Chapter-3: Laplace Transform

In the application of Laplace transform variable time is eliminated and a new domain is introduced.

In the modeling of dynamic systems differential equations are solved by using Laplace transform.

Properties of Laplace Transform

The Laplace transform contains no information  about f(t) for t<0. (Since t represents time this is  not a limitation)

Laplace transform is defined with an improper  integral. Therefore the required conditions are

the function f(t) should be piecewise continuous

the integral should have a finite value; i.e., the  function f(t) does not increase with time faster than  e -st decreases with time.

Laplace transform operator transforms a  function of variable t to a function of variable s.  e.g., T(t) becomes T(s)

The Laplace transform is a linear operator.

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