# Properties of the Laplace transform

9 videos

You know how to use the definition of the Laplace transform. In this tutorial, we'll explore some of the properties of the transform that will start to make it clear why they are so useful for differential equations.
This tutorial is paired well with the tutorial on using the "Laplace transform to solve differential equations". In fact you might come back to this tutorial over and over as you solve more and more problems.

### Laplace as linear operator and Laplace of derivatives

VIDEO
11:36 minutes

Useful properties of the Laplace Transform

### Laplace transform of cos t and polynomials

VIDEO
9:45 minutes

Laplace transform of cosine and polynomials!

### "Shifting" transform by multiplying function by exponential

VIDEO
11:17 minutes

A grab bag of things to know about the Laplace Transform.

### Laplace transform of the unit step function

VIDEO
24:15 minutes

Introduction to the unit step function and its Laplace Transform

### Inverse Laplace examples

VIDEO
19:15 minutes

Using our toolkit to take some inverse Laplace Transforms

### Laplace transform of the dirac delta function

VIDEO
12:13 minutes

Figuring out the Laplace Transform of the Dirac Delta Function