I really only think calculus notation is an issue. Calc 1 books absolutely demand that you view d/dx as an operator and not a ratio, likewise with the dummy variable and integration symbol. Then later the book teaches about unit normals and it’s implicitly acceptable and treat dx/dz and dy/dz as ratios.
i.e.
|u X v| = (1 + (dx/dz)^2 + (dy/dz)^2)^(1/2) = (dz^2 + dx^2 + dy^2)^(1/2).
This was extremely frustrating to me for a while until I accepted that this was how Leibniz did it, so if it’s good enough for him it’s good enough for me.
i.e. |u X v| = (1 + (dx/dz)^2 + (dy/dz)^2)^(1/2) = (dz^2 + dx^2 + dy^2)^(1/2).
This was extremely frustrating to me for a while until I accepted that this was how Leibniz did it, so if it’s good enough for him it’s good enough for me.