Apart from a brief encounter with synthetic geometry, Liouville did his first research in electrodynamics. He only published two short notes  and  on this subject and neither were particularly original or influential. Still, it is interesting to have a closer look at their genesis because it sheds light on the formation of Liouville as a scientist and illuminates the origin of his theory of differentiation of arbitrary order.
KeywordsHeat Flux Heat Equation Riccati Equation Wave Theory Total Heat Flux
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