Problem 1 This problem must be done by hand. Consider the following data set: Using these data points, compute the cubic spline interpolant for the function y = f(z). That is, compute the coefficients {a;, b;,;j,d;} for j = 0,1,2; to do so you will need to set up the system of four equations in four unknowns for the coefficients ;, 7 = 0, 1, 2, 3; use natural boundary conditions to reduce this system to only two equations for ; and 3. Then determine the other coefficients using the relations for b; and d;. Finally, once you have all the coefficients, evaluate the interpolant S(z) at the two points = 1.2 and z = 1.5