Taylor Series Section 5. Closing Thoughts

<body bgcolor="#ffffff"> <hr> <center> <table border="2"> <tr valign="top"> <td><a href="node4.shtml"><img height="44" width="44" src="/UCESIcons/tools/previous.gif"></a></td> <td><a href="taylor_series.html"><img height="44" width="44" src="/UCESIcons/tools/up.gif"></a></td> <td><a href="node6.shtml"><img height="44" width="44" src="/UCESIcons/tools/next.gif"></a></td> <td><a href="contents-node5.html"><img height="44" width="44" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="copyright.html"><img height="44" width="44" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces@krellinst.org"><img height="44" width="44" src="/UCESIcons/tools/feedback.gif"></a></td> </tr> </table> </center> <hr>  <h1>Section 5.   Closing Thoughts</h1> <p> As a mathematics educator, I have found that many students dislike the concept of Taylor polynomials and Taylor series. The primary reason for this appears to be the “less than aesthetic” look of the definition. Indeed, one must be careful to put the appropriate items <span class="nobr">(<i>x</i>, <i>c</i>, <IMG WIDTH=47 HEIGHT=19 ALIGN=absmiddle ALT="f^(n) (x)" SRC="img9.gif"> , etc.)</span> in the appropriate places.</p> <p> Even so, my hope is that more people will grow to better appreciate these objects. Often, our best efforts in mathematics produce only approximations, not exact results. In this light, Taylor polynomials and series offer a powerful tool for approximation, especially since polynomials are so “easy” to evaluate (at given input values), graph, differentiate, and integrate when compared to transcendental functions.</p> <hr> <address> James A. Sellers<br> <a href="mailto:sellersj@math.psu.edu">sellersj@math.psu.edu</a> </address> <hr> <center> <table border="2"> <tr valign="top"> <td><a href="node4.shtml"><img height="44" width="44" src="/UCESIcons/tools/previous.gif"></a></td> <td><a href="taylor_series.html"><img height="44" width="44" src="/UCESIcons/tools/up.gif"></a></td> <td><a href="node6.shtml"><img height="44" width="44" src="/UCESIcons/tools/next.gif"></a></td> <td><a href="contents-node5.html"><img height="44" width="44" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="copyright.html"><img height="44" width="44" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces@krellinst.org"><img height="44" width="44" src="/UCESIcons/tools/feedback.gif"></a></td> </tr> </table> </center> <hr> </body>