CRC Handbook of Lie Group Analysis of Differential Equations, Volume I

APPARATUS OF GROUP ANALYSIS: Lie Theory of Differential Equations: One Parameter Transformation Groups. Integration of Second-Order Ordinary Differential Equations. Group Classification of Second-Order Ordinary Differential Equations. Invariant Solutions. Generalizations: Lie-Baecklund Transformation Groups. Noether-Type Conservation Theorems. Non-Local Symmetry Generators via Baecklund Transformations. BODY OF RESULTS: Ordinary Differential Equations. Second Order Partial Differential Equations with Two Independent Variables. Evolution Equations I: Diffusion Equations. Evolution Equations II: General Case. Wave Equations. Hydro- and Gas- Dynamics. Hydrodynamic-Type Systems. Integrodifferential Equations. COMPUTER ASPECTS: Applications of Group Theory in Computation. Symmetry of Finite-Difference Equations. References. Indices.

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• Física Matemática
• Álgebra
• Matemática aplicada
• Cálculo diferencial e equações

Lie Algebras;Lie Group Analysis;Lie Groups;Ordinary Differential Equations;De Lie;Recursion Operator;Differential Equation;Lie Group Method;Conservation Laws;Lie;Contact Transformations;Point Transformations;Infinitesimal Operators;Arbitrary Functions;Symmetry Group;Partial Differential Equation;Symmetry Algebra;Arbitrary Constants;Differential Invariants;Canonical Variables;Local Symmetries;Quotient Algebra;BACKLUND TRANSFORMATIONS;Riemann Invariants;Lie Equations