# Merits of the Laplace transform

1. Apr 17, 2013

### IxRxPhysicist

Hey all,
Learning the Laplace transform and I get the point that it is a transformation but I would like to know what are some of the merits of the Laplace transform or more general why perform transformations in the first place. Any examples would be helpful.

2. Apr 17, 2013

### jasonRF

A standard use of Laplace transforms (and other integral transforms, for that matter) is to help solve differential equations. For certain kinds of ordinary differential equations (linear, constant coefficient) they turn the ordinary differential equation into an algebraic equation, and partial differential equations into ordinary differential equations. After you solve those simpler problems, you then need to perform the inverse transform to get the answer that you are looking for.

The wikipedia page has some examples at the bottom to help explain. Almost any differential equations book will also discuss this.

http://en.wikipedia.org/wiki/Laplace_transform

I hope that helps,

Jason

3. Apr 17, 2013

### IxRxPhysicist

That does help! Thanks!

4. Apr 18, 2013

### lightarrow

The Laplace transform is particularly useful in solving electrical/electronic networks with inductors and capacitors because it transforms time derivatives (inductors) in multiplication by the variable s and time integrals (capacitors) in division by s (the resistor doesn't introduce any difference), so the integro-differential equation of the net becomes simply an algebric equation.
You can do something similar with the Fourier transform, but with Laplace transform you can treat in a simple way even non periodic signals, for example Dirac Delta impulses, step functions and so on.