====== 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
  * [[https://en.wikipedia.org/wiki/Newton%27s_method|Netwon's method]], Wikipedia. Really nice explanation, animation of iteration of method, history, error analysis, and overview of what can go wrong.
  * [[http://mathworld.wolfram.com/NewtonsMethod.html|Newton's method]], Wolfram Alpha. Terse, error analysis, nice plots of Julia sets.
  * [[http://tutorial.math.lamar.edu/Classes/CalcI/NewtonsMethod.aspx|Newton's Method]], Paul's Online Math Notes. Nice wordy description of algorithm with illustrative graphs, with two examples.