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Re: Problems evaluating Grad
*To*: mathgroup at smc.vnet.net
*Subject*: [mg39425] Re: Problems evaluating Grad
*From*: adam.smith at hillsdale.edu (Adam Smith)
*Date*: Fri, 14 Feb 2003 03:24:25 -0500 (EST)
*References*: <b2fpvg$k66$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
The main difficulty here is that the package Calculus`VectorAnalysis`
assumes a default coordinate system Cartesian[Xx,Yy,Zz]. The current
Coordinate system used can be viewed by executing Coordinates[]. The
functions Grad, Div, Curl are very picky about the coordinates as
shown below
In[1]:=
<<Calculus`VectorAnalysis`
In[2]:=
Coordinates[]
Out[2]=
{Xx,Yy,Zz}
Below I get what I expect
In[3]:=
Grad[Xx+Yy]
Out[3]=
{1,1,0}
But using x and y instead of Xx and Yy gives me zero, since the
partial derivatives with respect to "Xx" and "Yy" of x+y are zero
In[4]:=
Grad[x+y]
Out[4]=
{0,0,0}
The solution to this is to set the default coordinates coordinates.
In[6]:=
SetCoordinates[Cartesian[x,y,z]]
Out[6]=
Cartesian[x,y,z]
Now for x+y things work as expected
In[8]:=
Grad[x+y]
Out[8]=
{1,1,0}
But your f[a,b] will still give zero because the partial derivatives
of a+b with respect to x and y are zero.
In[9]:=
f[x_,y_]:=x+y
In[10]:=
f[a,b]
Out[10]=
a+b
In[11]:=
Grad[f[a,b]]
Out[11]=
{0,0,0}
I am guessing that you really wanted Grad[f[x,y]]
In[12]:=
Grad[f[x,y]]
Out[12]=
{1,1,0}
Adam Smith
"Konrad Den Ende" <chamsterkonrad at bigfoot.com> wrote in message news:<b2fpvg$k66$1 at smc.vnet.net>...
> I'd like to detrmine Grad to a function so i go:
> <<Calculus`VectorAnalysis`
> f[x_,y_]:=x+y
>
> Grad[f[a,b]]
>
> I get no errors, but the answer is simply the same thing
> that i asked, as if no computation was done. What do i
> do wrong?
>
> Also - when i evaluated the examples in Help i got the same
> behavior. The answer that already is there gets exchanged
> to something else upon my evaluation. Namely, the question
> itself. What is that?!
>
> --
>
> Vänligen
> Konrad
> ---------------------------------------------------
> phone #1: (+46/0) 708 - 70 73 92
> phone #2: (+46/0) 704 - 79 96 95
> url: http://konrads.webbsida.com
> e-mail: chamsterkonrad at bigfoot.com
> -----------------------------------
>
> Sleep - thing used by ineffective people
> as a substitute for coffee
>
> Ambition - a poor excuse for not having
> enough sence to be lazy
> ---------------------------------------------------
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