This site contains a Java-based applet that uses the Newton’s (a.k.a. Newton-Raphson) method to find roots of real-valued functions.
To provide a numerical and graphical tool for better understanding of Newton’s method.
Target Student Population:
Students in a Calculus or Numerical Methods course or any other course that discusses linear approximation.
Prerequisite Knowledge or Skills:
Basic understanding of linear approximation and Newton’s method.
Type of Material:
This site can be used for individual exploration or as a part of an in-class demonstration.
Java enabled browser.
Evaluation and Observation
In numerical analysis, Newton's method (also known as the Newton–Raphson method), is a method for finding successively better approximations to the zeroes of a real-valued function. This site contains a JAVA based tool that implements Newton’s method to find a root of a user defined function. This tool produces both a numerically found root and a graphical representation of a function whose zero’s is being found and approximation steps. A user has control over the number of iterations, starting point, and the graphing window size.
The applet does not seem to produce accurate results (or a clear message) for functions that do not have zeros other than a disclaimer at the bottom. The applet can only handle a limited number of functions. For example, it does not seem to allow x^(1/3).
Potential Effectiveness as a Teaching Tool
This site could serve as a supplement to a Numerical Methods course. The applet can be used as an aid to a lecture or as a quick in-class demonstration. It could also be easily used as a part of a self-guided activity.
The user interface of the site is far from being intuitive. This certainly limits its effectiveness as a tool for self-guided activity. It also misses the mark on the student discovery of a key concept: why Newton’s Method can fail.
Ease of Use for Both Students and Faculty
The site has simple and rather minimalistic design. Once a user learns how to input a function and to use controls, the use of the tool becomes fast. Some instructions are presented and suggested activity is described.
It takes a while before an average user gets used to the input routine. Students are used to entering functions using the keyboard, so they may have a difficult time figuring out how to use the button operated applet. Also, there is no digital signature embedded in the applet so most students will have difficulty opening the applet.