Mathematics - Calculus - Multivariable - Vector calculus - Div, Grad, Curl and Theorems

10 steps: (1) GRADIENT: ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z). Turns scalar field into vector field pointing uphill. (2) DIVERGENCE: ∇·F = ∂Fx/∂x + ∂Fy/∂y + ∂Fz/∂z. Measures 'spreading out' at a point. (3) CURL: ∇×F. Measures 'rotation' at a point. (4) LINE INTEGRAL: ∫_C F·dr = work done by F along curve C. (5