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Topic: [ap-calculus] Series - a resource
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Benjamin Goldstein

Posts: 68
Registered: 8/21/11
[ap-calculus] Series - a resource
Posted: Sep 16, 2012 12:04 PM
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Colleagues,

Here is my annual pitch for my series chapter. Version 1.3, new for the
2012-2013 school year, has been posted to the designated deriver wiki.
(Click here: http://designatedderiver.wikispaces.com/BC+topics -- the
chapter is about half way down and is titled "Series Chapter v1.3.)
For those familiar with the chapter, not much is changed in the latest
version. There are a couple more problems on telescoping series, by
request, but mostly this revision was just about another layer of polish
and some error correction, both in the text and in the solutions.

For those new to the listserv, my chapter is a complete, stand-alone
chapter on the series topics for BC Calculus. It is organized differently
from how the material is treated in most textbooks. It starts with a
discussion of Taylor polynomials and then moves on to power series and
ultimately Taylor series. Convergence tests come in when they are needed --
to figure out intervals of convergence of power series. The idea is that by
starting with the more concrete ideas of Taylor polynomials, students will
be in a better place to appreciate what is happening when we extend to
infintely many terms in a Taylor series. This approach has been advocated
many times in this forum, and the feedback I have received on the chapter
has been positive. If you would like to know more about the chapter and the
thinking behind it, I encourage you to download it and read the preface.
You are free to use the chapter however makes sense to you. You can email
the entire document to students, post it on your course web pages, whatever
suits you. (I don't recommend printing it out for each kid, both because
that's a lot of paper and because I wouldn't want to lose the color in the
graphs.) I only ask that if you use the chapter, please send me feedback
(corrections, comments on areas that need clarification, thoughts on how
useful the text is, etc.). Since this is a personal project, not a work
project, please send emails to me at: bunderscoregoldstein at yahoo dot com.

Cheers,
Benjamin Goldstein

====
Course related websites:
http://apcentral.collegeboard.com/calculusab
http://apcentral.collegeboard.com/calculusbc
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