Gauss-Kronrod integration is an adaptation of Gaussian quadrature used on some graphing calculators, in particular the Texas Instruments graphing calculators where it is called fnInt. This mathlet outlines the mathematical computations involved and visually demonstrates the process the calculator uses to evaluate the integral. Visualization highlights possible shortcomings of the method. Examples are suggested in the mathlet for exploration of the method; an example of a troublesome integral with a work-around is included.

APPROPRIATE COURSES:

Calculus, numerical analysis

SOFTWARE SPECIFICATIONS:

This Java applet uses Swing components and requires Java Plug-in 1.1.1. Macs require Macintosh Runtime for Java(MRJ) and the SwingAll.jar file.

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This small collection of web pages discusses a nice extension to Gaussian quadrature that does not seem to be discussed in a large number of numerical analysis texts. It is of importance because it is apparently the method used by TI calculators, a fact that is sure to get the attention of students. The pages give some nice experimental exercises to help students see the need to transform functions from one interval to a standard one. It also uses a Java applet effectively to show graphically the way that Gauss-Kronrod Integration uses only half the nodes used by Gaussian quadrature.

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