This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts underlying principles a wide range of applications and various methods of solutions to PDEs. In addition to essential standard material on the subject the book contains new material that is not usually covered in similar texts and reference books. The text primarily serves as a textbook for the first two courses in PDEs or in a course on advanced engineering mathematics. It may also be used as a reference for graduate students researchers and professionals in modern applied mathematics mathematical physics and engineering. Readers will gain a solid mathematical background in PDEs sufficient to start interdisciplinary collaborative research in a variety of fields. Also by L. Debnath: Nonlinear Partial Differential Equations for Scientists and Engineers Second Edition ISBN 0-8176-4323-0.