These guys are fun.
...that's what my advisor had to say about the authors, most of them renowned astrophysicists. The content would be encountered in an undergraduate computational physics or numerical mathematics class, albeit there it would be both watered down and yet more formally presented. These guys give you the real deal theory complete with implementation albeit with informal insight to appeal to your intuition. For the physicist, C is probably the best language to learn the material, as we are not to be distracted with abstractions until first getting the job done, which is the purpose of this book.
Graduate numerical mathematics, which is basically methods to solve PDEs, are only barely touched upon in this book. As another professor first taught me, all those advanced methods in the end result in a linear system Ax=b. And so x=A^-1 b, which requires ways to invert the matrix A, which is best handled by the procedures described in this book. It is therefore the backbone of numerics.