Uploaded August 2016 | Updated September 2026, 2 weeks ago

---

In this video, I introduce the most basic parabolic PDE, which is the 1-D heat or diffusion equation. I show what it means physically, by discussing how it relates the concavity at a point (indicative of the average value of a function in the regions surrounding that point) to the time derivative.

In other words, the more different a parabolic PDE solution is from its surroundings, the more quickly it changes in order to better match/equilibrate with its surroundings. For example, the hotter your frying pan, the more quickly it loses heat to match the room temperature.

Questions? Ask in the comments below!

Prereqs: Basic ODEs, my ODE topics playlist, and a couple of my first two introductory PDE videos. For this lecture though, the bare minimum is a basic knowledge of PDEs (not necessarily how to solve them, just what they are) and some calculus.

Lecture Notes: drive.google.com/file/d/0B_urJu4cgDhMV19SczAycXk0LWc/view?usp=sharing&resourcekey=0-DxZ-pbWvkJR1ocpFzeNcEg

Patreon Link: patreon.com/user?u=4354534