Vector calculus | Mathematical notation | Differential operators
Del
Del, or nabla, is an operator used in mathematics (particularly 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 the standard derivative of the function as defined in calculus. When applied to a field (a function defined on a multi-dimensional domain), it may denote any one of three operators depending on the way it is applied: the gradient or (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. 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 (or nabla) 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: * Divergence: * Curl: (Wikipedia).
