From the catalogue:
Complex functions and integration, line and surface integrals, Fourier series, partial differential equations.

Joukovski map

This is the conformal map: \[ J(z)=z+\frac{1}{z} \] Shown is the mapping the circle $|z-a|=|1-a|$ (blue) to an airfoil (red). The number $a$ (the center) varies over an interval in the complex domain.
Animated Joukovsky map

D'Alembert's Solution of the Wave Equation with Maxima

String plucked in the middle

Solution to wave equation, string plucked in the middle

String plucked at 20% of the string length

Solution to wave equation, string plucked off-center