Applied Partial Differential Equations I with Theory

This course provides a rigorous introduction to partial differential equations and their applications. Emphasis will be placed on the theoretical foundations of partial differential equations and the mathematical formalism used to establish this 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; Linear algebra; APMA 0355 or equivalent.