Exercise "Interpolation"

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

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5. Implement a subroutine for cubic spline interpolation.
6. Implement a subroutine which calculates the derivative of a tabulated function by building a spline and then differentiating (analytically) the spline.
7. Implement a subroutine which calculates the antiderivative (the integral) of a tabulated function by building a spline and then integrating (analytically) the spline.