Property for sale in del, Spain

Facts About Del

Del, or nabla, is an operator used in mathematics, in particular in vector calculus, as a vector differential operator, usually represented by the nabla symbol ?. When applied to a function defined on a one-dimensional domain, it denotes its standard derivative as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), it may denote the gradient (locally steepest slope) of a scalar field (or sometimes of a vector field, as in the Navier–Stokes equations), the divergence of a vector field, or the curl (rotation) of a vector field, depending on the way it is applied.
Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. The del symbol can be interpreted as a vector of partial derivative operators, and its three possible meanings—gradient, divergence, and curl—can be formally viewed as the product with a scalar, a dot product, and a cross product, respectively, of the del "operator" with the field. These formal products do not necessarily commute with other operators or products. These three uses, detailed below, are summarized as:
Gradient:



grad
?
f
=
?
f


{\displaystyle \operatorname {grad} f=\nabla f}

Divergence:



div
?



v
?



=
?
?



v
?





{\displaystyle \operatorname {div} {\vec {v}}=\nabla \cdot {\vec {v}}}

Curl:



curl
?



v
?



=
?
×



v
?





{\displaystyle \operatorname {curl} {\vec {v}}=\nabla \times {\vec {v}}}