Green's Theorem

(1.7 hours to learn)


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.


This concept has the prerequisites:


  • 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)


MIT Open Courseware: Multivariable Caclulus (2010)


See also

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