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It’s difficult to see what Heaviside had in mind, but thanks for bringing it up. For instance, vector calculus was a very young discipline, and many of the operators currently in use (Div, Curl, the Laplacian) did not exist in Maxwell's time. Maxwell's equations are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. 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 equations are used in developing modern electrical and communications technologies.

Original 20 equations. Heaviside championed the Faraday-Maxwell approach to electromagnetism and simplified Maxwell’s original set of 20 equations to the four used today. With Maxwell's theories expressed in vectors, the scientific community began to appreciate the value of Maxwell's contributions. In the Wikipedia Quaternion article there is a section concerning, P.R.

Importantly, Heaviside rewrote Maxwell’s Equations in … Original Maxwell Equations - Maxwell's 20 Equations in 20 Unknowns - PDF; On Faraday's Lines of Force - 1855/56 Maxwell's first paper (Part 1 & 2) - Compiled by Blaze Labs Research (PDF) On Physical Lines of Force - 1861 Maxwell's 1861 paper describing magnetic lines of Force - Predecessor to 1873 Treatise Girard. Modern-Day 4 Equations. These are the familiar four equations that are usually referred to as Maxwell's equations.

Using his vector analysis, Heaviside turned Maxwell's original 12 equations into four. According to Tom Bearden [5], Maxwell's 1865 paper had its quaternion equations reduced to vector notation -- after a comparatively limited debate among some 30 scientists – a notation advocated by Heaviside, Gibbs, et al – after Maxwell was already dead. Maxwell's original paper [4] consisted of 20 equations with 20 unknowns.