No textbook is perfect. The 6th edition’s coverage of for nonlinear systems is present but less extensive than in dedicated ODE texts like those by Hirsch and Smale. Also, the chapter on partial differential equations necessarily compresses material that could fill an entire separate course. Students taking advanced PDEs may still need a supplementary text.
The text is structured into , moving from simple first-order equations to complex boundary value problems: No textbook is perfect