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Re: Piecewise and Integral
*To*: mathgroup at smc.vnet.net
*Subject*: [mg75239] Re: Piecewise and Integral
*From*: dh <dh at metrohm.ch>
*Date*: Sat, 21 Apr 2007 23:13:52 -0400 (EDT)
*References*: <f09g01$pe$1@smc.vnet.net>
$Version: 5.1 for Microsoft Windows (October 25, 2004)
Hi,
I am getting 10 as expected. Are you fooling yourself?
Daniel
zosi wrote:
> Hi,
>
> I have a problem that I considered (and still consider) trivial.
>
> Let us suppose I have defined a Gate
> (Period T and width \[Tau]= T/4), through Piecewise
> and extended it periodically (see from In[1] to In[6]).
> The Plot seems indicate that the extension is correct.
> Now let us calculate the coefficient a0 according to
> the usual formula In[13], having assumed that \[Lambda]=0 (In[12])
> The result Out[13] = 10 is correct.
>
> If I consider another case, i.e., I change the value of \[Lambda]=1/10,
> the result, 10, is again correct (as expected !).
>
> But, if I try \[Lambda]= T/2 the result is 5 (instead of 10). Why ?
> My interpretation is that the range
> \[Tau]< x \[LessEqual] T/2 is not evaluated.
> Infact, when I remove the ":" in In[3], the function is not defined
> in the last interval ( but correctly Plotted !).
>
> Any hint to obtain 10 when \[Lambda]= T/2 ?
> Thanks for your help
>
> G. Zosi
> Dipartimento Fisica Generale
> Universita di Torino
> Italy
>
> ----------------- begin -----------------------
>
> In[1]:= Clear["Global`*"] ; Remove["Global`*"];$Line=0;
>
> In[1]:= T=2;
>
> In[2]:= \[Tau]= T/4.
>
> In[3]:= f[x_] := Piecewise[ {{0, -T/2 \[LessEqual] x <- \[Tau]},
> {10, -\[Tau] \[LessEqual] x
> \[LessEqual]\[Tau]},
> {0, \[Tau]< x \[LessEqual] T/2}}]
>
> In[4]:= f[x_]:=f[x-T]/;x >T/2
>
> In[5]:= f[x_]:=f[x+T]/;x<-T/2
>
> In[6]:= Plot[f[x],{x,-2 T,2 T}];
>
> In[12]:= \[Lambda]=0
>
> In[13]:= a0 = (2/T)*Integrate[f[x],{x,-T/2. +\[Lambda] ,T/2.+\[Lambda]}]
>
> Out[13] = 10
>
> Now try with \[Lambda] = 1/10 and \[Lambda] = T/2
>
> --------------------- end --------------------
>
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