Doubt related to notation used in writing Maxwell's equations

[Hamiltonian]

Homework Statement:

not exactly a home work problem, just a small confusion as to what $\partial S$ and $\partial V$ mean in the equations given bellow.

Relevant Equations:

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What does $S=\partial V$ and $C=\partial S$ signify, usually I have only seen books writing $C$ when evaluating a line integral over a curve $C$ and $S$ when evaluating a surface integral over a surface $S$. Could someone clarify what $\partial S$ and $\partial V$ mean?

 

[Orodruin]

$\partial$ here is the boundary operator. In other words, $\partial V$ is the surface that is the boundary of the volume $V$ and $\partial S$ is the closed loop that is the boundary of the surface $S$.