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# Gradient and Differential Operators

The gradient vector operator is defined as .

The Laplacian scalar operator is defined as .

The four partial-differential operators, , form a covariant vector, called the covariant gradient operator

 (2.18)

Also, the contravariant gradient is defined as (notice the minus sign)

 (2.19)

Finally, the d'Alembertian is defined as

 (2.20)

Sometimes the symbol is used for the d'Alembertian.

Douglas M. Gingrich (gingrich@ ualberta.ca)
2004-03-18