It should give (-1)**n*f^(n)(0) (that is, (-1)**n*diff(f(x), x, n).subs(x, 0)), if I remember the formula correctly.
Aaron Meurer On Fri, Mar 11, 2016 at 9:00 AM, SAMPAD SAHA <sampadsa...@gmail.com> wrote: > Hi Aaron, > > I have a doubt . > > Do we want: > > > integrate(f(x)*DiracDelta(x, n), (x, -oo, oo)) would output as > > [image: Inline image 1] > > > > > Regards > Sampad Kumar Saha > Mathematics and Computing > I.I.T. Kharagpur > > On Wed, Mar 9, 2016 at 3:11 AM, Aaron Meurer <asmeu...@gmail.com> wrote: > >> DiracDelta(x, k) gives the k-th derivative of DiracDelta(x) (or you >> can write DiracDelta(x).diff(x, k)). >> >> It does look like the delta integrate routines could be improved here, >> though: >> >> In [2]: integrate(f(x)*DiracDelta(x), (x, -oo, oo)) >> Out[2]: f(0) >> >> In [3]: integrate(f(x)*DiracDelta(x, 1), (x, -oo, oo)) >> Out[3]: >> ∞ >> ⌠ >> ⎮ f(x)⋅DiracDelta(x, 1) dx >> ⌡ >> -∞ >> >> Since the integration rules for derivatives of delta functions are >> simple extensions of the rules for the delta function itself, this is >> probably not difficult to fix. >> >> Aaron Meurer >> >> On Mon, Feb 29, 2016 at 3:39 AM, Tim Lahey <tim.la...@gmail.com> wrote: >> > Hi, >> > >> > Singularity functions are actually extremely easy to implement given >> that we have a Dirac delta and Heaviside functions. Assuming that the Dirac >> delta and Heaviside functions properly handle calculus, it’s trivial to >> wrap them for use as singularity functions. The only thing that will need >> to be added is the derivative of the Dirac delta (assuming it’s not already >> there). I implemented singularity functions in Maple in less than an >> afternoon. >> > >> > I was a TA for a Mechanics of Deformable Solids course about 11 or 12 >> times and wrote it to help the students (as we have a site license for >> Maple). I also wrote a set of lecture notes on the topic. >> > >> > Cheers, >> > >> > Tim. >> > >> >> On Feb 26, 2016, at 4:29 PM, SAMPAD SAHA <sampadsa...@gmail.com> >> wrote: >> >> >> >> Hi Jason, >> >> >> >> Thank you for the explanation. It really helped me. >> >> >> >> So, basically we want to start it, firstly, by creating a module which >> would deal with the mathematical operations performed on Singularity >> Functions. After this whole module is prepared, we would focus on how to >> use this module for solving beam problems. Am I correct? >> >> >> >> Can you please explain me in brief that what are the mathematical >> operations we wanted to implement on that module? >> >> >> >> >> >> On Friday, February 26, 2016 at 4:54:59 PM UTC+5:30, SAMPAD SAHA wrote: >> >> >> >> Hi, >> >> >> >> I am Sampad Kumar Saha , an Undergraduate Mathematics and Computing >> Student at I.I.T. Kharagpur. >> >> >> >> I have gone through the idea page and I am interested in working on >> the project named Singularity Function. >> >> >> >> By going through the Idea, I understood that we want to add a package >> to Sympy which can be used for for solving beam bending stress and >> deflection problems using singularity function. Am I correct? >> >> >> >> We can by this way:- >> >> While solving we will be having the moment function as an input which >> we can arrange in the form of singularity functions and then integrate it >> twice to get the deflection curve and we can give the plot or the equation >> obtained of deflection curve as an output. >> >> >> >> I have gone through some documents available on internet which have >> brief studies on solving beam bending stress and deflection problems using >> singularity functions. >> >> >> >> References:- >> >> • Beam Deflection By Discontinuity Functions. >> >> • Beam Equation Using Singularity Functions. >> >> • Enhanced Student Learning in Engineering Courses with CAS >> Technology. >> >> Since there is just a brief idea given in the idea page, I have a >> doubt that what are the things other than solving beam bending stress and >> deflection problems to be implemented in the project? >> >> >> >> Any type of suggestions are welcome. >> >> >> >> >> ========================================================================================================================================== >> >> Regards >> >> Sampad Kumar Saha >> >> Mathematics and Computing >> >> I.I.T. 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