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.