MATH 2270 Lecture Notes - Dirac Delta Function, Partial Fraction Decomposition, Special Functions

• School: University of Guelph
• Department: Mathematics
• Course: MATH 2270
• Professor: Matthew Demers

Document Summary

4. 5 creating other functions from the heaviside function. The heaviside function is really interesting, because it can be used to create many other functions. To do this, we add or subtract two or more di erent heaviside functions to or from one another. If a < b and t 0, then a rectangular impulse r(t) can be created by r(t) = h(t a) h(t b) 0 t < a a t < b t b. Figure 4. 1: on the left, a graph of the rectangular impulse function r(t), with a = 1 and b = 2. This sort of function is sometimes depicted as appears on the right. Let a > 0 and t 0. Then, let a staircase function be given by stair(t) = h(t a) + h(t 2a) + h(t 3a) 0 t < a a t < 2a. 2a t < 3a t 3a. Figure 4. 2: on the left, a graph of stair(t) when a = 1.