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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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Algorithmic Lie Theory for Solving Ordinary Differential Equations (Paperback)
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Algorithmic Lie Theory for Solving Ordinary Differential Equations (Paperback)
Series: Chapman & Hall/CRC Pure and Applied Mathematics
Expected to ship within 12 - 19 working days
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Despite the fact that Sophus Lie's theory was virtually the only
systematic method for solving nonlinear ordinary differential
equations (ODEs), it was rarely used for practical problems because
of the massive amount of calculations involved. But with the advent
of computer algebra programs, it became possible to apply Lie
theory to concrete problems. Taking this approach, Algorithmic Lie
Theory for Solving Ordinary Differential Equations serves as a
valuable introduction for solving differential equations using
Lie's theory and related results. After an introductory chapter,
the book provides the mathematical foundation of linear
differential equations, covering Loewy's theory and Janet bases.
The following chapters present results from the theory of
continuous groups of a 2-D manifold and discuss the close relation
between Lie's symmetry analysis and the equivalence problem. The
core chapters of the book identify the symmetry classes to which
quasilinear equations of order two or three belong and transform
these equations to canonical form. The final chapters solve the
canonical equations and produce the general solutions whenever
possible as well as provide concluding remarks. The appendices
contain solutions to selected exercises, useful formulae,
properties of ideals of monomials, Loewy decompositions, symmetries
for equations from Kamke's collection, and a brief description of
the software system ALLTYPES for solving concrete algebraic
problems.
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