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Error approximation in Taylor Series

This lab is an exploration of some of the problems that come up when you approximate a function with a finite Taylor polynomial.

WARNING: THIS LAB IS NOT COMPLETE YET. I AM PUTTING IT UP FOR COMMENTS AND FOR MY OWN AMUSEMENT. I WILL EVENTUALLY POLISH THIS UP AND FINISH THE COMMENTARY, BUT THIS IS ALL THERE IS FOR NOW. YOU HAVE BEEN WARNED...

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Find the size of the interval, given the number of terms

In this section, we will examine the situation where we want to approximate our function with a given degree Taylor polynomial. We thus need to find out what domain this polynomial is guaranteed to fall within our error tolerence.

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A bounded set of derivatives (the easy case)

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Derivatives of any size (the hard case)

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Find the number of terms, given the size of the interval

In this section, we will examine the situation where we want to approximate our function over a given interval. We thus need to find out how many terms we need to take to guarantee our error is small enough.

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A bounded set of derivatives (the easy case)

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Derivatives of any size (the hard case)

Converted by *Mathematica*
May 12, 2003