Given by CSC Math Instructor Kyle Hickmann on February 4, 2010
In the last two or three decades there has been a great deal of research done in the mathematics of imaging using acoustic and electromagnetic waves. All of this work is rooted in the study of hyperbolic partial differential equations, the simplest of which is the one dimensional wave equation. We will show how this equation models the vibrations of a string stretched between two points. It will then be demonstrated that the motion of this string can be solved for. This is related to models for the propagation of acoustic waves through some medium. The relation of these models to imaging problems in medicine, geophysics, and sonar will then be discussed.