Applied Partial Differential Equations I

This course provides an introduction to partial differential equations and their applications, with an emphasis on techniques for solving PDEs rather than theory. We will learn how to use partial differential equations to solve problems that arise in practical applications by formulating questions about a real-world problem, creating a partial differential equation model that can help answer these questions, solving the resulting system using analytical, numerical, and qualitative methods, and interpreting the results in terms of the original application. Topics include the four fundamental PDEs (transport, wave, heat, and Laplace equations), solution techniques (Fourier transform, energy methods, separation of variables, maximum principles), and example applications. Prerequisites: Multivariable calculus; APMA 0350 or equivalent.