Computational mathematics is not mathematics as you know it! As I have learnt, you don't need to know every mathematics trick in the book to start using this, and you can take some of these ideas and start approximating a lot of physical phenomena.
This is a small work-through of how to model a diffusive process using a very simple computer code. It purposely doesn't cover some of the finer points, but it's a good start for those who maybe have always wanted to include different, interesting physical effects in their code but have been scared of the mathematics behind it.
I will add more to the series, hopefully allowing people to start feeling equipped to use more and more computational mathematics.