[Date Index]
[Thread Index]
[Author Index]
Re: Defining a total derivative
*To*: mathgroup at smc.vnet.net
*Subject*: [mg127788] Re: Defining a total derivative
*From*: "Dr. Wolfgang Hintze" <weh at snafu.de>
*Date*: Wed, 22 Aug 2012 05:19:21 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
*Delivered-to*: mathgroup-newout@smc.vnet.net
*Delivered-to*: mathgroup-newsend@smc.vnet.net
*References*: <k0nh82$avi$1@smc.vnet.net> <k11tv8$t7e$1@smc.vnet.net>
On 22 Aug., 08:24, S16 <sowna... at gmail.com> wrote:
> On Saturday, August 18, 2012 8:46:10 AM UTC+1, S16 wrote:
> > Hi,
>
> > I am very new to Mathematica, so need a bit of help!
>
> > I want to define a function (called say G) that is defined as
>
> > G = =E2=88=82/=E2=88=82x - ((=E2=88=82F/=E2=88=82x)/(=E2=88=82F/=E2=88=82=
>
> > y))*=E2=88=82/=E2=88=82y
>
> > Where F is some other function which will be defined.
>
> > So as you can see, G is a differenital operator. Want to define it so that I can just do G[ some function ] rather than repeatedly write out the whole thing.
>
> > Any help at all would be awesome!
>
> > -S16
>
> Sorry, my message came out formatted all wrong. I have actually managed to solve this issue- but have a different question.
>
> Say I have defined an operator G, which involves partial derivatives in x and y
>
> and I want to find expressions for G[G[ ]] , G[G[G[ ]]] - applying the operator multiple times. is there a way to define this on Mathematica (I want to put this in a package).
>
>
Let's take an example.
Define the operator g as
In[7]:= g = D[#1, x] + D[#1, y] &
Out[7]= D[#1, x] + D[#1, y] &
Test it
In[8]:= g[x + y]
Out[8]= 2
Chose a non trivial funcion
In[20]:= f = Sin[x*y]
Out[20]= Sin[x*y]
Now iterate g and apply it immediately to f
In[22]:= g[g[f]]
Out[22]= 2*Cos[x*y] - x^2*Sin[x*y] - 2*x*y*Sin[x*y] - y^2*Sin[x*y]
But this can be achieved more generally using Nest
In[23]:= Nest[g, f, 2]
Out[23]= 2*Cos[x*y] - x^2*Sin[x*y] - 2*x*y*Sin[x*y] - y^2*Sin[x*y]
Now the step you wanted. Definiting the interation of g without
applying it immediately.
In[27]:= gi[k_] := Nest[g, #1, k] &
Test it
In[28]:= gi[2][f]
Out[28]= 2*Cos[x*y] - x^2*Sin[x*y] - 2*x*y*Sin[x*y] - y^2*Sin[x*y]
Now the third iteration
In[29]:= gi[3][f]
Out[29]= (-x^3)*Cos[x*y] - 3*x^2*y*Cos[x*y] - 3*x*y^2*Cos[x*y] -
y^3*Cos[x*y] - 6*x*Sin[x*y] - 6*y*Sin[x*y]
Best regards,
Wolfgang
Prev by Date:
**Non-sequential composition of pure functions**
Next by Date:
**Re: Problem with NIntegrate**
Previous by thread:
**Defining a total derivative**
Next by thread:
**Re: Defining a total derivative**
| |