### Week 11 -- Sections 7.1-7.4

#### Short-term objectives

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

#### Long-term objectives

1. 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)
2. Understand the relation between determinant signs and the orientation (handedness) of coordinate systems. (Sec. 7.2)
3. Understand the relation between 3-vectors and antisymmetric matrices and the associated sign ambiguity. (Sec. 7.2)
4. 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)