Matlab is where I got my start in programming, so it will always hold a spot in my heart. It's great for numerical simulations, but now that I'm an R acolyte it's unlikely I'll go back to a piece of proprietary software.
As an undergraduate math major, I worked for several years on a differential equations project for my senior capstone.
Some of that work has made its way into a paper called Instabilities and Patterns in Coupled Reaction-Diffusion Layers, with my co-authors Anne Catllá
and Chad Topaz (Chad was also my advisor for my senior capstone).
Apart from the math (differential equations and algebraic manipulation, basically), I wrote a Matlab program to simulate the problem we were studying, and produced
both still images (like those seen in the paper) and movies showing the system over time.