This book is part of the series "Mathematics and Physics Applied to Science and Technology." It combines rigorous mathematics with general physical principles to model practical engineering systems with a detailed derivation and interpretation of results. The book presents the mathematical theory of partial differential equations and methods of solution satisfying initial and boundary conditions. It includes applications to acoustic, elastic, water, electromagnetic and other waves, to the diffusion of heat, mass and electricity, and to their interactions. The author covers simultaneously rigorous mathematics, general physical principles and engineering applications with practical interest. The book provides interpretation of results with the help of illustrations throughout and discusses similar phenomena, such as the diffusion of heat, electricity and mass. The book is intended for graduate students and engineers working with mathematical models and can be applied to problems in mechanical, aerospace, electrical and other branches of engineering.