One of the requirements is differential equations. I’ve taken the first 2 semesters of calculus for math and science but it was several years ago. I never got around to taking diff eq. Given the subject matter of the course, what level of expertise would I be expected to have and how difficult would it be to get up to speed?
I know this will be different for everyone, so I’ll just add that while I found some aspects of the first 2 semesters challenging, I wouldn’t classify any of it as ‘difficult.’
I think if you remember Calc I and II you’ll be alright. Differential Equations is basically just a methods course, there isn’t really an overarching theory. You just go through different differential equations by type (linear, first-order, seperable, etc) and learn to solve each type.
I’d think if you buy a diff-eq text, then as you go through the course and hit an equation whose solution you don’t understand, just flip to the appropriate chapter and figure it out.
(Circuts and electronics was one of the few courses whose lab I actually enjoyed though. Seems like it would be a lot less interesting without being able to build your own logics and such).
That’s the traditional approach. Some modern differential equations courses take an approach that leans more toward qualitative differential equations (i.e. classifying what kind of solutions your differential equations have, and what that tells you about the situation they’re modeling), numerical methods, and things like that that take advantage of the computer software currently available.
I don’t have a syllabus for this particular course (I’ve looked through the MIT OCW syllabus and assignments here), but I would expect that most of the differential equations used in most introductory circuits courses would be of the simplest possible type: linear differential equations with constant coefficients. (These are of the form
ysup[/sup] + c[sub]1[/sub]ysup[/sup] + … + c[sub]n[/sub]y = f(t)
where ysup[/sup] denotes the kth derivative of y WRT t, and c[sub]k[/sub] are constants. These are used to find the transient and AC behaviors of linear RLC circuits; most of them would be first or second order for pedagogy. Typical forcing functions f would be step functions and sine waves.)
Differential equations of this form can be easily solved using a method that takes only about a paragraph to describe. If you do a bunch of RLC circuit analysis problems you’ll get to understand them pretty well. It would be fairly common to have some discussion of these equations in the circuits course, but again I’m not sure what they’ve got planned for this MITx course.
A lot of the discussion of linear circuits takes place in the Laplace (complex frequency) domain, and understanding the transformation between time and frequency domains is also an important part of understanding RLC circuit behavior. This is covered in some DiffEq classes (like MIT’s 18.03) but I would also expect some discussion of the technique and its applications in a circuits class.
I appreciate everyone’s response but this is the sort of very specific information that I was looking for and your description lowers my anxiety level substantially, so thank you. That’s not to say that I understood every word, but I suspect that I can probably handle equations of the type you mentioned. Cheers.
I have a meager 2 cents’ worth to contribute here:
At my college, we took 3 semesters of Calc followed by one of D.E. It was allowed, but not recommended, that you could take those last two semesters in the other order. I started at that school on the half-semester, and due to scheduling, that’s how I ended up taking it.
Before I started D.E., I asked the profs for a recommendation. They suggested: During the semester break, study up on vectors and vector calculus, and on partial derivatives – taught in Calc III and used a lot in D.E. – I took that advice, and it served me well in D.E.
You’ll need to be really up to speed, especially in integration. If you’ve been away from it for a few years, some serious brushing-up may be in order.
My brother, who is much more into math than I was, once described the D.E. course as “a bag of tricks.”