This section is about applications of Taylor series, which
is something that I've been emphasizing from the beginning. You should
read the section, but there aren't a whole lot of "new" techniques
described in the section. It's more about showing how Taylor series
are used (which is very important, of course).
Emphasis is on the following:
- Error estimation: we're going to make mistakes, but how
bad will they be? Or can we get the errors under whatever limbo bar has
been established? This is often in the context of evaluating
a function at a point.
- A sensible use of a simplified version (Taylor polynomial)
of a function in some important domain (where the function
itself is "overly complicated"). This is often in the context
of replacing a function in a special domain.