In the previous chapter, we studied polynomial equations and their systems, and concentrated upon the special methods that are designed to harness their special structures. In the present chapter, we discuss general methods, which do not need special attributes in the equations on which they operate, and hence are applicable on all algebraic and transcendental equations. First, we deal with the problem of a single nonlinear equation in a single unknown. Next, we graduate to its multi-dimensional analogue: a system of nonlinear equations.
In this section, we are concerned with algebraic and transcendental equations, expressed in the form
f (x) = 0. (20.1)