The name nabla for the upside-down delta ∇ (aka an atled) comes from its shape: it is vaguely reminiscent of a harp, which is "nevel" in Hebrew. V and B being interchangeable under some western Semitic circumstances, the name nabla was given to the symbol.

∇ is merely a differential operator producing the partial derivatives in each variable. So for f:Rn→X,

∇f = (∂/∂x1,...,∂/∂xn)f
More mathematically, nabla (∇, ∇ in HTML) is a 3D vector that is composed of the three partial derivatives, this means :
( ∂/∂x, ∂/∂y, ∂/∂z)
It can be used to represent a number of vector operations on scalar fields or vector fields.
For instance,
  • grad F = ( ∂F/∂x, ∂F/∂y, ∂F/∂z) =( ∂/∂x, ∂/∂y, ∂/∂z)F= F
  • curl F= × F //not demonstrated because of the formatting limitations of E2
  • div F=∂Fx/∂x,∂Fy/∂y,∂Fz/∂z =( ∂/∂x, ∂/∂y, ∂/∂z).(Fx,Fy,Fz)= . F
  • Δ F=( ∂2F/∂x2, ∂2F/∂y2, ∂2F/∂z2) = ( ∂/∂x, ∂/∂y, ∂/∂z).( ∂/∂x, ∂/∂y, ∂/∂z)F = div grad F= ∇2F.
That pretty much sums it up, two vector field, two scalar fields, two applied on scalar fields, two applied on vector fields.

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