Maxwell Equation

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As a major contributor to the mathematics of vector calculus,

Oliver Heaviside was able to rewrite Maxwell's original 20 equations into a mathematically equivalent 4 equation form.

For Maxwell's equations, vector calculus formulations are much more mathematically convenient,
and have become the standard formulation to use.[1]


Wikipedia

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Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law,
form the foundation of classical electrodynamics, classical optics, and electric circuits.

These fields in turn underlie modern electrical and communications technologies.
Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents.

They are named after the physicist and mathematician James Clerk Maxwell,
who published an early form of those equations between 1861 and 1862.

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Vector calculus (or vector analysis) is a branch of mathematics concerned with
differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb{R}^3.

The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus,
which includes vector calculus as well as partial differentiation and multiple integration.

Vector calculus plays an important role in differential geometry and in the study of partial differential equations.

It is used extensively in physics and engineering,
especially in the description of electromagnetic fields, gravitational fields and fluid flow.