From 58c73fd511b77cb94124b71a4bb75c7ab6a6d8bc Mon Sep 17 00:00:00 2001
From: Elizabeth Hunt <elizabeth.hunt@simponic.xyz>
Date: Mon, 25 Sep 2023 10:36:23 -0600
Subject: add september notes & hw2 code / pdf

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 notes/Sep-20.org | 21 +++++++++++++++++++++
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+* Review & Summary
+Approx f'(a) with
+
++ forward difference $f'(a) \approx \frac{f(a+h) - f(a)}{h}$
+
++ backward difference $f'(a) \approx \frac{f(a) - f(a-h)}{h}$
+
++ central difference $f'(a) \approx \frac{f(a+h) - f(a-h)}{2h}$
+
+** Taylor Series
+given $C = \frac{1}{2}(|f''(\xi)|) \cdot h^1$
+
+with f.d. $e_{\text{abs}} \leq Ch^1$
+
+b.d.  $e_{\text{abs}} \leq Ch^1$
+
+c.d. $e_{\text{abs}} \leq Ch^2$
+
+$e_{\text{abs}} \leq Ch^r$
+
+$log(e(h)) \leq log(ch^r) = log(C) + log(h^r) = log(C) + rlog(h)$
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