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MathGroup Archive 2006

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Re: Errors at discontinuities

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65206] Re: Errors at discontinuities
  • From: "Narasimham" <mathma18 at hotmail.com>
  • Date: Sat, 18 Mar 2006 06:40:29 -0500 (EST)
  • References: <dvas2r$c27$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

My friend and I realized this soon after posting it (with c,d values
supplied). My practice it is to test evaluate and make any corrections
using plot itself as the guiding tool :)  and it works well with
continuous functions, so thought it was a valid enough replacement.
Thanks again.

David Park wrote:
> I think it is usually better practice to disentangle plotting from
> derivation. Prepare the function you are going to plot outside of the
> plotting statement. Then you can examine it, see if it is the form you want,
> do test evaluations and more easily correct things if necessary.
>
> a= 4 ; b = 3 ; tmax=10;
> fn[u_,lam_,A_]=A*ArcSin[Sin[ 2 Pi u/lam]]*2/Pi ;
>
> df[t_, a_, b_, c_, d_] = D[fn[t, a, b], t]/D[fn[t, c, d], t]
>
> Plot[df[t, 3, 4, 5, 5.65], {t, 0, tmax}];
>
> Also, in your plots c and d are never defined. I'm not certain if that
> completely answers your question, but at least we obtain a plot.
>
> David Park
> djmp at earthlink.net
> http://home.earthlink.net/~djmp/
>
> From: Narasimham [mailto:mathma18 at hotmail.com]
To: mathgroup at smc.vnet.net
>
> Errors appear at start / period cross-over points of  a triangular wave
> on t-axis  with  period a, amplitude b. Why does not
> Plot[  D[fn[t,3,4],t]  / D[fn[t,5,5.65],t] , {t, 0,tmax}] ; Or
> Plot[  D[fn[t,3,4],t]  , {t, 0,tmax}] ;
> work at beginning when the same works erroneously later on in sl1 and
> gets self-corrected  at sl2? And how to remedy the situation?  TIA
>
> a= 4 ; b = 3 ; tmax=10;
> fn[u_,lam_,A_]=A*ArcSin[Sin[ 2 Pi u/lam]]*2/Pi ;
> Plot[ fn[t,a,b], {t, 0,tmax}] ;
> Plot[  D[fn[t,a,b],t]  / D[fn[t,c,d],t] , {t, 0,tmax}] ;
> sl1=D[fn[t,a,b],t]/D[fn[t,c,d] ] ; Plot[ sl1 ,  {t, 0, tmax}] ;
> sl2= D[fn[t,a,b],t]/D[fn[t,c,d],t] ; Plot [sl2, {t, 0, tmax}] ;


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