1. Introduction

A very common problem in mathematics and physics is the problem of solving equations. Typically, equations have the form:

$$f(x)=g(x),$$

but when we bring $g(x)$ to the left and rename the resulting left-hand-side to $f(x)$, we get the equally general form:

$$f(x)=0.$$

So we see that determining a solution of an equation is essentially the same as finding a root of a function, that is, a zeroof the function.

In order to find a root $x$ of a function $f$, we often try to do this by manipulating the formula $f(x)=0$, e.g. by bringing terms to the other side. But there are many equations that we cannot solve in this way. Therefore, we have to try and find an approximation to the root $x$. In the next chapters, I will discuss some of the methods to do this.