A vector field is a vector-valued function defined on ℝ³ or some subset of ℝ³, though the notion can easily be extended to other dimensions. A field will usually be assumed to have continuous derivatives (see continuous function). Vector fields are common in physical applied mathematics—examples include gravitational field (see gravity), wind velocity, heat flux, electric field, and magnetic field—but may also be studied in their own right in multivariable calculus. Compare scalar field.