Map a rectangle conformally onto the upper half-plane:
Solution of the pendulum equation:
Check the solution:
Plot solutions:
Cnoidal solution of the KdV equation:
A numerical check of the solution:
Plot the solution:
Closed form of iterates of the Katsura-Fukuda map:
Compare the closed form with explicit iterations:
Plot a few hundred iterates:
Implicitly defined periodic maximal surface in Minkowski space:
Calculate partial derivatives:
Check numerically the equation for a maximal surface:
Plot the maximal surface in Euclidean space:
Solution of the Euler top equations for
:
Check the solutions numerically:
Plot the solutions:
Define a compacton solution of the nonlinear differential equation
:
Verify the solution:
Plot the compacton:
.
, where 
. 
is a doubly periodic function in 
with periods 
and 
, where 
is the elliptic integral EllipticK.
EXAMPLES
Basic Examples 
Scope 