### Week 3 -- Sections 2.4-3.2

#### Short-term objectives

- Construct the tangent hyperplane to the graph of a function from
R^n to R, and interpret it in terms of the approximate change in the
value of the function for a small change in its argument.
(Sec. 2.4)
- Use the gradient vector to determine the directions of fastest increase
and of level surfaces. (Sec. 2.4)
- Use the chain rule to calculate derivatives of composite functions
R -> R^n -> R, including functions that depend on a scalar variable
in two or more ways. (Sec. 2.4)
- Calculate 2 x 2 and 3 x 3 determinants and cross products. (Sec. 2.5)
- Use the algebraic properties of addition and scalar multiplication.
(Sec. 3.1)
- Recognize familiar classes of mathematical entities on which these
vector operations are defined. (Sec. 3.1)
- Determine whether a function [with domain R^n, P_n, or C^N(a,b)]
is linear, or affine. (Sec. 3.2)
- Find the matrix of a linear function from R^n to R^p. (Sec. 3.2)
- Recognize or construct the matrices representing simple
geometrical transformations in 2- and 3-dimensional space, such as
rotations, reflections, and shears.

#### Long-term objectives

- Distinguish the various geometrical representations/interpretations
of scalar-valued functions of a vector argument. (Sec. 2.4)
- Understand the concepts of vector space, domain, and codomain.
(Sec. 3.1)