This video describes how the Fourier Transform can be used to solve the heat equation. In fact, the Fourier transform is a change of coordinates into the eigenvector coordinates for the heat equation.

Book Website: http://databookuw.com
Book PDF: http://databookuw.com/databook.pdf

These lectures follow Chapter 2 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz

Amazon: https://www.amazon.com/Data-Driven-Sc...

Brunton Website: eigensteve.com