A useful generalization of an ordinary function is the delta function denoted
by d (t), which in mechanics can be used to describe an impulsive force at
time t/0, or in electric circuit theory the application of a very large voltage for a very short time at t/ 0. The delta function is not a function in the ordinary sense, but the result of a limiting process. The delta function
d (t/a ) can be considered to be the limit as h0/ at time t/a of a rectangular pulse of very large amplitude h , and very small width 1/h , so how-
ever large h becomes, the area of the pulse remains constant at h/(1/h)/1. A possible representation of the delta function at time t/a can be taken
as the limit as h0/ of the difference between the two step functions of amplitude h , with one located at t/a and the other located at t/a/ 1/h , as shown in Fig. 164.