Laplace transformation is a method for solving linear differential equations with constant coefficients based on given initial conditions. It can also be used for fault functions which give the value zero in the event of a negative argument. The operations and the differentiation and integration of time functions are converted, based on the form of transformation used, into algebraic operations with associated frequency functions. Laplace transformation is mainly used to solve differential equations in control technology.
With Laplace transformation, a function f(t) within the time range (original range) is assigned a function F(s) in the image or frequency range as part of a reversible but unique arrangement. This creates a unique but reversible relationship between the original function and the image function. It can be described using the following equation:
![dd595395c2b21a356edb03f034cdad77e5d19033 laplacetransformation_01.gif](/fileadmin/smc/files/dd595395c2b21a356edb03f034cdad77e5d19033.gif)
![5e6f700d8062ca5a386d901d56376890f696dba5 laplacetransformation_02.gif](/fileadmin/smc/files/5e6f700d8062ca5a386d901d56376890f696dba5.gif)
The variable s = σ + jω describes a complex frequency.