The math phys sequence follows Mathematical Physics by Kusse and Westwig closely. AEP 3200 covers chapters 1-8, and AEP 4200 covers chapters 9-11 (plus either 12 or 13, depending on the professor).

In terms of topics, AEP 3200 and AEP 4200 teach:

  • curvilinear coordinate systems
  • tensor calculus
  • the Dirac delta function
  • complex analysis: complex Taylor and Laurent series, contour integrals, Fourier and Laplace transforms
  • ODEs and PDEs: separation of variables, method of Frobenius, Laplace transform techniques, Green’s functions, wave and diffusion equations, Laplace’s equation, Hermitian operators, Sturm-Liouville operators, Bessel functions, Legendre polynomials, spherical harmonics

Math phys is heavily engineering-flavored; it provides you with a mathematical toolbox without focusing on any of the rigorous details. You will become comfortable with various techniques/calculations that will be useful in your physics courses, but you will not learn much of the theory, and you will not be doing proofs.

On the other hand, the courses from the math department emphasize rigor and theory. This is the route to take if you are looking for a deeper treatment of mathematical topics. Courses in complex analysis and differential equations are highly recommended alternatives to math phys.