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MathGroup Archive 2006

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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


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