1.2 - V ⋅n V n n ˆ V ≠u iˆ v ˆ w k j V ⋅ n = n||...

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Unformatted text preview: V ⋅n V n n ˆ V ≡ u iˆ + v ˆ + w k j ( ) V ⋅ n = n|| V| cos θ = u nx + v n y + w nz | ˆ n ≡ nx ˆ + ny ˆ + nz k i j ( ) ( ) θ V ⋅n V ⋅n n n n V V V ! " ∇= # ∂ ˆ ∂ ˆ ∂ ˆ i+ j+ k ∂x ∂y ∂z !$ ∇ ∇p ∇p ∇p = & & p p ∂ p ˆ ∂p ˆ ∂ p ˆ k i+ j+ ∂x ∂y ∂z " $ div V ≡ ∇ ⋅ V = ˆ V ≡ u iˆ + v ˆ + w k j ( ) ∂u ∂ v ∂w + + ∂x ∂ y ∂ z $% & ' curl V = ∇ × V = det ∂ ∂x u iˆ ∂ ∂y v ˆ j ∂ ∂w ∂v ˆ ∂ u ∂ w ˆ ∂v ∂u ˆ = − i+ − j+ − k ∂z ∂y ∂z ∂z ∂x ∂x ∂y w ˆ k ( " S (A ⋅ n dS)= (∇ ⋅ A )dV V % ...
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This note was uploaded on 04/07/2008 for the course AE 2020 taught by Professor Ruffin during the Summer '07 term at Georgia Tech.

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