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.