Educational materials on Youtube

Testing whether AI can solve a 4th-order, nonlinear, stiff vector PDE with negative viscosity.

Lecture on vectors and tensors using index notation

20-lecture series on undergraduate-level math (ODEs, PDEs, Fourier, Laplace, similarity transform, Bessel functions)

8-lecture series on graduate-level data-driven methods (machine learning, physics-informed neural nets, sparse regression, embedding)

My favorite lecture on nonlinear dynamics

The Einstein lecture

Particle dynamics simulator

Use your mouse to drag particles!

If you see nothing, hit the "Reset" button to initiate particles.

Generated by ChatGPT GPT-5 with single prompt:

Generate HTML interactive simulator of a periodic Stokesian dynamics simulation of 100 Brownian particles. I want to drag particles with my mouse and look at the response on all other particles in the simulator.

I want to apply common macroscopic flows on them. Add a toggle that turns hydrodynamic interactions on and off.

NOTE: ChatGPT gave me a much simpler simulation with RPY pairwise only. This is NOT a Stokesian dynamics simulation. It's still important to know physics.

Using AI to build intuition in math courses