Piecewise and Integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg75189] Piecewise and Integral*From*: zosi <zosi at to.infn.it>*Date*: Fri, 20 Apr 2007 00:33:22 -0400 (EDT)

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 --------------------