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MathGroup Archive 2003

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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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