On the Flow of Heat in a Rod Composed of Two Materials, Due to an Impulsive Source

In Heat conduction problems we require solutions of the equation

k^∂2v/ _∂x²=^∂v /_∂t

which satisfy the initial and boundary conditions. Following Heaviside, we replace ^∂/_∂t by the operator p (= k_q^{2</sup) and regard p (or q) as obeying the laws of algebra.}