The equation of mean mass conservation is, in vector notation:

The eight original Maxwell's equations can be written in modern vector notation as follows:

The hydraulic gradient can be expressed in vector notation, using the del operator.

The general formula for higher dimensions can be quickly arrived at using vector notation.

As expected, the analysis using vector notation results in a straight confirmation of the previous analysis:

It manages without vector notation and doesn't touch perturbation theory.

He wrote six out of the nine formulas, which at that time were not expressed in vector notation, nor using linear algebra.

This formula defines the integral on the left (note the dot and the vector notation for the surface element).

Including the other two equations, in modern vector notation, they can form a set of eight equations.

It will be convenient to switch over to three-dimensional vector notation.