[Date Index]
[Thread Index]
[Author Index]
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 --------------------
Prev by Date:
**Re: Dirac Delta Function: Basics**
Next by Date:
**Re: neat way to program minimum of sum**
Previous by thread:
** Re: Importing and retaining graphics**
Next by thread:
**Re: Piecewise and Integral**
| |