Re: New Analytical Functions - Mathematica Verified

*To*: mathgroup at smc.vnet.net*Subject*: [mg66960] Re: New Analytical Functions - Mathematica Verified*From*: "Mohamed Al-Dabbagh" <mohamed_al_dabbagh at hotmail.com>*Date*: Mon, 5 Jun 2006 03:48:15 -0400 (EDT)*References*: <200605280104.VAA23436@smc.vnet.net> <200606011055.GAA20733@smc.vnet.net> <e5osg1$hvp$1@smc.vnet.net> <e5rf0d$h4r$1@smc.vnet.net> <e5ttg9$eef$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

dhky at shaw.ca wrote: > How does Mathematica handle the derivative of a function such as x^5? > IF > it finds the derivative symbolically then evaluates it. > [eg. second derivative of x^5 = 20x^3 then at x=12.2 the result is > 36316.96] > If I was a Mathematica developer, I would prefer finding the derivative symbolically first then substitute for the required x. This will give perfect solution. The reason is that in numerical analysis, finding derivative is much harder and error-prone operation than integration. Derivative in numerical analysis is a real nightmare, and errors can grow dangerously contrary to integration. You may refer to a numerical analysis reference and read more about numerical derivation and its disadvantages. The higher the derivative, the more dangerous are the numerical errors. In our specific problem in hand, Fractional Part is NOT done according to a certain formula in Mathematica AND in other algebraic systems. It is done by a rather complicated chopping and "trimming" procedure. The result I derived will provide the mathematical formula for Fractional Part such that there will be no need for processor-side load necessary to neutralize sign then isolate the integer from fractional part. Using my result that: the derivative of Fractional Part of any function is the same as derivative of that function, will further simplify (one) operation associated with fractional parts, i.e., providing the derivatives. So there will be no need for using fractional part costly operations when the derivative is needed! Mohamed Al-Dabbagh http://dabbagh2.fortunecity.com/disc

**References**:**Re: New Analytical Functions - Mathematica Verified***From:*"Mohamed Al-Dabbagh" <mohamed_al_dabbagh@hotmail.com>