Can't decide between PDEs or Vector Analysis

srl17

I am working on a dual undergrad degree program, with my primary degree being Electrical Engineering. This fall will start the last semester to get my B.S. in Math completed. For the engineering side I am taking Electromagnetics and Signals and Systems Analysis this semester.

I need only to take Number Theory and one other math course to complete the math degree. I've already taken real and complex analysis, Advanced Calculus, Abstract Algebra and all the fun theory courses. I am torn between PDEs and Vector Analysis as I can see both being useful for Engineering and in the context of Electromagnetics. Both courses have applied sections on Maxwell's Equations so that doesn't help me in my decision.

Any suggestions/arguments on which course to take would be appreciated.

Thanks

joshmccraney

i spoke first hand with university of washington for prep for aerospace engineering at grad level (similar yet not exact) and they specifically mentioned pdes being a large component.

srl17

Yeah, that's the impression I have gotten for any mechanical based engineering. I am leaning towards PDEs since Maxwell's Equations, which are PDEs, are the fundamental basis for electricity. I just think it weird that I would get advanced standing grad credit if I take vector analysis, but nothing for PDEs.

I'm not concerned about earning grad credit as an undergrad, but was using the Math classes that give me advanced standing at my University as a guide towards which math classes to take while fleshing out my B.S. in Math.

ahsanxr

What does the PDE class cover? In my experience its usually a bunch of very important topics like Fourier analysis, Special Functions and of course PDE's usually involving separation of variables. Hell my PDE class even spent a couple of weeks on vector calculus. So definitely check out what each class is covering. And do you really need a whole semester to cover vector calculus from an applied math perspective? I'd go for PDE if my assumptions about what each class covers is correct.

srl17

The detailed syllabi aren't posted for either class.

Here is the small course description for PDEs:
The objectives of the course are to provide students with the techniques necessary for the formulation and solution of problems involving PDE's and to prepare students for further study in PDE's. The three main types of second order linear PDE's--parabolic, elliptic, and hyperbolic--are studied. In addition, the tools necessary for the solution of PDE's such as Fourier series and Laplace transforms, are introduced.

And for Vector Analysis
Topics which will be covered include: vector algebra, vector differentiation and integration, divergence, gradient, curl, the theorems of Green, Gauss and Stokes, and curvilinear coordinate systems. There will be an emphasis upon problem solving and applications in electromagnetic theory and fluid flow.

So PDEs looks like a better bet since I had to teach myself alot of the vector topics while taking Complex Analysis. I'm sure neither class will give me as much a headache as Measure Theory and Lebesgue Integration did in A. Calc 2

Thanks all for the advice

Jorriss

This is kind of strange I think.

Is the Vector analysis a second course in vector calculus?

You've already seen divergence theorem, stokkes theorem, line integrals and all that jazz correct? You definitely need to know the big theorems of vector calculus before PDEs, albeit, it's probably easy enough to teach yourself if necessary.

nicholls

I see both of these courses as crucial for anybody who wants to further study electromagnetism.

It seems strange that you are forced to choose between them. If you have no experience with vector calculus (which seems very strange for anyone in elec eng/math) then definitely vector calculus is a priority. If you already know fairly well what curl, gradient, divergence, stokes theorem and all that fun stuff is then you should be good to go onto PDEs.

PDEs uses vector calculus, particularly when it comes to Maxwell's equations, so you will need vector calc before you learn PDEs (not in general, but it would be a very good idea, otherwise the problems you can solve will be limited).