This text has many advantages over most other introductions to partial differential equations.

Illustrations

PDEs are physically motivated and geometrical objects; they describe curves, surfaces, and scalar fields with special geometric properties, and the way these entities evolve over time under endogenous dynamics. To understand PDEs and their solutions, it is necessary to visualize them. Algebraic formulae are just a language used to communicate such visual ideas in lieu of pictures, and they generally make a poor substitute. This book has over 300 high-quality illustrations, many of which are rendered in three dimensions. In the online version of the book, most of these illustrations appear in full colour. Also, the website contains many animations which do not appear in the printed book.

Most importantly, on the book website, all illustrations are freely available under a Creative Commons Attribution Noncommercial Share-Alike License. This means that you are free to download, modify, and utilize the illustrations to prepare your own course materials (e.g. printed lecture notes or beamer presentations), as long as you attribute the original author. Please visit <http://xaravve.trentu.ca/pde>.

Physical motivation

Connecting the math to physical reality is critical: it keeps students motivated, and helps them interpret the mathematical formalism in terms of their physical intuitions about diffusion, vibration, electrostatics, etc. Chapter 1 of this book discusses the physics behind the heat, Laplace, and Poisson equations, and Chapter 2 discusses the wave equation.