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. > >