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MathGroup Archive 1995

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Re: How to parametric plot deriv of interpolating func?

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1581] Re: How to parametric plot deriv of interpolating func?
  • From: rubin at msu.edu (Paul A. Rubin)
  • Date: Sat, 1 Jul 1995 03:48:09 -0400
  • Organization: Michigan State University

In article <3sg42m$8ji at news0.cybernetics.net>,
   "Ronald J. Riegert" <riegerrj at esvax.dnet.dupont.com> wrote:
->	I have recently started working with NDSolve and just 
->encountered Mathematica interpolating functions for the first 
->time.  The Mathematica book says that these can be dealt with 
->just like any other function, but I'm having difficulty using 
->their derivatives in parametric plots.  
->	In particular, I use NDSolve to solve the second-order 
->differential equation diffeq for x[t], and call the result 
->soln:
->
->soln=
->   NDSolve[{diffeq,x[0.]==0.,x'[0.]==1.},x,{t,0.,50.}][[1,1]]
->
->This gives the interpolating function:
->
->x -> InterpolatingFunction[ {0.,50.}, <>]
->
->I'm interested in plotting D[x[t],t], so I do:
->
->Plot[Evaluate[D[x[t] /. soln,t]],{t,0.,50.}]
->
->which works fine.  However, I'm really want to use D[x[t],t] 
->in a parametric plot, so I test by entering:
->
->ParametricPlot[{t, Evaluate[D[x[t] /. soln,t]]},{t,0.,50.}]
->
->which should give the same graph as the above Plot command.  
->Instead, it produces a bunch of error messages.  
->	My question, therefore, is how do I go about using the 
->derivative of an interpolating function in a parametric plot?
->
->Ronald J. Riegert
->DuPont Experimental Station
->riegerrj at esvax.dnet.dupont.com
->
->
You need to Evaluate the entire first argument:

     ParametricPlot[Evaluate[{t, D[x[t] /. soln,t]}],{t,0.,50.}]

ParametricPlot has attribute HoldAll, so Mma hold the first argument, which 
is the part enclosed in braces.  Basically, it didn't see your Evaluate 
until after substituting 0. for t.  I think.

Paul

**************************************************************************
* Paul A. Rubin                                  Phone: (517) 432-3509   *
* Department of Management                       Fax:   (517) 432-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
* East Lansing, MI  48824-1122  (USA)                                    *
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entirely different.                                    J. W. v. GOETHE


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