This text is designed for a one-semester or two-quarter course in partial differential equations given to third- and fourth-year students of engineering and science. It can also be used as the basis for an introductory course for graduate students. Mathematical prerequisites have been kept to a minimum — calculus and differential equations. Vector calculus is used for only one derivation, and necessary linear algebra is limited to determinants of order two. A reader needs enough background in physics to follow the derivations of the heat and wave equations.