How to Prepare for Differential Equations?

[sheldonrocks97]

Hello,

I am going into my first semester at university in the fall and I have already completed Calc I and II and linear algebra and I am finishing up Calc III over the summer.

So I was talking to the chair of the EE department at my university and he recommended I take ODEs my first semester.

The problem is, I've never solved a differential equation in my life, and I don't know much about them. And combined with that fact that it will be my first 300 level class, that makes me nervous.

My question is, how should I prepare for this class? I have been looking up videos on separable ODEs and first order linear ODEs, but I was wondering what else I should study to prepare myself to take this class. I know that you need to be strong in integration and differentiation, but other than that I'm not sure how to prepare.

Thanks for the help!,

Austin

 

[SteamKing]

If you know y' = x, what is y? That's a pretty simple ODE. It's also separable, which can easily be seen by writing y' in differential form.

If you've done integration by parts, you've already solved some simple differential equations (you know v' and you have to find v by integration).

As long as you are current on integration techniques and know your derivatives, you'll be OK. For linear first order ODEs, you should review the exponential function (e^x) and how to differentiate and integrate it. Review solving polynomial equations of degree two and higher (i.e., know the quadratic formula and how to factor a polynomial). Later on, you'll be exposed to series solutions of certain ODEs, but I wouldn't worry too much about them just yet.

 

[sheldonrocks97]

If you know y' = x, what is y? That's a pretty simple ODE. It's also separable, which can easily be seen by writing y' in differential form.

If you've done integration by parts, you've already solved some simple differential equations (you know v' and you have to find v by integration).

I never thought of it like that! I guess those are differential equations now that I think about it. Thanks!

 

[verty]

I would look at complex numbers and complex exponentials, and finding real and imaginary parts of complex rationals, for example (a + ib)^2 / (c + id), what is the real part? And when you learn ODE's, focus on the general solutions or broadest ideas, what works in general. Anyway, that's all I can think of.

 

[sheldonrocks97]

I would look at complex numbers and complex exponentials, and finding real and imaginary parts of complex rationals, for example (a + ib)^2 / (c + id), what is the real part? And when you learn ODE's, focus on the general solutions or broadest ideas, what works in general. Anyway, that's all I can think of.

I never would have thought to look at that, but I'll keep that in mind, too. Thanks!