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.