The present book examines a number of physical and technical prob­ lems which involve second-order partial differential equations. Consider­ able attention is also given to the theory of such equations. In addition, the text includes several chapters and sections of a general nature (indicated by an asterisk). The material in these sections does not as yet have direct application; nonetheless, it is important for an understanding of contemporary scientific literature on mathematical physics.Among the applications studied are the vibrations of strings, membranes, and shafts; electric oscillations in lines; the electrostatic prob­ lem; the basic gravimetric problem; the emission of electromagnetic waves and their distribution along wave guides and in horns; the emission and dispersion of sound; gravity waves on the surface of a liquid; heat flow in a solid body, and so forth. Solutions are given to both very simple and more complicated problems, making it possible for the reader to master the methods considered in the book and also the physics of the phenomena in question. In almost every chapter, there are problems whose basic pur­ pose is to develop the reader's technical skill.Approximate methods for solving problems in mathematical physics are not discussed, since their exposition would require a considerable in­ crease in the size of the book. Also excluded are certain specialized prob­lems (for example, those associated with the physics of atomic reactors) that have arisen only in the last few years.Translation editor Herbert J. Eagle