# Mathematical Formulas - Vector Operators

This section contains a summary of vector operators expressed in each of the three major coordinate systems:

• Cartesian (,,)
• cylindrical (,,)
• spherical (,,)

Associated basis vectors are identified using a caret (

) over the symbol. The vector operand

is expressed in terms of components in the basis directions as follows:

• Cartesian:
• cylindrical:
• spherical:

## Divergence

Divergence in Cartesian coordinates:

Divergence in cylindrical coordinates:

Divergence in spherical coordinates:

## Curl

Curl in Cartesian coordinates:

Curl in cylindrical coordinates:

Curl in spherical coordinates:

## Laplacian

Laplacian in Cartesian coordinates:

Laplacian in cylindrical coordinates:

Laplacian in spherical coordinates:

Ellingson, Steven W. (2018) Electromagnetics, Vol. 1. Blacksburg, VA: VT Publishing. https://doi.org/10.21061/electromagnetics-vol-1 CC BY-SA 4.0

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