Suppose two numbers which the products of their one$-$step increments are added to an initial value of the

second number.

$($a$)$ Draw the flow chart of this summing process provided that the initial value of the second number will be

the same for all incremental steps of the second number.

$($b$)$ Build and write on the answer sheet a m$-$script running the algorithm of the problem describing Part $($a$)$

$($c$)$ Add explanation $($comment$)$ for each line of this MATLAB Code.

$($d$)$ Show the screen shot after running the m$-$script when the initial value of the first number is $1$ and that of

the second number is $5$ and the final values of the increments for the first and second numbers are $2$ and $3$

respectively and with one$-$step increment.

Table shows the density $()$ of $N_2$ as a function of pressure $(P)$ at $T=200K.$

$($a$)$ Using these data, build a $m-$script to estimate the virial coefficients of the virial equation of state given by;

$Z=\frac{P}{RT}=1+B+C{}^2+D{}^3$

where $R$ is the gas constant $(=0\mathrm{.}08206$liter$*at\frac{m}{\text{m}\text{o}\text{l}*K}).$

$($b$-$i$)$ Plot also $P(atm)$ vs $($mol$/$liter$)$ graph including the curve fitting the data and the data by using also the

same $m-$script.

$($b$-$ii$)$ Insert the title of the plot

$($b$-$iii$)$ Indicate as axis labels the related variables on the $x-$ and $y-$axis.

$($b$-$iv$)$ Insert a legend indicating the fitted curve and the data.

For the following equations;

$x=e^{-{}_{i}t}sint$;$y=e^{-{}_{i}t}cost$;$z={}_{i}t$

$($a$)$ Sketch the flow$-$chart of a program which generates three$-$dimensional curve of these equations

$($b$)$ Write a m$-$script generating a three$-$dimensional curve as the parameter $t$ is varied and;

$($c$)$ Add comments in your m$-$script.

$($d$)$ Run the $m-$script over some range by entering values from $t=0$ to $t=10$ and with;

$($d$-$i$){}_1=-0\mathrm{.}05,{}_1=-0\mathrm{.}05,{}_1=1$

$($d$-$ii$){}_2=-0\mathrm{.}01t,{}_2=-0\mathrm{.}1t,{}_1=2$

$($d$-$iii$){}_3=-0\mathrm{.}05t,{}_3=-0\mathrm{.}05t,{}_3=0\mathrm{.}1$

$($e$)$ Show the screenshot of the plot.

$($e$-$i$)$ Add title to the plot.

$($e$-$ii$)$ Add labels for axes

$($e$-$iii$)$ Add legend representing the generated curves

Good Luck..