lizfcm/notes/Sep-20.org

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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. $e_{\text{abs}} \leq Ch^2$
$e_{\text{abs}} \leq Ch^r$
$log(e(h)) \leq log(ch^r) = log(C) + log(h^r) = log(C) + rlog(h)$