I'm trying to understand the math of animation nodes (Omar's helping) to create surfaces, and I was very curious how I could use AN to create parametric functions.I used the _surface_z addon for to create some surfaces. So how do I get parameterized functions in AN? It's possible? 
Here's a great example of the "gabriel's horn"http://mathworld.wolfram.com/GabrielsHorn.html and Funnel”http://mathworld.wolfram.com/Funnel.html.
Parametric surfaces are very easy to create. A parametric surface is defined by two parameters—usually denoted by $u$ and $v$—that have a certain range and a parametric equation that maps those parameters to a 3D vector. To discretize the surface, we let $u$ and $v$ range in their defined range with a certain uniform step size and apply the parametric equations to get the locations. An implementation of your second example is as follows:
To construct a surface from that, just use the polygons of a grid, because the structure of the output points is inherently similar to that of the grid:
The first example is a subset of what we just created, where it is simply defined to have the X equation to be $u$ and the Y equation to be $v$. Or more simply, it can be treated as a multi-variable function of the x and y locations of a grid points. In fact, the second example can also be described as a multi-variable function of the x and y locations of a circle mesh of a high inner loop count. You can implement this yourself as a practice.
I personally think there is another approach. Simply use falloff to decide how to deform the mesh. It's also possible to make the shape more complex depending on your falloff, and curve interpolation settings.
