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Re: beginner question regarding units in equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123945] Re: beginner question regarding units in equations
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Mon, 2 Jan 2012 02:42:27 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201112310701.CAA17278@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

Amen.

Bobby

On Sun, 01 Jan 2012 01:29:47 -0600, W Craig Carter <ccarter at mit.edu> wrote:

>
> I feel compelled to put in my 2 cents worth on this topic.  I hope that
> I am barking at the choir here, but perhaps a student might be
> listening.
>
> Every year in my set of materials science and engineering lectures, I
> try to emphasize that the *first* thing a student should do when
> performing a calculation is "non-dimensionalize, non-dimensionalize,
> non-dimensionalize."  This is a minority opinion in engineering.  It is
> never correct to take the Log or the Sine of a dimension. *Every* ideal
> spring can be written as F/(k xo) = 1 - x/x0 = 1-xbar, the
> characteristic frequency of any harmonic oscillator should be normalized
> by dividing through by Sqrt[k/m] (or its equivalent) and so on.
>
> There is no physics in units---only relative quantities.  The units
> packages are useful for determining if a quantity has been
> non-dimensionalized when formulas extracted from texts, etc.
>
> For example, this avoids frustrating errors that appear when, for
> example, FindFit[data,Exp[-a (x-b)^2],{a,b},x] when data might be
> student scores centered around 500:
>
>
>
> W Craig Carter
> Professor of Materials Science, MIT
>
>
>
> On Dec 31, 2011, at Sat, Dec 31, 11 ---2:01 AM, Bill Rowe wrote:
>
>> On 12/30/11 at 7:09 AM, szhorvat at gmail.com (Szabolcs Horv=C3=A1t) wrote:
>>
>>> On 2011.12.29. 8:53, RDog wrote:
>>
>>>> Many civil engineering equations are empirically derived and
>>>> therefore the units dont work out exactly. How does Mathematica
>>>> handle units in equations and especially in empirical equations
>>>> where there may be parameters set to weird exponetial powers. Does
>>>> the program use units at all in equations or does the user need to
>>>> keep track?
>>
>>> Mathematica does not know about units.  It does not keep track of
>>> units by default.  So you don't need to worry about units not
>>> matching.
>>
>>> There is the Units` package which provides some limited support for
>>> units, but I have never used it seriously.  I think that not using
>>> units explicitly in your program will be the most productive way to
>>> work.
>>
>> There is another package AutomaticUnits available at
>> <http://library.wolfram.com/infocenter/MathSource/7655/>
>>
>> that significantly improves upon the Units package. Along with
>> other things you can do:
>>
>> << AutomaticUnits`
>>
>> radius = r Centimeter;
>> area = Pi r^2;
>> Plot[area, {r, 0, 2}]
>>
>> and get the desired plot without worrying about the units. A
>> much better solution than the Units package.
>>
>>
>
>


-- 
DrMajorBob at yahoo.com



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