From the course: Complete Guide to Differential Equations Foundations for Data Science

Unlock this course with a free trial

Join today to access over 25,300 courses taught by industry experts.

What is the Laplace transform?

What is the Laplace transform?

From the course: Complete Guide to Differential Equations Foundations for Data Science

Start my 1-month free trial Buy for my team

What is the Laplace transform?

“

- [Instructor] In this chapter, you will explore a very important mathematical concept, Laplace transforms. These transforms are key to simplifying many differential equations. Let's start off by exploring what Laplace transforms are. The Laplace transform is named after the French mathematician Pierre-Simon de Laplace. He wrote about generating functions in 1814, and the integral form of the Laplace transform became a result of that. Augustin-Louis Cauchy and Bernhard Riemann both helped this transform develop. Plus, Robert Hjalmar Mellin was the first to apply this transform to the study of differential equations and functions. Let's review a few definitions before I dive into showing you about Laplace transforms. First, let's explore what a piecewise continuous function is. A piecewise continuous function has a finite amount of breaks on an interval where each open subinterval is continuous and always reaches a finite limit at all of its end points. Let's look at an example of…

Contents