Partial Differential Equations of Mathematical Physics

Abstract

Chapters 2 through 4 of this text developed solution methods for physical problems that are governed by ordinary differential equations. The purpose of Chapters 7 through 9 is to extend these methods to problems that are governed by partial differential equations. Partial differential equations have been the subject of vigorous mathematical research for over 250 years and remain so today. A systematic and complete coverage of this subject is far beyond the scope of this text. Instead, the equations to be solved here will be introduced in the context of several explicit applications. This has the advantage of leading to both the differential equations and the auxiliary conditions (initial conditions, boundary conditions) that are needed to single out the unique solutions to specific physical problems. These ideas are developed in the present chapter. The actual solution procedures are presented in Chapters 8 and 9.