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How did Fourier know an infinite number of frequencies were required to solve the heat equation?

What we assume to be "the general solution" has evolved and refined over time. There is an argument to be made that Fourier did not strictly know that this would give the general solution, ...
Georg Essl's user avatar
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How did Fourier know an infinite number of frequencies were required to solve the heat equation?

English translation of Fourier's Analytical Theory of Heat is accessible on Internet Archive. His reasoning for a stationary plate problem, which is his first example of applying trigonometric series,...
Conifold's user avatar
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Why was FFT needed to detect Soviet nuclear tests?

On the first question I can answer in general terms. Any analysis of wave phenomena is based on Fourier transform. In our case, the data are obtained from seismographers, and the goal is to find the ...
Alexandre Eremenko's user avatar

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