Green's Function
An impulse response function used to solve inhomogeneous linear differential equations subject to specified boundary conditions.
Governing formula
L G(x, x') = δ(x - x'), y(x) = ∫ G(x, x') f(x') dx'
SI unit
Impulse Response Function
In depth
Green's functions represent the field or response produced by a point source represented by a Dirac delta function δ(x - x'). Integrating the Green's function against an arbitrary source distribution f(x') yields the exact general solution.
Examples in the real world
Solving Poisson's electrostatic equation ∇²V = -ρ/ε₀ using Green's function G(r, r') = 1 / (4π |r - r'|).