Useful properties of the Laplace Transform.
Laplace transform of e^at.
Table of Laplace Transforms. In this video, I show the Laplace transform for a few common functions. No theory or derivations here, just a quick reference that I will refer to in other videos.
The Inverse Laplace Transform. In this video, I give an important theorem related to the inverse Laplace transform, give a definition about the inverse Laplace transform and find the inverse Laplace transform of a function.
Laplace Transform is a Linear Operator - Proof. In this video I quickly prove the important property that the Laplace transform is a linear operator. This says that to take the Laplace transform of a linear combination of functions we take the Laplace transform of each term separately and add the result.
This video shows how to apply the First shifting theorem of Laplace transforms. Several examples are presented to illustrate how to take the Laplace transform and inverse Laplace transform and are seen in university mathematics.