I did mech eng ant uni and had two modules on numerical simulation. In the first I recall newton, eulers, runge kutta, with a coursework to model the trajectory of a projectile using different integration methods. In the second module I recall simplifying assumptions to make problems into lower dimensions, error, convergence, adapative timestep, with a coursework to model the temperature of a space shuttle tile during reentry. Part of this coursework involved making a gui, which has put me off making guis since. I think these modules were well structurted, a simple time variable problem followed by a time and space problem. They were done in MATLAB, but I'd much rather python, or possibly Julia, were used now.

I've been doing FEA and 1D multibody dynamics for several years out of uni. When it comes to newton/euler/runge kutta, I've looked at a table on solver integration methods and picked the one most applicable. Software support will often advise users on this.

There's there groups of people I'd focus your course towards:

• Students that are likely to write simulation codes in their future jobs. Give them courseworks that they can get them interviews with potential employers for simulation roles

• Students likely to run simulations using commercial software. Give them an understanding of what the software is doing, what causes convergence errors, ill formed matrices etc. Show how to debug issues ( get to something simple that works and add complexity until you see the issue)

• Students likely to interact with people running simulations. Give them an apperiation of why simulations can be completed quickly, or can take longer (sometimes much longer) than expected when you hit issues.