# Vector Field

A vector field is a function that assigns a vector to each point of Euclidean space. Vector fields arise in differential equations and differential geometry.

Vector field is a college-level concept that would be first encountered in a multivariable calculus course.

### Prerequisites

Differential Equation: | A differential equation is an equation that involves the derivatives of a function as well as the function itself. |

Vector: | (1) In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. (2) In topology, a vector is an element of a vector space. |