$1$ A prismatic beam $[$E$]=$ constant$],$ of length $L,$ is loaded mid$-$span by load P$.$ Derive by any first principles method:

$($a$)$ Sketch the deflected shape, SFD and BMD

$($b$)$ Calculate the slope at the supports, and

$($c$)$ The mid$-$span deflexion. Show the deflexion is: $w\frac{l^3}{48}El.$

$($d$)$ If $L=8m$ and $P=100kN$ : determine the end slope and the mid$-$span deflexion.

Please help, show all work and drawings.