Oliver Heaviside - Innovations and Discoveries

Innovations and Discoveries

Heaviside did much to develop and advocate vector methods and the vector calculus. Maxwell's formulation of electromagnetism consisted of 20 equations in 20 variables. Heaviside employed the curl and divergence operators of the vector calculus to reformulate 12 of these 20 equations into four equations in four variables (B, E, J, and ρ), the form by which they have been known ever since (see Maxwell's equations). He invented the Heaviside step function and employed it to model the current in an electric circuit. He invented the operator method for solving linear differential equations, which resembles current Laplace transform methods (see inverse Laplace transform, also known as the "Bromwich integral"). The UK mathematician Thomas John I'Anson Bromwich later devised a rigorous mathematical justification for Heaviside's operator method.

Heaviside advanced the idea that the Earth's uppermost atmosphere contained an ionized layer known as the ionosphere; in this regard, he predicted the existence of what later was dubbed the Kennelly–Heaviside layer. He developed the transmission line theory (also known as the "telegrapher's equations"). He also independently discovered the Poynting vector.