RE: Differentiating functions of vectors
- To: mathgroup at smc.vnet.net
- Subject: [mg9449] RE: [mg9424] Differentiating functions of vectors
- From: jmthomas <jmthomas at cybercable.tm.fr>
- Date: Thu, 6 Nov 1997 02:39:58 -0500
- Sender: owner-wri-mathgroup at wolfram.com
Your function is
f[ a_ , b_ ] := a . b
but I need to know the kind of data structure that a and b refer to: are
= they vectors (like the dot suggests)? If it is the case,
differentiating = with respect to a certain argument implies in fact
tensor analysis, = which is not present as a standard routine set in
mathematica. See = MathTensor, references are given to it in wolfram
Research site. If a and b are just reals or complexes, you can use:
op1=Derivative[1,0][#]&
op2=Derivative[0,1][#]&
If f[a_,b_]=2a+b you will get
op1[f]=2&
and op2[f]=1&
----------------------------------------------- Jean-Marie THOMAS
Conseil et Audit en Ing=E9nierie de Calcul jmthomas at cybercable.tm.fr
www.cybercable.tm.fr/~jmthomas
-----Original Message-----
From: Loris Bennett [SMTP:loris at ferro.physik.TU-Berlin.DE] To:
mathgroup at smc.vnet.net
Sent: Wednesday, November 05, 1997 7:57 AM To: mathgroup at smc.vnet.net
Subject: [mg9424] Differentiating functions of vectors
--------------E197FA4B98680772E12058D3
Hello,
If I have a function such as
f[ a_ , b_ ] := a . b
how do I differentitate w.r.t a certain component without having to
specify
the components of the vector explicitly? I had hoped something like
fa[ a_ , b_ ] = D[ f [ a . b ] , a[[1]]]
would work, but it doesn't..
All help greatly appreciated.
Loris