Intro PDE Visualiser

This app is designed for a first classroom encounter with partial differential equations. The aim is deliberately modest: students should see that a PDE is a rule about how a function changes in different directions.

The app avoids complicated solution methods and focuses on five simple ideas:

  1. a PDE can say that a function does not change in one direction;
  2. integrating one partial derivative leaves an arbitrary function, not just an arbitrary constant;
  3. two derivative rules must be mutually consistent if they are to describe one function;
  4. proposed solutions can be tested by substitution;
  5. transport and wave equations have simple shape-based interpretations.
PDE idea
x-shape G(x)
y-shape F(y)
0.2 3
display

Goals

We want to think of seeing PDEs as not just symbols and toward seeing them as directional tests on surfaces and shapes.