# Convolutions in the S-Plane with Applications

**Project level:** Honours

It is well known that the Laplace transform of a time-domain convolution of two functions is the product of the individual Laplace transforms. A similar 'dual' property is that a convolution type contour integral of two Laplace transform yields the time domain product. This property is not as explored in applications as the first property. Specifically in applied probability it can be used to obtain explicit results related to "time-domain" products - that were otherwise not achievable of certain performance functions. The purpose of this project is to explore this exciting property. The student needs to have working knowledge of complex analysis. Knowledge of probability is of secondary importance.