Partial differential equations (PDEs) play a vital role in mathematics and its applications. They can be used to model real-world phenomena such as the vibrations of a stretched string, the flow of heat in a bar, or the change in values of financial options. My aim in writing this post is to give you a brief glimpse into the fascinating world of PDEs using the improvements for boundary value problems in
DSolve and the new
DEigensystem function in
Version 10.3 of the Wolfram Language.
The history of PDEs goes back to the works of famous eighteenth-century mathematicians such as
Euler,
d'Alembert, and
Laplace, but the development of this field has continued unabated during the last three centuries. I have, therefore, chosen examples of both classical as well as modern PDEs in order to give you a taste of this vast and beautiful subject.