Learn how to solve Partial Differential Equations (PDEs) using Laplace Transforms, focusing on the heat equation for a semi-infinite domain. Explore the relationship between classic methods and modern problems, apply the Laplace Transform with respect to time, and solve ODEs with forcing through homogeneous and particular solutions. Discover how to handle initial and boundary conditions, and understand the solution in both frequency and time domains. This 40-minute video tutorial by Steve Brunton provides a comprehensive breakdown of the problem-solving process, offering valuable insights for students and professionals in applied mathematics and engineering.