What a PDE Is: Equations That Remember Their Neighbours

Deep End Era. Engineering with Sankalp · Oct 12, 2026 · 58m

A flow-assurance engineer's CFD solver blows up at two in the morning, and she asks a retired applied mathematician whether that is numerics or physics. Through their weekly calls, the episode builds the basics needed for the Navier-Stokes arc. ODEs remember their own past, while PDEs remember their neighbours. Transport moves shapes along, and its nonlinear form (Burgers) forms shocks in finite time. Heat smooths, and gives the square-root-of-time diffusion law. Waves echo, and Laplace's equation describes equilibrium. The episode covers Hadamard's three conditions (existence, uniqueness…