After completing this section, students should be able to do the following.

  • State the definition of the curl of a vector field in two dimensions.
  • State the definition of the curl of a vector field in three dimensions.
  • Understand how curl measures local rotation in two dimensions.
  • Understand that curl need not measure gobal rotation.
  • Compute circulation: the flow of a vector field along a curve.
  • State Green’s Theorem.
  • View Green’s Theorem as a fundamental theorem of calculus.
  • Use Green’s Theorem as a planimeter.
  • State the definition of the divergence of a vector field in any dimension.
  • Understand how divergence measures local expansion.
  • Understand that divergence need not measure gobal expansion.
  • Compute flux: the flow of a vector field across a curve.
  • State the flux form of Green’s Theorem.