More mathematically, nabla (∇, ∇ in HTML
) is a 3D vector
that is composed of the three partial derivative
s, this means :
( ∂/∂x, ∂/∂y, ∂/∂z)
It can be used to represent a number of vector operations on scalar field
s or vector field
- 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.