Should it be decided that more than one function is executed by a single entity, then a convention for representing function sharing is employed.
Another traditional convention for representing functions emphasizes hierarchical relationships using a tree diagram.
Users of graphics calculators will be well aware, however, of the immense power of representing functions
in multiple ways, in the form of symbols, tables and graphs--the so-called 'rule of three'-- and the many learning opportunities these provide for students.
For PDEs with complicated geometries, the finite-element method (FEM) is a popular approach to representing functions
. One could, of course, represent functions on such geometries using a (high-order) finite-element basis and carry out Algorithm 1, but it is not clear whether such a FEM-based infinite Arnoldi variant of Algorithm 1 would be computationally feasible (because it requires the solution of a PDE at each iteration).
I was specifically interested in the kinds of instructional decisions I made to help the students overcome constraints in their interpretations of functions originating in dynamic physical models, and of tables and equations representing functions
originating in dynamic physical models.