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This book consists of two parts. Part 1 gives an account of the methods for solving typical problems in mathematical physics and an introduction to integral equations. Part 2 deals with the appli­ cations of these methods to problems requiring the use of special functions. Extensive use is made in this book of the Dirac (5-function. Generalised functions are introduced and their applications are described. Each chapter concludes with a number of problems illustrating the main text (altogether 150 problems with answers are given). This text was designed for students of physics and engineering and was based on a course given at the Department of Theoretical and Experimental Physics of the Moscow Engineering-Physics Institute