La Workplace Transformation Application: The Laplace Transform

Introduction

Laplace Transformation Application

The Laplace Transform was first used and named after by its discoverer Pierre Simon Laplace. Pierre Simon Laplace was a French Mathematician and Astronomer, who had a lot of influence in the development of mathematics, statistics, physics, and astronomy. He contributed greatly to classical mechanics, by converting the old geometrical analysis to one based on calculus, which opened up application of his formulas to a broader range of problems. He also developed the Bayesian interpretation of probability in the field of statistics. However, what is a Laplace transform?

Basically, a Laplace transform will convert a function in some domain into a function in another domain, without changing the value

Since equations having polynomials are easier to solve, we employ Laplace transform to make calculations easier. We use Laplace transform on a derivative to convert it into a multiple of the domain variable. Thus with Laplace transform n^th degree differential equation can be transformed into a n^th degree polynomial. One can easily solve the polynomial to get the result and then change it into a differential equation using inverse Laplace transform. Like a good transform, Laplace transform converts a given differential equation (or a signal in practical life) to a polynomial, which is easier for the user to solve. Also, the final functions is equal in value to the initial function. Hence, nothing is gained, nothing is lost.

Laplace transformation application is common in engineering education to find the perspective that the Laplace transform is just a theoretical and mathematical concept (outside of the real world) without any application in others areas. The transforms are considered as a tool to make mathematical calculations easier. However, it is important to notice that “frequency domain” is possible appreciate also in the real world and applied in other areas like, for example,

The pure sounds consist in only frequency (for example the “beep” of a computer) and are not common in the nature. The majority of the “real” sounds consist in thousands of different frequencies emitted at the same time. This let us to distinguish between a natural sounds (rich in resonance) from an artificial (with not many components). The natural sounds like our voice, the music, the noise, etc. they do not consist in a frequency but in a band of frequencies with many fundamentals and other harmonies that produce rebound and resonance in the