dt, with limits ranging from 0 to infinity. Laplace transform is formulated as the integration of the product of the function with e -st. For instance, F (s), A (s), G (s), X (s), etc. It can also be represented as the capital letter of the function related to frequency 's'. Whenever you encounter any function written inside the capital letter L, instantly identify that it is the Laplace transform of a function. This transform converts any signal into the frequency domain 's', where the complexity of the problem reduces. The Laplace transform will change the differential equation into an easy-to-solve algebraic function. Let the function be f(t) (piecewise continuous), therefore the Laplace transform of the function f(t) will be L f(t) or F(s). A piecewise continuous function is a function that has a finite number of breaks, and this consistency remains till the function reaches infinity. To understand Laplace transform, we must first learn about piecewise continuous function.
In studying the dynamic control system, the characteristics of the Laplace transform and the inverse Laplace transformation are both employed. In electronics engineering, the Laplace transformation is very important to solve problems related to signal and system, digital signal processing, and control system. The Laplace transformation is the most effective method for converting differential equations to algebraic equations. The Laplace transform is named after Pierre Simon De Laplace, a famous French mathematician (1749-1827) who formulated a transformation that can convert one signal into another using a set of laws or equations. Laplace transform - Formula, Calculator, Inverse Laplace Transform and Applications
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