Vector Identities

# Vector Identities - Vector Identities Gradient 1(f g = f g...

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Vector Identities Gradient 1. v ( f + g ) = v f + v g 2. v ( cf ) = c v f , for any constant c 3. v ( fg ) = f v g + g v f 4. v ( f/g ) = ( g v f f v g ) /g 2 at points v x where g ( v x ) n = 0. 5. v ( v F · v G ) = v F × ( v ∇ × v G ) ( v ∇ × v F ) × v G + ( v G · v ) v F + ( v F · v ) v G Divergence 6. v ∇ · ( v F + v G ) = v ∇ · v F + v ∇ · v G 7. v ∇ · ( c v F ) = c v ∇ · v F , for any constant c ,8. v ∇ · ( f v F ) = f v ∇ · v F + v F · v f 9. v ∇ · ( v F × v G ) = v G · ( v ∇ × v F ) v F · ( v ∇ × v G ) Curl 10. v ∇ × ( v F + v G ) = v ∇ × v F + v ∇ × v G 11. v ∇ × ( c v F ) = c v ∇ × v F , for any constant c 12. v ∇ × ( f v F ) = f v ∇ × v F + v f × v F 13. v ∇ × ( v F × v G ) = v F ( v ∇ · v G ) ( v ∇ · v F ) v G + ( v G · v ) v F ( v F · v ) v G Laplacian 14. v 2 ( f + g ) = v 2 f + v 2 g 15. v 2 ( cf ) = c v 2 f , for any
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