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課程簡介 :
We will begin with many concrete models
of ODEs and PDEs in dynamical system theory and quantum mechanics. From
the given models, we examine their invariant transformations, Lie
groups and invariants. Using invariants corresponding to the Lie algebra
structure, we seek ways to reduce the ODEs and PDEs to lower order systems
and sometimes even Explicit solutions of the physical model, and the
physical implications.
This course utilizes only basic knowledge in ODEs, PDEs and algebra.
Students do not need extensive prerequisites in these subjects.
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Two
useful references are:
[1] Lie Groups, Lie Algebras, and Some of Their Applications, by Robert
Gilmore, Wiley-Intersccience, New York, 1974.
Reprinted by
Dover, 2006.
[2] Group Theory and the Coulomb Problem, by M. J Englefield, John
Wiley and Sons, 1972
* ISBN: 0471241652
We will also use some more recent references by R. Gilmore and C.
Letellier.
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