Suggested activities:

Write a Matlab program to define the structure matrix $A$ in $(2\mathrm{.}34).$ Then, using the

MatlaB $\backslash$command or code of your own design, solve the system for the displacements $y_i$

using $n=10$ grid steps.

Plot the solution from Step $1$ against the correct solution

$y(x)=(\frac{f}{24}EI)x^2(x^2-4Lx+6L^2),$ where $f=f(x)$ is the constant defined above.

Check the error at the end of the beam, $x=L$ meters. In this simple case the derivative

approximations are exact, so your error should be near machine roundoff.

Rerun the calculation in Step $1$ for $n=10*2^k,$ where $k=1,$dots,$11.$ Make a table of the

errors at $x=L$ for each $n.$ For which $n$ is the error smallest? Why does the error begin to

increase with $n$ after a certain point? You may want to make an accompanying table of the