Green's Functions are heavily emphasized in graduate programs in engineering, applied math and physics. They're a useful way in solving many differential equation related problems in many fields. Unfortunately, for many (like me), the Green's Function (and it's uses) seemed restricted to 'textbook' problems. Not anymore.
I had to get this book for use at work. Even though Green Functions were introduced to me in graduate school, it was never a tool I got accustomed to. Because of the necessity (and now ease of use) of the Green's Functions, I had to learn to use it effectively. Now, with Duffy's book, I'm using as a tool in solving many E'nM and photonic problems.
Duffy's book on Green's Functions with Applications really develops the Green's Function mathematically based on physical and historical needs. At first, I thought the book might lead me into too 'mathematical' of a diversion than I cared for. Fortunately, this book balances mathematical rigor and practical use. Duffy further presses the uses of Green's Functions by introducing it into applications. These applications give a good run down on the concepts and techniques needed to apply it to other problems. Duffy book doesn't alienate the readers, and gives plenty of examples to allow the student to work out problems on their own.
Don't cut yourself short. Green's Functions are a useful tool, and Green's Functions with Applications by Dean G. Duffy is an effective way of learning to be fully competent with this tool (Green's Functions). A definite plus to self-learners and practicing professionals (and students).