Kanwal R.P. Linear Integral Equations: Theory and Technique

Academic Press, 1971. - 296 pages.Many physical problems which are usually solved by differential equation methods can be solved more effectively by integral equation methods. Indeed, the latter have been appearing in current literature with increasing frequency and have provided solutions to problems heretofore not solvable by standard methods of differential equations. Such problems abound in many applied fields, and the types of solutions explored here will be useful particularly in applied mathematics, theoretical mechanics, and mathematical physics.Each section of the book contains a selection of examples based on the technique of that section, thus making it possible to use the book as the text for a beginning graduate course. The latter part of the book will be equally useful to research workers who encounter boundary value problems. The level of mathematical knowledge required of the reader is no more than that taught in undergraduate applied mathematics courses. Although no attempt has been made to attain a high level of mathematical rigor, the regularity conditions for every theorem have been stated precisely. To keep the book to a manageable size, a few long proofs have been omitted. They are mostly those proofs which do not appear to be essential in the study of the subject for purposes of applications.