Application

Introduction:

•  The Laplace transform is named in honor of mathematician and astronomer Pierre-Simon Laplace, who used the transform in his work on probability theory.

• Like the Fourier transform, the Laplace transform is used for solving differential and integral equations.

• Laplace transform is a widely used integral transform.

• Laplace transform is just a shortcut for complex calculations.

 Real Life Applications:

•    The Laplace transform turns a complicated nth order differential equation to a corresponding nth degree polynomial.
  
  
• In physics and engineering, it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems.

• The Laplace transform is one of the most important equations in digital signal processing and electronics.

•  In Nuclear physics, Laplace transform is used to get the correct form for radioactive decay.

• It has also been applied to the economic and managerial problems, and most recently, to Materials Requirement Planning (MRP) 

• The Laplace transform reduces a linear differential equation to an algebraic equation, which can then be solved by the formal rules of algebra