Lecture 7.
Taylor Series.
Today I discussed Taylor series. I wrote
out the general form of the Taylor series. Our one example was a Taylor series
expansion of ex at 0. The Taylor series is something that will turn
up often in this course. It is essential that you grasp the idea of using a
small number of terms of the Taylor series to get a Taylor polynomial
approximation. Don't let the expression representing the residual or the
truncation error intimidate you. It is useful for obtaining a bound on the
actual error.
Our first
application of Taylor series to our course is to Newton's root finding
algorithm. We derived Newton's algorithm using a Taylor expansion, and obtained
some insight on the Newton's algorithm's quadratic rate of convergence.
Posted: Tue - September 27, 2005 at 11:46 AM