Re: I do not understand
- To: mathgroup at smc.vnet.net
- Subject: [mg25435] Re: [mg25381] I do not understand
- From: David Withoff <withoff at wolfram.com>
- Date: Sun, 1 Oct 2000 02:44:20 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
> Hello,
>
> ySer=Series[y[t],{t,0,3}]
>
> If I apply this rule like this
> (y[t]+y'[t])/.y[t]->ySer
> both y[t] and y'[t] changes appropriately
>
> If I apply
> y'[t]/.y[t]->ySer
> nothing happens
>
> Why is that?
Because combining series expansions with other functions automatically
causes expansions of those other functions. For example:
In[1]:= expr = Series[Exp[x], {x, 0, 3}]
2 3
x x 4
Out[1]= 1 + x + -- + -- + O[x]
2 6
In[2]:= Cos[x] + x expr
2 3 4
x x 5 x 5
Out[2]= 1 + x + -- + -- + ---- + O[x]
2 2 24
The operation (y[t]+y'[t])/.y[t]->ySer does not make a
substitution in y'[t], but adding ySer to y'[t] causes y'[t]
to be expanded.
Dave Withoff
Wolfram Research