Advanced Electromagnetic Theory I

This is the graduate-level deep dive into Maxwell's equations, where you stop treating electromagnetics as a set of recipes and start deriving wave behavior from first principles in whatever coordinate system and medium the problem demands. Expect heavy analytical homework — solving wave equations in rectangular, cylindrical, and spherical geometries, working through waveguides and cavities, and formulating radiation and scattering problems using auxiliary potentials and EM theorems. It's the foundation course for anyone going into antennas, microwaves, photonics, or computational EM, and the mathematical machinery you build here is what later courses on numerical methods and high-frequency techniques assume you already own.