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Is there any published, somewhat comprehensive, list of (almost?) all the many ways in which the Leibniz notation ($dx,$ $P(dx),$ $d\mu(x),$ $du\wedge dv,$ etc., etc.) gets used in the various areas of mathematics?

(I posted this question here on m.s.e. and it was closed although nobody verbally expressed any specific objections to it or even hinted at such.)

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    $\begingroup$ from what I read on MSE it was closed as not being clear enough --- I'm not sure that asking the same question here will be helpful. $\endgroup$
    – Carlo Beenakker
    Commented Aug 9, 2020 at 19:46
  • $\begingroup$ It's also clearly not research level (although lots of also clearly-not-research-level historical questions do well on MO anyway). $\endgroup$
    – LSpice
    Commented Aug 9, 2020 at 19:51
  • $\begingroup$ @CarloBeenakker : Do you have any guesses as to what someone might find unclear about this? $\endgroup$
    – Michael Hardy
    Commented Aug 10, 2020 at 0:11
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    $\begingroup$ At least for me, the question is not clear since there is a distinction between, for example: the original notation used by Leibniz; the formalization of this notation (Robinson et al.); the derived notations inspired by the concept of differential in other branches, etc. Perhaps you could be more specific in what aspects are you interested about this. $\endgroup$
    – efs
    Commented Aug 14, 2020 at 15:09
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    $\begingroup$ "At any rate what I had in mind has more to do with what Leibniz and Robinson have in common". If you have that in mind, well, ask that. $\endgroup$
    – efs
    Commented Aug 14, 2020 at 17:39

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Not quite sure in which direction you are hoping for an answer, but to set a first data point I offer the Pantheon of Derivatives

Part 1 – Directional Derivatives
Part 2 – Manifolds
Part 3 – Vector Bundles
Part 4 – Lie Theory
Part 5 – Theorems

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  • $\begingroup$ Maybe this is similar to what I had in mind. (Every day I am appalled by the frequent crude typesetting solecisms in MathJax and LaTeX by otherwise literate mathematicians, and these pages are consistent with that. At one point I see $2\mathrm{max}\Big\{ \cdots\cdots\Big\}$ instead of $2\max\Big\{\cdots \cdots \Big\}$ and wonder why people don't know about things like this. But the content looks very interesting otherwise.) $\endgroup$
    – Michael Hardy
    Commented May 8, 2022 at 17:47

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