Maxima by Example: Ch. 7, 8, 9, 10, and 11

On 29 Apr 2009, Dave Feustel  wrote:
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Have you thought about including a chapter on tensor calculus and
differential geometry with reference to General Relativity?
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Hi Dave,

I have thought of writing such a chapter, but not in this
series of tutorials for the beginning serious user of Maxima.

Maxima needs more intelligent discussions of both math and
science topics, with enough quality and depth to attract the
attention of college instructors.

I initially wrote several chapters around the focus of
computational physics, but when I saw the kinds of
questions appearing on the Mailing List, I realised that
a general introduction to the use of Maxima would be
much more helpful, and would also encourage me to learn
more about the subtleties of Maxima.

I still have a part of my brain thinking about another
series of chapters, for another "book", concentrating
on physics, which happens to be what I am most
familiar with.

 I taught general relativity for beginners
(using Bernard Schutz: A First Course in General
Relativity) and cosmology for beginners (at the
level of J. N. Islam: An Introduction to Mathematical
Cosmology) for a mixture of physics seniors and
graduate students at Cal. State, Long Beach.

(But most of my teaching experience was with
plasma physics, astrophysics, and elementary
particle phenomenology.)

I am sure there are both lurkers and active participants
who are better qualified to write a good technical
introduction to both differential geometry and
general relativity (with Maxima embedded) than yours truly.

As to Myron Evans "Grand Covariant Unified
Field Theory (GCUFT)", a quick google brought
up an apparently serious critic who (with colleagues)
has lavished time and energy on refuting this theory:
 Gerhard W. Bruhn, Department of Mathematics,
Darmstadt University of Technology,
 see the page:
http://www.mathematik.tu-darmstadt.de/~bruhn/GCUFT.html

and also the short pdf file," Some fatal shortcomings
of the ECE theory":
http://www.mathematik.tu-darmstadt.de/~bruhn/connection170209.pdf

A Feb. 08 posting by Bruhn on the
http://arxiv.org/ preprint site for physics and math is:
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arXiv:0705.3030
http://arxiv.org/PS_cache/arxiv/pdf/0705/0705.3030v2.pdf
The Evans Lemma of Differential Geometry
February 1, 2008
Abstract:
The Evans Lemma is a basic tool for Evans GCUFT or ECE Theory [2].
Evans has given two proofs of his Lemma. The first proof in [1] is shown to
be invalid due to dubious use of the covariant derivative D?. A second proof
in [2, Sec.J.3] is wrong due to a logical error.
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Ted Woollett