3Blue1Brown

Solution to the block collision puzzle from last video.

The third and final part of the block collision sequence.

This rule seems random to many students, but it has a beautiful reason for being true.

How do you study what cannot be solved?

The heat equation, as an introductory PDE. And to continue my unabashed Strogatz fanboyism, I should also mention that his textbook on nonlinear dynamics and chaos was also a meaningful motivator to do this series, as you'll hopefully see with the topics we build to.

(Sine waves / boundary condition) + linearity + Fourier = Solution

Fourier series, from the heat equation to sines to cycles.

Because why not?

Euler's formula intuition from relating velocities to positions.

The famous (infamous?) Problem 2 on the 2011 IMO

A story of the value in mathematical play.