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.

## 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.

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

### String plucked in the middle

### String plucked at 20% of the string length