i$)$ A vertical force $P={15}_{k}N$ acts on the end of a cantilever beam with a rectangular crosssection width of $15cm$ and a height that changes linearly. Divide the beam length into $20$ equal parts and calculate the deflection and rotation at the midpoint of the beam using the finite difference method. $L=4m,h_0=30cm,h_L=15cm,E=10$GPa

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ii$)$ When the loading and support conditions are as shown in the figure $($uniformly distributed load and simply supported at the right end$),$ find the values and locations of the maximum deflection, maximum positive rotation, maximum positive moment, and maximum positive shear force. Again, divide the system into $20$ equal parts for your calculations.