# Jean-Marie Duhamel

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French mathematician and physicist

Jean-Marie Constant Duhamel Born (1797-02-05)5 February 1797 Saint-Malo, Ille-et-Vilaine, France Died 29 April 1872(1872-04-29) (aged 75) Paris, France Known for Duhamel's formula Duhamel's integral Duhamel's principle Vibroscope Scientific career Fields Mathematics Physics Thesis De l'influence du double mouvement des planètes sur les températures de leurs différents points (1834)

**Jean-Marie Constant Duhamel** ([/ˌdjuːəˈmɛl/](https://en.wikipedia.org/wiki/Help:IPA/English);[1] French: [\[dy.amɛl\]](https://en.wikipedia.org/wiki/Help:IPA/French); 5 February 1797 – 29 April 1872) was a [French](/source/French_people) [mathematician](/source/Mathematician) and [physicist](/source/Physicist).

His studies were affected by the troubles of the [Napoleonic era](/source/Napoleonic_era). He went on to form his own school *École Sainte-Barbe*. [Duhamel's principle](/source/Duhamel's_principle), a method of obtaining solutions to inhomogeneous linear evolution equations, is named after him. He was primarily a mathematician but did studies on the mathematics of [heat](/source/Heat), [mechanics](/source/Mechanics), and [acoustics](/source/Acoustics).[2] He also did work in calculus using infinitesimals. Duhamel's theorem for infinitesimals says that the sum of a series of infinitesimals is unchanged by replacing the infinitesimal with its principal part.[3]

In 1853 he published about an early recording device he called a [vibroscope](/source/Vibroscope). Like other similar devices, the vibroscope was a type of measuring device similar to an [oscilloscope](/source/Oscilloscope), and could not play back the etchings it recorded.[4]

## Honours

- [19617 Duhamel](/source/19617_Duhamel), [asteroid](/source/Asteroid) named after him

## See also

- [Duhamel two-point function](/source/Bogoliubov_inner_product)

- [Raabe–Duhamel's test](/source/Convergence_tests#Raabe–Duhamel's_test)

## References

1. **[^](#cite_ref-1)** ["Duhamel"](http://www.dictionary.com/browse/duhamel). *[Random House Webster's Unabridged Dictionary](/source/Random_House_Webster's_Unabridged_Dictionary)*.

1. **[^](#cite_ref-2)** [John J O'Connor and Edmund F Robertson. The MacTutor History of Mathematics archive](http://www-history.mcs.st-andrews.ac.uk/Biographies/Duhamel.html)

1. **[^](#cite_ref-3)** H. J. Ettlinger (1922) "A Simple Form of Duhamel's Theorem and Some New Applications", [American Mathematical Monthly](/source/American_Mathematical_Monthly) 29(7): 239–50

1. **[^](#cite_ref-4)** Burgess, Richard James (2014). [*The History of Music Production*](https://books.google.com/books?id=qMKiAwAAQBAJ). Oxford University Press. p. 3. [ISBN](/source/ISBN_(identifier)) [978-0199357178](https://en.wikipedia.org/wiki/Special:BookSources/978-0199357178). Retrieved 1 August 2019.

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