### Week 4 -- Sections 3.3-3.5

#### Short-term objectives

- Recognize discontinuities and places of nondifferentiability in
functions R^n -> R^p, and evaluate routine limits of such functions.
(Sec. 3.3, 3.4)
- Construct the differential to a function R^n -> R^p at a point,
and use it to estimate the change in the function's value for a
small change in its argument. (Sec. 3.4)
- Calculate differentials and partial derivatives of composite functions,
R^n -> R^m -> R^p. (Sec. 3.5)

#### Long-term objectives

- Distinguish the various geometrical representations/interpretations
of vector-valued functions of a vector argument. (Sec. 3.3)
- Understand the "best linear approximation" interpretation of partial
derivatives. (Sec. 3.4)
- Understand how the chain rule follows naturally from the "best linear
approximation" interpretation. (Sec. 3.5)