This notes are aimed at students of Higher Education Institutions. They cover partial differential equations (differential equations with partial derivatives) with applications to large categories of physical problems.

The two main methods for solving partial differential equations are thoroughly developed: the method of separable variables and the method of integral transforms. Each of these methods is presented as simply as possible, so that it can be immediately understood by the reader.

The exercises and their solutions are presented in a suitable manner so that the reader can grasp the method, while also clarifying some essential and significant details. It is advisable that the reader consults our books during the study of this material: COMMON DIFFERENTIAL EQUATIONS, FUNCTIONS OF MULTIPLE VARIABLES, AND MATHEMATICAL ANALYSIS I, to which there are relevant references.

Our teaching experience gives us hope that this will serve as a good starting point for the study of partial differential equations.

GIANNIS GAROUTSOS [Excerpt from the text of the preface]