Some Useful Properties of Laplace Transforms

Transform of a step function if U t) is a unit step function 

Transform of an impulse function the Dirac delta or unit impulse function is given as 

As can be seen from the sketch, as s — 0, the rectangular pulse Kit - to) gets taller and thinner, but the limit does not exist. Even though the limit does not exist in the usual sense, one can still derive useful properties of the impulse function. For example. 

In order for this operational method to be useful to chemical engineers, there must be convenient ways to invert the transform. That is, it is necessary to be able to perform the operation 

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