Del operator

From Chemepedia

The del operator also known as nabla is an important operator in vector based calculus. Its strength is that it is independent of the coordinate system, and it therefore allows a general representation of microscopic balances.

Coordinate systems: Definitions

  • Cartesian coordinates are defined by
  • Cylindrical coordinates are defined by
  • Spherical coordinates are defined by where is the azimuth and is the polar angle (See figure).
Representations of in spherical coordinates
Relationship between the coordinate systems
Cartesian Cylindrical Spherical
Cartesian
Cylindrical
Spherical

Common Del formula

Operation Cartesian coordinates Cylindrical coordinates Spherical coordinates
Vector field
Gradient of a scalar
Divergence of a vector field
Curl of a vector field
Laplacian of a scalar field
Differential displacement
Differential normal area
Differential volume