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The differential element or just differential of a quantity refers to an infinitesimal change in said quantity, and is defined as the limit of a change in quantity as the change approaches zero.

Differentials are useful in the definitions of both derivatives and integrals; for example, the derivative of with respect to is defined as

When transforming coordinates, the value of a differential element is computed using the determinant of the Jacobian matrix.

Formulae for differential elements[]

Line elements[]

  • (scalar line element)
  • (tangential vector element)
  • (normal vector element)

Area elements[]

Surface elements[]

  • (scalar surface element)
  • (normal vector surface element)

Volume elements[]

  • (three-dimensional Cartesian coordinates)
  • (cylindrical coordinates)
  • (spherical coordinates)
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