Vector Fields

A weather map doesn't just say 'it's windy.' At every dot on the map it draws a little arrow — which way the wind blows and how hard. That is a vector field: a rule that hands you a vector at every point of space. Water currents, magnetic fields, the pull of gravity, the flow of heat — all of them are vector fields. Multivariable calculus is the language for measuring what these fields do.