1. Understanding vector fields, divergence, and curl vector fields
The divergence and curl of a vector field


2. Understanding line integrals
The integral of a scalar function with respect to arc length
The line integral of a vector field in the plane
The line integral as an integral with respect to arc length
The differential form notation
Curves in R3
Precise definitions and proofs


3. Conservative vector fields
The fundamental theorem for line integrals
Conditions for a field to be conservative


4. Parametrized surfaces
Parametrized surfaces
Normal vectors, tangent planes and orientation
The orientation of a surface and an expression for the normal vector (optional)


Index.