Numerical Analysis vs Applied Analysis

[jbrussell93]

I'm a sophomore physics major and will be choosing classes for next semester in a couple of weeks. I was planning on taking mathematical methods because I've often heard that it makes a big difference going into the upper level classes but unfortunately, it isn't being offered next year. It has been offered every fall semester since 2006 but for some reason they aren't offering it anymore! Anyway, I now have an extra slot open and I was thinking about taking either numerical or applied analysis. It seems that numerical analysis would be more beneficial for the modeling research that I'm doing especially since I haven't taken any programming classes. On the other hand, applied analysis looking much more interesting and directly relevant to physics, though I must admit a bit intimidating... I'll probably only have the option to take one or the other so I'd like some opinions on which might be more beneficial.

For some background, I'm interested in geophysics and seismology research. I'm planning on going to graduate school for physics (geophysics).

Numerical Analysis:
Machine arithmetic, approximation and interpolation, numerical differentiation and integration, nonlinear equations, linear systems, differential equations, error analysis. Selected algorithms will be programmed for solution on computers.

Applied Analysis:
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.

 

[Lavabug]

Without a doubt, the second essential for any physics major. I had the equivalent as a sophomore student and I'm surprised it's not a mandatory course for you. You absolutely need it to do any sort of QM or boundary value problems in EM.

I'm guessing the second course is mostly theory + proof based. If you're spending a lot of time on you're research and are actually learning programming in a scientific context, don't take the numerical course. What you're doing is more effective for learning programming IMO, and you could easily teach yourself those subjects as they're pretty elementary (unless they're taught with full-blown rigor), there tons of succinct course notes for those subjects out there (check MIT OCW).

 

[jbrussell93]

Without a doubt, the second essential for any physics major. I had the equivalent as a sophomore student and I'm surprised it's not a mandatory course for you. You absolutely need it to do any sort of QM or boundary value problems in EM.

Do you think applied analysis is necessary to take as soon as possible? It is offered every semester where as numerical analysis is only offered in the fall. I'll probably have space to take applied analysis later on in my senior year but if it's going to be beneficial early on then I'll try to take it now.

 

[Lavabug]

Not taking it before QM will needlessly make it harder. A good course in QM will assume you know about vector spaces, linear algebra, Fourier transforms, orthogonal functions, and have a solid handle on PDE's by separation of variables (same goes for potential problems in EM). EM might require Laplace transforms if you do a lot of AC circuit theory. At least, this was my case.

So yeah unless you want to spend a lot of time self-studying these subjects and risk falling behind, I suggest you take the course. I'm surprised it isn't a requirement.

 

[jbrussell93]

Not taking it before QM will needlessly make it harder. A good course in QM will assume you know about vector spaces, linear algebra, Fourier transforms, orthogonal functions, and have a solid handle on PDE's by separation of variables (same goes for potential problems in EM). EM might require Laplace transforms if you do a lot of AC circuit theory. At least, this was my case.

So yeah unless you want to spend a lot of time self-studying these subjects and risk falling behind, I suggest you take the course. I'm surprised it isn't a requirement.

I think you have persuaded me! I was also considering taking a plate tectonics class to help with my geology minor and develop my geophysics background, but this class sounds more important for my success as a physics major.

Appreciate the advice.

 

[Lavabug]

No worries.

As an anecdote, the equivalent course for me was called "mathematical methods 5"(2nd term 2nd year), while the following (last) "math" course I took was much like your numerical analysis, in my 2nd term of my junior year (though it was 40-60 theory and application).