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In what work did Jacobi introduce the jacobian, and what was his motivation for doing so?

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I don't know about the motivation, but it was introduced in his article Ueber die Functionaldeterminanten (Journal für die reine und angewandte mathematik, bd. 22, 1841). However, Jacobians had already been studied by Cauchy in 1815.

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    $\begingroup$ The motivation is described at length in the article of Stackel, in the same file that you linked. It follows Jacobi's article. $\endgroup$ – Alexandre Eremenko Dec 11 '17 at 0:16
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    $\begingroup$ @AlexandreEremenko Thank you. I failed to notice it. $\endgroup$ – José Carlos Santos Dec 11 '17 at 7:17
  • $\begingroup$ Was Jacobi aware of Cauchy's use of jacobians? $\endgroup$ – user109871 Dec 11 '17 at 13:13
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    $\begingroup$ @user109871 He doesn't seem to mention Cauchy in his article. $\endgroup$ – José Carlos Santos Dec 11 '17 at 13:18

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