Vector Integration

Conservative field

A vector field for which there exists a scalar function f such that ∇f=F.

Gradient field

A vector field F for which there exists a scalar function f such that ∇f=F in other words, a vector field that is the gradient of a function; such vector fields are also called conservative.

Potential function

A scalar function f such that ∇f=F.

Line Integral

1.

Green’s Theorem

Gauss Divergence Theorem

Let E be a simple solid region and S is the boundary surface of E with positive orientation. Let F be a vector field whose components have continuous first order partial derivatives. Then,

Example 3: Use the Divergence Theorem to evaluate

Stoke’s Theorem