Use d'Alembert's formula to solve the boundary value problem for a string of unit length, subject to the given conditions.
I can't get this to work with LaTeX so I hope this makes sense.
f(x) = 2x if 0 ≤ x ≤ 1/2
f(x) = 2(1-x) if 1/2 < x ≤ 1
g(x) = x
The Attempt at a Solution
I've been able to do previous problems up until this one. Previous problems were all a single function that was 2 periodic. This one I am not sure where to start. I at least thought the g* wouldn't be too hard since it's only x, but there is an example that shows the same thing and they have completely different integration limits.
I think my whole problem is even/odd extensions. I am not the best at them and plan to go back and study them again since they are a couple sections back.
Any tips to get this one even started?