### Week 9 -- Sections 5.5, 6.1

#### Short-term objectives

- Find the differential (or Jacobian matrix) of a nonlinear
function from that of its inverse. (Sec. 5.5)
- Find normal vectors to the coordinate surfaces (or lines) of a
curvilinear coordinate system. (Sec. 5.5)
- Find the differential (or partial derivatives) of a multivariable
function defined implicitly. (Sec. 5.5)
- Test whether a function of two vector variables qualifies as an
inner product. (Sec. 6.1)
- Use the Schwartz, triangle, and norm-difference inequalities.
(Sec. 6.1)

#### Long-term objectives

- Appreciate the implicit and inverse function theorems in
matrix-algebra terms. (Sec. 5.5)
- Become alert to the algebraic and geometrical symptoms of breakdown
of existence, uniqueness, or smoothness of inverse and implicit
functions. (Sec. 5.5)
- Understand the concepts of inner product, norm, and metric (on
spaces more general than R^n) and how each is a specialization of
the next. (Sec. 6.1)