Vector Calculus
A branch of mathematics dealing with multivariable differentiation and integration of vector fields in 3D Euclidean space.
Governing formula
∇f (Grad), ∇ · F (Div), ∇ × F (Curl), ∇²f (Laplacian)
SI unit
Differential Operators
In depth
Vector calculus provides the mathematical language of field theories in physics. Differential operators (del ∇) measure local field rate of change (gradient), local expansion/contraction (divergence), and local rotational circulation (curl), unified by fundamental integral theorems.
Examples in the real world
Formulating Maxwell's electrodynamic field equations and fluid dynamics Navier-Stokes continuity equations.