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9 votes

What are some good references elucidating the discovery/creation of Fourier Series?

Contrary to what the name suggests, Fourier series were not invented/discovered by Fourier. They were considered by Euler and Bernoullis, in relation to the one dimensional wave equation, not the heat ...
Alexandre Eremenko's user avatar
7 votes

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

First of all, one has to notice that the work of Fourier predates all modern notions of function. The notion of function was first clarified by Dirichlet, in his attempt to justify Fourier's arguments....
Alexandre Eremenko's user avatar
7 votes

Substantiating claimed Fourier quote about “an arbitrarily capricious graph”

You can find the quote (or something similar) in multiple places in the Théorie analytique de la chaleur, for example in Chapter I, paragraph (article) 14: "L'examen de cette condition fait ...
user6530's user avatar
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6 votes
Accepted

What are some good references elucidating the discovery/creation of Fourier Series?

§1.1 (+ supplement) of Bressoud’s A radical approach to real analysis, recommended here just recently, does pretty much exactly what you want.
Francois Ziegler's user avatar
6 votes

What are some good references elucidating the discovery/creation of Fourier Series?

The book Introduction to the Theory of Fourier's Series and Integrals by H. S. Carslaw answers your questions in the first chapter on the History of this subject. Many commonly held false beliefs are ...
DisintegratingByParts's user avatar
6 votes
Accepted

History behind the heat equation

Heat equation was first formulated by Fourier in a manuscript presented to Institut de France in 1807, followed by his book Theorie de la Propagation de la Chaleur dans les Solides the same year, see ...
Conifold's user avatar
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5 votes

Was Fourier inspired by Ptolemy?

Fourier was not inspired by Ptolemy or by mechanics. His work where he developed Fourier series and invented Fourier transform was about heat. He never mentions Ptolemy (or any astronomer). The ...
Alexandre Eremenko's user avatar
5 votes

What does the Fourier transform have to do with heat?

Not to sway others from providing a better answer from more interesting sources, but I think one clue can be found in the current version of the Wikipedia article for Joseph Fourier himself: There ...
natevw's user avatar
  • 197
2 votes

Were the kilogram, the grave, etc. meant to be units of weight, units of mass, or was it ambiguous at the time?

I would choose #2. The commission reported that Lavoisier and Hauy used a beam scale to determine the mass of the unit volume of water. A beam scale measures mass. As it was the standard weighing ...
jkien's user avatar
  • 1,901
2 votes

Different conventions between Fourier Transform and Characteristic Function

I agree: the main difference is the minus sign in the exponent. The other differences are cosmetic. For a probability measure, we normalize $$ \hat{\mu}(\omega) = \int e^{i \omega x} d \mu(x) $$ ...
Gerald Edgar's user avatar
  • 10.3k
2 votes

Different conventions between Fourier Transform and Characteristic Function

There is a fourth convention $$\hat{f}(s)=\frac{1}{2\pi}\int e^{-its}f(t)dt,$$ which is used sometimes.
Alexandre Eremenko's user avatar
1 vote
Accepted

Are there any portraits of Joseph Fourier other than this one?

Here is a caricature of Fourier and Legendre: http://www.numericana.com/fame/legendre-fourier.jpg (This is the only existing portrait of Legendre).
Alexandre Eremenko's user avatar
1 vote

History behind the heat equation

The first mathematician who did this accurately and with all detail was Joseph Fourier. Though he had predecessors. (One can almost never answer the question "who did this first", so on my ...
Alexandre Eremenko's user avatar
1 vote

Did Fourier use heated metal rings as experimental evidence to justify his mathematical discoveries?

The essential part of the answer (page references) is contained in the comment of @Conifold. However his general conclusion is plain wrong, and I would like to put the things straight. A scientist ...
Alexandre Eremenko's user avatar
1 vote

Substantiating claimed Fourier quote about “an arbitrarily capricious graph”

I think the conclusion here is that there is no proof that the claimed Fourier quote is an actual Fourier quote (in any language). However, (1) Absence of proof is not proof of absence. (2) ...
Daniel J. Greenhoe's user avatar
1 vote

What are some good references elucidating the discovery/creation of Fourier Series?

I know a book that is completely devoted to the history and development of trigonometric series (including of course Fourier series). But it is not in English, it is in Russian. It gives a rather ...
James Warthington's user avatar

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