Preface 1. Introduction and summary 2. PDE systems, pfaffian systems and vector field systems 3. Cartan's local existence theorem 4. Involutivity and the prolongation theorem 5. Drach's classification, second order PDEs in one dependent variable and Monge characteristics 6. Integration of vector field systems n satisfying dim n' = dim n + 1 7. Higher order contact transformations 8. Local Lie groups 9. Structural classification of 3-dimensional Lie algebras over the complex numbers 10. Lie equations and Lie vector field systems 11. Second order PDEs in one dependent and two independent variables 12. Hyperbolic PDEs with Monge systems admitting 2 or 3 first integrals 13. Classification of hyperbolic Goursat equations 14. Cartan's theory of Lie pseudogroups 15. The equivalence problem 16. Parabolic PDEs for which the Monge system admits at least two first integrals 17. The equivalence problem for general 3-dimensional pfaffian systems in five variables 18. Involutive second order PDE systems in one dependent and three independent variables, solved by the method of Monge Bibliography Index.
Preface 1. Introduction and summary 2. PDE systems, pfaffian systems and vector field systems 3. Cartan's local existence theorem 4. Involutivity and the prolongation theorem 5. Drach's classification, second order PDEs in one dependent variable and Monge characteristics 6. Integration of vector field systems n satisfying dim n' = dim n + 1 7. Higher order contact transformations 8. Local Lie groups 9. Structural classification of 3-dimensional Lie algebras over the complex numbers 10. Lie equations and Lie vector field systems 11. Second order PDEs in one dependent and two independent variables 12. Hyperbolic PDEs with Monge systems admitting 2 or 3 first integrals 13. Classification of hyperbolic Goursat equations 14. Cartan's theory of Lie pseudogroups 15. The equivalence problem 16. Parabolic PDEs for which the Monge system admits at least two first integrals 17. The equivalence problem for general 3-dimensional pfaffian systems in five variables 18. Involutive second order PDE systems in one dependent and three independent variables, solved by the method of Monge Bibliography Index.
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