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

All visualization below are done using Maxima computer algebra system (CAS).

Cart simulation

This is a simulation of a differential equation for the displacement $y=y(t)$ of a cart ensemble, consisting of a cart of mass $m$, a spring with spring constant $k$ and a damper with damping constant $b$. \[ m\,y'' + b\,y'+k\,y = f(t) \] where \[ f(t)=f_0\,\sin(2\pi\omega\,t)\] i.e. the cart is subjected to an external periodic force.
Animated cart simulation

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