Definition of Laplace Transform
Let be a given function which is defined for . If there exists a function so that
then is called the Laplace Transform of , and will be denoted by . Notice the integrator where is a parameter which may be real or complex.
The symbol which transform into is called the Laplace transform operator.
Laplace transformation is a powerful method of solving linear differential equations. It reduces the problem of solving differential equations into algebraic equations. For more information about the application of Laplace transform in engineering, see this Wikipedia article and this Wolfram article.