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Short Calculus
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- Constructivist Calculus Sun, 2011-03-06 13:21
- week 3: post mortem Thu, 2011-02-24 17:47
- week 2: what's up Wed, 2011-02-02 18:54
- Week 1: resources Mon, 2011-01-31 21:20
- Meeting times - and initial introductions Mon, 2011-01-31 21:09
Week 1: resources
Today, no discussion of sequences would be complete without mentioning the Online Encyclopedia of Integer Sequences: http://oeis.org/Seis.html although in calculus we will tend to be more interested in sequences that "converge", in other words, sequences whose terms get closer and closer to a given number. That's a bit tricky to do with just integers.
If you want to dive right into the technical definition, you can look at http://en.wikipedia.org/wiki/Cauchy_sequence. As for actual exercises on the topic www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_ch13.pdf is one example. Let's find a few more, but, mainly, let's get to work!
I'll look forward to discussion of first examples and any questions at http://metameso.org/vanilla/index.php?p=/categories/short-calculus.
Some other resources that are near and dear to me come from PlanetMath.
You can search with Google: http://www.google.com/search?q=sequence%20site:planetmath.org
And if you log in, you can set your default "view" mode to LaTeX sources -
http://planetmath.org/?method=src&from=objects&name=Sequence&op=getobj
Note that to create an account on PlanetMath you temporarily need to disable Javascript to make it past the Captcha (shrug). I think it's worth it to get the LaTeX view mode!!
You can then copy content directly from PlanetMath into our forum --
http://metameso.org/vanilla/index.php?p=/discussion/14/definition-of-a-s...
(Some of these definitions may be a bit advanced for our purposes -- but getting a look at the LaTeX source is well worthwhile.)
PS. In detail: Once you've made your login on PlanetMath, you can browse to
http://planetmath.org/?op=editprefs and then scroll down to "appearance" and select "TeX source" as the "Encyclopedia rendering style" -- then hit update at the bottom of the page.
You'll have no shortage of LaTeX examples then :) But you can also get examples by looking at the source of the Calc book on Wikibooks that I mentioned earlier --
http://en.wikibooks.org/wiki/Calculus