### Week 11 -- Sections 7.1-7.4

#### Short-term objectives

- Calculate n x n determinants by a cofactor expansion. (Sec. 7.1)
- Simplify determinants by row operations. (Sec. 7.1)
- Calculate areas and volumes of parallelepipeds in n dimensions,
using determinants and cross products. (Sec. 7.2)
- Calculate areas and volumes, and other integrals, in curvilinear
coordinate systems. (Sec. 7.3)

#### Long-term objectives

- Understand the algebraic structure of determinants, inverses, and
solutions of linear systems, as given by the permutational definition
of determinants and Cramer's rules. (Sec. 7.1)
- Understand the relation between determinant signs and the
orientation (handedness) of coordinate systems. (Sec. 7.2)
- Understand the relation between 3-vectors and antisymmetric matrices
and the associated sign ambiguity. (Sec. 7.2)
- Understand the geometrical and physical meaning of surface integrals,
and distinguish between scalar integrals (with respect to surface area)
and vector (flux) integrals. (Sec. 7.4)