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Re: Defining differential operators question


tgoetze at my-dejanews.com wrote:

> I would like to be able to define a family of differential operators
> that act on a function being passed in. For simplicity sake, I will
> assume that the functions being passed in are functions of one
> variable.
> 
> Suppose that given a list L={a0,a1,a2,a3}, that the differential
> operator defined by L, acts on a function F by:
> 
> a0*F + a1*F' + a2*F'' + a3*F'''

Here is one solution using MapIndexed:

 In[1]:= NewD[l_List,f_]:=Function[x,Evaluate[
	Plus@@MapIndexed[#1 Derivative[First[#2]-1][f][x]&,l]]]

 In[2]:= g[x_] := x^3

 In[3]:= NewD[{a0,a1,a2,a3},g]
 Out[3]=
	                  3          2
	Function[x$, a0 x$  + 3 a1 x$  + 6 a2 x$ + 6 a3]

 In[4]:= %[1]
 Out[4]= a0 + 3 a1 + 6 a2 + 6 a3

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul at physics.uwa.edu.au  AUSTRALIA                       
http://www.physics.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________


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