Dimensional Analysis, 2013

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Lectures at the Refresher Course in Statistical Mechanics,
Homi Bhabha Center for Science Education, November 2013. 

Dimensional Analysis, 2013

The course

This course was addressed to teachers of physics.  It advanced one answer
to the question of how to get the heart of a new subject as quickly as
possible.  The particular answer involved dimensional arguments as the
core technique. 

Dimensional analysis was introduced in the first two lectures using some
examples.  It was shown how dimensional analysis simplifies problems and
allows discovery of new phenomena. 

In the next two lectures Gauss' approach to measurements and units was
introduced, and was applied to developing natural units.  Examples of
standard physics were analysed using these techniques. 

In the final two lectures we discussed asymptotic scaling and the breaking
of scaling using the example of Rayleigh-Benard convection and fractals
respectively.  The notion of breaking of scaling was then applied to critical
phenomena.