Math (Subject) GRE without Diff EQ

[jeffasinger]

I just realized I won't have the chance to take a class in differential equations before I have to submit my math graduate school applications, so there's no way I'll have the class beforehand. I've taken pretty much every other topic mentioned, and will review heavily on the calculus (it's been awhile), but how much will this matter?

What sort of Differential Equation questions are typical for the Math GRE? How difficult would it be to just self-teach myself that (small?) portion of Diff EQ?

 

[deluks917]

My school has a weekly math GRE prep session which I attend once in awhile. As far as I can tell there are almoswt no questions on differential equations that aren't seperable. This page seems to say the same thing http://http://math.scu.edu/~eschaefe/gre.html" . In addition you couldn't be asked to solve a system of DE's or do variation of parameters when you have 3 minutes a question. Still I'd look at an engineeering or physics book and read the basic intro to De's section. It certainly shouldn't take you much more then a week to cover this stuff (the harder stuff like series solutions/Laplace transforms etc.) are highly unlikely to be on the test.

 

[snipez90]

I asked basically the same question over a month ago and got no replies. From looking at Princeton Review, I gathered at least this much appears on the exam:

-Basic DE's (immediate integration)
-Solutions to f' = f, y'' + y = 0 (this was not explicitly in the text, but I figured everyone knows this)
-Separable DE's
-Homogeneous equations (the function is homogeneous)
-Exact equations
-Using integrating factor for non-exact equation (in particular two well-known types of integrating factors in this case, namely when (M_y - N_x)/N is a function of x alone and a similar case, where the DE is M*dx + N*dy = 0 and subscripts denote partial derivative wrt that variable)
-First-Order Linear Eqs.
-Higher-Order Linear Eqs. w/ Const. Coefficients

I would try to understand at least one of the well-known methods for finding a particular solution to higher order linear equations, which would probably be the only thing you actually have to learn. I recommend looking at the Boyce and Diprima text for practice, and ideally this should serve as a calculus refresher, as far as the computational aspects go. Good luck.

 

[jeffasinger]

Thanks all,
It sounds like with a little self study I won't have a problem.

 

[rezeew]

I understand your concern about not being able to take a class in differential equations before submitting your graduate school applications. However, I want to assure you that it is possible to perform well on the Math GRE without having taken a class in differential equations.

Firstly, the Math GRE covers a wide range of topics, and differential equations are just one small part of the test. While it is important to have a strong understanding of calculus, as you mentioned you will be reviewing, the majority of the test will focus on other topics such as algebra, geometry, and statistics.

In terms of the specific types of differential equation questions that may appear on the Math GRE, they are typically basic and do not require advanced knowledge. They may involve solving first-order or separable differential equations, or finding particular solutions to given differential equations. These types of questions can be easily self-taught with the help of online resources or review books.

Of course, taking a class in differential equations would provide a more comprehensive understanding of the topic, but it is not necessary for success on the Math GRE. With diligent self-study and review of calculus, you can still perform well on the exam. I wish you the best of luck in your graduate school applications.