Objectives: In this tutorial, we examine Newton's Method and see the
geometry underlying the derivation of the algorithm. We also look at a few examples that illustrate the method.
After working through these materials, the student should be able
- to understand graphically the derivation of Newton's Method,
- to apply Newton's Method to find the roots of a function.
Algorithm. Let f be a differentiable function. Choose
a point x1 near a root of f. Define recursively
If the point x1 is chosen sufficiently close to the root then the xn's
are successively better approximations of the root.
- Drill problems on using Newton's Method.