Re: simple Sin

*To*: mathgroup at smc.vnet.net*Subject*: [mg89891] Re: simple Sin*From*: dh <dh at metrohm.ch>*Date*: Tue, 24 Jun 2008 03:25:47 -0400 (EDT)*References*: <g3nh5n$cg$1@smc.vnet.net>

Hi, the numerical approximation you get from NDSolve is not valid outside the specified domain. Therefore, you can not expect it to have symmetry. For the same reason, the series representations differ. hope this helps, Daniel Narasimham wrote: > It is surprising a bit, by numerical computation Sin[ t] has a > different series representation, is not even an odd function of t ! > Looks like has a different chemistry. > > NDSolve[{y''[t] + y[t] == 0, y'[0] == 1, y[0] == 0 }, y, {t, 0, 2 Pi}] > sin[u_] = y[u] /. First[%] > Plot[sin[t] - Sin[t], {t, 0, 2 Pi}] > > Series[{sin[t], Sin[t]}, {t, 0, 8}] > > Also, why do we not get an expansion of sin as Series[Im[Exp[I*t]], > {t, 0, 8}] ? > > TIA > > Narasimham > -- Daniel Huber Metrohm Ltd. Oberdorfstr. 68 CH-9100 Herisau Tel. +41 71 353 8585, Fax +41 71 353 8907 E-Mail:<mailto:dh at metrohm.com> Internet:<http://www.metrohm.com>