Chapter 14 Vibration and Diffusion in One – Dimensional Media

In this chapter, we study the solutions, both analytical and numerical, to the two most important equations of one-dimensional continuum dynamics. The heat equation models the diffusion of thermal energy in a body; here, we analyze the case of a one-dimensional bar. The wave equation describes vibrations and waves in continuous media, including sound waves, water waves, elastic waves, electromagnetic waves, and so on. Again, we restrict our attention here to the case of waves in a one-dimensional medium, e.g., a string, or a bar, or a column of air. The twoand three-dimensional versions of these fundamental equations will be analyzed in the later Chapters 17 and 18.