Theory of Differential Equations : Partial Differential Equations (Paperback)

12. General integrals of equations of orders higher than the first; 13. Linear equations of the second order in two independent variables: the Laplace-transformations; 14. Adjoint equations: linear equations having equal invariants; 15. Forms of equations of the second order in two independent variables having their general integrals in explicit finite form; 16. Equations of the second order in two independent variables having an intermediate integral; 17. Ampere's method applied to equations of the second order in two independent variables; 18. Darboux's method and other methods for equations of the second order in two independent variables; 19. Generalisation of integrals; 20. Characteristics of equations of second order: intermediate integrals; 21. General transformation of equations of the second order; 22. Equations of the third and higher orders, in two independent variables; 23. Equations of the second order in more than two independent variables, having an intermediate integral; 24. Equations of the second order in three independent variables, not necessarily having an intermediate integral; Index to Part IV.