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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.
• ## 1: Introduction to Partial Differential Equations

In this course we shall consider so-called linear Partial Di&fflig;erential Equations (P.D.E.’s). This chapter is intended to give a short de&filig;nition of such equations, and a few of their properties. However, before introducing a new set of de&filig;nitions, let me remind you of the so-called ordinary di&fflig;erential equations ( O.D.E.’s) you have encountered in many physical problems.