Master Mathematical Techniques for Physics: PHYS 508 vs MATH 442

[iacephysics]

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.

 

[Andy Resnick]

Phys 508 is the mathematical structure needed to more closely examine mechanics, E&M and QM. Since you claim to not have a good grasp of those subjects, I would think that the course will not (yet) meet your needs- you won't have the context yet, and it will seem like a lot of confusing math.

Math 442 may be a better fit, especially if you feel weak in those areas. However, it's also likely to be divorced from physics- the emphasis may be on determining when a solution exists, rather than obtaining a solution.

Why not talk to the profs? Explain what you are looking for in a course, see what they have to say.