Important results in the theory of PDEs regarding boundaryvalue problems are trace and extension theorems. Since the trace operator essentially acts by restriction to the boundary of the domain, I was wondering how it got the name "trace": who came up with this name, when and why?
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2$\begingroup$ The trace operator restricts a function to the boundary of the domain, so one can say that it "traces the boundary of the function". $\endgroup$ – Carlo Beenakker Oct 10 '17 at 14:42

$\begingroup$ Tracing being a primitive precomputer method of image reproduction :) $\endgroup$ – J.J. Green Oct 10 '17 at 14:49

2$\begingroup$ Not sure the historical order of terminology, but for example in do Carmo's book on curves and surfaces, the trace of a parametrised curve is it's image. One "traces" the curve in space to get the image as one might trace a picture onto a new sheet of paper. Then @CarloBeenakker comment extends that notion to tracing a function along the boundary which is itself the trace in (do Carmo's sense) of the inclusion of the boundary into the domain. $\endgroup$ – Paul Bryan Oct 11 '17 at 0:06

$\begingroup$ Now crossposted to History of Science and Mathematics, see hsm.stackexchange.com/q/6603/4703 $\endgroup$ – Jules Lamers Oct 17 '17 at 15:09