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Algunas fórmulas comunes en análisis vectorial
1. ( )f g f∇ + = ∇ +∇g
2. ( )cf c f∇ = ∇ , para una constante c
3. ( )fg f g g∇ = ∇ + ∇f
4. ( ) ( ) 2f g g f f g g∇ = ∇ − ∇ , en los puntos donde ( ) 0g x ≠
5. ( )div div div+ = +F G F G
6. ( )rot rot rot+ = +F G F G
7. ( ) ( ) ( ) rot rot∇ ⋅ = ⋅∇ + ⋅∇ + × + ×F G F G G F F G G F
8. ( )div divf f f= + ⋅F F F ∇
9. ( )div rot rot× = ⋅ − ⋅F G G F F G
10. div rot 0=F
11. ( )rot rotf f f= +∇F F ×F
12. ( ) ( ) ( )rot div div × = − + ⋅∇ − ⋅∇F G F G G F G F F G
13. 2rot rot grad div= −F F ∇ F
14. rot 0f∇ =
15. ( ) ( )2 2∇ ⋅ = ⋅∇ + ×F F F F F Frot
16. ( ) ( )2 2 2 2fg f g g f f g∇ = ∇ + ∇ + ∇ ⋅∇
17. ( )div 0f g∇ ×∇ =
18. ( ) 2 2f g g f f g g f∇⋅ ∇ − ∇ = ∇ − ∇
19. ( ) ( ) ( )⋅ × = ⋅ × = ⋅ ×H F G G H F F G H
20. ( )( ) ( )( ) ( )⋅ ×∇ × = ⋅ ⋅∇ ⋅ − ⋅ ⋅∇H F G H G F H F G
21. ( ) ( ) ( )×⋅ × = ⋅ − ⋅F G H F H G H F G
NOTA: f y g denotan campos escalares; F, G y H denotan campos vectoriales