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Download e-book for iPad: Algorithmic Lie Theory for Solving Ordinary Differential by Fritz Schwarz

By Fritz Schwarz

ISBN-10: 158488889X

ISBN-13: 9781584888895

even though Sophus Lie's concept was once nearly the one systematic approach for fixing nonlinear traditional differential equations (ODEs), it used to be infrequently used for sensible difficulties as a result gigantic quantity of calculations concerned. yet with the appearance of desktop algebra courses, it turned attainable to use Lie idea to concrete difficulties. Taking this process, Algorithmic Lie concept for fixing usual Differential Equations serves as a necessary creation for fixing differential equations utilizing Lie's conception and comparable results.

After an introductory bankruptcy, the booklet presents the mathematical starting place of linear differential equations, overlaying Loewy's concept and Janet bases. the subsequent chapters current effects from the idea of continuing 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 booklet establish the symmetry periods to which quasilinear equations of order or 3 belong and remodel those equations to canonical shape. the ultimate chapters clear up the canonical equations and bring the final suggestions every time attainable in addition to offer concluding feedback. The appendices comprise strategies to chose workouts, worthwhile formulae, homes of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a quick description of the software program process 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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