  In most introductory numerical analysis textbooks, the treatment of a single
nonlinear equation often consists of a collection of all-purpose methods that
frequently do not work or are inefficient. These textbooks neglect to teach the
importance of adapting a method to the given problem, and consequently also
neglect to provide the tools to accomplish this.
  Several general techniques are described here to incorporate the specific
structure or properties of a nonlinear equation into a method for solving it.
This can mean the construction of a method specifically tailored to the
equation, or the transformation of the equation into an equivalent one for
which an existing method is well-suited. The techniques are illustrated with
the help of several case studies taken from the literature.
