The emphasis in this book is placed on techniques for solving partial differential equations found in physics and engineering but discussions on existence and uniqueness of solutions are included. Several different methods of solution are presented, with the primary emphasis on the classical method of separation of variables. Secondary emphasis is placed on transform solutions, as well as on the method of Green's functions. The derivation and analysis of heat, wave and potential equations are covered in chapter one, and throughout the book the physical interpretation of mathematical results is stressed. A background of elementary calculus and differential equations is necessary.