- #1
eljose
- 492
- 0
could actually the Cauchy theorem be applied to [tex] R^{2} [/tex] of course with some restrictions..namely
-The differential form must be invariant under rotation in the plane
-The differential form must come from a gradient [tex] \nabla{S}=f/(|r|-a) [/tex]
with this using the same techniques by Cuachy we could se the equality:
[tex] \Int_{C}dq.F(x,y)//(|r|-a)=2\piF_{r}(a) [/tex]
this means somehow that the integral over a curve on RxR is equal to the normal component evaluated at the point r=a where r is the modulus of the vector (x,y,z)
-The differential form must be invariant under rotation in the plane
-The differential form must come from a gradient [tex] \nabla{S}=f/(|r|-a) [/tex]
with this using the same techniques by Cuachy we could se the equality:
[tex] \Int_{C}dq.F(x,y)//(|r|-a)=2\piF_{r}(a) [/tex]
this means somehow that the integral over a curve on RxR is equal to the normal component evaluated at the point r=a where r is the modulus of the vector (x,y,z)