Questions tagged [fourier]

Jean-Baptiste Joseph Fourier (1768-1830) was a French mathematician and physicist best known for initiating the investigation of Fourier series, which eventually developed into Fourier analysis and harmonic analysis, and their applications to problems of heat transfer and vibrations.

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What did Fourier mean by stating that every function can be decomposed into sine and cosine functions?

Fourier stated that every function can be decomposed into sine and cosine functions. Was he referring to periodic functions only? To a certain class only? I ask, because it seems clear (at least to me)...
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Was Fourier inspired by Ptolemy?

Ptolemy invented a system to describe the periodic motion of the planets by epicycles. Fourier did something similar for periodic motion in mechanics. Every such motion can be thought of as ...
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What does the Fourier transform have to do with heat?

For example the current version of the Fourier analysis article on Wikipedia says the study is: […] named after Joseph Fourier, who showed that representing a function as a sum of trigonometric ...
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Different conventions between Fourier Transform and Characteristic Function

While it is clear that there are several conventions for Fourier transforms of intragrable functions on $\mathbb{R}$, I don't think I have ever seen anything different from the three following ...
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How did Fourier determine the coefficients of Fourier series?

I was reading a chapter of Fourier's seminal work "Analytic Theory of Heat". The third chapter of this book was translated by the famous Stephen Hawking in his book "God created the ...
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Did Fourier use heated metal rings as experimental evidence to justify his mathematical discoveries?

In his answer to a previous question Alexandre Eremenko pointed out that Joseph Fourier in his book Analytic Theory of Heat gave all kinds of arguments in favor of the following mathematical ...
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History behind the heat equation

Who was the first mathematician/physicist to derive the heat equation $u_t=\Delta u$ and when? Was it already known to explain most diffusion phenomena? How much time passed between the first ...
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Were the kilogram, the grave, etc. meant to be units of weight, units of mass, or was it ambiguous at the time?

It is sometimes stated that the early metric units of 'weight' really were meant to be exactly that: units of weight (i.e. force), not mass. However, is that really so? In fact, did the people ...
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Origin of the Fourier transform (1878)

I located Joseph Fourier's book, Analytical Theory of Heat (1878), but at first glance it looks like it is all about heat. What did Fourier call the Fourier transform? When did he first use it?
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Substantiating claimed Fourier quote about “an arbitrarily capricious graph”

The following quote (in English) is fairly widely attributed to Fourier, but I can't substantiate it. An arbitrary function, continuous or with discontinuities, defined in a finite interval by an ...
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What are some good references elucidating the discovery/creation of Fourier Series?

I've always grappled with anything related to Fourier since my undergrad days. Recently, when revisiting why I learned what I did, I discovered how Fourier's desire to understand the flow of heat ...