Question

Can someone please explain how the Fourier odd and even extensions could be used to solve differential equations? I understand how to do the extensions, but am not sure when/how to apply that knowledge.

Answer 1

cant really say because im actually taking the course now

but from what i have seen, its used to simplify the solution for laplace equation or heat equation, etc, which are 2nd order diff eqs

Answer 2

@nincompoop pls make sensible answers

Answer 3

The idea is that Fourier series allow you to decompose a periodic function as well as its derivatives into the sum of sine/cosine parts with meaningful coefficients. That's a really basic way of looking at it so if you need more depth try searching via Google or ask your professor for help.