Correct Enunciation – Del. ?, ?, ?

multivariable-calculusterminology

I've come across various different symbols being pronounced as "del". What is the internationally accepted del? If not internationally, then what's the English/American(specify which one if they are different) one that most lecturers/&c use?

  • $\partial$: I have heard $\frac{\partial}{\partial x}$ being called "del by del x", and (rarely) "dou by dou x" and "der by der x". $\partial$ can be used without a fraction (einstein notation), in which case it gets confusing.
  • $\nabla$: Called Nabla or del. This has four different uses, which can be easily distinguished while reading out loud, but it gets confusing when the first and last uses (grad and covariant derivative) get mixed up with $\partial$ and $\delta$
    • Gradient/grad: $\vec{\nabla}\phi$ (phi is a scalar). Read as "nabla phi", or "del phi".
    • Divergence/div: $\vec{\nabla}\cdot\vec{v}$ Pretty clear, can be read as "nabla dot" or "del dot"
    • Curl/rot: $\vec{\nabla}\times\vec{v}$ Also clear, can be read as "nabla cross" or "del cross"
    • Covariant derivative: $\vec{\nabla}_{\vec{u}}\vec{v}$: Can be read as "del v" or "nabla v" . I've seen it called "del u v" also.
  • $\delta$ : Read out as "delta", but I've heard it used as "del" as well.

This entire thing has confused me. My questions are:

  1. Which one can be correctly called "del"? I'm fine with div/curl being read out as del, as the dot/cross can be read out as well. The confusion is between the convariant derivative, grad, partial derivative, and lowercase delta. Or is it just a matter of context?
  2. Where did this confusing terminology come from in the first place? Why name something del when we already have a bunch of other dels? A timeline of the dels would be appreciated, but not necessary :-).

Best Answer

For what it's worth, in the community I hang out with, we generally just say "partial ecks" for $\partial_x$, and when we are feeling even lazier and when the context is clear, we call the same operator "dee-dee ecks", as if it were the ordinary $\frac{d}{dx}$.

$\nabla$, however, is always "nabla", unless it is used for the gradient of a function, in which case we say "gradient of eff" for $\vec{\nabla} f$.

In class, however, if the expression is embedded in prose (say as part of a theorem statement), I would never read the symbol. I would instead say what it means. So while I may write

Important, we always have $\partial_x\partial_y f = \partial_y\partial_x f$

I would say,

Important, we always have that partial derivatives commute.

Or if I write

Therefore $\partial_x f = 0$

I would say

Therefore the partial derivative of eff with respect to ecks is zero.

Or if I write

By the Maxwell's equations, $\nabla\cdot E = 0$

I would say

By the Maxwell's equation, ee is divergence free.

The only time I might read the symbols as symbols is if I am performing a computation on the board and am just copying stuff directly from my notes. In those cases I honestly cannot remember what I would usually say.

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