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Mathematics

Big-O Notation

Mike Forni, retired
Posted 10 years ago

I have recently been exposed to Big-O notation in an online calculus class (Prof Ghrist/Calc II) in relation to Taylor series. I do not really understand how or when to use Big-O (like O(x^2)).Can someone please explain or direct me to an online resource that covers Big-O notation in detail. Thanks for any help.
POSTED BY: Mike Forni
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For more than you ever want to know about O notation, see http://en.wikipedia.org/wiki/Big_O_notation#Use_in_computer_science

Very briefly, suppose f(x) can be represented by an infinite series: f(x) = a0 + a1 x + a2 x^2 + … Call fn(x) the approximation containing the terms of the series up to x^n. Then we can write f(x)=fn(x) +O(x^{n+1}), which means that |f(x)-f_n(x)|/x^{n+1} -> 0 as x -> 0.
POSTED BY: S M Blinder

Not sure this is a Mathematica question.... As for on-line resources, type "math large O notation" into Google and you will get lots of helpful links...
POSTED BY: David Reiss
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