Slope fields are a powerful tool for checking the validity of derivatives,
antiderivatives, and solutions to differential equations. While the graphical resolution
and processing speed of a TI83 limit the usefulness of the techniques somewhat,
it is still a handy tool to have loaded in one's calculator on examination day.
A related technique, known as 'Euler's Solution' after the eighteenthcentury Swiss
mathematician Leonhard Euler, traces a particular solution curve from a given set
of initial coordinates. By applying regression models to the data accumulated while
tracing an Euler's solution, it is occasionally possible to determine an expression
that will approximate Euler's curve. Again, given the platform (TI83, that is),
the likelihood of this actually yielding useful results is slim, but it's interesting
to explore.
Note: This program uses the calculator's 'Y0', 'Y9', and 'Y8' graphing
functions in it's calculations, and will overwrite any equations previously stored
there.
