- #1
Rasalhague
- 1,387
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What does "to 2nd order" mean?
http://www.mathpages.com/rr/s2-11/2-11.htm
I thought "to second order" meant an approximation consisting of the initial terms of the Taylor series up to and including the second derivative term. For example, it seems to be used that way in the Wikipedia article Taylor series, in the section "Taylor series in several variables" [ http://en.wikipedia.org/wiki/Taylor_series ]. Is the quote above using an unusual definition of second order, or have I misunderstood something here?
In the limit as the number n of sides of the polygon increases and the angle a approaches zero, the value of [itex]\cos \alpha[/itex] approaches 1 (to the second order), and the value of [itex]\sin \alpha[/itex] approaches [itex]\alpha[/itex].
http://www.mathpages.com/rr/s2-11/2-11.htm
I thought "to second order" meant an approximation consisting of the initial terms of the Taylor series up to and including the second derivative term. For example, it seems to be used that way in the Wikipedia article Taylor series, in the section "Taylor series in several variables" [ http://en.wikipedia.org/wiki/Taylor_series ]. Is the quote above using an unusual definition of second order, or have I misunderstood something here?