III.16 Differential Forms and Integration, Terence Tao: Page 178.

0-forms, 1-forms, 2-forms, etc. are called differential forms.

Fundamental scalar function operations are addition, pointwise product and differentiation.  These can be generalized to differential forms.

An example of a solid or surface of a sphere is used to show the relationship between 3-forms and 2-forms.

There are sign changes related to antisymmetry in the derivation rule for differentiation.  The differentiation operator is nilpotent, d(dw) = 0.

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