Partial di?erential equations (PDEs) is a topic worthy of your study. It is a subject about di?erential equations involving unknown functions of several variables; the derivatives are partial derivatives. As such, it is a subject that is intimately connected with multivariable calculus. To be successful you should have a good command of the concepts in the calculus of several variables. So keep a calculus text nearby and review concepts when needed. The same comments apply to elementary ordinary di?erential equations (ODEs). An appendix at the end of the book reviews basic solution techniques for ODEs. If you wish to consult other sources, the texts by Farlow (1993) and Strauss (1994) are good choices. A mathematics book must be read with a pencil and paper in hand. Elementary books ?ll in most steps in the exposition, but more advanced books leave many details to the reader. This book has enough detail so that you can follow the discussion, but pencil and paper work is required in some portions. Verifying all the statements and derivations in a text is a worthwhile endeavor and will help you learn the material. Many students ?nd that studying PDEs provides an opportunity to hone their skills and reinforce concepts in calculus and di?erential equations. Further, studying PDEs increases your understanding of physical principles in a monumental way. The exercises are the most important part of this text, and you should try to solve most of them. Some require routine analytical calculations, but others require careful thought. We learn mathematics by doing mathematics, even when we are stymied by a problem. The e?ort put into a failed attempt will help you sort out the concepts and reinforce the learning process. View the exercises as a challenge and resist the temptation to give up. It is also a good habit to write up your solutions in a clear, concise, logical form. Good writing entails good thinking, and conversely