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Re: Directional derivative in content MathML?

From: Stan Devitt <jsdevitt@stratumtek.com>
Date: Tue, 20 May 2003 17:22:38 -0400
Message-ID: <3ECA9C9E.6020405@stratumtek.com>
To: Robert Miner <RobertM@dessci.com>
CC: brentmh@ece.rice.edu, www-math@w3.org, lizzardg@rice.edu

I don't know if this was what you had in mind, but
given u=(x,y,z) with x,y and z all functions of s,
I would write df(x,y,z)/du  *du/ds  as something like

<apply>
    <plus/>
    <apply>
      <times/>
      <apply><partialdiff/><bvar><ci>x</ci></bvar>
        <apply><ci>f</ci><ci>x</ci><ci>y</ci><ci>z</ci></apply>
      </apply>
      <apply><partialdiff/><bvar><ci>s</ci></bvar>
        <apply><ci>x</ci><ci>s</ci></apply>
      </apply>
    </apply>
    <apply>
      <times/>
      <apply><partialdiff/><bvar><ci>y</ci></bvar>
        <apply><ci>f</ci><ci>x</ci><ci>y</ci><ci>z</ci></apply>
      </apply>
      <apply><partialdiff/><bvar><ci>s</ci></bvar>
        <apply><ci>y</ci><ci>s</ci></apply>
      </apply>
    </apply>
    <apply>
      <times/>
      <apply><partialdiff/><bvar><ci>z</ci></bvar>
        <apply><ci>f</ci><ci>x</ci><ci>y</ci><ci>z</ci></apply>
      </apply>
      <apply><partialdiff/><bvar><ci>s</ci></bvar>
        <apply><ci>z</ci><ci>s</ci></apply>
      </apply>
    </apply>
</apply>

I would write the gradient of f evaluated at (a,b,c) as

<apply>
  <apply><grad/><ci>f</ci></apply>
  <vector><ci>a</ci><ci>b</ci><ci>c</ci></vector>
</apply>

and if u is a unit vector I would write the directional derivative of f
in the direction uu=(u,v,w)  (a unit vector) at (a,b,c) as:

<apply>
  <apply>
    <times definitionURL="dotproduct"/>
    <apply><grad/><ci>f</ci></apply>
    <vector><ci>a</ci><ci>b</ci><ci>c</ci></vector>
  </apply>
  <vector><ci>u</ci><ci>v</ci><ci>w</ci></vector>
</apply>

>  
>
Received on Tuesday, 20 May 2003 17:20:32 GMT

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