Finite representation of impulse functions: In solving differential equations

TRANSIENT PROBLEMS, such as closing a switch at a certain time, or throwing a load on a machine suddenly, or applying an impulse to a system, involve the use of discontinuous functions. These may be expressed in one type of notation by multiplying any given function by the Heaviside Null Unit Function H(x,x0), which is equal to zero when x < x0 and is equal to unity when x > x0. Similarly, in studying the fields due to point sources in a continuous medium the impulse function which is the derivative of the Null Unit Function H′(x, x0) arises.