This book is a rarity because Farlow actually succeeds in explaining how to model physical problems using PDE's. This is a volume for engineers rather than mathematicians, so expect clarity rather than pages of ugly and worthless abstractions. It's not exhaustive, but, given the price, you wouldn't be justified in demanding a detailed treatment of all the intricacies of a subject as vast as PDE's. As a pedagogical tool, Farlow stresses the physical origin of PDE's , so many problems include units and very insightful diagrams. For example, unlike many other authors, Farlow reveals the intuitive meaning of the LaPlacian, which is a noteworthy distinction reminiscent of the writing of Tristan Needham, the author of Visual Complex Analysis. If your primary interest is real understanding rather than an adeptness at manipulating meaningless symbols, this book contains all the physical motivations necessary to advance your ambitions.