ABSTRACT
The homogeneous equation for the wave operator (or the d’Alembertian ) c ≡ ∂2
∂t2 − c2∇2 describes, e.g., the dynamics of a vibrating string in R × R+, of a
drum membrane or surface of a lake in R2 × R+, or of a sound wave in air, or an electromagnetic wave in vacuum in R3 × R+. Here c denotes the speed of sound or light. The wave equation propagates signals with velocities less than or equal to c. Unlike the diffusion equation, the wave equation is not affected by a change in the sign in the time variable, and so in this sense it is reversible. We will discuss Sturm-Liouville system for 1-D wave equation, which is followed by finding Green’s functions for 1-D, 2-D and 3-D wave equations, and other applications.
