Jean Baptiste Joseph Fourier, who flourished in Revolutionary and Napoleonic France, was a mathematician
and public figure whose solution
of certain "heat problems" essentially frames all of modern analysis (or at least so [CL] proposes).  "Fourier analysis", as he appears
to have understood it, deals with the decomposition of functions into their harmonic components, that is, expression as a sum of 
characteristic sinusoids or equivalent trigonometrics.