How important really is Differential Equations?

[blockRed]

So i have started looking at some PhD econ program admission FAQs and math recommendations/ requirements recently. Lo and behold, diff eq appears, and much more than once!

Now i am a little nervous. I know more math is better, but i've been told/read here that ODE is the most marginal of classes. As a result, this is a class i haven't taken.

Should i be worried?

[AREStudentHopeful]

I wouldn't be worried. It's helpful, but unless you're doing certain types of macro or financial econ, you generally don't need a whole lot beyond the basic diff EQ you learn in Calc III. From what I've seen in natural resource econ (in case that's your thing) the most you use in dynamic optimization is still only the most basic stuff. That being said, an A in Diff Eq is still nice to see for admissions

[blockRed]

From Minnesota's website (bolding is mine):

"Courses in real analysis, differential equations, optimization, topology, probability or measurement theory are all particularly helpful in preparing for graduate studies"

[AREStudentHopeful]

Minnesota also has quite a few faculty who's interests lie in finance or mathematical econ so that doesn't surprise me. From what I've seen and heard, Minnesota in generally "harsher" with respect to math used in their program when compared to similar schools. Like I said, I'm not saying it's not helpful, but I also think that unless you plan on going into the fields I mentioned, you shouldn't have too much of a problem teaching yourself what you need to know beyond Calc III.

[blockRed]

Minnesota also has quite a few faculty who's interests lie in finance or mathematical econ so that doesn't surprise me. From what I've seen and heard, Minnesota in generally "harsher" with respect to math used in their program when compared to similar schools. Like I said, I'm not saying it's not helpful, but I also think that unless you plan on going into the fields I mentioned, you shouldn't have too much of a problem teaching yourself what you need to know beyond Calc III.

I don't think Diff Eq is hard, but i am surprised at how many program websites it comes up as pseudo-required/ looked upon really favorably. Minnesota is somewhat expected, but here's NYU:

"You should definitely have taken single-variable and multivariate calculus. It is expected that you would have a background in linear algebra, and an exposure to probability and statistics. Many of our applicants also have a background in difference or differential equations, and they have been exposed to rigorous thinking in limits, continuity, and basic topological concepts (openness, compactness, etc.). There are a good number of applicants who have more than this: e.g., some measure theory and exposure to rigorous probability theory and stochastic processes."

So it's on their list, between Calc/LA and RA.

[AREStudentHopeful]

I'm just commenting in regard to its usefulness. I'm not saying that programs wouldn't look favorably on it if you've taken it; they would. However, if you already have RA, Topology, or things like that, I think the MB of adding ODE is very little with respect to admissions chances (not that I'm endorsing taking math just for the purposes of admissions, I'm not - in my opinion, that's called mathterbation).

[_nanashi]

Differential Equations isn't really used, but often the reason its valuable is that in a basic differential equations course, you will learn what a difference equation is. Difference equation is crucial to anyone doing finance, or empirical macroeconomics. They are used in Time Series Econometrics, which is the key tool for these subjects. If you don't have diff eq, I really wouldn't worry about it. I would however make sure I knew difference equations from Chiang, or Enders.

If your worried about coursework, for preperation. I'd be making sure I understood Calculus, Functions Matrix Algebra, Probability/Math Stats (with Calculus) inside and out. For signaling Real Analysis, Measure, Topology are the usual suspsects depending on how good you are in pure math, what you want to do, and where you want to do. The one value of Analysis (and I am more skeptical than most of its value) is that it forces you to learn to read mathematics, and forces you to understand the finer details of calculus, inductive logic which helps a lot long term.

[OneArmedEcon]

LOL. Mathterbation. I love it.

[corolla09]

I don't think its terribly necessary. It may be listed since most math major requirements have you take Diff Eq. I did not take the course and would not find it very useful for much grad work. However it may be more important for top-10. If you find a better course (i.e. more math stats) I would contemplate taking that instead.

[Olm]

Okay kiddies, gather 'round the campfire and listen to this story:

You need calculus, linear algebra, stats, and you need to know how to do proofs. Anything else you need can be picked up later.