Introducing Convolutions: Intuition + Convolution Theorem

In this lesson, I introduce the convolution integral. I begin by providing intuition behind the convolution integral as a measure of the degree to which two functions overlap while one sweeps across the other. I demonstrate this intuition by showing that the convolution of two box functions is a triangle.
I then move on to proving the Convolution Theorem for Fourier Transforms, and discussing how it compares to the Convolution Theorem for Laplace Transforms. The proof for Fourier Transforms is relatively simple, but the proof for Laplace Transforms is a bit more difficult (if you really want to see the Laplace Transform proof, I can make another video but I've put it off for now).
Questions/requests? Let me know in the comments! Hopefully the intuition I provided was sufficiently clear.
Prereqs: Very basic knowledge of Fourier and Laplace Transforms (i.e. you just need to know what they are and what they're used for), ODEs, and integration. Playlist: • Topics in Ordinary Dif...
Lecture Notes: drive.google.c...
Patreon: www.patreon.co...
Twitter: / facultyofkhan
Special thanks to my Patrons for supporting me at the $5 level or higher:
Jose Lockhart
Yuan Gao
Justin Hill
Marcin Maciejewski
Jacob Soares
Yenyo Pal
Chi
Lisa Bouchard