Divergence and Curl

Divergence and Curl

We can use the partial derivatives of the components of a vector field \(\vec{F}\) to define related quantities (the curl and the divergence), each of which provides valuable information about the geometric properties of \(\vec{F}\text{.}\) These will be used later in the course as we try to generalize the fundamental theorem of calculus to higher dimensions.

This worksheet introduces the divergence and the curl of a vector field \(\vec{F}\text{,}\) introducing the geometric interpretation as well as the algebraic definition needed to calculate divergence and curl. It also lays the foundation for the curl and divergence tests.