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Re: beginner question regarding units in equations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg123948] Re: beginner question regarding units in equations
  • From: W Craig Carter <ccarter at mit.edu>
  • Date: Sun, 1 Jan 2012 02:29:47 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201112310701.CAA17278@smc.vnet.net>

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.
>
>




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