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More generally, we define the differential <math>d\omega</math> by extending the above definition by [[linearity]].
More generally, we define the differential <math>d\omega</math> by extending the above definition by [[linearity]].
<!--"Cohomological" is the correct spelling! Please don't keep breaking it-->
==Cosmological properties of the differential==
==Cohomological properties of the differential==
The [[operator]] ''d'' has the important property that <math>d\circ d = 0</math>. This essentially follows from the equality of mixed [[partial derivative]]s. The following simplest example illustrates the general proof: Let <math>f(x,y)</math> be a smooth function in two variables. Then
The [[operator]] ''d'' has the important property that <math>d\circ d = 0</math>. This essentially follows from the equality of mixed [[partial derivative]]s. The following simplest example illustrates the general proof: Let <math>f(x,y)</math> be a smooth function in two variables. Then