## 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;