Talk:List of vector identities

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Thanks. I've been trying to learn TeX and this is how I'm doing it. I know some purists might not appreciate that.

People don't know what this is just by looking at it. A couple sentences exposition would help.-LtNOWIS 04:44, 6 Apr 2005 (UTC)

I changed Green's first identity because the notation was incorrect. All these are the same:

\left( {\vec \nabla {\rm f} \cdot \vec \nabla {\rm f}} \right) = \left[ {\frac{{\partial f}}{{\partial x}},\frac{{\partial f}}{{\partial y}},\frac{{\partial f}}{{\partial z}}} \right] \cdot \left[ {\frac{{\partial f}}{{\partial x}},\frac{{\partial f}}{{\partial y}},\frac{{\partial f}}{{\partial z}}} \right] = \left( {\frac{{\partial f}}{{\partial x}}} \right)^2 + \left( {\frac{{\partial f}}{{\partial y}}} \right)^2 + \left( {\frac{{\partial f}}{{\partial z}}} \right)^2 = \left\| {\vec \nabla {\rm f}} \right\|^2

but

\left( {\vec \nabla {\rm f}} \right)^2

doesn't exist, and

\vec \nabla {\rm f}^2 = \left[ {\frac{{\partial f^2 }}{{\partial x}},\frac{{\partial f^2 }}{{\partial y}},\frac{{\partial f^2 }}{{\partial z}}} \right] = 2f\left[ {\frac{{\partial f}}{{\partial x}},\frac{{\partial f}}{{\partial y}},\frac{{\partial f}}{{\partial z}}} \right] = 2f\vec \nabla {\rm f}

is something completely different. Joaoliveira 31-aug-2006 20:00 UTC