
11.5.2.6 Fourier method
Problem:
Solve the boundary-value problem for the homogeneous wave equation:
\[
\begin{array}{l}
u_{t t}=a^{2} u_{x x}, \quad a=1, \quad u(0, x)=\frac{x}{2}, \\
\frac{\partial u}{\partial t}(0, x)=u(t, 0)=u(t, l)=0 .
\end{array}
\]