  The theorems of vector analysis (divergence theorem, etc.) are typically
first applied in the undergraduate physics curriculum in the context of the
electromagnetic field and the differential forms of Maxwell's equations.
However, these tools are analyzed in depth several courses later in the
junior-senior level. I discuss here a "bridge" problem, using the language of
vector calculus in a mechanics setting to understand Archimedes' principle as a
consequence of hydrostatic equilibrium and the superposition of the external
forces. It is my hope that this treatment will help students better integrate
and understand understand these and similar vector analysis results in contexts
beyond electromagnetism.
