- #1

Rasalhague

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*Lecture Notes on General Relativity*, p. 12, he writes:

*In spacetime the simplest example of a dual vector is the gradient of a scalar function, the set of partial derivatives [of the function] with respect to the spacetime coordinates, which we denote by "d":*

[tex]\mathrm{d}\phi = \frac{\partial \phi}{\partial x^{\mu}} \hat{\theta}^{(\mu)}[/tex]

http://preposterousuniverse.com/grnotes/

Is it just a coincidence of notations that [tex]\mathrm{d}\phi [/tex] looks like a differential (an infinitesimal quantity)? I take it it's important to distinguish between these two concepts (differential and gradient) even though they might be written using the same symbol?