Math 753/853 Newton's method

Newton's method is an algorithm for finding solutions $x$ of a nonlinear equation $f(x) = 0$, where $f$ is differentiable. In general $f$ and $x$ can be multidimensional ($f: \mathbb{R}^n \rightarrow \mathbb{R}^n$), but for now we'll just consider the one-dimensional case.

Some excellent online resources for Newton's method