Green's Theorem

(1.7 hours to learn)

Summary

Green's Theorem is a theorem relating the integrals of the curl and the divergence of a vector field over a closed region to a line integral along its boundary.

Context

This concept has the prerequisites:

Goals

  • Know the definitions of curl and divergence
  • Prove two versions of Green's Theorem:
    • relating line integrals to curl
    • relating flux to divergence
  • Be able to apply Green's Theorem to compute:
    • the area of a closed region
    • line integrals
    • flux across a curve
  • Use Green's Theorem to show that conservative vector fields have zero curl

Core resources (read/watch one of the following)

-Free-

MIT Open Courseware: Multivariable Caclulus (2010)

-Paid-

See also

-No Additional Notes-