The above two video from numberphile are trying to motivate real analysis (I think?). The latter continues on from the former.
Presenter's argument goes kind of like this:
He first considers the real number line and talks about measuring distance between numbers
4-3=1
Then he talks about...
Lowly engineer here. I am struggling - I think like many - to develop intuition on DEs.
From looking at the history and applications of DEs, general themes that come to mind are, conservation, energy (eg. isochrone problem), causality, feedback (control systems), etc.
However, I can't seem to...