When we pluck a guitar string or strike a drum, the resulting vibrations follow precise mathematical laws governed by differential equations. While these equations can be notoriously difficult to solve directly, mathematicians have developed clever geometric transformations that reveal hidden patterns in their solutions. This talk explores the Prüfer transformation, a technique that converts complex oscillation problems into simpler geometric relationships involving angles and distances. We'll see how this approach not only makes theoretical analysis more elegant but also provides practical tools for predicting when and where vibrations occur. The method applies to a broad class of problems that arise in physics and engineering, including systems where energy is not conserved situations that traditional methods struggle to handle.
Join us on Monday, Sept. 29, at 3:10 p.m. in Hayes 109 to hear this exciting presentation from Shalmali Bandyopadhyay, assistant professor of mathematics at the University of Tennessee at Martin. We hope to see you there!