Exercise "Interpolation"

1. Implement a function which makes a Lagrange polynomial interpolation of a table {x[i],y[i]} at a given point z.
2. Implement a function for the linear spline interpolation.
3. Implement a function for the quadratic spline interpolation.
4. Hint: location of the index i: x[i]<z<x[i+1] must be done using the binary search.
5. Create your own individual interesting interpolation examples -- a step function perhaps, a function with a pole, or what not.

Ideas for the project

1. Cubic spline
   • Implement a function for cubic spline interpolation.
   • Implement a function which calculates the derivative of a tabulated function by building a spline and then differentiating (analytically) the spline.
   • Implement a function which calculates the antiderivative (the integral) of a tabulated function by building a spline and then integrating (analytically) the spline.