I'm working on a problem, but I don't really understand how to solve it. I'm given a number of (xi,yi) co-ordinates, and need to find the cubic spline with periodic boundary conditions that interpolate them, s(x). Then I need to find the value of s(t) where t is a specific value x0<t<xn, and also all the values of s"(xi). (I'm intentionally leaving off the specific values, i want to know how to solve the problem, but not be given the solution for the problem) What I'm having a problem with is that neither my textbook (Elementary Numerical Analysis 3ed, Atkinson), does not really go over periodic boundaries, nor can I find any sort of algorithm for solving a spline function by hand online. I need a step-by-step approach.