  Previously, we have introduced a very small number of examples of what we
call Ouroboros functions. Using our already established theory of Ouroboros
spaces and their functions, we will provide a set of families of Ouroboros
functions that bolster our overall understanding of the Ouroboros spaces. From
here, we extend the theory of Ouroboros functions by introducing Ouroboros
functionals and Ouroboros functional spaces. Furthermore, we re-frame the
expected value of a random variable as an Ouroboros functional, which proves to
be more intuitive in view of probabilistic measure theory. We then show that
these Ouroboros functions have additional applications, as they are general
solutions to certain elementary linear first order partial differential
equations (PDEs). We conclude by elaborating upon this connection and
discussing future endeavors, which will be centered on answering a given
hypothesis.
