Visualization of complex physical phenomena with Mathematica(R): opportunities for use in education

Classroom instruction in the physical sciences and engineering entails the introduction of complex principles that can be extremely difficult to relate to one's past experiences. These principles are most often set forth as mathematical equations, which can be manipulated and solved to arrive at a particular result, and so come to describe and predict the behavior of the systems they represent. Certain physical phenomena, however, are of such nature and complexity that visualization of the system becomes necessary in order to fully understand the underlying processes. This fact is emphasized by the many plots and diagrams that permeate scientific and engineering literature. Often, time-varying data is plotted at discrete time intervals in order to visually convey the temporal behavior of a particular process. In light of the complexity of scientific and engineering problems, and considering the availability of advanced computer software capable of providing visualization of many of these problems, it is the purpose of this paper to present several illustrations of how certain complex physical phenomena can be visualized using the animation capability of a particular software package, Mathematica.