Hot and Cold Metal: Executable or Text Version
This program numerically solves the Heat Equation in 2 dimensions for a "cold" metal plate with a "hot" pattern on its surface (or vice versa). An analytical solution of this equation in requires rather advanced mathematics, but a numerical solution is far simpler. Of course, it's only an approximation, but it's near enough. For an outline of the method I use, click HERE for a Word document I've prepared.
Fireworks: Executable or Text Version
This is a trivial looking program which uses some fairly advanced mathematics simply for the sake of accuracy! As it flies through the air it meets AIR RESISTANCE. I have taken account of the effects of air resistance, modeled as proportional to the square of the speed of the firework.