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Focusing on Lie's theory, this book provides a comprehensive introduction to solving differential equations. It explores Loewy's theory, Janet bases, and the continuous groups of a 2-D manifold, along with Lie's symmetry analysis and equivalence problems. The text categorizes symmetry classes for quasilinear equations of order two or three, transforming them into canonical form for solution. Appendices offer selected exercise solutions and formulae, while a dedicated website provides software for complex algebraic calculations.
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Algorithmic Lie Theory for Solving Ordinary Differential Equations, Fritz Schwarz
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- 2019
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