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...

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.

A bounded set of derivatives (the easy case)

Derivatives of any size (the hard case)

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.

A bounded set of derivatives (the easy case)

Derivatives of any size (the hard case)

Converted by Mathematica May 12, 2003