As this book deals with advanced topics in engineering mathematics, which undergraduate students in engineering and postgraduate students in mathematics and allied disciplines have to study as part of their course requirements, the title of Advanced Engineering Mathematics has been considered more suitable. This well-organized and accessible text discusses in detail the advanced mathematical tools and techniques required for engineering problems. The book begins with Fourier series and goes on to give an indepth analysis of Fourier transform, Mellin transforms and Z-transforms. It then examines the partial differential equations with an emphasis on the method of separation of variables applied to the solution of initial boundary value problems involving the heat, wave and Laplace equations. Discrete mathematics and its applications are covered in a separate chapter as the subject has wide applications in computer science. In addition, the book presents some of the classical problems of the calculus of variations, including the brachistochrone problem. The text concludes with a discussion on tensor analysis which has important applications in the study of continuum mechanics, theory of relativity, and elasticity. Intended primarily as a text for undergraduate students of engineering, postgraduate students of mathematics (M.Sc.), and master of computer applications (MCA), the book would be of great benefit also to practising engineers.