| Textbook sections | Topics | Hours (approx.) |
| 1.4 |
Vectors in 2 and 3 dimensions: The cross product.
| 2 |
| 3.1-3.4 |
Vector-valued functions: Parametrized curves, arclength, curvature
and torsion. Vector fields, gradient, divergence, curl, the Del operator.
| 8 |
| 4.2-4.4 |
Maxima and minima in several variables: extrema of functions and their classification,
Lagrange multipliers.
| 4 |
| 5.1-5.6 |
Multiple integration:
Review of double and triple integrals, change of variables, improper
integrals, integration in higher dimensions, applications.
| 6 |
| 6.1-6.3 |
Line integrals: scalar and vector line integrals, Green's
theorem, conservative vector fields.
| 6 |
| 7.1-7.3 |
Surface integrals and vector analysis: parametrization of surfaces,
scalar and vector surface integrals, Gauss's and Stokes's theorems.
| 8 |
| 8.1-8.3 |
Vector analysis in higher dimensions: introduction to differential
forms.
| if time permits |