Vector calculus is multivariate [real analysis]
? in (usually) 2 and 3 dimensions.
The field consists of a suite of formulas and problem solving techniques very useful for
engineering and
Newtonian physics.
Most of the analytic results are more easily understood using the machinery of
differential geometry, for which vector calculus forms a subset.
Vectors live in a space called a "vector space" over a given field?.