Stiff differential equations johndcook.com/blog/2020/02/0…

Differential equations date back almost as far as calculus, to the late 1600's.

Power series solutions for DIFFERENTIAL equations lead to DIFFERENCE equations for the coefficients.

Ripples and hyperbolas johndcook.com/blog/2020/11/0…

In R^n, Δ u is the sum of the second derivatives of u with respect to each variable.

Laplace's equation: Δu = 0.

Oscillations in RLC circuits johndcook.com/blog/2022/04/0…

Heat (or diffusion) equation: u_t - Δu = 0

Schrödinger's equation: i u_t + Δu = 0

Solving the wave equation on a disk johndcook.com/blog/2021/06/1…

Michael Corleone initially intended to be a math professor. (In the book, not the movie.)

Scalar reaction-diffusion equation: u_t - Δu = f(u)

Laplace's equation was first studied by Laplace around 1780, Stigler's law of eponymy not withstanding.

Finding a vector potential whose curl is given johndcook.com/blog/2022/12/0…

Huygens-Fresnel principle en.wikipedia.org/wiki/Huygens%E…

Operator calculus johndcook.com/blog/2022/10/1…

Thank you for following @Diff_eq

'The history of transistors is the history of solving Schrödinger's equation in various materials.' -- Leon Lederman