Dx as change in distance vs dx as infinitesimal x?

[jaredvert]

dx as change in distance vs dx as infinitesimal x?

Why are they the same notation?Sent from my iPhone using Physics Forums

 

[dipole]

Because they're the same thing. What meaning exactly would $dx$ have otherwise?

If at time $t$ you have some position $x(t)$ then Newton's Law tells you how a small change in position is related to the velocity of the particle - namely $x + dx = x + v(t)dt$, where $v(t)$ satisfies the equation $m\frac{dv}{dt} = F$.

 

[sophiecentaur]

An actual change in distance is often denoted by δx or Δx, to distinguish it from the infinitesimal dx, which is part of Calculus. dy/dx really means the limit of δt/δx as δx approaches zero. In Science, we are often too sloppy about these notations as there may be pitfalls when you don't stick to the 'rules' precisely.