Does the $\partial$ mean something when it is used as the boundary of a set?

Question

I'm currently studying the divergence theorem and usually the boundary of a set $\Omega$ is called $\partial \Omega $, which I found curious because the $\partial$ symbol is used in partial derivatives. Does this have a meaning or it is just a traditional way of writing it? Thanks

Answer 1

The short answer is yes there is something being hinted at there. It is the tip of a very big iceberg though...starts with the fundamental theorem of calculus on the real line and goes via divergence and Stokes's theorem, to general differential forms, de Rahm cohomology and beyond. Depending on your level, this note by Tao may be interesting https://www.math.ucla.edu/~tao/preprints/forms.pdf

Answer 2

You might find the more general discussion here on mathoverflow helpful. The answer is yes, but it's going to depend on your level of familiarity with more advanced calculus.