Laplace Transforms of Unit Step Function
Laplace Transforms of Unit Step Function:
Unit Step Function ( Heaviside Function ): The unit step function or Heaviside Function u (t - a) is defined as follows:
Where a ≥ 0; The graph of this function is shown below and where a is the positive constant.
Properties associated with the Unit Step Function:
Proof: (1) Using the definition of Laplace Transform, we have;
(2) Heaviside Shifting Theorem:
Where u (t - a) is the unit step function.
Proof: By definition we have;