Re: Re: Q
- To: mathgroup at smc.vnet.net
- Subject: [mg41492] Re: [mg41478] Re: Q
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 22 May 2003 06:57:34 -0400 (EDT)
- References: <CB927881-8BA1-11D7-86EA-000393671006@earthlink.net>
- Sender: owner-wri-mathgroup at wolfram.com
>Paul, that's amazing!
Thanks :-) Personally, I've always found the way that Solve works
with Series one of the most beautiful and elegant design features of
Mathematica.
>Please give us an explanation of how that works.
Adding an O[t] term coerces a function into its Maclaurin series, e.g.,
f[t] + O[t]^2
Solve understands how to work with Series equations, e.g.,
Solve[f[t] + O[t]^2 == t, {f[0],f'[0]}]
You can, if you like, use LogicalExpand first to see the equations
that Solve is using.
LogicalExpand[f[t] + O[t]^2 == t]
Cheers,
Paul
>On Wednesday, May 21, 2003, at 08:04 AM, Paul Abbott wrote:
>
>>The following code determines the f'[0],..., Derivative[m][f][0] in
>>terms of f[0] as replacement rules (which is usually better than
>>assigning them as numerical values):
>>
>> m=4;
>>
>> Solve[f'[t] - g[f[t]] + O[t]^m == 0,
>> Table[Derivative[n][f][0], {n, m}]]