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

Laplace as linear operator and Laplace of derivatives

Laplace transform of cos t and polynomials

"Shifting" transform by multiplying function by exponential

Laplace transform of t: L{t}

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

Laplace transform of the unit step function

Inverse Laplace examples

Dirac delta function

Laplace transform of the dirac delta function