Fritz Schwarz's Algorithmic Lie Theory for Solving Ordinary Differential PDF

By Fritz Schwarz

even though Sophus Lie's conception was once almost the one systematic strategy for fixing nonlinear usual differential equations (ODEs), it used to be infrequently used for useful difficulties as a result of the huge quantity of calculations concerned. yet with the appearance of desktop algebra courses, it grew to become attainable to use Lie conception to concrete difficulties. Taking this process, Algorithmic Lie idea for fixing traditional Differential Equations serves as a important advent for fixing differential equations utilizing Lie's idea and similar results.

After an introductory bankruptcy, the e-book offers the mathematical beginning of linear differential equations, protecting Loewy's thought and Janet bases. the next chapters current effects from the idea of constant teams of a 2-D manifold and talk about the shut relation among Lie's symmetry research and the equivalence challenge. The middle chapters of the booklet determine the symmetry periods to which quasilinear equations of order or 3 belong and rework those equations to canonical shape. the ultimate chapters resolve the canonical equations and bring the final suggestions each time attainable in addition to supply concluding feedback. The appendices include suggestions to chose workouts, valuable formulae, homes of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a quick description of the software program procedure 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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