Forsyth A.R. Theory Of Differential Equations. Part 4: Partial Differential Equations. Volume 5

Cambridge: At the University Press, 1906. — 478 pages.Introduction: two existence theorems.
Cauchy's theorem.
Linear equations and complete linear systems.
Non-linear equations.
Equations of the first order.
The method of characteristics for two independent variables.
Singular integrals.
The method of characteristics in any number of independent variables.
Lie's method.
The equations of theoretical dynamics.