What is the Codifferential and How Can it be Calculated for 1-Forms?

[zetafunction]

codifferential what is it ??

given an 1-form i know how to calculate the exterior derivative 'd'

however how could i calculate the codifferential ?? i mean the adjoint operator of 'd'

if possible help me with the example $$A= fdx+gdy$$ where f and g are functions of the variable (x,y)

for the case of the exterior derivative $$dA=rotA$$ (rotational) however i do not have any idea of how to define the codifferential of a $$\delta A$$

 

[lavinia]

what about the codifferential using the Hodge star operator?

 

[element4]

Adjoint operators are usually defined using inner products. As Lavinia suggests, it is therefore natural to use the Hodge star operator in this case. See http://en.wikipedia.org/wiki/Hodge_dual#The_codifferential" page.