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