Questions related to Laplace Transform

1. What is the main purpose of Laplace transforms?
2. What are the real life applications of Laplace transform?
3. What is the logic behind Laplace transform?
4. Which function has no Laplace transform?

What is the main purpose of Laplace transforms?

The Laplace transform is used to solve differential equations. It is accepted widely in many fields. We know that the Laplace transform simplifies a given LDE (linear differential equation) to an algebraic equation, which can later be solved using the standard algebraic identities.

What are the real life applications of Laplace transform?

Laplace transform is an integral transform method which is particularly useful in solving linear ordinary dif- ferential equations. It finds very wide applications in var- ious areas of physics, electrical engineering, control engi- neering, optics, mathematics and signal processing.

What is the logic behind Laplace transform?

The Laplace transform describes signals and systems not as functions of time but rather as functions of a complex variable s. When transformed into the Laplace domain, differential equations become polynomials of s.

Which function has no Laplace transform?

It must also be noted that not all functions have a Laplace transform. For example, the function 1/t does not have a Laplace transform as the integral diverges for all s. Similarly, tant or et2do not have Laplace transforms.