Baron Jean-Baptiste-Joseph Fourier (21 March 1768 – 16 May 1830), born in poor circumstances in Auxerre, introduced the idea that an arbitrary function, even one defined by different analytic expressions in adjacent segments of its range (such as a staircase waveform) could nevertheless be represented by a single analytic expression. This idea encountered resistance at the time but has proved to be central to many later developments in mathematics, science, and engineering. It is at the heart of the electrical engineering curriculum today. Fourier came upon his idea in connection with the problem of the flow of heat in solid bodies, including the earth.
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