This is an excellent introduction into numerical methods for integrating conservation laws. The book begins with an introduction to the mathematics theory of one dimensional hyperbolic equations that must be understood by anyone attempting to solve problems of this type. The book discuss classical methods for their numerical solution (such as the Lax-Wendroff method) and existing properties of such methods in resolving discontinuous flow patterns. If you desire the numerical solution to conservation laws or hyperbolic equations in general you must read this book.
Solutions & Notes:
I am in the process of transcribing my notes from this book into a solutions manual. You can find my first attempts and my scanned in handwritten notes below.