of each group member. If you are less then $4$ students in the group just permute the digits.

$$ You need to plot in your OCTAVE$/$MATLAB code the arcade and the door $($use the plotting command for the doors: Rectangle $($position$,[$x$\_$pos, y$\_$pos, door$\_$width, door$\_$hight$],$linewidth$,$ value$)$

x$\_$pos, y$\_$pos: are the left$-$bottom position of the door.

Details of the work:

$1.$ Write a code for Bisection or Newton $($you can use the ones we implemented in class$).$ Using OCTAVE$/$MATLAB functions or any code from the net or other groups will result in a zero in the project. $(2$pt$)$

$2.$ Write a code to solve the Doors problems $($find contact coordinates. You can simply complete the code developed in $1.$ Need to submit one code for each case $(4$ codes$).(2$pt$)$

$3.$ Each code needs to solve the problem and plot the arcade and the rectangle$/$square door in one frame. $(2$pt$)$

$4.$ Each code needs to plot the error curve $($you must use ETF$)$ in a separate

frame. $(1$pt$)$

$5.$ Write a report were you explain your work and your conclusion using the provided template.

$(3$pts$)$

What to submit:

$1.$ One code for each door case. The codes have to contain comments, and plotting commands. When we run the code, it hase to plot the ETF error in one figure, and in another figure the arcade and the door.

$2.$ Report $($using the template$)$: It has to contain: Explanations of your work for each door, figures $($Errors and arcades with doors$),$ and conclusions.

Important

$$ Put all files in a single folder and submit is as a single zipped file $($use standard tool for zipping$).$

$$ The zipped folder has to be named as: MAT$444$prijecID. Put the ID of one of group members, and only one submit ion per group

$$ The folder must contain the report in PDF$,$ and the $4$ codes in OCTAVE$/$MATLAB format $($if the code doesn$$t run the project will not be corrected$).$

$$ If the submission procedure is not respected the project will not be corrected.

Note: Marks will be deducted for uncommented and non$-$running codes $($codes with bugs$)($programs$).$