3 ms·
You're making a good point. However, taking inspiration from differential topology (and differential forms in particular), the notation dx can be made sense of
by codethief 4y ago
You're making a good point. However, taking inspiration from differential topology (and differential forms in particular), the notation dx can be made sense of once you interpret x as a coordinate function x: M -> R on a manifold. So in a sense you are replacing the variable x with a function x (whose parameter is usually left unspecified).
- LudwigNagasena 4y agoYeah, it’s the standard way to do it. But there is a reason the 7th point is called “stay away from differentials.” It’s cryptic and unintuitive for many people. I wonder whether name binding concepts from CS theory a la lambda calculus can be leveraged for an alternative formalization.
- selimthegrim 4y agoI think usually slightly alternate definition of derivative is used - https://en.wikipedia.org/wiki/Total_derivative https://en.wikipedia.org/wiki/Total_derivative