Question

I'm in the midst of solving the heat equation with boundary conditions. My question is that I'm left with what looks like a Fourier Sine Series but I'm not sure. It's in the format

sin[(2n+1)*pi*x/(2L)]

as opposed to the normal

sin(n*pi*x/L)

Can I still use the same method of finding the coefficient?

Answer 1

u have done some mistake so far

Answer 2

ok

Answer 3

there is nothing wrong with that
u must have boundary condition like this to get that
\[0\le x \le L\\ T(x=0)=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{\partial T }{\partial x } (x=L)=0\]
method is the same

Answer 4

Those are the boundary conditions. I just wasn't sure if setting up the integral was the same. Thanks @mukushla