#### Sequences as functions

A sequence can be generated by a function from the integers to the real numbers.
There are two ways to establish whether a sequence has a limit.

#### The alternating series test

Alternating series are series whose terms alternate in sign between positive and
negative. There is a powerful convergence test for alternating series.

#### Vector-valued functions

#### The cross product

The cross product is a special way to multiply two vectors in three-dimensional
space.

#### Parameterizing by arc length

We find a new description of curves that trivializes arc length computations.

#### Functions of several variables

#### Functions of several variables

We introduce functions that take vectors or points as inputs and output a
number.

#### Approximating with the gradient

We use the gradient to approximate values for functions of several variables.

#### Differentiability

We introduce differentiability for functions of several variables and find tangent
planes.

#### Interpreting the gradient vector

The gradient is the fundamental notion of a derivative for a function of several
variables.