Re: Q
- To: mathgroup at smc.vnet.net
- Subject: [mg41398] Re: Q
- From: "Carl K. Woll" <carlw at u.washington.edu>
- Date: Sun, 18 May 2003 05:01:00 -0400 (EDT)
- Organization: University of Washington
- References: <ba5176$sfi$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Stepan,
Here is one approach:
Derivative[1][f][t_]:=F[f[t]]
f[0]=f0;
Now, to get f'''[0], for example, just use:
In[3]:=
D[f[t],{t,3}]/.t->0
Out[3]=
2 2
F[f0] F'[f0] + F[f0] F''[f0]
If you want to assign values to f'[0], f''[0], etc., then simply use:
In[5]:=
Derivative[n_][f][0]:=D[f[t],{t,n}]/.t->0
Now, we have, for example:
In[7]:=
f''''[0]
Out[7]=
3 2 3 (3)
F[f0] F'[f0] + 4 F[f0] F'[f0] F''[f0] + F[f0] F [f0]
You could also use the memo-izing version
Derivative[n_][f][0]:=Derivative[n][f][0]=D[f[t],{t,n}]/.t->0
so that you don't have to do the D operation every time.
Carl Woll
Physics Dept
U of Washington
"Stepan Yakovenko" <yakovenko at ngs.ru> wrote in message
news:ba5176$sfi$1 at smc.vnet.net...
> HI!
>
> I've got an equation f'[t]=F[f[t]].
> F[] is known and analytic, (say
> F[x]=x*x). I know f[0]=f0. f0 is
> a number. I want to get all f'[0],
> f''[0], f'''[0], ... assigned
> to their numberical values that can be
> unambiguously found after differentiating
> the source equation as many times as
> needed.
>
>
> --
> Try "win /t" to run Windows in text mode
>
>