$3\mathrm{.}2$ Derive the Lagrange cubic interpolation functions for a four$-$node $($one$-$dimensional$)$

element $($with equally spaced nodes$)$ using the alternative procedure based on inter$-$

polation properties listed in Eqs. $(3\mathrm{.}2\mathrm{.}23)$ and $(3\mathrm{.}2\mathrm{.}24).$ Use the local coordinate $\stackrel{}{x}$ for

simplicity.