Partial differential equations, PDEs, are central to our understanding of physics. Wave equations model the propagation of sound, light, and water waves; the Schrödinger equation predicts the properties of atomic and molecular systems; the diffusion equation describes the flow of particles or energy. Numerical solution of a wide variety of PDEs makes it possible to demonstrate the similarities and differences between the various equations, thereby forming a bridge between the classical mechanics of the 19th century and the quantum mechanics of the 20th. It was, however, necessary to limit certain features of the program to the classical wave equation in order to limit the scope and size of the code. For instance, quantum mechanical operators are not discussed since they are treated extensively elsewhere in the CUPS series.
The reader may wish to consult a book on mathematical methods for scientists, as well as standard texts on optics, quantum mechanics, and thermal physics while working through the computer exercises accompanying program WAVE. Texts which provide extensive treatments of oscillatory and wave phenomena are also available.[10,7,2]