Unveiling Solutions to Partial Differential Equations through Separation of Variables

Tyler Berry

This presentation explores the application of the separation of variables method in solving partial differential equations, with a focus on the heat equation and wave equation. The separation of variables technique involves breaking down a partial differential equation into simpler ordinary differential equations by assuming a solution in the form of a product of functions of individual variables. By applying this method to the heat equation and wave equation, we demonstrate how it enables the decomposition of complex problems into more manageable components, facilitating the derivation of solutions through systematic steps. Through detailed examples and analysis, we showcase the efficacy of the separation of variables method in providing analytical solutions to these fundamental equations governing heat propagation and wave dynamics.

• Tyler Berry graduated from Darlington High School and is a senior dual-degree math and engineering major. In the fall, Tyler will continue his studies at Clemson University, where he will pursue a degree in electrical engineering.