Matrix Theory. 3 Credits. Basic properties of matrices, determinants, vector spaces, linear transformations, eigenvalues, eigenvectors, and Jordan normal forms. Introduction to writing proofs. Applied Analysis. 3 Credits. Solution of the standard partial differential equations (wave, heat, Laplace's eq.) by separation of variables and transform methods; including eigenfunction expansions, Fourier and Laplace transform. Boundary value problems, Sturm-Liouville theory, orthogonality, Fourier, Bessel, and Legendre series, spherical harmonics. I've taken the standard calc, ODE, statistics, and mathematical methods. I haven't had a formal linear algebra course though I've gotten some exposure in my other courses. I've had little exposure to solving PDEs so I'm leaning towards applied analysis. What do you guys think is the more essential math course for a physics major?