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The Method of Equivalence and its Applications (Paperback)
Loot Price: R1,968
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The Method of Equivalence and its Applications (Paperback)
Series: CBMS-NSF Regional Conference Series, 58
Expected to ship within 12 - 17 working days
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The ideas of Elie Cartan are combined with the tools of Felix Klein
and Sophus Lie to present in this book the only detailed treatment
of the method of equivalence. An algorithmic description of this
method, which finds invariants of geometric objects under infinite
dimensional pseudo-groups, is presented for the first time. As part
of the algorithm, Gardner introduces several major new techniques.
In particular, the use of Cartan's idea of principal components
that appears in his theory of Repere Mobile, and the use of Lie
algebras instead of Lie groups, effectively a linear procedure,
provide a tremendous simplification. One must, however, know how to
convert from one to the other, and the author provides the Rosetta
stone to accomplish this. In complex problems, it is essential to
be able to identify natural blocks in group actions and not just
individual elements, and prior to this publication, there was no
reference to block matrix techniques. The Method of Equivalence and
Its Applications details ten diverse applications including
Lagrangian field theory, control theory, ordinary differential
equations, and Riemannian and conformal geometry. This is the only
book to treat this subject in such depth and to include the
algorithm, the use of principal components, and the use of
infinitesimal analysis on the Lie algebra level. This volume
contains a series of lectures, the purpose of which was to describe
the equivalence algorithm and to show, in particular, how it is
applied to several pedagogical examples and to a problem in control
theory called state estimation of plants under feedback. The
lectures, and hence the book, focus on problems in real geometry.
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