How to use Lie Groups in differential equation

> From: 'Joal Heagney'
> Subject: RE: [Maxima] How to use Lie Groups in differential equation
> 
> > Hi all. I remember somebody saying in this news group that 
> Lie Groups 
> > (symmetry analysis) was a general purpose approach to solving 
> > differential equations. I've been googling the web for a 
> week now in 
> > order to understand how this works, and now have a bit of an 
> > understanding of what an algebra/group is (and specifically 
> what Lie 
> > algebras and groups are).

The following text is from 1897 and available online.
(See below for one link):

Ordinary Differential Equations, by James Morris Page 

This book is quite readable as a DiffEq text and includes
significant material (multiple sections with multiple 
chapters each, and references to this material elsewhere
within other chapters.)

One might easily miss it, due to it's age.

> However, each time I try to understand how Lie algebra applies to 
> differential equations, I slam into a wall of mathematical symbolism.

This book is low on symbolism compared to modern
texts -- comparable to a normal ODE text perhaps.

> So, does anyone have any links to free resources that covers 
> this topic 
> at a 2nd/3rd year university level? Preferably with some 
> worked examples? :)

I estimate this is approximately at the 2-3 year level,
typical of other ODE texts.  Certainly not much higher
based on my casual inspection.


Online sources include:
Ordinary Differential Equations, by James Morris Page 
(frame- and JavaScript-dependent page images at Cornell)
http://onlinebooks.library.upenn.edu/webbin/book/browse?type=lccn&key=QA345%
20.B16%201897a
[DjVu formatted copies apparently exist too.]

Also available from that page:

Introductory Treatise on Lie's Theory of 
Finite Continuous Transformation Groups, 
by John Edward Campbell 
(frame- and JavaScript-dependent page images at Cornell)

An Introduction to the Lie Theory of One-Parameter Groups,
by Abraham Cohen 
(frame- and JavaScript-dependent page images at Cornell)


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Herb Martin, MCSE, MVP
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