Vector Calculus

Question 1

Scalar Field vs Vector Field

Answer 1

Scalar => ∇f = (fx,fy,fz)
Vector => ∇ = (∂/∂x, ∂/∂y, ∂/∂z)

Question 2

Divergence of a Vector Field

Answer 2

Measures how much F spreads out from a point.

∇·F = ∂F1/∂x + ∂F2/∂y + ∂F3/∂z

∇·F =/= F·∇

Question 3

Curl of a Vector Field

Answer 3

∇xF = l i j k l
l ∂/∂x ∂/∂y ∂/∂z l
l F1 F2 F3 l

Calculate like a matrix

Question 4

u·∇ Operator

Answer 4

u·∇ = u1(∂/∂x) + u2(∂/∂y) + u3*(∂/∂z)