How much math is needed before taking ODE?

[riaudo]

I am a junior in high school taking AP Calc AB. This is the highest level of math offered at my high school (everyone else in my class is a senior)

I want to start taking math classes at my community college. Currently I take College Chemistry I there (fall semester) and it's going very well. I want to take another class during the spring semester.

I looked in the math catalog and the only math class they offer at the time I can take it (after school in the evenings) is Ordinary Differential Equations.

Can I take this class with a basic knowledge of calculus? If I can differentiate and integrate, would I be okay taking ODE? Also, how hard would ODE be at a community college level?

Thanks for the help!

 

[dacruick]

ODEs would be a great course for you to take!

I took one calculus course in university before taking ODEs and it went fine for me. I don't think it will be too difficult for you at all. I would say that the integrations and differentiations in ODEs are actually easier than the ones you will perform in calc 1. You should do fine, and even if you don't, what do you have to lose?

 

[romsofia]

Depending on the course, you might need calc 2 because of series solutions. Check to make sure you won't be using series solutions if you're going to attempt this.

 

[S_Happens]

ODE uses a lot of techniques of integration from Calc 2, such as partial fractions and integration by parts. Partial fractions isn't anything difficult, but it's definitely easier when you already know those techniques and can concentrate just on the ODE info.

I would want to be completely comfortable with Calc 2 before jumping in at a big university, but a small community college may be manageable if interaction with the professor is easy.

Calc 2 is almost certainly a prerequisite for ODE, so you'd have to talk to someone about getting placed in the class. Go ahead and talk to the professor(s) and head of the dept to see what they think or if they'd even let you.

 

[riaudo]

I've started to teach myself other integration techniques like integration by parts. I guess I'll wait until the professor's name is put on the website so I can check ratemyprofessor to see if he's a good teacher and if that's the case I'll just explain my situation and see what he thinks.

Thanks!

 

[S_Happens]

Well, I meant that with Calculus 2 being a prerequisite, you'll almost certainly have to talk to the head of the math dept to get special permission to even take ODE (IF you are allowed), so I'd look into that early.

Another word of warning, basically anything from Calc 2 will be fair game if it's a prerequisite. The list starts getting long when you keep adding things you need to learn. Some things are easy to learn simultaneously (partial fractions, improper integration, etc) but some things are/can be quite difficult and require a lot more practice (integration by parts, integration by trig substitution, Taylor polynomials, etc.). I've encountered all of this so far in my ODE class, and the pace is such that it's necessary to know that material ahead of time. My tests are 50 minutes long, so there's no time to waste trying to figure something out.

The bottom line is that all of my professors so far haven't been satisfied simply with mastery of the current material. They feel that we should be able to do all the calc2, calc 1, and pre-calc/trig that we previously learned to be able to succeed in the current class. Sometimes it bothers me as it doesn't always add to what we're doing, but that's how it's done where I am. I'm all for building on previous material, but that's not really what I'm complaining about although I'm not going into detail. I'm all for mastery of a subject rather than a brain dump to pass a test (for those who might misunderstand my previous statements).

 

[HallsofIvy]

Much of introductory differential equations focuses on Linear differential equations, and the fundamental theory for them is heavily Linear Algebra. I would recommend Linear Algebra as a prerequisite for Differential Equations.

 

[S_Happens]

It might depend on the class itself. Even though we've only been dealing with linear DEs, there hasn't really been any Linear Algebra needed. My class is technically select ODE and Linear Algebra and we haven't touched anything officially Linear Algebra yet.

The exception mainly being that the Wronskian is a determinant, but they simply said "Here's how to calculate the Wronskian...".

I'd consider MY experiences to be mostly techniques of solving differential equations, so almost a plug and chug style. Mind you, my prof does go through many proofs, but in the end, all the work just gets down to following simple methods to solve certain equations. So, again, MY experience has been that calculus 2 is used heavily and you're expected to already know it, while any Linear Algebra necessary has been taught at the same time.

After we finish up Laplace Transforms, we'll do some select Linear Algebra before going to systems of Linear DEs. I'm not sure what a full blown Linear Algebra class covers without looking, but we'll do basic systems of equations, matrix operations, determinants, and up to eigenvalues and eigenvectors. I'm familiar with all of it up to eigenvalues and eigenvectors, so off the top of my head I wouldn't consider that to be enough material simply for one class.

Again, MY experience.

 

[HallsofIvy]

Well, the fundamental concept used in elementary differential equations is that the set of all solutions to a linear homogeneous nth order differential equation forms a vector space of dimension n so you can find n "independent" solutions as a basis for the solution set and so write the general solution. None of that will even make sense without Linear Algebra.

 

[S_Happens]

I deleted "from a practical standpoint" from the end of my last statement before posting, but I think it brings up an important distinction for why we will have differing opinions.

I certainly agree that it is rooted in Linear Algebra. From an "understand the concepts down to the bare bones" point of view, sure it would be great to know. From the point of view of passing the class or being able to take away practical material, it doesn't really matter. I am an engineer and much more interested in application than proof. I'm perfectly fine with my professor telling me exactly what you just said and then showing me the methods used, limitations, and applications.

Don't get me wrong, and I'll again state, that I'm not simply interested in a passing grade without understanding. It's just that application and the end result, in this case, are more important to me. I can't imagine a person that couldn't be successful in ODE simply for the deep rooted reason that you posted above. I don't think the same argument could be made about calculus 2. There is no question that you'll need many of the methods of integration in solving DEs.