Question

what is laplace transformation​

Answer 1

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Meaning :

In mathematics, the Laplace transform is an integral transform named after its inventor Pierre-Simon Laplace. It transforms a function of a real variable t to a function of a complex variable s. The transform has many applications in science and engineering. The Laplace transform is similar to the Fourier transform.

Purpose / Uses :

The purpose of the Laplace Transform is to transform ordinary differential equations (ODEs) into algebraic equations, which makes it easier to solve ODEs. ... The Laplace Transform is a generalized Fourier Transform, since it allows one to obtain transforms of functions that have no Fourier Transforms.

Properties:

Laplace transforms have several properties for linear systems. The different properties are: Linearity, Differentiation, integration, multiplication, frequency shifting, time scaling, time shifting, convolution, conjugation, periodic function. There are two very important theorems associated with control systems.

There are two theorems related to Laplace transformation :

• Initial value theorem (IVT)
• Final value theorem (FVT)

In short,

Laplace transformation is nothing but a shortcut method of solving differential equation.

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