# Laplace transform

Contents

Transforms and the Laplace transform in particular. Convolution integrals.

## Laplace transform

We now use one of the coolest techniques in mathematics to transform differential equations into algebraic ones. You'll also learn about transforms in general!

## Properties of the Laplace transform

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 transform to solve a differential equation

You know a good bit about taking Laplace transform and useful properties of the transform. You are dying to actually apply these skills to an actual differential equation. Wait no longer!

## The convolution integral

This tutorial won't be as convoluted as you might suspect. We'll see what multiplying transforms in the s-domain give us in the time domain.