lizfcm/notes/Sep-20.org

• Review & Summary
  • Taylor Series

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. $e_{\text{abs}} \leq Ch^2$

$e_{\text{abs}} \leq Ch^r$

$log(e(h)) \leq log(ch^r) = log(C) + log(h^r) = log(C) + rlog(h)$