I have performed non-trivial scientific calculations, in university and beyond, for almost 15 years. Until the end of undergraduate school, this was mostly done by hand. Optimizing the trajectory of a heavy ball or solving the heat equation are problems with analytical solutions, and thus can be solved with pen(cil) and paper. However, there were instances when numerical tools had to be used, rather than analytical ones. This occurred, for example, when replacing models of the physical world wit...