For 10 points, name the mathematical operator that is equal, in Cartesian 3-space, to the sum of the partial derivatives of the components of a vector field with respect to the appropriate coordinate, and is often symbolized del dot.
For a general tensor field, this operator is equal to the comma operator plus the sum over indices of the product of the connection coefficients and tensor components; in that context, it is also known as the semicolon or covariant derivative. Vector fields that vanish under this operator are known as (*) solenoidal, and its operation on the gradient yields the Laplacian. For 10 points, name the mathematical operator that is equal, in Cartesian 3-space, to the sum of the partial derivatives of the components of a vector field with respect to the appropriate coordinate, and is often symbolized del dot.
For a general tensor field, this operator is equal to the comma operator plus the sum over indices of the product of the connection coefficients and tensor components; in that context, it is also known as the semicolon or covariant derivative.
{div}ergence [accept {covariant derivative} or {semicolon} derivative before they’re mentioned; prompt on {del dot} or {grad dot} or {nabla dot}]