Dirac Delta Function: Basics

*To*: mathgroup at smc.vnet.net*Subject*: [mg75174] Dirac Delta Function: Basics*From*: Gopinath Venkatesan <gopinathv at ou.edu>*Date*: Thu, 19 Apr 2007 04:34:36 -0400 (EDT)

Hello Friends I browsed some of the previous posts in this forum on Dirac Delta function, and found some interesting distributions used to represent the delta function, at the below website: <http://mathworld.wolfram.com/DeltaFunction.html> Also when I tried using one of the distribution, Fourier series approximation (shown below), I was getting very different solutions for different entries of upper limit of k, even at higher values of upper limits. DeltaF(x - a) = 1/(2*Pi) + (1/Pi)*Sum[Cos[k*a]*Cos[k*x] + Sin[k*a]*Sin[k*x], {k, 1, Infinity}] (here DeltaF is DiracDelta). Does anyone here can give me suggestions on using right distributions and parameters. Thanks. Also Can I use the DiracDelta[] function available in Mathematica itself. How does Mathematica calculate them. I am not integrating the equation containing DiracDelta[], so as seen from the Mathematica examples, I think it is doing Laplace transformations. Any help/directions to resources are appreciated. Thanks, Gopinath Graduate Student University of Oklahoma