A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model. PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics.
- In this course we shall consider so-called linear Partial Diﬀerential Equations (P.D.E.’s). This chapter is intended to give a short deﬁnition of such equations, and a few of their properties. However, before introducing a new set of deﬁnitions, let me remind you of the so-called ordinary diﬀerential equations ( O.D.E.’s) you have encountered in many physical problems.