Algorithmic Lie Theory for Solving Ordinary Differential Equations

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Introduction
Linear Differential Equations
Linear Ordinary Differential Equations
Janet's Algorithm
Properties of Janet Bases
Solving Partial Differential Equations
Lie Transformation Groups
Lie Groups and Transformation Groups
Algebraic Properties of Vector Fields
Group Actions in the Plane
Classification of Lie Algebras and Lie Groups
Lie Systems
Equivalence and Invariants of Differential Equations
Linear Equations
Nonlinear First-Order Equations
Nonlinear Equations of Second and Higher Order
Symmetries of Differential Equations
Transformation of Differential Equations
Symmetries of First-Order Equations
Symmetries of Second-Order Equations
Symmetries of Nonlinear Third-Order Equations
Symmetries of Linearizable Equations
Transformation to Canonical Form
First-Order Equations
Second-Order Equations
Nonlinear Third-Order Equations
Linearizable Third-Order Equations
Solution Algorithms
First-Order Equations
Second-Order Equations
Nonlinear Equations of Third Order
Linearizable Third-Order Equations
Concluding Remarks
Solutions to Selected Problems
Collection of Useful Formulas
Algebra of Monomials
Loewy Decompositions of Kamke's Collection
Symmetries of Kamke's Collection
Alltypes Userinterface
References
Index
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