This poster session will highlight the use of visualization tools for understanding calculus and topological concepts. We take a novice’s view of understanding open sets in the plane in order to define continuity of functions. This highlights why continuity within a neighbourhood is important for differentiability. In multivariate calculus, we expand on differential calculus notions of derivatives and the limits that define them, by growing from one dimension with two directions of movement towards a point, to two dimensions and an infinite number of ways to move towards a point. This work is done on top of the backdrop of the usual topology on the real plane. This research project is an investigation of applying the Plus Topology on the plane as a backdrop for continuity and differentiability as discussed in a multivariable calculus class.

I would like to use a computer to display interactive Desmos and Maple graphs that will not be interactive on the poster, but the interactivity is valuable. If I can get a table or something on which to set my computer, that would be amazing