Electrical Engineering ⇒ Topic : Laplace transformation

LAPLACE TRANSFORMATION

Differential equations can be solved either by classical method or by Laplace transform method. The classical method is based on time-domain analysis and Laplace transform method is based on the time-domain analysis. The classical method for solving differential equations becomes quite cumbersome when used for network involving higher order differential equations.

Therefore in such cases Laplace transform is preferred.

Solution of differential equations by Laplace transformation involves three steps, similar to numerical calculations by logarithms.

Taking of the transform which automatically takes into consideration the initial condition.

Rearranging the algebraic equation thus obtained, using algebraic partial fraction (if necessary) to bring every term into the standard form available in the Laplace transform table.

Finding the desired complete solution. This table helps in finding transforms as well as inverse transform.

The Laplace transformation is denoted by the script letter L. The Laplace transform of any function of f (t) is given by the expression

                                                                          ...............  (1)

                                                    Laplace Transform Table

where f^-1 is the integration of function.

Inverse Laplace Transformation

The mathematical process of passing from the complex variable expression to the time expression is-called an inverse transformation. The rotation for the inverse transformation is L^-1,so that

                                                                                  .................. (2)