# 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 t: L{t}

VIDEO 9:06 minutes
Determining the Laplace Transform of t

### Laplace transform of t^n: L{t^n}

VIDEO 10:16 minutes
Laplace Transform of t^n: L{t^n}

### 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

### Dirac delta function

VIDEO 17:48 minutes
Introduction to the Dirac Delta Function

### Laplace transform of the dirac delta function

VIDEO 12:13 minutes
Figuring out the Laplace Transform of the Dirac Delta Function