The del operator (∇) is an operator commonly used in vector calculus to find derivatives in higher dimensions. When applied to a function of one independent variable, it yields the derivative. For multidimensional scalar functions, it yields the gradient. If either dotted or crossed with a vector field, it produces divergence or curl, respectively, which are the vector equivalents of differentiation.
There are six ways del can be used to compute second derivatives of multivariable functions.
- The divergence of the gradient, also know as the Laplacian
- The vector Laplacian, equal to the Laplacian of each component of the vector
- The curl of the gradient, always equal to 0 (see irrotational vector field)
- The gradient of the divergence
- The divergence of curl, always equal to 0 (see incompressible vector field)
- The curl of the curl