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Oliver Heaviside invented what is called "symbolic calculus" which was a mathematically non-rigorous (at that time) but very effective way of solving differential equations that occur in physics and engineering. Later it was justified using Laplace transform and distributions theory. Heaviside function plays an important role in his formalism, analogous to ...


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"Oliver Heaviside ... what he was doing, why he developed his step function"? A short answer is that Heaviside was interested, as a practical electrical engineer, in transient effects in complex electrical circuits as well as in steady effects. Examples of 'transient' problems: What happens when a switch is flipped (closed), and the circuit is an intricate ...


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Since I have no shame, I screen-shotted the reference that J.G. found:


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This gives the four equations in the form Heaviside came up with: $$\varepsilon E = \rho$$ $$\nabla \times E = - \mu \frac{\partial H}{\partial t}$$ $$\nabla \cdot \mu H = 0$$ $$\nabla \times H = k E + \varepsilon \frac{\partial E}{\partial t}$$ where $E$ represents the electric field, $H$ represents the magnetic field, $\varepsilon$ is the permittivity, $...


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