2.1Sequences as functions
A sequence can be thought of as a function from the integers to the real numbers.
There are two ways to establish whether a sequence has a limit.
Vector-valued functions
20.1The cross product
The cross product is a special way to multiply two vectors in three-dimensional
space.
23.2Parameterizing by arc length
We find a new description of curves that trivializes arc length computations.
24.3Parametric plots
Tangent and normal vectors can help us plot make interesting parametric
functions.
Functions of several variables
25.1Functions of several variables
We introduce functions that take vectors or points as inputs and output a
number.
29.1Linear approximation
We extend the ideas of linear approximation to functions of several variables.
36.2Integrals with trivial integrands
We study integrals over general regions with and integrand equaling one.
38.3Computations and interpretations
We practice more computations and think about what integrals mean.
Vector-valued functions of several variables
41.2Green’s theorem as a planimeter
A planimeter computes the area of a region by tracing the boundary.