## § Green's functions

• Can solve $L y(x) = f(x)$.
• $f(x)$ is called as the forcing operator.
• $L$ is a linear diffeential operator. That is, it's a differential operator lik $\partial_x$ or $\partial_t \partial_t$. See that $\partial_t \partial_t$ is linear, because $\partial_t \partial_t \alpha f + \beta g = \alpha (\partial_t \partial_t f) + \beta (\partial_t \partial_t g)$