Our goal in written Mathematical Methods for Engineers is to answer "Initial boundary value problems, and Wave equation in spherical and cylindrical coordinates". This book is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. The present book is based on lectures given by the author to students of various colleges studying mathematics. In designing this course the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. Therefore in most cases, we did not give rigorous formal proofs of the theorems. The rigorousness of proof often fails to be fruitful and therefore it is usually ignored in practical applications. The book can be of use to readers of various professions dealing with applications of mathematics in their current work. The subject matter is presented in a very systematic and logical manner. It contains material which you will find of great use, not only in the technica1 courses you have yet to take but also in your profession after graduation, as long as you do.