### Week 1 -- Sections 1.1-1.4

### Learning Objectives (Skills)

#### Short term ("This will be on the test.")

- Find a parametric representation for a plane (defined by an equation
or by geometric conditions). (Sec. 1.2)
- Find the tangent vector (and tangent line) to a parametrized curve at
a point, and interpret it in terms of the approximate change of the
vector-valued function for a small change of the parameter. (Sec. 1.4)

#### Long term ("Why are we studying this?")

- Recognize the vector operations of addition, scalar multiplication,
and dot product in various contexts: (Sec. 1.1)
- geometrical or physical vectors
- nongeometrical numerical (finite-dimensional) vectors
(e.g., business applications)
- functions (infinite-dimensional vectors)

- Appreciate the difference between points and vectors, and the
dependence of the vector operations in physical space upon the choice of
origin. (Sec. 1.3)
- Distinguish the various geometrical representations/interpretations
of vector-valued functions. (Sec. 1.4)