Theory of Differential Equations : Partial Differential Equations (Paperback)

1. Introduction: two existence-theorems; 2. Cauchy's theorem; 3. Linear equations and complete linear systems; 4. Non-linear equations: Jacobi's second method, with Mayer's developments; 5. Classes of integrals possessed by equations of the first order: generalisation of integrals; 6. The method of characteristics for equations in two independent variables: geometrical relations of the various integrals; 7. Singular integrals and their geometrical properties: singularities of the characteristics; 8. The method of characteristics in any number of independent variables; 9. Lie's methods applied to equations of the first order; 10. The equations of theoretical dynamics; 11. Simultaneous equations of the first order.