Differential

In calculus, a differential refers to an infinitesimal (i.e., an infinitely small) quantity.

For instance, for some vector $\vec{L}$ in ${\mathbb{R}}^2$, we can represent $dz$ as with the tangent plane: $dz=f_x(x,y)dx+f_y(x,y)dy$ And as:

$$dl=d{l}_x\hat{x}+d{l}_y\hat{y}$$

Multi-dimensional

We could also represent the differential surface area $dS$:

$$dS=d{l}_{x}d{l}_y=dxdy$$

In polar coordinates, since $\theta$ is in radians, not metres, we must also convert by multiplying with $r$:

$$dS=rd\theta dr$$