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From: Dan_Ciarniello@cc.sfu.ca
Newsgroups: comp.sys.handhelds
Subject: RE: HP48: User-defined derivative problems
Message-ID: <2904833@cc.sfu.ca>
Date: 26 Feb 91 23:32:38 GMT
Lines: 48
Return-path: <Dan_Ciarniello@cc.sfu.ca>
To: handhelds@gac.edu


 > We have some problems to define discrete Heaviside step function
 > U(t) and it's derivative Unit impulse SIGMA(t) in the same
 > directory, and after that use: 'dt(U(5*t))' EVAL.
 
 > We have defined U(t) like: \<< \-> t 'IFTE(t\>=0,1,0)' \>>
 >          and derU(t) like: \<< \-> t dt 'SIGMA(t)' \>>
 >         and SIGMA(t) like: \<< \-> t 'IFTE(t==0,1,0)' \>>
 
 > Now, if we try to derivative 'U(a*5)' the HP48 will say
 > following:
 >            der Error
 >            Undefined Local Name
 >            4:
 >            3:
 >            2:         'U(a*5)'
 >            1:              'a'
 
 > Can someone help us solving this problem.
 
 When I tried this, I did not get an error when trying to differentiate
 U(a*5).  Instead, what I got was the following:
 
               'IFTE(a*5\>=0,\.da(1|(t=a*5)),\.da(0|(t=a*5)))'
 
 It would seem that if a user-defined function is differentiable using
 built-in functions, the user-defined derivative is not used.
 
 To get this to work, redefine U(t) as
 
                    \<< \-> t
                      \<< 'IFTE(t\>=0,1,0) EVAL \>>
                    \>>
 
 This is not differentiable according to the 48.  Differentiating this
 function without having derU(t) defined gives:
 
                    'derU(a*5,5)'
 
 If derU(t) and SIGMA(t) are defined one gets:
 
                    'IFTE(a*5==0,1,0)'
 
 which is, of course, SIGMA(a*5)
 
 Hope this helps,
 Dan.
 
?