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diff --git a/notes/Sep-20.org b/notes/Sep-20.org new file mode 100644 index 0000000..ba067bb --- /dev/null +++ b/notes/Sep-20.org @@ -0,0 +1,21 @@ +* 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. $e_{\text{abs}} \leq Ch^2$ + +$e_{\text{abs}} \leq Ch^r$ + +$log(e(h)) \leq log(ch^r) = log(C) + log(h^r) = log(C) + rlog(h)$ |