I’ll start off exactly where I stopped in the previous post: I will tell you my solution to the problem my PDEs lecturer (and later master’s thesis advisor) Paneah gave us:

Problem: Find all continuously differentiable solutions to the following functional equation:

(FE) $latex f(t) = fleft(frac{t+1}{2} right) + f left(frac{t-1}{2} right) ,, , ,, t in [-1,1] .$

Before writing a solution, let me say that I think it is a fun exercise for undergraduate students, and only calculus is required for solving it, so if you want to try it now is your chance.

Continue reading Where have all the functional equations gone (part II) →