Partial differential equations (with 25 figures) - Fritz John (1910- (Spriger-Verlag, 1981)
The book identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. It discusses real functions of several variables, the Cauchy-Kowalevski theorem, a second proof foe existence of solutions of the initial value problem for symmetric hyperbolic systems, solutions of the Dirichlet problem in higher dimension, a proof of Widder's theorem on non-negative solutions of the equation. Finally, the book presents H. Lewy's construction of a linear differential equation without solutions