What Is the Intuitive Explanation of the Laplace Transform?

[member 428835]

hello pf!

i am wondering if anyone here knows of a geometric, intuitive explanation for the laplace transform? if so, please direct me to the source of if you could, explain to me your understanding?

thanks!

 

[homeomorphic]

The Laplace transform always bothered me. It took me a very long time to understand it deeply.

Here's a start.

http://ocw.mit.edu/courses/mathemat...ure-19-introduction-to-the-laplace-transform/

Also, it helps to understand Fourier transforms and Fourier series. That gives you more physical/geometric intuition. Once you understand that stuff, you can interpret Laplace transforms in terms of them. Places to get intuition about Fourier series/transforms would include signal processing books, or if you want a more mathematical approach that's still pretty intuitive, you could look at Discourse on Fourier Series by Lanczos.

 

[member 428835]

thanks homeomorphic!

 

[micromass]

See this: https://www.physicsforums.com/showthread.php?t=461628 The videos in that thread basically show that the Laplace transform is the continuous extension of power series. Much in the same way that Fourier transforms are the continuous analogue of Fourier series.