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We have used graphical analysis with fences and funnels to
study the Airy equation. We described a number of useful
transformation methods, in particular, the method of finding a
balancing transformation.
Through the help of computer exploration
and the appropriate application of these transformations,
a number of qualitative questions and many
quantitative ones about the asymptotic behavior of solutions of Airy's
equation have been completely answered. This serves as a useful illustration
for students of how sophisticated hardware and software interacts with
powerful mathematical methods to produce a meaningful understanding of
mathematical concepts. It is worthwhile to reiterate that the methods
used in this analysis relied very heavily on computer graphics; indeed,
the results were obtained without ever writing down a
formula for 
!
Contents
Next:References
Up:A New Look at
Previous: A backwards funnel.