Basic background info (which may not be useful):I will be a junior in physics this fall. I am done with all undergraduate level classical mechanics, E&M and quantum mechanics courses. I think I want to do experimental physics. I have been working under an AMO physics professor whose research is about ultracold atoms and quantum optics. I have been building electronic apparatuses for the experiment and laying out circuit boards most of the time, nothing closely related to physics yet. I definitely want to go to a good grad school. Meanwhile, I don't think I have a solid grasp of the materials from my physics classes, especially E&M and quantum, since I didn't push myself at all and only got by doing only the minimum work needed to get good grades on the homework and exams, which were not difficult at all. So, Say I take this course PHYS 508 Mathematical Physics I Core techniques of mathematical physics widely used in the physical sciences. Calculus of variations and its applications; partial differential equations of mathematical physics (including classification and boundary conditions); separation of variables, series solutions of ordinary differential equations and Sturm-Liouville eigen problems; Legendre polynomials, spherical harmonics, Bessel functions and their applications; normal mode eigen problems (including the wave and diffusion equations); inhomogeneous ordinary differential equations (including variation of parameters); inhomogeneous partial differential equations and Green functions; potential theory; integral equations (including Fredholm theory). Topics are illustrated with realistic physics problems; a broad range of illustrative examples are explores; applications are emphasized. Prerequisite: MATH 241 or MATH 380; MATH 285 then, then should I still take this course MATH 442 Intro Partial Diff Equations Introduces partial differential equations, emphasizing the wave, diffusion and potential (Laplace) equations. Focuses on understanding the physical meaning and mathematical properties of solutions of partial differential equations. Includes fundamental solutions and transform methods for problems on the line, as well as separation of variables using orthogonal series for problems in regions with boundary. Covers convergence of Fourier series in detail. 4 hours of credit requires approval of the instructor and completion of additional work of substance. Prerequisite: One of MATH 284, MATH 285, MATH 286, MATH 441.