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New PDF release: Algorithmic Lie Theory for Solving Ordinary Differential

By Fritz Schwarz

although Sophus Lie's thought was once almost the one systematic approach for fixing nonlinear usual differential equations (ODEs), it was once hardly used for sensible difficulties due to the significant quantity of calculations concerned. yet with the appearance of laptop algebra courses, it turned attainable to use Lie thought to concrete difficulties. Taking this procedure, Algorithmic Lie thought for fixing traditional Differential Equations serves as a helpful creation for fixing differential equations utilizing Lie's thought and similar results.

After an introductory bankruptcy, the publication offers the mathematical origin of linear differential equations, masking Loewy's idea and Janet bases. the next chapters current effects from the idea of constant teams of a 2-D manifold and speak about the shut relation among Lie's symmetry research and the equivalence challenge. The center chapters of the publication establish the symmetry periods to which quasilinear equations of order or 3 belong and rework those equations to canonical shape. the ultimate chapters clear up the canonical equations and bring the final strategies at any time when attainable in addition to supply concluding comments. The appendices comprise strategies to chose workouts, beneficial formulae, homes of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a short description of the software program approach ALLTYPES for fixing concrete algebraic problems.

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Algorithmic Lie Theory for Solving Ordinary Differential Equations (Chapman & Hall/CRC Pure and Applied Mathematics) by Fritz Schwarz

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