[CS-FSLUG] Calculus

[Clinton Evans]

Perhaps the first examples I gave, center-of-gravity and moment of inertia, 
are good ones to consider. Look them up on wikipedia or Eric Weinstein's 
world of Physics for the equations. The definitions come directly from the 
definition of the definite integral. The practical calculation uses integral 
calculus for simple shapes or numerical integration for more complex 
geometries.

In my work, I use diffraction theory for calculating the performance of a lens 
system. Geometric ray-tracing (lots of vectors but not much calculus) tells 
me the shape of the wavefront emerging from the lens. Then, I use the 
Huygens-Fresnel Integral (look it up on google for the equations) to 
calculate the the form of the image spot -- known in optics speak as the 
point-spread function.

This theory also leads to a related calculation for the modulation transfer 
function. It is like a frequency response for an amplifier except the 
frequency is in cycles per mm instead of cycles per second and provides a 
fairly rigorous assessment of a lens' image quality. The calculation uses an 
autocorrelation integral of the emerging wavefront from the lens. Here is a 
reference:

http://publib.upol.cz/~obd/fulltext/Physica-40-41/acta6.pdf

An optics text book would give a better account but this paper shows the 
general idea.

I also use least-squares optimization methods routinely. A google search will 
give the general idea but the plot depends on lots of linear algebra applied 
to a matrix of partial derivatives -- calculus.

Clinton


On Thursday 25 May 2006 10:58, Yama Ploskonka wrote:
> Thank you, Clinton, yet much of what you say is FOAF evidence.
>
> As a physicist working in optics, do you have one - not asking for more
> of your time - one example of something specific _you_ have calculated
> using calculus?  Just one.  Equation very much appreciated.  To make it
> more enticing:  I will hang that one on my wall, by the computer, and
> get my wife to explain it to me until I get it.  I mean, I'm supposedly
> a bright kid, I should be able to get that Calculus...
>
> I hope that NDA is not a problem with you as it is with Dave...
>
> Thanks
>
> Yama
>
> Clinton Evans wrote:
> > I use calculus routinely in the course of my work.
>
> <FOAF>
>
> > It is an immensely useful
> > tool for a wide range of problems. Every time a mechanical engineer works
> > out a center of gravity or a moment of inertia he uses calculus. Every
> > time an electrical engineer works an AC network problem, he uses
> > calculus. In terms of dollars per equation, Every time an orbital
> > mechanics person works out how to get a space craft to Neptune, he uses
> > calculus.
> >
> > Maxwell's Equations are the most economically important piece of physics
> > in the past 200 years and calculus is at the heart of the theory. It is
> > fundamental to everything from radio through power generation and
> > transmission to physical optics. It also provided the most important clue
> > leading to relativity. Talking of relativity, calculus is also
> > fundamental to general relativity.
>
> </FOAF>
>
> > I am a physicist and work in optics.  My use of calculus is so diverse it
> > is hard to know where to start but here is a short list:
> >
> > Optical Coatings
> > Polarization
> > Optimization
> > Radiometry
> > Diffraction Theory
> > Geometric Optics (Fermat's Principle)
> >
> > Quite apart from its utility, calculus is also interesting. It has its
> > own beauty and is as worthy of study as anything in literature, the arts
> > or any phenomenon of the physical world.
> >
> > Clinton
> >
> > On Wednesday 24 May 2006 13:24, Yama Ploskonka wrote:
> >> David Aikema wrote:
> >> <snip>
> >>
> >>> With degrees in French Lang & Lit, and certification as an elementary
> >>> school teacher, I'm unsurprised that you speak of not having used
> >>> calculus outside of school.
> >>
> >> ouch!
>
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-- 
Clinton