Green's Theorem in normal form | MIT 18.02SC Multivariable Calculus, Fall 2010

Green's Theorem in normal form

Instructor: Joel Lewis

View the complete course: http://ocw.mit.edu/18-02SCF10

License: Creative Commons BY-NC-SA
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Category:

Education

Tags:

• multivariable calculus
• vectors
• matrices
• partial derivatives
• double integrals
• line integrals
• triple integrals
• surface integrals

[faithx92]

When get wrote down ∫∫ div(F)dA, I believe he may have meant ∫∫ curl(F)dA. Since the former is Gauss's divergence theorem. However, since the vector field is symmetrical, the answer happened to be right. Thanks a lot for your hard work!

[frade001]

[5:15] Did he just fart?

[DoctorFastest]

@faithx92 ∫∫ div(F)dA is correct. Green's theorem is the analog of the divergence theorem for two dimensional vector fields.

Perhaps you are confused because Green's theorem can also be generalized to Stokes theorem. Namely, if you go from the plane the three dimensional space. In that case it is the *other* side of the equation you reference that will be replaced by the curl.

[herrGaman]

These clips are great help, thanks!