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) * ************************************************************************** Mathematicians are like Frenchmen: whenever you say something to them, they translate it into their own language, and at once it is something entirely different. J. W. v. GOETHE