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If there was ever an article that needs this template, this is it. It's a case of "grad students showing off". But here it is.
{{math-a}}
Let <math>f:M\rightarrow \mathbb{R}</math> be a [[smooth]] [[function]] on a [[manifold]]. The '''differential''' (or '''exterior derivative'''), <math>df</math>, is a [[covector field]] on ''M'' defined as follows: for ''v'' a [[tangent]] [[vector]] at a point <math>p</math>
Let <math>f:M\rightarrow \mathbb{R}</math> be a [[smooth]] [[function]] on a [[manifold]]. The '''differential''' (or '''exterior derivative'''), <math>df</math>, is a [[covector field]] on ''M'' defined as follows: for ''v'' a [[tangent]] [[vector]] at a point <math>p</math>