This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Greens functions from scratch. Greens functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Greens function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Greens function approach. For the first time, Greens functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.