Can't decide between PDE or ODE or both

[proximaankit]

Hey everyone
I am going to be a freshman this fall (in college). I am currently having a dilemma in choosing my math class. In high school I took classes all the way up to Honors Differential Equations (ODE). In June I went to the university and signed up for Ordinary Differential Equation since they could not give me an exception for Partial Differential Equations. However, I have been talking with the advisor so that is bound to change.

Regardless, all that time since june has made me question myself a bit. I am afraid of PDE being too hard (I know (-_-) ). I mean I don't know what to expect since this is my freshman year. My time management skills are hit or miss (although I do not know how living in college might change that). I am currently signed up for 15 CHrs as a physics major. With the PDE added it will be 18 CHrs. I really enjoyed my Calc III and DiffEQ classes at my high school although I did end up with A-. I want to take PDE but I am scared of messing up early on (I also think that I may forgotten little bit of ODE but I do have book and notes to review).

Please tell about your experience with PDE and if you have any opinions, suggestions or etc on the matter please post them.

So should I take PDE, ODE or both? Also do you have any tips for a freshman.

Thank You Very much

 

[caldweab]

My experience and advice is take the course because you'll see them all through the curriculum. Your fluids and heat transfer classes are all PDEs. They aren't that bad really, you can pick up http://https://www.amazon.com/Diffe...r=1-2&keywords=partial+differential+equations for a good start.

 

[lurflurf]

The difficulty of a class depends only loosely on the subject. If it is one of those silly pde classes that is mostly separation of variables it should be manageable. Only a few thing from ode class are needed. If you have already taken an ode class it is a waste to take another that duplicates it. Is this ode class similar to the one you took or is it a different class?

 

[Floid]

If you are just going in as a freshman and have credit for all your Calculus classes you are already way ahead of the curve. It can't hurt to take a class that covers material you have already taken (ODEs) to give yourself time to adjust to college and then take PDEs next semester.

 

[WannabeNewton]

I was in the almost the same situation as you. Unless the ODE class is a proof based ODE class (which I'm guessing it isn't) I really don't see much point in repeating it; my own adviser told me that I would be bored to tears if I took a non-proof based ODE class after having already taken one in HS (I found the one in HS to be unbearably boring as well) so I just tested out with a proficiency exam hence I agree with lurf with regards to that. The reason I said "almost the same situation" is because I was given the option to take applied PDEs but I didn't take it as I was much more interested in pure math classes (and for me a purely proof based PDE class would be waaaaaaaaaaaay out of the question at the first semester freshman level).

 

[proximaankit]

The difficulty of a class depends only loosely on the subject. If it is one of those silly pde classes that is mostly separation of variables it should be manageable. Only a few thing from ode class are needed. If you have already taken an ode class it is a waste to take another that duplicates it. Is this ode class similar to the one you took or is it a different class?

Well back in my high school Differential Equations it was dual enrollment class (which I did not pay for at the time) and so you would get the credit at a state university.

Also looking at the college description describes pretty much what I did:

"First- and second-order methods for ordinary differential equations including: separable, linear, Laplace transforms, linear systems, and some applications."

Since it was my senior year I did not get to cover some stuff at the end in depth. For example, numerical analysis and solving differential equations using eigenvalues and eignevectors (these we did cover to some degree, again not very deeply, i.e. no complex eigenvalues).

Oh by the way here is a description for my PDE class:

"Derivation of the heat, wave, and potential equations; separation of variables method of solution; solutions of boundary value problems by use of Fourier series, Fourier transforms, eigenfunction expansions with emphasis on the Bessel and Legendre functions; interpretations of solutions in various physical settings."

Ya the Fourier series and transformation sound kind troublesome from what I have heard.

 

[thegreenlaser]

Well back in my high school Differential Equations it was dual enrollment class (which I did not pay for at the time) and so you would get the credit at a state university.

Also looking at the college description describes pretty much what I did:

"First- and second-order methods for ordinary differential equations including: separable, linear, Laplace transforms, linear systems, and some applications."

Since it was my senior year I did not get to cover some stuff at the end in depth. For example, numerical analysis and solving differential equations using eigenvalues and eignevectors (these we did cover to some degree, again not very deeply, i.e. no complex eigenvalues).

Oh by the way here is a description for my PDE class:

"Derivation of the heat, wave, and potential equations; separation of variables method of solution; solutions of boundary value problems by use of Fourier series, Fourier transforms, eigenfunction expansions with emphasis on the Bessel and Legendre functions; interpretations of solutions in various physical settings."

Ya the Fourier series and transformation sound kind troublesome from what I have heard.

If you haven't done much linear algebra (vector spaces, eigenvalues, eigenvectors) and you haven't done Fourier series or Fourier transforms before, the eigenfunction expansion stuff might be kind of difficult for you. It shouldn't be impossible, but you might find that there are a lot of new ideas getting thrown at you all at once, and you might get more out of the class if you wait until you have some more math experience.

 

[lurflurf]

Fourier series and transformation are sometimes included in calculus or ode, most pde classes start from the beginning though. In fact some classes spend half of the class on Fourier series and transformation before they do any pdes.
That looks like the description of a typical applied pde class. It is as good as any class past calculus to take first.

 

[proximaankit]

Oh by the it looks like my university refers to ODE as the mathematically rigorous version of (non-partial) differential equation. Here is the description for the actual ODE (which is higher than differential equation and pde.

Math 430 Ordinary Differential Equations I:
Picard existence theorem, linear equations and linear systems, Sturm separation theorems, boundary value problems, phase plane analysis, stability theory, limit cycles, and periodic solutions.

Preqs for M430 is Math 221 which is the basically the same differential equations that I took in high school.

Just for info PDE is called Introduction to Partial Differential Equations and it is Math 324.

Also i hope they do not do Fourier stuff in the Math 221. I will also talk to a advisor about this.

 

[Astronuc]

Hey everyone
I am going to be a freshman this fall (in college). I am currently having a dilemma in choosing my math class. In high school I took classes all the way up to Honors Differential Equations (ODE). In June I went to the university and signed up for Ordinary Differential Equation since they could not give me an exception for Partial Differential Equations. However, I have been talking with the advisor so that is bound to change.

Regardless, all that time since june has made me question myself a bit. I am afraid of PDE being too hard (I know (-_-) ). I mean I don't know what to expect since this is my freshman year. My time management skills are hit or miss (although I do not know how living in college might change that). I am currently signed up for 15 CHrs as a physics major. With the PDE added it will be 18 CHrs. I really enjoyed my Calc III and DiffEQ classes at my high school although I did end up with A-. I want to take PDE but I am scared of messing up early on (I also think that I may forgotten little bit of ODE but I do have book and notes to review).

Please tell about your experience with PDE and if you have any opinions, suggestions or etc on the matter please post them.

So should I take PDE, ODE or both? Also do you have any tips for a freshman.

One should master ODEs before PDEs. What topics were covered in ODE class in high school?

Did one do Second Order ODEs? Power Series Solutions and Special Functions? Systems of First Order ODEs? Laplace Transforms?

 

[vela]

Does the physics department offer a mathematical methods course? That's usually where physics majors learn this material. It's not going to be proof-based, but taking a proof-based ODE or PDE course probably won't help you that much in the long run (not that it hurts to take it either). I'd think taking a course in real analysis would be more useful, especially if you don't know how to write formal proofs yet.

 

[proximaankit]

In the high school DiffEq class these were the following topics that I covered:

1. First Order (no Picard Methods, or Ricatti and Clairaut equations) and their applications
2. Higher Order Differential Equations and their applications
3. Cauchy-Euler Equation, Power Series Solution
4. Laplace Transformation
5. Systems of linear DE (Laplace Transform, Operator, and Eigenvalue methods)
6. Numerical Analysis (Euler, Imp. Euler and Runge-Kutta method)

However, the last two topics were the ones that I did not get to cover in depth and clarity. For example for the eigenvalues we did not cover complex ones, or as in the case of numerical analysis in which I only spent few days.

@vela

Yes the mathematical department does offer Mathematical Methods in Physical Science but I want to save that for next semester

Also just out of curiosity why do you think real analysis will be helpful or useful. I tried to do analysis for a while by myself and the result was not the pretty Although with a proper guidance it does seem quite fun.

 

[WannabeNewton]

With regards to real analysis, it's required if you're interested in mathematical physics; it's useful simply because it helps your proof writing abilities tremendously (if this is something you care about). Finally, it's just a really beautiful subject.

 

[atyy]

Also i hope they do not do Fourier stuff in the Math 221. I will also talk to a advisor about this.

From the physics point of view, the Fourier stuff is very important, as are the eigenvalue methods. The eigenvalue methods for linear odes make life easy by "diagonalizing" the equation so that you have variables in which the equations are "uncoupled". The Fourier transform is an eigenvalue method for linear pdes.

 

[proximaankit]

The Fourier stuff is very important, as are the eigenvalue methods. The eigenvalue methods for linear odes make life easy by "diagonalizing" the equation so that you have variables in which the equations are "uncoupled". The Fourier transform is an eigenvalue method for linear pdes.

Yes I agree to but do you think they do the Fourier series and decomposition in a regular differential equations (Math 221 at my university). Also how important is complex eigenvalues.

 

[atyy]

Yes I agree to but do you think they do the Fourier series and decomposition in a regular differential equations (Math 221 at my university). Also how important is complex eigenvalues.

Complex eigenvalues are just the same as real eigenvalues with respect to how to solve the equation. Real eigenvalues mean your solution is exponentially decaying or exploding. Complex eigenvalues just mean that your solution is rotating since exp(ix)=cos(x) + i sin(x). So they are very important, but one can quite blindly apply them in the same way as real eigenvalues.

 

[lurflurf]

Just relax. If you had an ode class and understood it you will be fine. It is usual that different classes cover slightly different things. Just review it for a day, you don't need to retake a whole class just because you do not know some small thing. If that were true everyone would need to take every class ten times.