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## Main Question or Discussion Point

When I first came across differentials, I was told that they could be thought of as infinitesimal changes. However, I can't get my head around how they're actually used to model physical problems. For example, if ##x## is the x-coordinate of a moving body, then ##dx## is an infinitesimally small change in position. More generally, if ##\vec{r}## is the position vector of a body, then ##d\vec{r}## is an infinitesimally small change in position. What I don't understand is how we think of things like distance, mass, and area in terms of differentials. For example, we think of ##dA## as an infinitesimally small area; ##dm## as an infinitesimally small mass; and ##ds## as an infinitesimally small distance. Why do we avoid the concept of "change" when talking about mass, area, and distance (to name a few)?