This applet illustrates the use of Newton's Method to approximate solutions to a particular equation involving the square of cosine. The user can choose an initial approximation and then observe Newton's Method step-by-step.
Type of Material:
A Java-enabled browser.
Identify Major Learning Goals:
To illustrate the convergence of Newtons Method to the solution of a particular equation.
Target Student Population:
Students in Calculus I.
Prerequisite Knowledge or Skills:
Understanding the use of the first derivative in determining tangents to curves.
Evaluation and Observation
This applet does a good job of showing how the selection of different initial points affects the convergence of Newtons Method to a solution.
The site could use an introductory paragraph explaining Newtons Method and perhaps providing a derivation of the basic formula.
Potential Effectiveness as a Teaching Tool
This applet is a well-designed visual aid for a one-time in-class demonstration. The applet is a nice, large size, the function is well-chosen with several roots, and the viewing rectangle is quite appropriate.
The function to which Newtons Method is applied cannot be modified. That obviously limits somewhat the effectiveness of the applet. Also, enhancements such as a zoom capability and a counter for the number of iterations would have been beneficial.