In this tutorial we are going to take a look at Newtons Method for approximating the roots of an equation. The idea of the method is as follows: we will start with an initial guess which is reasonably close to the true root, then the function is approximated by its tangent line (which can be computed using the tools of calculus), and we will compute the x-intercept of this tangent line (which is easily done with elementary algebra). This x-intercept will typically be a better approximation to the function's root than the original guess, and the method can be iterated. So, first, we will see how this method looks like and then we will do some examples.
To use this method
to approximate a solution to an equation, first put your equation in
Understand how to
visualize Newtons Method iterations geometrically.
Realize that on
some problems the choice of your initial guess is critical.
Keep lots of
digits in your intermediate results!
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.