Talk:gradient

Deletion discussion

The following information passed a request for deletion.

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== gradient ==

I wondered whether RFV would be more appropriate, but ultimately decided to put this here. I claim these three definitions:

3. (calculus) Of a function y = f(x) or the graph of such a function, the rate of change of y with respect to x, that is, the amount by which y changes for a certain (often unit) change in x.
4. (physics) The rate at which a physical quantity increases or decreases relative to change in a given variable, especially distance.
5. (mathematical analysis) A differential operator that maps each point of a scalar field to a vector pointed in the direction of the greatest rate of change of the scalar. Notation for a scalar field φ: ∇φ

are redundant to each other, and they are somewhat doubtful. The definition labelled "analysis" is the one that agrees the most with what I have been taught and with w:Gradient; a slightly better-written version of it would encompass the other two. The sense labelled as "calculus" looks like something synonymous with derivative; although a plain derivative can be considered a special case of gradient (when you identify a one-dimensional vector space with its underlying scalar field, which is usually the field of real numbers), I doubt that gradient is actually used this way. The "physics" sense reads as synonymous with the first. As far as I know, physicists use "gradient" the same way mathematical analysts do (unless they use it in an everyday meaning); there is no separate physical sense of gradient. — Keφr 17:52, 25 January 2015 (UTC)

I agree that these are not really fully independent meanings, but I'm sure we can find cites for all three of them, and some users will not be familiar with differential operators. I don't think it would be helpful to delete any one of them, and combining all three would make a rather clumsy paragraph. The OED has all three separate senses (plus some others that we don't have). Perhaps the "physics" sense is not specific to physics -- it is also used in other sciences. Dbfirs 21:53, 27 January 2015 (UTC)

Keep. I've made a couple of edits to the entry, but I'm sure it can be further improved. Would you like cites for the senses you doubt? Dbfirs 08:04, 1 February 2015 (UTC)

Kept; no consensus to delete. bd2412 T 16:17, 25 February 2015 (UTC)