ABSTRACT
At the end of this chapter, you should be able to:
• define the Heaviside unit step function • use a standard list to determine the Laplace transform of H (t − c) • use a standard list to determine the Laplace transform of H (t − c). f (t − c) • determine the inverse transforms of Heaviside functions
In engineering applications, functions are frequently encountered whose values change abruptly at specified values of time t . One common example is when a voltage is switched on or off in an electrical circuit at a specified value of time t . The switching process can be described mathematically by the function called the Unit Step Function – otherwise known as the Heaviside unit step function. Figure 98.1 shows a function thatmaintains a zero value for all values of t up to t = c and a value of 1 for all values of t ≥ c. This is the Heaviside unit step function and is denoted by:
f (t) = H(t− c) or u(t – c)
where the c indicates the value of t at which the function changes from a value of zero to a value of unity (i.e. 1).
